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Today's students have a critical need to learn and understand math vocabulary. It no longer passes the test to just memorize functions and do calculations, but not be able to explain how the work was done.
Hands On Equations Hands-On Equations is the ideal first introduction to algebra for elementary and middle school students. Not only will these students have fun and be fascinated with the program, their sense of self-esteem will be dramatically enhanced as they experience success with sophisticated looking algebraic equations. Supported Platforms Apple Supported Devices iPad ver 4.+ Release Date March 2012
Product Summary Take a look at TI's next-generation handheld designed especially for grades 6-8. The TI-73 Explorer joins our popular line of handheld technology, providing a larger screen alternative for teachers who feel limited by the two-line display of other fraction and scientific models. The TI-73 Explorer is completely compatible with existing TI-73 classroom accessories and related curricular materials for upper elementary through lower middle grades, from fractions through pre-algebra. Enhance your student's learning experience with the new TI-73 Explorer, which serves as a bridge between the TI-15 Explorer and the TI-84 Plus Silver Edition. General Information Product Type Graphing Calculator Manufacturer Part Number 73/CLM/2L1 Manufacturer Website Address Manufacturer Texas Instruments, Inc Product Model TI-73 Product Name Explorer TI-73 Graphing Calculator Product Line Elementary Brand Name Texas Instruments Display & Graphics Display Screen 8 Line x 16 Character Memory Standard Memory 32 KB RAM Battery Information Power Source Battery
This textbook is suitable for graduate students in engineering and also for use in a senior-level course. Some knowledge of the use of ordinary and partial differential equations to describe problems related to engineering analysis is assumed, as is a rudimentary knowledge of matrix algebra. The book is divided into twelve chapters, each being devoted to some mathematical problems, and four appendices are included to describe reference material. The author starts with an elementary example of the deflection of a tightly stretched wire under a distributed load. This example is sufficient to: (a) refresh the reader on some aspects of differential equations that will prove important for understanding approximate solutions, (b) introduce the concept of approximate solutions, and (c) actually define and illustrate the finite element method (FEM). The next chapters are devoted to linear second order ordinary differential equations, a finite element function for two dimensions, Poisson's equation (FEM approximation, applications). One chapter is devoted to higher-order elements difficulties arising in maintaining continuity of the approximating function between elements. Chapter 9 presents a FEM program for two-dimensional boundary value problems. All codes are written in MATLAB script, which can be run on the student version of MATLAB. Also, a number of applications related to various fields of engineering is provided. In the exercises at the end of most chapters, there is a section on "Numerical experiments and code development" with problems that encourage students to test the codes. All codes, example data files, and auxiliary codes are available for download on the website for this book. Reviewer: Pavol Chocholatý (Bratislava)
Trigonometry 0201703386 9780201703382 Trigonometry: This text is designed for a variety of students with different mathematical needs. For those students who will take additional mathematics, the text will provide the proper foundation of skills, understanding, and insights necessary for success in further courses. For those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in the world today. Many of the applied problems in this text are actually real problems that people have had to solve on the job. With an emphasis on problem solving, this text provides students with an excellent opportunity to sharpen their reasoning and thinking skills. With increased critical thinking skills, students will have the confidence they need to tackle whatever future problems they may encounter inside and outside the classroom.This text is technology optional. With this approach, teachers will be able to offer either a technology-oriented course or a course that does not make use of technology. For departments requiring both options, this text provides the advantage of flexibility. «Show less Trigonometry: This text is designed for a variety of students with different mathematical needs. For those students who will take additional mathematics, the text will provide the proper foundation of skills, understanding, and insights necessary for success... Show more» Rent Trigonometry today, or search our site for other Dugopolski
Pre-assessment will include a discussion of electronic basics to determine how much knowledge the students already have of electronics and batteries. Since this unit is intended for students beginning their study of electronics, it is reasonable to expect that many of the students will have very little pre-existing knowledge about the subject. A mathematics-related pre-assessment will also occur, using some of the calculations necessary for the unit. The mathematics pre-assessment could be issued again after the unit, to see if students' arithmetic skills improved.
In this differentiation instructional activity, students select from a list of differentiation rules which one they have to use to find the derivative of the given equation. They evaluate one integral exactly. Directions are written to solve a related rate problem step by step. There are five example problems to practice solving for related rates. Use of the Chain Rule and/or implicit differentiation is one of the key steps to solving these word problems. Students review vocabulary words for calculus. In this calculus lesson, a list of vocabulary words is provided for students to review. Students may use this list as a review of important terms to know for calculus. Young scholars calculate the velocity of object as they land or take off. In this calculus lesson, students are taught how to find the velocity based on the derivative. They graph a picture the represent the scenario and solve for the velocity.
Basic Algebra, Like Terms, Add and Subtract Expressions Part 1 This class is intended for the novice student who wants to learn algebra beginning with the basis. This video will teach you how to learn three basic components of beginning algebra.This class will teach: Definitions, Collecting Like Terms, and Adding and Subtracting Algebraic Expressions.
Overview of Sheltered Algebra Unit This Algebra I unit on writing and graphing linear equations is designed as a model for sheltered instruction for English language learners. It was developed for Algebra I class in a large urban high school. Classes have eighteen to twenty-five students and are scheduled in blocks of ninety minutes. The teacher has been trained by TEXTEAMS (Texas Teachers Empowered for Achievement in Mathematics and Science) Algebra I: 2000 and Beyond Institute. Part of the institute's goal is for teachers to possess strategies that meet the needs of diverse student populations. Teachers use concrete learning experiences to build mathematical concepts and reasoning that are meaningful to the student. The Algebra I TEXTEAMS training inspires many of the activities in this unit, which is available through regional educational service centers. Technology has been integrated throughout the unit. In particular, students will be using a calculator based ranger (CBR) and graphing calculators. This technology is part of the TEKS and will be used in TAKS. Teachers are encouraged to receive training through the school district of the regional educational service centers on the use of the graphing calculator. A website has also been provided through Region IV ESC. The unit was designed as a model for sheltered instruction; however, it is good for all students due to the engaging activities and strong emphasis on vocabulary and accessing student's prior knowledge. The presentation, materials, and pacing of this lesson have been further modified with second language acquisition strategies to accommodate a diverse class of native English speaking students and LEP students with a wide range of backgrounds and various levels of English proficiency (beginning, intermediate, and advanced). The sequence of lessons within the unit is only a suggestion. Teachers may need to make adjustments based on their students, resources, training and time. Lessons are not necessarily designed to be completed in one class period and may vary from the suggested length of time. The individual teacher determines the time needed to ensure that the students are learning. 1 Writing and Graphing Linear Equations Algebra One Lesson Slope Writing Linear Equations Given Slope and Y-Intercept TEKS c2A, c2B TAKS Objective 3 b1B, c2A, c2B, c2D, c2E, c2F Objective 1 Objective 3 Writing Linear Equations Given a Table, a Graph, the Slope, the Y-Intercept, Two Points, and a Verbal Description b1B, c2A, c2B, c2D, c2E Objective 1 Objective 3 Graphing Lines c2D Objective 3 Evaluating Changes in Slope and Y-Intercepts of Graphs, Equations, and Problem Situations c1C, c2C, c2E, c2F Objective 3 Practicing Changes in Slope and Y-Intercept of Graphs, Equations, and Problem Situation c1C, c2C, c2E, c2F Objective 3 The above TEKS are specifically related to this unit; however, there are ongoing TEKS that are utilized in spiraling the instruction. 2 Inter-disciplinary Information for Algebra One Science Writing and Graphing Linear Equations with Science's Motion Unit The use of the calculator based ranger (CBR) in Algebra translates perfectly to the speed lesson in Science. The students can take their knowledge from lesson 1 using the CBR and Ranger Program to apply it to the lesson associated with calculating speed. 3 Algebra One Unit Writing and Graphing Linear Equations Lesson Plan 1 Finding slope using graphs, tables, and two points Content Objectives The student will learn how to find slope given a graph, table, and two points. The student will understand and develop features of all four types of slopes. The student will use physical representations of the scenarios and work in pairs to work through the activity. SIOP Component(s): Preparation In order for the LEP student to best understand the content objectives, it is essential that it be clearly stated in simple language. The objectives should be given both orally and in written form. Language Objective The student will understand and define the following vocabulary: motion detector, rate, point, line, rise, run, graph, and slope. SIOP Component(s): Preparation It is important in the sheltered instructional setting to establish academic language objectives. LEP students not only learn content, but they acquire academic English skills in reading, writing, listening, and speaking. Special emphasis is placed on the development of math-specific vocabulary. Metacognitive Objectives The student will use a motion detector (CBR) to discover features of slope. The student will use a chart to organize information regarding slope. The student will work in cooperative groups for the Linear Motion activity. 4 Motion detector (calculator based ranger, commonly referred to as CBR)  Assessment: Linear Motion – transparency (TEXTEAMS Algebra 1: 2000 and beyond pages 95 - 96)  Overhead graphing calculator  Student graphing calculators  Graph paper  Rulers  Slope Characteristic Chart SIOP Component(s): Preparation A variety of materials make the lesson clear, meaningful, and help provide concrete examples for the LEP student. Procedure Allow approximately two ninety-minute class periods (1) Prior knowledge should include plotting ordered pairs, simplifying fractions, independent and dependent variables, and finding patterns. SIOP Component(s): Building Background It is important to access students' prior knowledge. If there are knowledge gaps, steps should be taken to build the necessary background. This can be done through mini-lessons that precede the whole-group lesson. (2) The teacher needs to define the following terms as they come up in the lesson: motion detector, rate, point, line, rise, run, graph, and slope. 5 SIOP Component(s): Building Background, Comprehensive Input, Strategies, Interaction Vocabulary used in math is very specific and often difficult to define. The key terms to be defined and discussed in this lesson have multiple meanings. The teacher assists students in distinguishing the meaning that applies to the content, modeling correct usage. Students are encouraged to use the appropriate terms in class work and discussion. Have students create vocabulary cards using the verbal word association strategy. Teachers may reinforce vocabulary with posters or other visual representations in the classroom. (3) At this point, the class will go through the activity, ―Walk This Way.‖ The classroom should be set up with an aisle down the middle, wide enough for a student to easily walk down without distraction from other students. The motion detector should face the aisle from the front of the room and be connected to an overhead-graphing calculator. Make sure that all students can see both the student walking down the aisle and the data projected from the calculator on a screen in front of the room. SIOP Component(s): Comprehensible Input, Strategies The classroom setting is designed to ensure that all students, including LEP students, are involved and encouraged to participate. Setting up the demonstration with the motion detector clarifies the content objective and makes instruction more meaningful through an authentic experience. (4) Explain to students that the motion detector works similarly to the way a police radar gun works by sending out an ultrasonic pulse that measures distance from the motion detector over a period of time. The data the motion detector retrieves will be displayed as a graph on the overhead projector. 6 SIOP Component(s): Comprehensible Input (5) To set up the motion detector for this activity, run the CBR Ranger program and follow the following steps: 1. Link the Ranger Program from the CBR to the graphing calculator. 2. Open the Ranger Program and press enter. 3. Go to main menu and enter number 1 setup/ sample. 4. Set up the next screen as follows: Realtime: Time: Display: Begin on: Smoothing: Units: yes 15 distance enter none feet 7 5. Put the arrow on start now at the top right hand corner. Face the motion detector toward the student walking and press enter. Have students volunteer to walk in front of the motion detector. Have each student walk differently—slow, fast, away from the motion detector, toward the motion detector, stand still, etc. After doing a few of these examples discuss how each style of walking affected the graph. For example, a slow walker has a very flat graph whereas a fast walker has a very steep graph. This is also a good time to review independent and dependent variables. SIOP Component(s): Lesson Delivery The teacher acts as a facilitator allowing students to discover the effect when rate, time, or direction are changed. With this activity, students are motivated and interested because they are actively involved and, through repetition, patterns develop and students can predict the results. (6) At this point, have a student come up with a scenario and then predict what the graph should look like. After the class has completed the discussion, have a student represent the scenario in front of the motion detector and determine if the class prediction is correct. For example, a student starts 8 feet from the motion detector and walks slowly toward the motion detector for 5 second. The student then stands still for 6 seconds and walks back quickly for 4 seconds. Distance in feet Time in seconds Do a few scenarios so that the students get a good understanding of what affects a line and how to draw it as a graph. 8 SIOP Component(s): Comprehensible Input, Strategies Having the students supply the scenario makes instruction more meaningful to them. Students take ownership in their own learning. (7) Pair students to answer the first three questions on the Assessment: Linear Motion transparency. Also assign one problem from problems 4-7 and one problem from problems 8-11 to each pair. As they finish working their problems, have each pair choose one problem to answer on the transparency. Discuss the answers as a class and review all that was discovered through the above activity. SIOP Component(s): Interaction The teacher has lowered the anxiety level in the classroom for the LEP students by allowing them to work in a small group and to choose the problems they want to work on. The demonstration with the whole-class group provides a common, shared experience for the students. Changing to pair work not only allows the LEP student an opportunity to use and practice new knowledge but also 9 By sharing their work with the whole group, students have the results of more than just working one problem. In addition, students gain confidence by sharing their own work. (8) Pass out a sheet of graph paper to each student. Have each student plot two ordered pairs on their graph paper and connect them using the ruler. Walk around the class as the students are doing this to make sure that all four types of slope (positive, negative, zero, and undefined) are being represented. If not, draw that specific slope on a sheet of graph paper to use later. SIOP Component(s): Building Background, Review/Evaluation The teacher takes this opportunity to assess the students' skills and prior knowledge as he/she monitors their work. (9) Have students compare their lines to their neighbor's lines and talk about the differences and similarities. Have the students discuss some of the differences and similarities as a class and write them down on the board or on a transparency to use later. SIOP Component(s): Strategies, Lesson Delivery In this activity, the student has an opportunity to share and learn from peers before being asked for input. Graphic organizers or T-charts are effective strategies for students to learn for recording their thoughts before the class discussions. The teacher may want to make directions more specific, requesting two similarities and two differences in the lines. When the teacher begins to record responses for similarities and differences, all students will be able to participate and contribute. 10 (10) Have each student take his or her ordered pairs and find the slope. The students do not know the concept of slope yet but lead them to discover how to find it. First have the students subtract their y values and their x values. Then have the students set up a fraction with y over x and simplify if necessary. Make the connection to match the graph activity completed earlier. Discuss with the students how this number represents the rate at which their line is moving up or down just like the graph was affected by how fast or slow someone walked. SIOP Component(s): Building Background, Review/Evaluation It's important to reinforce content-specific vocabulary. For example, when the student is asked to set up a fraction, use the terms numerator and denominator. Some students may have the concept but have not connected the word to the concept because of limited English skills. Using actions, visual aids, and gestures helps to define terms for LEP students. (11) Have students compare their answers and lines with their neighbor's lines and talk about the similarities and differences. Discuss this as a class and come up with some generalizations. Write this down on the board or on a transparency to use later. SIOP Component(s): Comprehensible Input Some LEP students may not have the vocabulary to understand classroom instructions. For example, similarities and differences may be difficult for students with very limited English skills. It is important that the teacher explains the task in several ways. Graphic organizers can be especially helpful for students to organize their thoughts. 11 (12) Have the class organize their graphs by categories on the board or wall. As they are organizing the graphs, see what type of categories they are using. Hopefully, the students will be categorizing the lines by the types of slope (positive, negative, zero, and undefined). This is where the lines the teacher drew will be important to include so that all four types will be represented. The teacher may have to lead the students in that direction based on what they are doing. SIOP Component(s): Strategies Students can easily discriminate between graphs in this activity by using feature analysis. The graphs though created by different students and using different data, are excellent visuals. With this strategy, students will identify similarities and differences in the lines that are produced. (13) At this point pass out the characteristic chart to each student. Begin by talking about the four types of slope. Ask the students which group would represent positive slope, negative slope, zero slope, and undefined slope. Once all categories are labeled, have the students draw a sketch of each in the second row of the chart. SIOP Component(s): Strategies Taking the feature analysis one step further, the teacher provides students with a graphic organizer to help categorize and label the different slopes. Graphic organizers provide an excellent tool to make the connection between graphic representations of the slope with the appropriate labels. (14) Review what the similarities and differences are of the four types of slope. Use the ones written on the board or on the transparency as a springboard to get the students started if necessary. As the features are discussed, have them fill in the third row of the chart. 12 Features: Rises to the right Goes up hill Steeper m > 1 Flatter 0< m <1 (reading from left to right) Features: Features: Falls to the right Horizontal Goes down hill Straight Across Steeper m < -1 Flatter -1< m <0 (reading from left to right) Features: Vertical Goes up and down (15) Begin discussing the three ways to find slope: graphing, tables, and two points. Begin with graphing. Talk about how to look at two distinct points on the line and look at the rise (change in y) and the run (change in x). Write the slope as a fraction of y/x and simplify if necessary. Work through a couple of examples on the board or on a transparency. 2 3 Two points: (1, 5) and (-1, 2) The graph rises 3 and runs 2 so the slope is 3/2. (16) Now discuss how to find slope given a table. Use an example problem of a table and talk about how to find the differences of the y values and the differences of the x values to find the patterns. Write the slope as a fraction of y/x and simplify if necessary. x -3 -1 1 3 y -1 2 5 8 -1 - -3 = 2 3–1=2 2 - -1 = 3 8–5=3 After finding the patterns of the table by looking at the differences, the slope can be identified by 3/2. 13 (17) Finally discuss how to find slope given two points. Put an example of two points on the board and have the students discuss and predict how to solve for slope. Work through the problem and write the slope as y/x. Two points: (1, 5) and (-1, 2) 5–2=3 1 - -1 2 or 2 – 5 = -3 = 3 -1 – 1 -2 2 It is key to remember that it does not matter which order pair gets subtracted first, just that both ordered pairs are subtracted in the same order. Keep all three examples on the board and/or transparency so the students can use them as a tool to do their own examples. (18) Put the students in groups of three. Each group will work out a type of problem (positive, negative, zero, or undefined) all three ways (graphing, table, and algebraically). Assign each group a type of slope to work with. Give them about 15 minutes to work the problems and have them put the examples on a blank transparency. Have each group explain its example to the class. Once all the groups have completed the activity, choose one of each type of slope to use as an example to fill in the rest of the chart. Give students time to finish up their charts. As they are completing the charts, walk around and answer any questions. (19) End the lesson with an overall discussion of the chart and slope. SIOP Component(s): Review/Evaluation In summarizing the lesson, the teacher stresses that students are able to use three different methods to find the slope. Students realize that through the use of different methods, they can arrive at the same slope. Technology Application The motion detector (CBR) is used to investigate slope. The teacher can show what a positive and negative slope look like by using a graphing calculator. 14 through discussion and group work. A formal assessment will be given during the lesson through the completion of the chart and group presentations Find a graph or a table in a newspaper, magazine, or the Internet. Find the slope and explain the characteristics of that slope. 15 SIOP Component(s): Review/Evaluation16 17 18 Slope Characteristic Chart POSITIVE SLOPE NEGATIVE SLOPE ZERO SLOPE UNDEFINED SLOPE FEATURES: FEATURES: FEATURES: FEATURES: EXAMPLES: GRAPH: EXAMPLES: GRAPH: EXAMPLES: GRAPH: EXAMPLES: GRAPH: Table: Table: Table: Table: Slope: Two points: Slope: Two points: Slope: Two points: Slope: Two points: 19 Algebra One Unit Writing and Graphing Linear Equations Lesson Plan 2 Writing linear equations given slope and y-intercept Content Objective The student will use a motion detector to write in his/her own words: slope, y-intercept, rate of change, and rate. The student will read, record, and interpret information on tables and graphs. SIOP Component(s): Preparation It is important in the sheltered instructional setting to establish academic language objectives. LEP students not only learn content, but also acquire academic English skills in reading, writing, listening, and speaking. Special emphasis is placed on development of math-specific vocabulary. Metacognitive Objectives The student will use technology to enhance learning. The student will create and use graphic organizers (tables, graphs). SIOP Component(s): Preparation Metacognitive strategies that students acquire will continue to help them even when the teacher is not there to guide them. Strategies enable the student to plan, monitor, and evaluate learning independently. 20 Materials  ―What's My Trend?‖ student activity sheet - transparency and student copies (TEXTEAMS Algebra 1 2000 and Beyond page 167)  ―What's My Trend?‖ graph page – transparency and student copies  ―What's My Trend?‖ assessment – transparencies and student copies (TEXTEAMS Algebra 1 2000 and Beyond page 168 – 169)  Motion detector (CBR)  Overhead graphing calculator  Student graphing calculators  Measuring device SIOP Component(s): Preparation A variety of materials make the lesson clear, meaningful, and help provide concrete examples for the LEP student. Procedure Allow approximately two ninety-minute class periods (1) Prior knowledge should include slope (positive, negative, zero, undefined, steep, and flat), independent and dependent variables, domain and range, plotting and identifying ordered pairs, and patterns. SIOP Component(s): Building Background In the sheltered math class, it is important to activate and assess students' prior knowledge by reviewing vocabulary and key concepts. Teachers should not assume that students make connections automatically. It is necessary to explicitly create a link from prior knowledge or previous lessons to new lessons. In some cases, teachers think that LEP students lack comprehension or memory skills, but this may happen from a lack of or failure to activate prior knowledge. 21 SIOP Component(s): Comprehensible Input Remember that many math concepts are abstract; therefore it is important that LEP students are able to define terms in their own words rather than parrot the teacher or text. (2) At this point, the class will go through the activity, ―What's My Trend?‖ The classroom should be set up with an aisle down the middle wide enough for a student to easily walk down without distraction from other students. The motion detector should face the aisle from the front of the room and be connected to an overhead graphing calculator. Make sure that all students can see both the student walking down the aisle and the data projected from the calculator on a screen in front of the room. This is the same setup as the previous lesson. SIOP Component(s): Preparation, Lesson Delivery The classroom setting is designed to ensure that all students, including LEP students, are involved and encouraged to participate. Setting up the demonstration with the motion detector clarifies the content objective and makes instruction more meaningful through an authentic experience. (3) First pass out the student activity sheet (page 167) and graph page for students to write on throughout the lesson. To start the activity, the teacher begins with the first problem on the student activity sheet. Explain the scenario. ―Start 2 feet away from the motion detector and walk away at 1.5 ft/sec.‖ Have a student physically demonstrate the action by starting exactly 2 feet away from the motion detector and walking down the aisle from the motion detector approximately 1.5 ft/sec. Remind students that the motion detector works similar to the way a police radar gun works by sending out an ultrasonic pulse that measures distance from the motion detector over a period of time. After the students understand the scenario and how the motion detector works, have students complete the table. 22 t 0 1 2 3 t d 2 3.5 5 6.5 2 + 1.5(t) = d SIOP Component(s): Comprehensible Input Auditory information is sometimes difficult for LEP students to process. Through the use of visuals like the motion detector and graphing calculator, instruction becomes comprehensible. The step by step process in the demonstration guides LEP students from a real experience to articulating the same information in a table, in a graph, and orally. SIOP Component(s): Building Background, Comprehensible Input, Strategies SIOP Component(s): Strategies Using a graphic organizer such as a table to organize the data from the motion detector helps LEP students focus their attention and make connections between ordered pairs and the points on the graph. (4) Looking back to the previous lesson, have the students discuss or predict how they think the graph will look. Sketch a graph of the ordered pairs on the provided grid paper and draw the line that is represented by those ordered pairs. Have the students define the independent and dependent variables as well as the domain and range. The teacher should also graph it on large grid paper to help demonstrate the slope and y-intercept. Using the graph, determine the slope and the y-intercept and compare those values to the table. 23 Distance (feet) t 0 1 2 3 t Time (seconds) Point out that the differences of the y values over the differences of the x values is the slope/rate and the starting point is the y-intercept which is always at x or (t) = 0. d 2 3.5 5 6.5 2 + 1.5(t) = d 1–0=1 2–1=1 3–2=1 3.5 – 2 = 1.5 5 – 3.5 = 1.5 6.5 – 5 = 1.5 The above differences give us 1.5/1 which is the slope/rate and the y-intercept/starting point is 2. SIOP Component(s): Comprehensible Input Even though students have been taught to graph ordered pairs and lines in a previous lesson, it is important that the teacher model the skill. LEP students need the visual to reinforce and ensure understanding. LEP students sometimes experience difficulty in understanding instruction when teachers interchange terms with the same meaning. For example, y values over x values and y/x, both mean that the value of y is divided by the value of x. It is often necessary to clarify terminology by defining it in several different ways. (5) Have the students explain in words what happened. For example the total distance is 1.5 times the number of seconds plus the starting point of 2 feet. Then have the students write an equation that represents the written description (y = 2 + 1.5t or y= 1.5t + 2). The graphing calculator can be used to represent the table, graph, and 24 equation. To see how this works see technology applications for this lesson. SIOP Component(s): Practice The verbal expression provides LEP students with practice in using English. Math has a language of its own. Students learn to express a verbal statement in algebraic terms. (6) Now begin working on table 2. Have the students predict what the graph might look like given the scenario. Have a student volunteer to walk away from the motion detector at a constant rate. The data will be portrayed as a line on the graphing calculator. Use the trace function to get the distance at each second. Problem 2: Walk slowly away from the motion detector at a constant rate. 1–0=1 2–1=1 3–2=1 t 0 1 2 3 t d 2.5 3.1 3.9 4.6 2.5 + .7(t) = d 3.1 – 2.5 = .6 3.9 – 3.1 = .8 4.6 – 3.9 = .7 Use the knowledge learned from the first table to find the slope and y-intercept. To find the slope on this table you will have to average the differences of the y values and divide them by the differences of the x values (.6 + .8 + .7 = .7 slope = .7/1). SIOP Component(s): Review/Evaluation Along with learning the identified key content terms, LEP students may need other words defined. For example, in this lesson it may be necessary to review and define the term average. 25 (7) Have the students graph the table and write a description of the scenario in words and then write the same thing as an algebraic equation in slope-intercept form. Continue this same process for each table. When all the tables are complete, put the students into pairs and have them work through the assessment: ―What's My Trend?‖ handout (page 168–169). Walk around to answer questions and to keep each pair on target. As a whole class, discuss the worksheet and go over the answers. (8) SIOP Component(s): Interaction The demonstration with the whole-class group provides a common, shared experience for the students. Changing to pair work not only allows the LEP student an opportunity to use and practice new knowledge but also to SIOP Component(s): Review/Evaluation (9) Once the assessment is completed the teacher will discuss slopeintercept form (y = mx + b) and compare it to the equations the students wrote. Have them determine that ―m‖ is the slope/rate and ―b‖ is the y-intercept/starting point. After they understand the 26 connection to slope-intercept form, introduce standard form (ax + by = c). Discuss each form as linear equations and give examples of how to transform an equation from standard form to slope-intercept form. SIOP Component(s): Practice It is important to note that with the demonstration and activities, the student not only develops an understanding of rates of change but can also express the information as a table, as a graph, in a verbal description, and finally as an algebraic equation. The skills have not been taught in isolation but combine to present the concept and show the relationship between the different skills. The gradual process of taking concrete examples to define abstract concepts scaffolds instruction so that the LEP student can exhibit increasing independence in learning. Technology Applications The motion detector (CBR) and graphing calculator will be used to learn and help write linear equations. This is accomplished using the Lists, Scatter Plots, y =, and linear regression. This can be done for all of the tables in this activity. The steps to accomplish this are as follows: 1. Push the STAT button and push enter on Edit. 2. The list screen should appear with L1, L2, etc. 3. Plug in the values for time into L1 and the values for distance into L2. 27 4. Push STAT PLOT by entering 2nd Y=. 5. Push enter on 1 and set up the screen to On, scatter plot: (first graph), Xlist: L1, Ylist: L2, Mark: any. 6. Push Window and set up your view window to include all the x values and all the y values. Give a few below the lowest numbers and few above the highest numbers. 7. Push Graph 8. Test your graph by plugging in your equation into y= and graph. 28 9. A linear regression can be found by going to Stat – Calc – 4:Linear Regression (ax + b). This gives you the most accurate equation for your data. SIOP Component(s): Building Background when the pairs are working on the assessment worksheet. The teacher should walk around and answer questions and informally rate the students' understanding. A formal assessment (additional practice) could be given to assess individual understanding of the concept. The handout may also be used as additional practice or an alternative assignment for LEP students because it does not require extensive reading in English. 29 The students will develop a graph for a given scenario by inputting their own points and scales. In the extension, each student will have to fill in the table, determine the rates, write a description, and write an equation in slopeintercept form and standard form. 30 What's My Trend? Graph Page 1. 2. 3. 4. 5. 6. 31 Additional Practice Given the situation plot a graph; write a description, and an equation. 1. Susan started 3 feet from the motion detector and walked away at a constant rate of 2 ft/sec. t 0 1 2 3 t Description: Equation: 2. Use the given table to plot a graph, write a description, and an equation. t 0 1 2 3 t Description: Equation: Write an equation in slope-intercept form for each problem. Distance (feet) Distance (feet) Time (seconds) 3. 4. d 8 7.2 6.2 5.3 Distance (feet) Time (seconds) d Distance (feet) Time (seconds) Time (seconds) 32 5. slope: -3 y-intercept: 5 6. slope: ½ y-intercept: -2 7. slope: 4 y-intercept: 0 33 Transform each from standard form into slope-intercept form. Identify the slope and y-intercept in each. 8. 8x + y = 12 9. x – y = 9 Equation: Slope: Y-intercept: 10. 4x + 2y = -10 Equation: Slope: Y-intercept: 11. 3x – y = 6 Equation: Slope: Y-intercept: Equation: Slope: Y-intercept: 34 Extension Fill in the blank grid below with a graph that demonstrates you riding in a car. Label the time and distance scales to help determine your graph. Using your scale and your graph fill in the table then write an equation and write a description. 20 Distance ( ) 15 10 5 0 5 Time ( 10 ) 15 20 2. Fill in the table. Time 0 5 10 20 t Distance 3. Write the equation for your graph and table. 4. Write a description represented by your graph, table, and equation. 35 Algebra One Unit Writing and Graphing Linear Equations Lesson Plan 3 Writing linear equations given a table, a graph, the slope, the y-intercept, two points, and a verbal description Content Objectives The student will discover how to take a written description to fill in a table, draw a graph, and write a symbolic equation. The student will also take a table and draw a graph, write a symbolic equation, and a verbal description scales, rate of change, constant rate, motion detector (CBR), slope and y-intercept. The student will understand how to write a symbolic equation and verbal description physical representation of the scenarios and collaborate with a partner on the activity. The student will complete tables and graph data. 36 SIOP Component(s): Preparation Metacognitive strategies that students acquire will continue to help them even when the teacher is not there to guide them. Strategies enable the student to plan, monitor and evaluate learning independently. Materials  ―Wandering Around‖ Activity 1 sheets - transparencies and student copies (TEXTEAMS Algebra 1 2000 and Beyond pages 158 - 159)  ―Describe the Walk‖ Activity 2 sheets – transparencies and student copies (TEXTEAMS Algebra 1 2000 and Beyond pages 160 - 161)  Writing Equations Chart – transparency and student copies  Additional Practice  Quiz SIOP Component(s): Preparation A variety of materials make the lesson clear, meaningful, and help provide concrete examples for the LEP student. Procedure Allow approximately two ninety-minute class periods (1) Prior knowledge should include the use of the motion detector, independent and dependent variables, finding slope from a table or graph, plotting and identifying ordered pairs, patterns, slope-intercept form, standard form, and filling in a table given a rate and a starting point. SIOP Component(s): Building Background Linking previous lessons to new learning can activate prior knowledge. Students do not automatically make connections, and the teacher may need to explicitly point out past learning. (2) The teacher needs to define the following terms: scale, rate of change, constant rate, motion detector, slope, and y-intercept. 37 SIOP Component(s): Building Background The teacher selects and focuses on critical key terms that will be used in the lesson. The vocabulary is defined as students work through the activity. Students will define the terms as the lesson progresses. Reinforcement will be oral, written, and visual. (3) First review the lesson on writing an equation given the slope and yintercept by leading the students in completing the first part of the writing equations chart. Example: slope = 3, y-intercept = -2; equation: y = 3x – 2 SIOP Component(s): Building Background Skills learned in a prior lesson are reviewed and linked to new concepts, building and reinforcing prior knowledge. (4) At this point the class will go through Activity 1: Wandering Around. Each student needs a copy of the handout, and the teacher needs to use the overhead copies to complete the activity. In this activity the student will look at a situation and fill in a table, a graph, a written symbolic equation, and a verbal description. The teacher will begin with a review of how the motion detector worked and the type of information it produces. If necessary, the teacher could do an example with the use of the motion detector to help remind the students how it works. The teacher will begin with the first problem by having a student read and walk through the scenario. ―Ryan was walking away from the motion detector at 2 feet per second. You missed where he started but you know that he was at the 9 foot mark when the timer called out the 3rd second.‖ Have a student demonstrate walking away from the motion detector and stop after 3 seconds and 9 feet away. This helps the students understand exactly what the scenario is explaining. After the students (5) 38 understand the scenario walk them through completing the table and graphing the ordered pairs. t 0 1 2 3 4 d 3 5 7 9 11 Distance (feet) Time (seconds) The teacher will need to discuss the independent variable (time which is on the x-axis) and dependent variable (distance which is on the yaxis) along with the scales of the graph. SIOP Component(s): Comprehensible Input, Strategies, Lesson Delivery Students are actively engaged in problem solving. The teacher has the student reading the problem and acting out the problem. For LEP students that are struggling with English reading comprehension, this activity promotes understanding. The class participates in going through the stepby-step procedures for completing the table and graphing the data. (6) The teacher will need to lead the student to write the equation using the slope (rate) and the y-intercept (starting point). The teacher should show that the differences of y (distance) over the differences of x (time) is the slope and the starting point where x = 0 (time = 0) is the y-intercept. The equation should be written in slope-intercept form (d = 2t + 3 or y = 2x + 3). SIOP Component(s): Comprehensible Input Throughout this activity, the teacher models the reasoning process by verbalizing whatever comes to mind. This helps the student make connections and see the importance of the process rather than the product. (7) Now work on the second problem exactly as the first problem. In this problem the student is walking toward the motion detector, which 39 means the slope is going to be negative. Have the students fill in the table, graph, and write the equation. ―Madeline was walking toward the motion detector at 3 feet per second. You missed where she started, but you know that she was at the 9 foot mark at the 2nd second.‖ Distance (feet by 2's) Time (seconds) t 0 1 2 3 y = -3x + 15 d 15 12 9 6 SIOP Component(s): Comprehensible Input, Strategies Multiple examples are provided for students to develop a better understanding of the concepts. Each example has been selected to demonstrate a variety of situations that may occur. When students work independently they can refer to the models and notes from the class activity. (8) At this time the teacher can use the writing equations chart and begin making the connection on how to write an equation given the slope and a point. Algebraic example: slope is -3 and goes through the ordered pair (2,9) Using y = mx + b, plug in -3 for m, 2 for x, and 9 for y. Solve the equation for b. 9 = -3(2) + b 9 = -6 + b 15 = b So the equation of the line would be y = -3x + 15. 40 SIOP Component(s): Practice The teacher provides the student with ample guided practice. Problems used in practice are specifically chosen to link with the next concepts that will be introduced to the student. (9) Problems three and four are done exactly the same way as above except in these problems the scenarios provide two points. The students will have to determine the slope and the y-intercept from the table and write an equation. After completing these problems, the teacher can use the writing equations chart and begin making the connection on how to write an equation given two points. ―You looked up and Chet was walking. He was at the 6 foot mark at the 1st second and the 1 foot mark at the 2nd second.‖ Distance (feet) Time (seconds) t 0 1 2 3 y = -5x + 11 d 11 6 1 -4 Algebraic Example: given the two points (1,6) and (2,1) First the student must find the slope. 1 – 6 = -5 2–1 1 Using y = mx + b, plug in -5 for m, and either 2 for x, and 1 for y or 1 for x and 6 for y. Solve the equation for b. 1 = -5(2) + b 6 = -5(1) + b 1 = -10 + b 6 = -5 + b 11 = b 11 = b So the equation of the line would be y = -5x + 11. 41 (10) In Activity Two the students will take the information from the table to graph the points, as well as write a symbolic equation and a verbal description. The symbolic equation will be written the same as the other activity using the slope and y-intercept, point and y-intercept, or two points. The written verbal description should be similar to the scenarios written in Activity One. Distance (feet by 3's) Time (seconds) t 0 1 2 d 15 21 27 Symbolic equation: given the y-intercept and several points First the student must find the slope. 21 – 15 = 6 1–0 1 Using y = mx + b, plug in 6 for m and 15 for b. So the equation would be y = 6x + 15. Verbal description: Sam started 15 feet from the motion detector and walked away from it 6 feet per second. SIOP Component(s): Comprehensible Input, Practice In this problem the teacher adds an additional skill, practice writing verbal descriptions for given data. This may seem difficult for some LEP students however, the teacher can refer to the description in prior problems to model writing. (11) Put the students in pairs to finish working the last three problems. As the students are working, the teacher should walk around and answer any questions. As the groups finish, have each group write in one part of the problem (graph, symbolic equation, and verbal description) on 42 the transparency to show the entire class. This will allow for discussion and summary of the entire lesson. SIOP Component(s): Interaction, Lesson Delivery The large group summary allows students to participate and share information. Even if a student does not understand all of the concepts or could not complete the entire task, students could still contribute. Technology Applications A graphing calculator can be used in several ways to check the students' work. The students can check their equations and graphs by looking at the table and graphs on the graphing calculator. Inputting their equation into the y = screen and then pushing graph will check their graph and pushing 2nd graph will check their table. Remember to set up the window with the values on your table (remember to go below a few and above a few). The screens below will help demonstrate the above process. Additional help is available on the Region IV website graphing calculator tutorial. SI 43 Assessment An informal assessment will be given during the lesson when the pairs are working on the activity sheet and writing up their answers on the transparencies. The teacher should walk around and answer questions and informally rate the students understanding. A formal assessment will be given to assess individual understanding of the concept in the form of additional practice. Another formal assessment will be given the following class period in the form of a quiz Depending on the needs of the students, the teacher determines if and how to best use the additional practice assignment or if it is needed. The practice may be used as a tutorial for students who need the extra time and attention to better understand the concepts. Extensions Each student needs to find a table or a graph in a newspaper, magazine, or on the Internet. The student will find the slope (rate) and the y-intercept (starting point) and write a symbolic equation and a verbal description matching their data. 44 SIOP Component(s): Building Background, Comprehensible Input, Strategies, Practice, Lesson Delivery45 Writing Equations Chart Type Given the slope and the y-intercept Problem Given: slope = 3 y-intercept = -2 Plug in 3 for m and –2 for b Solution Y = 3x –2 Or Y = 3x + -2 Given the slope = –3 ordered pair = (2,9) Y = -3x + 15 slope and an Ordered pair Plug in – 3 for m, 2 for x, and 9 for y 9 = -3(2) + b 9 = -6 + b 15 = b Given two two ordered pair (1,6) and (2,1) Y = -5x + 11 Ordered pairs Find slope 1 – 6 = -5 2–1 1 Plug in –5 for m, 2 for x and 1for y, or 1 for x and 6 for y 1 = -5(2) + b 6 = -5(1) + b 1 = -10 + b 6 = -5 + b 11 = b 11 = b Distance (feet) Given a Graph Find the y-intercept and slope y-intercept is 3 slope is 2 Time (seconds) Y = 2x + 3 Given a Table Find the slope by difference of y over the difference of x Find the y-intercept where x = 0 x y 0 3 slope is 4 1 7 y-intercept is 3 2 11 Y = 4x + 3 46 Writing Equations Chart Type Given the slope and the y-intercept Given the slope and an Ordered pair Problem Solution Given two Ordered pairs Given a Graph Given a Table 47 Additional Practice Label the table and graph. Fill in the table, sketch the graph, and write a symbolic rule for the situation (write the equation for the table and graph). 1. Sean was walking away from the motion detector at 3 feet per second. You missed where he started, but you know that he was at the 15 foot mark when the timer called out the 4th second. TABLE GRAPH RULE 2. Stacey was walking toward the motion detector at 2 feet per second. You missed where she started, but you know that she was at the 4 foot mark at the 2nd second. TABLE GRAPH RULE 3. Jessica started 3 feet from the motion detector. You looked up and she was at 11 feet at the 2nd second. TABLE GRAPH RULE 4. You looked up and Aaron was walking. He was at the 4 foot mark at the 1st second and the 1 foot mark at the 2nd second. TABLE GRAPH RULE 48 Label the table and graph. Sketch the graph. Write a symbolic rule and a description of the walk. 5. 0 1 2 TABLE TIME DISTANCE GRAPH 1 3 5 RULE 6. 0 1 2 TABLE TIME DISTANCE GRAPH 1 5 9 RULE 7. 1 2 3 TABLE TIME DISTANCE GRAPH 6 4 2 RULE 8. 0 1 2 TABLE TIME DISTANCE GRAPH 0 3 6 RULE 9. 2 4 6 TABLE TIME DISTANCE GRAPH 4 2 0 RULE 49 10. 1 3 5 TABLE TIME DISTANCE GRAPH 2 4 6 RULE 50 QUIZ Label the table and graph. Fill in the table, sketch the graph, and write a symbolic rule for the situation (write the equation for the table and graph). 5. Sean was walking away from the motion detector at 2 feet per second. You missed where he started but you know that he was at the 10-foot mark when the timer called out the 4th second. TABLE GRAPH RULE 6. Sue was walking toward the motion detector at 3 feet per second. You missed where she started but you know that she was at the 5-foot mark when the timer called out the 1st second. TABLE GRAPH RULE Label the table and graph. Sketch the graph. Write a symbolic rule and a description of the walk. 3. 0 1 2 TABLE TIME DISTANCE GRAPH 5 9 13 RULE 51 4. 2 3 4 TABLE TIME DISTANCE GRAPH 5 7 9 RULE 52 Algebra One Unit Writing and Graphing Linear Equations Lesson Plan 4 Graphing lines Content Objective The student will learn how to graph a line given two points, slope and point, and Objective The student will understand and define the following vocabulary: graph, coordinate plane, x and y- axis, slope and y-intercept Objective The students will use a concrete model (transparency lines and coordinate plane) to graph and work in pairs to complete the activity. SIOP Component(s): Preparation Metacognitive strategies that students acquire will continue to help them even when the teacher is not there to guide them. Strategies enable the student to plan, monitor, and evaluate learning independently. 53 Materials  Large grid paper  Regular graph paper  Transparency lines or spaghetti (if using the transparency lines make a transparency of this handout and separate each line)  Graphing activity SIOP Component(s): Preparation A variety of materials make the lesson clear, meaningful, and help provide concrete examples for the LEP student. Procedure Allow approximately 1 ninety-minute period (1) Prior knowledge should include the understanding of slope, y-intercept, ordered pairs, and basic graphing on a coordinate plane. SIOP Component(s): Review/Evaluation In this lesson, the teacher reviews terms and concepts previously taught in the unit. It is important to establish a strong foundation before proceeding and making links to new tasks. LEP students will benefit from having the important terms repeated and reinforced. (2) Pass out a sheet of graph paper to each student. Then give the students two points (such as (-2, 3) and (4, 2)) and ask them to graph the line. Label the line A. Then give the students a slope and a point (such as m = 2 and (-2, -5)) and have them graph that line. Label that line B. Have the students discuss and review the process they used to graph both lines A and B. 54 SIOP Component(s): Review/Evaluation, Interaction In reviewing the procedures for graphing lines, the teacher has the student making the graph, talking about the task in his/her own words. This reinforcement of the procedure demonstrates real understanding rather than mimicking memorized responses. If a student is having difficulty verbalizing the procedure, the teacher can paraphrase the student's words using appropriate terminology and clarifying ideas. (3) Review slope-intercept form focusing the review on slope ―m‖ and yintercept ―b‖. Refer back to the previous lesson and discuss how the yintercept is the beginning point (the starting point in previous activity) and the slope is the rate (the rate in the previous activity). To help graph y = mx + b, stress that one starts with begin with ―b‖ and move with ―m‖. Take time to do some examples for them. (Example Problem Transparency) SIOP Component(s): Strategies; Comprehensible Input The teacher provides students with an additional strategy, a mnemonic device that is used to help students recall information. Time should be spent in explaining the alternate representation of the letters m and b. This tool can be helpful for LEP students because the words are easily understood and represent the action on the graph. (4) The following activity will help reinforce and practice graphing. Pair up all students. Pass out a large coordinate plane and a transparency line or spaghetti to each student. Give them a problem (Example Problem Transparency) and have them use the transparency line or spaghetti to graph on the large coordinate plane. Have the pairs check their answer with each other to determine the correct answer. They can also use a graphing calculator to check their graphs. Continue doing practice problems until the class has a good grasp of graphing lines. 55 SIOP Component(s): Comprehensible Input, Practice LEP students build comprehension and understanding by practicing skills in a variety of activities. Even though students have been exposed to the skill and practiced graphing, changing the format of the practice keeps the student's interest and actively engaged in learning. (5) At this time pass out the graphing game. Each pair needs a set of cards and a scorecard. Place the cards equation side up. Both students make sure the equation is in slope intercept form and then graph the equation using their large grid paper and transparency lines/spaghetti. When both students have completed the graph, check it by looking at the back of the card. If the student gets it correct, they give themselves two points. If it is incorrect, they lose a point. Continue play for 5 minutes. After 5 minutes, have the students total up their score and record it on the scorecard. Have the winners rotate around the room to another partner and continue play. This activity will allow the students to practice graphing and help peers teach each other. SIOP Component(s): Interaction, Practice, and Strategies The game format provides yet another way for students to actively participate and interact with peers while getting additional practice and immediate feedback on their understanding of graphing. Technology Applications The graphing calculator can be used in this lesson to check their graphs. They could use them before the activity when they are in partners. They could also be allowed to use them in the game to check their answers before they look at the back of the card. If the calculator is used they might only get 1 point instead of 2 points. See lesson 3 for information on how to check equations and graphs. 56 as the pairs are working on the practice problems and during the game. A formal assessment could be given during the game by looking at the scorecards Extensions Each student will write an equation and graph it for all four types of lines (positive, negative, horizontal, vertical). 57 Transparency Lines 58 59 Example Problems (2,4) and (-1,0) (-2, -3) and (3, 6) slope = 3, (1, 3) slope = ½, (-2, 3) slope = -4, (-3, -4) slope = 1, (2, 5) Y = 2x + 2 Y=½x+3 Y = 4x - 1 Y = 1/4x - 2 Y = -2x + 2 Y = -1/2 x – 2 Y = -4x + 3 Y = -1x – 3 Y=x Y = -x 2x + y = 4 2x + 4y = -8 x + y = -2 x + 3y = 6 x – 2y = 10 60 Name: _____________________ Name: __________________________ Game 1: Your score Their score Game 1: YourName: ______________________ Game 1: Your score Name: _____________________ Game 1: Your score Their61 y = 2x + 4 3x – y = -1 y=x–4 2x – y = 1 y=x+3 x – y = -4 y = 4x - 7 2x – y = 0 62 y = -2x + 4 3x + y = 1 y = -x – 4 2x + y = - 1 y = -x + 3 x+y=4 y = -x 2x + y = 0 63 y = 1/2x + 4 2x – 3y = -3 y = 2/3x – 4 x – 2y = 2 y = 3/4x + 3 x – 3y = 12 y = 3/4x x – 2y = 0 64 y = -1/2x + 4 2x + 3y = 3 y = -2/3x – 4 x + 2y = -2 y = -3/4x + 3 x + 3y = -12 y = -3/4x x + 2y = 0 65 (2, 4) and (-1, 2) (-3, -4) and (0, 2) (3, 0) and (-6, 0) Slope = 3 Point = (-1, 0) Slope = -2 Point = (3, 2) Slope = 1/2 Point = (-2, -3) Slope = - 2/3 Point = (3, 1) Slope = - 1 Point = (2, 2) 66 67 Algebra One Unit Writing and Graphing Linear Equations Lesson Plan 5 Evaluating changes in slope and y-intercept of graphs, equations, and problem situations Content Objective The student will learn to evaluate how changes students will use a graphing calculator to discover how transformations affect graphs, equations, and problem situations. Students will work in pairs to practice problems. 68 Problem Situation Activity – transparency and student copies  Student graphing calculators  Overhead graphing calculator SIOP Component(s): Preparation A variety of materials make the lesson clear, meaningful, and help provide concrete examples for the LEP student. Procedure Allow approximately 1 ninety-minute class period (6) Prior knowledge should include the understanding of slope, y-intercept, table, and graphing on a coordinate plane. SIOP Component(s): Building Background In this lesson, the teacher reviews terms and concepts previously taught in the unit. It is important to establish a strong foundation before proceeding and making links to new tasks. LEP students will benefit from having the important terms repeated and reinforced. (7) Review graphing of a linear equation from slope-intercept form focusing on slope as a rate and y-intercept as the starting point. 69 SIOP Component(s): Review/Evaluation It is important to continually reinforce vocabulary and concepts to ensure that all students are developing a clear understanding of the content objectives. Teachers may need to revise, reword, and/or redirect instruction to spiral content understanding. (8) Begin teaching transformations by beginning with the parent function y = x. Draw a picture of the graph and begin answering each of the discussion questions. The teacher should guide the students through the use of the graphing calculator to check each answer. What would happen to the graph and the equation if I moved it up two units? y=x+2 y-intercept would change to 2; slope would be the same What would happen to the graph and the equation if I moved it down 4 units? y=x–4 y-intercept would change to -4; slope would be the same What would happen to the graph and equation if I added 6 to the y-intercept? y=x+6 y-intercept would change to 6; slope would be the same What would happen to the graph and equation if I subtracted 10 from the yintercept? y = x – 10 y-intercept would change to -10; slope would be the same What would happen to the graph and equation if I multiplied the slope by 1? y = -x y-intercept stays the same; slope changes to -1 which changes the direction of the line What would happen to the graph and equation if I multiplied the slope by 4? y = 4x 70 y-intercept stays the same; slope changes to 4 which makes the graph steeper What would happen to the graph and equation if I multiplied the slope by 1/2? y = -1/2x y-intercept stays the same; slope changes to –1/2 which changes the direction of the line and makes the graph flatter What would happen to the graph and equation if I multiplied the slope by -1 and added 3 to the y-intercept? y = -x + 3 y-intercept changes to 3; slope changes to -1 which changes the direction of the line All of these questions are examples of transformations of linear equations. At this point pair up the students and have them work through another example (such as y = 2x + 1) answering the same questions. Each pair should write the new equation and draw a graph for each question. When they finish this problem, have them use the graphing calculators to check their equations and graphs. SIOP Component(s): Strategies, Interaction, Review and Evaluation The questioning technique used by the teacher is designed to help students explore transformations. Answers are not linguistically demanding so that students with limited oral skills in English can participate. The teacher has walked students through the process, asking questions and thinking aloud. The LEP student benefits from following the thought process. This allows students an opportunity to ask their own questions as they develop. The activity also allows for self-evaluation and immediate feedback when students check the equations and graphs on the graphing calculator. (9) Pass out the Problem Situation Activity to each student. Read the scenario aloud in class and ask a student to explain what the scenario is saying. Have the students fill in the table, write an equation, and graph a line for the scenario. 71 Time (weeks) 0 1 2 3 4 5 Equation: y = 20x + 1050 Amount Saved by $10's Begin with 1050 Process $1050 1(20) + $1050 2(20) + $1050 3(20) + $1050 4(20) + $1050 5(20) + $1050 Amount Saved $1050 $1070 $1090 $1110 $1130 $1150 Weeks by 1's SIOP Component(s): Comprehensive Input, Practice The application problem is clearly stated and the topic is relevant to high school students. This attracts the student's attention and helps to keep him/her actively focused on completing the table and graphing the results. (10) Begin answering the questions on the worksheet. How would the equation and graph change if Tim made $200 during the summer? y = 20x + 200 72 The y-intercept (starting point) is lower and the slope is the same. How would the equation and graph change if Tim received $10 a week for chores? y = 10x + 1050 The y-intercept is the same but the slope is smaller (less steep). Compare the slopes and y-intercepts in the following two equations. In the first equation the slope is smaller (less steep) and the y-intercept is greater. What changes in the scenario resulted in a change in the steepness of a line? the slope What changes in the scenario resulted in a change in the starting point of a line? the y-intercept SIOP Component(s): Lesson Delivery The questions on the handout provide an opportunity for LEP students to practice writing in a very natural way. Responses do not require extensive academic writing skills but communicate essential information and ideas. (11) Close the lesson by discussing how transformations affect a graph, an equation, the slope, and the y-intercept. SIOP Components(s): Strategies In summarizing the lesson, students are encouraged to reflect and consider the observations they made in both a real world and a hypothetical problem. The teacher monitors and guides responses and may need to paraphrase student responses to model the appropriate math vocabulary and English usage. 73 Technology Applications The graphing calculator can be used throughout this lesson to check their equations and graphs. To help the understanding of transformations, the graphing calculator can be used to investigate steepness, flatness, and varying starting points through the discussion in class. A formal assessment can be assessed through the Problem Situation Activity sheet 74 Formal assessment evaluates the individual student's comprehension and learning of the lesson's objectives. In addition, the assessment measures the student's procedural knowledge for problem solving. Extensions Develop a scenario with a table, graph, and equation. Use that information to describe 4 changes in slope and y-intercept from the scenario. Write the new equations for each change. 75 Problem Situation Activity Tim worked all summer mowing lawns and made $1050. When school starts, Tim cannot work anymore but his parents pay him $20 a week for doing chores around the house. Instead of spending his money Tim has decided to save his money to purchase a car next year. 1. Make a table that represents the above scenario. Time (weeks) Process Amount Saved 2. Write an equation that represents how much money Tim will have saved after t weeks. 3. Sketch a graph. 76 4. How would the equation and graph change if Tim made $200 during the summer? 5. How would the equation and graph change if Tim received $10 a week for chores? 6. Compare the slopes and y-intercepts in the following two equations. y = 12x + 500 y = 20x + 250 7. What changes in the scenario resulted in a change in the steepness of a line? 8. What changes in the scenario resulted in a change in the starting point of a line? 77 Algebra One Unit Writing and Graphing Linear Equations Lesson Plan 6 Practicing transformations in slope and y-intercept of graphs, equations, and problem situations Content Objective The student will learn to evaluate how changes a graphing calculator to discover how transformations affect graphs, equations, and problem situations. The students will work in pairs to practice problem solving. The student will reflect and evaluate his/her participation in the different stations as to the ease and difficulty of the task. 78 SIOP Component(s): Preparation Metacognitive strategies that students acquire will continue to help them even when the teacher is not there to guide them. Strategies enable the student to plan, monitor and evaluate learning independently. Materials  Stations (Sheets for stations 1 – 6)  Station Worksheet  4 dice (2 with numbers 1- 6, 2 with positives and negatives)  Grid paper  Transparency lines  Student graphing calculators SIOP Component(s): Preparation A variety of materials make the lesson clear, meaningful and help provide concrete examples for the LEP student. Procedure Allow approximately 1 ninety-minute class period (1) Prior knowledge should include the understanding of transformations. SIOP Component(s): Building Background Transformation is an important concept in mathematics. The teacher presents the word's meaning within the content area. The word is modeled by the teacher and defined by its use with familiar skills. (2) Review transformations by graphing, writing equations, and through problem situations. 79 SIOP Component(s): Building Background, Comprehensive Input Through the use of guided instruction of transformations, teachers activate, assess, and reteach content before beginning the station activities. (3) Put the students into pairs. Pass out the station worksheet to each student. Explain the six stations and how to rotate around them. SIOP Component(s): Comprehensive Input, Lesson Delivery Directions for the stations offer step-by-step instructions and clearly explain the process. It is best to simplify sentence structure in text used in directions. SIOP Component(s): Interaction Students work through the stations with a partner. This allows for collaboration and ample opportunities to communicate and learn from peers. Station 1: The students will use the grid paper and transparency lines. The student will graph the original problem with the transparency line and then translate line according to the instructions. The student will need to graph the original problem, graph the new problem and write the new equation on the station worksheet. (Similar to lesson 4) Station 2: The students will use a numbered die and a sign die. The original problem will be posted at the station. The student rolls the numbered die and the sign die twice. The first roll of each goes with the slope the second roll of each goes with the y-intercept. The number for the slope is what you multiply the slope by to find the new slope and the number for the y-intercept is what you add or subtract to find the new number. After the student gets the new equation they graph it and write a verbal description to explain the changes of the new equation on the station worksheet. (Similar to lesson 5) Example: y = 2x + 3 original problem First roll = 4 and + Second roll = 2 and – 80 y = 8x + 1 new problem ~ multiply positive 4 to the slope and subtract 2 from the y-intercept Graph the new equation. The new equation is steeper and remained positive and the y-intercept is smaller. Station 3: The students will use graphing calculators to explore the effects of changing slope and y-intercepts. This station will have 3 sets of 4 equations to graph and then a couple of questions to answer based on the graphs. The graphs and answers to questions should be written on the stations worksheet. Station 4: The students will look at a problem situation and fill in a table, a graph, write an equation, and answer some questions based on a scenario. Each answer should be placed on the station worksheet. (Similar to lesson 5) Station 5: The students will review graphing lines given in slope-intercept form and standard form. Each equation needs to be written and graphed on the station worksheet. (Similar to lesson 2) Station 6: The students will review writing an equation given a graph, table, or slope and y-intercept. Each equation needs to be written and graphed on the station worksheet. SIOP Component(s): Strategies, Interaction, Practice, Lesson Delivery Actively working at the different stations with a partner engages the LEP student in a variety of activities where they can express understanding of content objectives. This classroom setting also reduces the linguistic demands on students' limited English skills. (4) After the stations are complete, have the students discuss the station that was the hardest and the station that was the easiest. This should allow for some good discussion of concepts. 81 SIOP Component(s): Planning Time has been built into the lesson for student self-evaluation. Students are asked to think about and give their opinion as to the ease and difficulty of each of the stations and the reasoning behind it. This also offers the teacher an opportunity to further assess the needs of students who may need more attention or tutorials. Technology Applications The graphing calculator is used on station 3 to discover more about transformations done while observing the students as they work through the stations. The teacher may want to use a chart similar to the one on page X to identify students who need extra assistance. A simple check system identifies students who successfully completed the different stations. A formal assessment will be done through the station worksheet 82 Formal assessment evaluates the individual student's comprehension and learning of the lesson's objectives. In addition, the assessment measures the student's procedural knowledge for problem solving. Extensions Develop an example of a station that could be used to help practice transformations. 83 STATION 1 Use the grid paper and transparency line to graph the following equations and then to make transformations to those equations. 1. y = 2x + 4 Translate this graph down 2 units. Graph the new line. Write the new equation. 2. y = (1/2)x – 3 Translate this graph up 4 units. Graph the new line. Write the new equation. 3. 2x + y = 6 Translate this graph down 2 units. Graph the new line. Write the new equation. STATION 2 84 Roll each die twice. The first roll of each goes with the slope the second roll of each goes with the y-intercept. The number for the slope is what you multiply the slope by to find the new slope, and the number for the y-intercept is what you add or subtract to find the new number. Write the new equation and a verbal description explaining the changes from the original equation. Example: y = 2x + 3 original problem First roll = 4 and + Second roll = 2 and – y = 8x + 1 new problem ~ multiply positive 4 to the slope and subtract 2 from the y-intercept Graph the new equation. The new equation is steeper and still positive and the y-intercept is smaller. Problems: 1. y = 3x + 1 2. y = 4x - 4 3. y = -6x + 8 4. y = -2x STATION 3 85 Use a graphing calculator to graph the following equations on the same graph. Answer the following questions for each. 1. Graph: y=x y = 2x y = 4x y = 8x Questions: a. How are these lines alike? b. How are these lines different? c. What happens to the graph as "m" gets bigger? (y = mx + b) 2. Graph: y=x y = 1/2x y = 1/4x y = 1/8x Questions: a. How are these lines alike? b. How are these lines different? c. What happens to the graph as "m" gets smaller? (when m is between 0 and 1) 3. Graph: y=x y = 2x y = 2x + 3 y = -2x - 2 Questions: a. Explain how 2 and -2 in front of the "x" change the graph compared to y = x? b. Explain what the y-intercepts of 3 and -2 do to the graph? STATION 4 86 Read the scenario below and answer all the questions. Susie received a gift of $50. She also gets $10 a week for doing chores around the house. Instead of spending her money Susie has decided to save her money to purchase a new ring. 1. Make a table that represents the above scenario. Time (weeks) Process Amount Saved 2. Write an equation that represents how much money Susie will have saved after t weeks. 3. Sketch a graph. 4. How would the equation and graph change if Susie got $100? 5. How would the equation and graph change if Susie received $15 a week for chores? 6. Compare the slopes and y-intercepts in the following two equations. y = 15x + 50 y = 5x + 100 STATION 5 87 Sketch a graph of the following lines. Make sure they are in slopeintercept form ( y = mx + b). 1. y = -3x – 2 2. y = -1/3 x - 3 3. 4x – 2y = 6 4. 3x + 4y = -8 5. x + y = -3 STATION 6 88 Write an equation given a table, graph, two points, or slope and yintercept. 1. 0 1 2 3 4 2 4 6 8 10 2. slope = -2 y-intercept = 3 3. 4. (2, 4) (4, 12) 5. -1 1 3 5 7 Station 1: 6. (0, 4) (1, 3) 0 3 6 9 12 Station Worksheet 89 1. 2. 3. new equation: new equation: new equation: Station 2: 1. equation: 2. equation: 3. equation: 4. equation: description: description: description: description: Station 3: 1. 2. 3. Questions: a. b. c. Station 4: Questions: a. b. c. Questions: a. b. 90 Time (weeks) Process Amount Saved 2. equation: 3. graph: 4. 5. 6. Station 5: 1. 2. 3. 4. 5. Station 6: 1. 2. 3. 4. 5. 6. 91
Book Description: Learn math the easy way with ELEMENTARY ALGEBRA! Study sets at the end of every chapter will improve your ability to read, write, and communicate mathematical ideas. Difficult concepts are made clear with a five-step approach to problem-solving: analyze the problem, form an equation, solve the equation, state the result, and check the solution. Prepare for exams with numerous resources located online and throughout the text such as live online tutoring, tutorials, the book companion website, chapter summaries, self-checks, practice sections, and reviews. Take advantage of the accompanying Video Skillbuilder CD-ROM that will save you class preparation time through video lessons, web quizzes, and chapter tests.
Resources for math teachers Resources for Algebra 1 and Algebra 2 Using the internet as a teaching tool Algebra 1 Algebra 2 General HELP 1- HOTMATH will help you with many step-by-step solutions to the odd problems of almost every textbook 2- PURPLE MATH Offers a variety of complete lessons with quizzes and extra tutorials. These are just some topics your students can use. There are many more topics. 3- Fee is required 4- 5- Search for the lesson that you want. Copy the hyperlink and then import that video to your computer by using a free software from For the first time only: a- Go to b- Download the Free Ipod Video Converter 2.92 c- Install or run the program and create an icon on your desktop (Just to find it) d- Open the Free IPOD converter e- f- Click on the Youtube icon g- Paste the link of the video that you want to show your students h- Click that you want to automatically convert your video to an Ipod format (mp4) i- Make sure to select the folder for your file (Go to parameters) j- Click download now k- 6- Use your textbook websites 7- Test for Juniors and Seniors: KEMPT. To get there type or go to
November 09, 2006 The Learning Curve From the Learning Curve: Learning Curves: Honors: Multivariable Calculus: What textbook would you use to teach honors Calc 3? Already rejected: Apostal for being too linear-algebra-y and Hurley for being out of print. Too linear-alebra-y? How can a multivariable calculus textbook be too linear-algebra-y? Multivariable derivatives and integrals are linear maps in an algebra-like space, aren't they? 2 Comments: All of Apostol's books are excellent, as long as the student is up to the task (as they would be at Berkeley, or in any Honors program). As far as the notion of too-much linear algebra, multivariate calculus can't be taught properly without a good grounding in linear algebra, so that's a red herring. The gradient is a vector, the Hessian is a symmetric matrix, multivariate transformations inherit their local properties from the associated Jacobian matrices, etc., etc., etc. Linear algebra is an organic part of multivariate calculus, whether we like it or not! A Honors course in multivariate calculus that doesn't include a solid grounding in the relevant linear algebraic underpinnings does not merit the "honors" designation!
Chapter 1: Introduction to Spreadsheet Models for Optimization Chapter 1 Introduction to Spreadsheet Models for Optimization This is a book about optimization with an emphasis on building models and using spreadsheets. Each facet of this theme—models, spreadsheets, and optimization— has a role in defining the emphasis of our coverage. A model is a simplified representation of a situation or problem. Models attempt to capture the essential features of a complicated situation so that it can be studied and understood more completely. In the worlds of business, engineering, and science, models aim to improve our understanding of practical situations. Models can be built with tangible materials, or words, or mathematical symbols and expressions. A mathematical model is a model that is constructed—and also analyzed—using mathematics. In this book, we focus on mathematical models. Moreover, we work with decision models, or models that contain representations of decisions. The term also refers to models that support decision-making activities.
To help you plan your class schedules for the rest of this academic year, here is a list of what the Math Department will be offering at the 300 and 400 level for Winter and Spring quarters. In all cases, you should pay attention to the prerequisites listed in the catalog: A couple of special notes: Math 465 and 466 will not be offered this year. Also, there will be three topics courses, Math 480, offered in Spring. And, there are two additional courses for those interested in teaching, Math 421/422 and Math 497. Descriptions for all of these follows. This two-quarter course is intended for students interested in becoming Secondary School mathematics teachers. There are three main goals in this class. The content goal is that you gain a more comprehensive understanding of two of the fundamental concepts of calculus: the mathematics of change (Math 421) and reasoning about infinite processes (Math 422). The communication goal is that you learn to communicate your understanding and insights about calculus. The learning process goal is that you reflect on your experience as a student in a way that increases your effectiveness as a math teacher. The text for this course is a draft of the book "Making Sense of Calculus" by Stephen Monk, a national leader in mathematics education and recently retired mathematics professor at UW. These courses will be similar in tone to Math 411/412 (Algebra for Teachers) and Math 444/445 (Geometry for Teachers). You should have completed the Mathematics Basic Requirement for the Teacher Preparation Option (Math 124, 125, 126, 307, 308) before taking Math 421. The principal subject of algebra is the solution of polynomial equations. The familiar solution of a quadratic or degree two polynomial equation by the quadratic formula was discovered independently in several cultures many centuries ago. It is now a standard part of secondary mathematics education, but typically students do not study higher degree polynomial equations from the same perspective. In this course we will do so, as we take a close look at the most central results in the early history of algebra. These include: • The solution of quadratic polynomial equations. The quadratic formula will be examined from three different perspectives. • The solution of cubic, or degree three, polynomial equations. This was obtained in the sixteenth century by several Italian mathematicians and represents the most dramatic advance in algebra to have taken place for centuries. • The solution of quartic, or degree four, polynomial equations. This was also obtained by Italian mathematicians, later in the sixteenth century. • The fundamental role of complex numbers in the solution of cubic equations. Even if one is interested only in real number solutions to cubic equations with real number coefficients, the method of solution developed in the sixteenth century led inevitably to the introduction and study of complex numbers. We will see why this was so and learn how to use them. • The attempt to solve polynomial equations of higher degree, culminating around 1800 with Gauss's proof of the Fundamental Theorem of Algebra. Underlying these topics is the idea that the coefficients of a polynomial encode information about that polynomial's roots. Our goal is to learn how to use the coefficient data to unravel this hidden information. Another goal of the course is the development of experience in grappling with mathematical argument. There will be weekly assignments in which students will be asked to read mathematical arguments, develop an understanding of the arguments, write out the arguments in more detail, and write arguments from scratch. Some class time each week will be dedicated to small group discussions of these assignments. We will not cover a large amount of material, aiming instead for an in-depth understanding of a few key results. Math 480 COURSE DESCRIPTION Spring 2009 INTRODUCTION TO DYNAMICAL SYSTEMS. TEXT: R. Devaney, A First Course in Chaotic Dynamical Systems, Addison- Wesley, 1992. WHAT IS A DYNAMICAL SYSTEM? Dynamical systems is a branch of mathematics that attempts to understand processes in motion. Such processes occur in all branches of science. For example, the motion of planets is a dynamical system, one that has been studied for centuries. Some other systems are the stock market, the world's weather, and the rise and fall of populations. Some dynamical systems are predictable, whereas others are not. The reason for this un- predictable behavior has been called "chaos." One of the remarkable discoveries of the modern mathematics is that very simple systems—even as familiar as quadratic functions—may be chaotic and behave as unpredictably as the stock market or as wildly as a turbulent waterfall. ABOUT THIS COURSE: The aim of the course is to show a "window" into some fairly recent mathematics. The emphasis will be on mathematical ideas and concepts. This is a course in discrete dynamical systems, which is basically iteration, or composing a function with itself over and over. We are interested in the long- term behavior of a system. Often complexity of the system calls for qualitative reasoning as opposed to looking for specific analytic solutions. Continuous dynamical systems, which arise from differential equations, are closely related to, and have many common features with, discrete dynamical systems. The plan is to cover most of the book, which will be supplemented by handouts and material from other sources. One of the main themes will be the dynamics of the quadratic family Qc (x) = x2 + c depending on the parameter c, first when c and x are real, and later when c and x are complex. We will study how the long-term behavior of the system changes from stable and predictable to chaotic. PREREQUISITES: Math 327/8 or Math 334/5/6, or permission of the instructor. More of an issue is general "mathematical maturity." This will be a (mostly) proof-based course, so it is highly desirable to be familiar with proof methods, such as proofs by induction, contradiction, and contraposition; basics of set theory (set algebra, countable and uncountable sets); ϵ-δ definitions of convergence and other elements of Introductory Analysis. 480B MWF 2:30 TIME: MWF at 2:30pm Instructor: William Stein TITLE: Algebraic, Scientific, and Statistical Computing, an Open Source Approach Using Sage DESCRIPTION: This is a course about using free open source software to support computation in the mathematical sciences. Topics include Sage, Python, Cython, debugging and profiling code, computing with algebraic structures (groups, rings and fields), exact and numerical linear algebra, numerical optimization, basic statistical computing, and 2d and 3d graphics. > > 480C MW 2:30-3:50 > > Math 480: The Mathematical Theory of Knots. > Time: MW 2:30-4:20. > Instructor: Judith Arms > > Prerequisites: Math 310 and 326, OR Math 335, OR permission of > instructor. > > Text: The Knot Book, by Colin Adams. > > Topics: Knot and link presentations and Reidemeister moves; > prime, composite, and altenating knots; tabulating knots; > knot invariants such as colorability, stick number, genus, > and knot polynomials; selected additional topics, if time permits. > One highlight of the course will be the proof of Tait's conjecture > on alternating knots using polynomial invariants that were > discovered in the 1980's. > > Grades will be based on homework, classwork (some in groups), a take-
Easy Input Tool Entering your math problem has never been easier. Use the keyboard to enter common math symbols or insert special symbols and expressions using the toolbar. Filter by subject to find the symbols most relevant to you. Problems are recognized and then formatted as they appear in your math textbook. Select Your Topic Complex problems mean that you could have many different answers. Use the dropdown topic selection menu to select the topic that most closely matches what you are looking for. Step-by-step answers. Instantly. Math Instant answers returns your answer plus step-by-step solutions to even the most complex problems. Roll over unfamiliar terms in each of the steps to get an explanation of what they mean. Want to see a graph? Instant math allows you to graph your solutions too.
Put the fun back into mathematics by demystifying confusing symbols and terminology. Think of Math Anxiety Relief for Nearly Everyone as your personal journey leading to an eventual understanding of calculus, using everyday language to introduce new concepts in small manageable steps. This book is for you if you want to learn the language of Science, Technology, and Engineering and it is intended to complement traditional text books in Mathematics. You'll enjoy the extensive use of color diagrams, pictures, and graphs that are used throughout the book. Microsoft Excel is introduced early in the book to show how mathematics can be made visual. Excel's hidden equation solving talents are revealed.
The Bedside Book of Algebra The Bedside Book of Algebra A fun and interactive introduction to algebra and the way in which it affects the world around us. The book features clear and concise explanations of key concepts to demonstrate the principles of the various disciplines at work in the real world. There are exercises that challenge the reader to consider the concepts presented and help them learn how they relate to common experiences. The book profiles key figures throughout history and presents dozens of fun facts in each discipline and it is written by specialists in their field in an accessible and fun style that will appeal to both the expert and the layperson.
Portfolios Mathematical Portfolios The purpose of the portfolio The purpose of the portfolio is to provide students with opportunities to be rewarded for mathematics carried out under ordinary conditions, that is, without the time limitations and pressure associated with written examinations. Consequently, the emphasis should be on good mathematical writing and thoughtful reflection. The portfolio is also intended to provide students with opportunities to increase their understanding of mathematical concepts and processes. It is hoped that, by doing portfolio work, students benefit from these mathematical activities and find them both stimulating and rewarding. The specific purposes of portfolio work are to: develop students' personal insight into the nature of mathematics and to develop their ability to ask their own questions about mathematics. provide opportunities for students to complete extended pieces of mathematical work without the time constraints of an examination. enable students to develop individual skills and techniques, and to allow them to experience the satisfaction of applying mathematical processes on their own. provide students with the opportunity to experience for themselves the beauty, power and usefulness of mathematics. provide students with the opportunity to discover, use and appreciate the power of a calculator or computer as a tool for doing mathematics. enable students to develop the qualities of patience and persistence, and to reflect on the significance of the results they obtain. provide opportunities for students to show, with confidence, what they know and what they can do.
Math Models Mathematical Models with Applications 1A Mathematical Models with Applications1A is a one-semester course designed to help students to build on their knowledge of algebra and expand their understanding through mathematical experiences. Students use interactive media and content to develop an understanding of real-life applied problems involving money, data, chance, patterns, design, and science. Scope and Sequence
Description: This math class is a pre-algebra math class. We use the book Discovering Algebra which is a book that uses real life situations to teach algebra. In addition to this book we will use hands on activities and activities using the TI-73 calculator. Although our focus will be algebra we will also be covering the 7th grade curriculum which also covers number sense and geometry. Every activity chosen will focus on challenging the students to think creatively. Class: Math Description: This general math class covers such topics as number sense, geometry, and algebra. I will use many different learning strategies such as hands on activities, higher order thinking strategies, and using TI-73 activities that correlate with the curriculum. Class: Science Description: The 7th grade science curriculum covers a wide variety of topics such as: atmosphere and the weather, biology of the human body, heredity and genetics, and motion and forces. Students have created a bracket for the NCAA Championships and have found statistics for each team in their region. Between 3/15 & 4/3 the students will answer questions about the statistics they have already found. Students will be able to take a math concept (statistics) and connect it to the real world.
So pretty much the calculus class my class offers goes beyond the scope of calculus AB which in itself goes beyond Calculus I. My math teacher told me I only need to look over 2 chapters to be ready for the BC test so I figured I might as well do it since I'm pretty good at math. The question would be what next? My counsler seems to not know what's next she mentioned I might take Calculus for Engineers 1 and 2 online but that seems really redundant to me. So what are my options? I'd suggest a multi-variable calculus course at your local college. Stats is good, if you haven't already taken it, but math people will tell you stats isn't "real" math sometimes. (I've heard my own D say this). Calculus BC is usually equivalent to a year of freshman calculus in college. The usual follow-on courses, which should be available in your local community college, are: * multivariable calculus * linear algebra * differential equations Note that linear algebra and differential equations are often combined into one course, so if they are offered separately at your local community college, take both if you decide to take either, so that you won't have to partially repeat it to get the rest of the course. Other possibilities (these are all typically semester-long courses, except for AP statistics in high school): * AP statistics in high school or non-calculus-based statistics at a community college (often not worth subject credit for majors that also require calculus) * calculus-based statistics at a community college (more likely to be given subject credit, but rarely offered at community colleges) * discrete math at a community college (often recommended or required for computer science majors)
Algebra, says Devlin, is a language, a very precise language written in symbols, and it's everywhere: in nearly all electronic devices, every statistic and each Internet search engine - and, indeed, in every train leaving Boston. "You can store information using it. You can communicate information using it," Devlin said. "Google has made billions capitalizing on algebra." Yet our schools don't always do a very good job teaching it, Devlin said. Instead of showing students the possibilities and beauty algebra offers, they ultimately steer frustrated and bored students away from math and the 21st century careers that use it - the opposite of the intended result. ... Algebra, by the dictionary's definition, is essentially abstract arithmetic, letters and symbols representing relationships between groups, sets, matrices or fields. It's a way to find a piece to a puzzle using the pieces you already have in place. It comes in very handy for engineers, financial analysts and sociologists, not to mention World of Warcraft video game players, some of whom use algebraic formulas to decide which weapon is more effective under certain circumstances - perhaps another hook to lure unsuspecting teens into seeing the useful side of algebra. ... Laptop computer. The computer is just an implementation in electrical circuits of a special form of algebra (called Boolean algebra) invented in the 19th century. Ordinary algebra is used to design and manufacture computers, and is at the heart of how to program them. Cell phone. A cell phone is a particular kind of computer. An important feature of cell phones is that your phone receives all the signals sent to every cell phone in the region, but only responds to signals sent to your phone. This is achieved by using signal coding systems built on algebra. Parking cop. Today's parking enforcement officers may carry equipment connecting them directly to a central vehicle database that registers your parking fine before you get back to the car and see the ticket on the windshield. Without algebra, such a system could not exist. Hybrid car. Modern cars often come equipped with GPS, a highly sophisticated system that is designed using enormous amounts of mathematics that builds on algebra. Delivery truck. Large retail chains use mathematical methods to determine the routing and scheduling of their delivery trucks; algebra is fundamental to those methods. Stoplight. These days, stoplights are centrally controlled by computers, so there is even algebra involved in turning the light from red to green. IPod. This is a math device in your hand. The iPod stores music using sophisticated mathematics built on algebra. And the iPod shuffle mechanism uses regular school algebra to order your songs randomly. ... Even though it is a very pro-algebra article, my favorite quote was by an unknown source: "Algebra ... the intensive study of the last three letters of the alphabet." Share this: I had to solve two problems for myself today. I am posting my solutions here, mainly for my own reference but maybe somebody out there might have the same issues to be solved. The first problem I faced was installing a network printer so that it would be available to all users on that machine. This is probably a minor problem for seasoned IT pros, but since I am not one, it took some investigating. I learned that local printers are installed automatically for all users, while network printers are associated with user profiles. This means that when you install a network printer it is only available to the user profile that you used when installing. The solution is to install the network printer as a local printer. In other words, go to Control Panel .. Printers. Click "Add a printer". Select that you want to install a local printer. At this point you will create a new port, using a Standard TCP/IP port. You'll need to have the IP address of the printer to do this and you'll also want to have the drivers handy. Since it is installed as a local printer it will now be available to all users when they log in. The bug I still haven't worked out, though some of you may have an idea, is that even though I have selected it to be the default printer in my profile, it is not necessarily the default printer for other users. If is the first printer installed, no problem, but otherwise it is not the default for other users.
YourTeacher.com ( offers a comprehensive library of online math lessons covering College Algebra, with a personal math teacher inside every lesson, available on demand!... ... YourTeacher.com ( offers a comprehensive library of online math lessons covering College Algebra, with a personal math teacher inside every lesson, available on demand! Every lesson features video examples, interactive practice, multiple choice self-tests, and more
This website is housed at the School of Mathematics and Statistics, University of St. Andrews, Scotland. There is a biographies index, which has biographical information, arranged alphabetically by the person's last name or arranged by time periods, beginning with pre-500 A.D. Each biography is signed by the article's author, and a list of References is also provided for further research. There is also a History Topics index, with topics broken down into math in various cultures and math topics--i.e., algebra, mathematical physics, etc. This website includes historical biographies of women in mathematics, a list of links to professional societies in mathematics, K-12 teaching materials, the full text to proceedings from the International Conference on Technology in Collegiate Mathematics (1994-2003), and a indexed page of links to other websites on various math topics search website "Math Archives" is the home to the Electronic Proceedings of the International Conference on Technology in Collegiate Mathematics. This is an annual conference, and the Math Archives has full text of the papers from 1994 to 2003. There is both an author and subject indexUSA.gov is the U.S. government web portal to all federal, state, tribal, and local government web resources and services. USA.gov is intended to help people navigate government information, procedures, and policies. A to Z of Mathematics: A Basic Guide Print Location: Ref QA93 .S49 2002 Using the language of a general reader, this book discusses the basic skills required for understanding math. A number of examples show not only how to work a math problem but also why the problems are solved that way.Facts on File Calculus Handbook Print Location: Ref QA303.2 M36 2003 Intended use is for middle school, high school and college students taking single-variable calculus. It's a comfortingly slim book. There are included a number of well-known calculus theoremsAn international non-profit organization dedicated to advancing science around the world by serving as an educator, leader, spokesperson and professional association. In addition to organizing membership activities, AAAS publishes the journal Science (earlier issues online), as well as many scientific newsletters, books and reports, and supports programs that raise the bar of understanding for science worldwide. AAAS also provides some career reosources that are of general interest. American Mathematical Society Founded in 1888 to further mathematical research and scholarship, the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life. Aim is to advance the participation of girls and women in the sciences, from biomedicine to mathematics and the social sciences, in engineering, and in the technologies, in all areas and at all levels. Organized in 1920, the National Council of Teachers of Mathematics is now the world's largest group of its kind. You can find content standards for teaching mathematics here, as well as weekly problems and games for you to try with students of all agesQuotations Dictionary of Quotations in Mathematics Print Location: Ref QA99 .D53 2002 A book of quotes on mathematics, divided into topical chapters. The goal of the book is to make students aware that there is a higher reason for doing mathematics than simply solving a problemInstitute of Mathematical Statistics Worldwide organization whose purpose is to spread awareness on the applications and developments of statistics and probability. Student membership is free. You can also get full text on many of the articles found within the recent issues of four IMS publications: Annals of Applied Probability, Annals of Probability, Annals of Statistics, and Statistical ScienceMathGuide The MathGuide is an Internet-based subject gateway to scholarly relevant information in mathematics, located at the Lower Saxony State- and University Library, Göttingen (Germany).AI
... Customers Who Bought This Also Bought More About This Book geometry, the geometric theorems involved with congruence, quadrilaterals, proportional line segments, special triangles and fundamental locus theorems. This book requires the use of the Geometer's Sketchpad, Version 5, a registered trademark of Key Curriculum Press. The book was supported by Key Curriculum Press with a grant to the authors. This is a revised version of the previously published "Explorations and Discoveries in Mathematics Using the Geometer's Sketchpad Version 4, Volume 3"
The Fundamental Theorem of Algebra The Fundamental Theorem of AlgebraI think that by asking these types of questions you will help yourself to understand complex concepts intuitively. So keep it up. The quadratic formula gives us the real and complex roots of a 2nd degree polynomial. We can not use it to solve higher degree polynomials. Sometimes the quadratic will just give us one answer for x. This is a case where we have found a root with multiplicity 2. This concept is a bit tough to explain. Here is a link to give an exact definition. See if you can understand it: Wikipedia. Complex analysis will certainly help, but I think the real meat and potatoes is in a general field of mathematics that some people refer to as Abstract Algebra. The Fundamental Theorem of Algebra Quote by V0ODO0CH1LD Thanks! Would you say I should learn complex analysis first or abstract algebra? Or are the two unrelated enough that it won't matter? The two have small intersection at the introductory level. Neither are prerequisites for the other. But I have found that there are junior level complex analysis classes, while algebra does not come till senior level. The two have small intersection at the introductory level. Neither are prerequisites for the other. But I have found that there are junior level complex analysis classes, while algebra does not come till senior levelRight, since complex analysis is not considered on the main track, some people take algebra without ever having taken complex analysis. There is some flexibility in paths through a math department. For instance, a computer scientist might conceivably take algebra (maybe combinatorics is even more likely) but not complex analysis, while the the closely related field of electrical engineering might use more from complex analysis.There's a formula for 2nd degree equations -- quadratics. There's a formula for third-degree equations (cubics). There's a formula for fourth degree equations (quartics). But there is NO general formula for solving 5th degree equations or higher. To learn about that, you'd study abstract algebra. What you'd learn from complex analysis is a proof that every polynomial of degree n has n complex roots. But there are other proofs that don't explicitly use complex analysis. But from complex analysis you'd understand why the n roots of the polynomial zn = 1 are the vertices of a regular n-gon in the plane -- a very cool fact indeed. So it sounds like you'd be more interested in abstract algebra if you want to learn about formulas for finding roots; and complex analysis if you're interested in the roots in general. Here's a fascinating article about the beautiful images you get when you plot all the roots of various classes of polynomials.
Precalculus is a preparatory course for calculus and covers the following topics: algebraic, exponential, logarithmic, trigonometric equations and inverse trigonometric identities. Prerequisite: Grade of b or higher in MATH 150, or a score of 24 or above on the math portion of the ACT or 540 or above SAT score or a passing score on the Columbia College math placement exam. G.E. Prerequisite(s) / Corequisite(s): Grade of B or higher in MATH 150, or a score of 24 or above on the math portion of the ACT or 540 or above SAT score or a passing score on the Columbia College math placement exam. Course Rotation for Day Program: Offered Fall and Spring. Text(s): Most current editions of the following: Most current editions of the following: Trigonometry By Stewart, Redlin, & Watson (Brooks-Cole) Recommended Precalculus By Blitzer, R. (Prentice Hall) Recommended Course Objectives To demonstrate fundamental technical skills and clear understanding of the basic concepts of algebraic and transcendental functions. To solve real-world problems using algebraic and transcendental functions. To identify connections between mathematics and other disciplines. To use appropriate technology to enhance their mathematical understanding and to solve real-world problems. Measurable Learning Outcomes: • Determine if a relation is a function. • Identify the domain and range of a function. • Use the graph of a function to identify characteristics of the function such as symmetry and intervals of increasing, decreasing, and constant behavior. • Recognize graphs of common functions and graph transformations of these common functions. • Combine functions arithmetically and through composition and identify the domain of the resulting functions. • Describe and explain the fundamental concepts associated with inverse functions, including the definition of one-to-one functions and the graphical interpretation of inverses. • Define, evaluate and graph trigonometric functions • Define, evaluate and graph inverse trigonometric functions. • Solve rational and polynomial equations including those with complex numbers. Solve simple problems using the Law of Sine and the Law of Cosines to compute angle measures and side lengths of triangles. Know the basic trigonometric identities, addition formulas, double- angle formulas, and half-angle formulas for the sine and cosine functions. Solve basic trigonometric equations. Simplify exponential and logarithmic expressions and solve exponential and logarithmic equations. *Solve applied problems using exponential and logarithmic functions
Specification Aims To introduce students to representations of groups over the field of complex numbers. Brief Description of the unit In the second and third year course units on group theory we have seen that abstract groups are quite complicated objects. One of the most fruitful approaches to studying these objects is to embed them into groups of matrices (to "represent" the elements of an abstract group by matrices). The advantage of this approach lies in the fact that matrices are concrete objects, and explicit calculations can easily be performed. Even more importantly, the powerful methods of linear algebra can be applied to matrices. The course is devoted to representations of finite groups by matrices with entries in the field of complex numbers. Learning Outcomes On successful completion of this course unit students will know the basic properties of complex representations of finite groups and be able to use them in examples; understand the relationship between a representation and its character; know the basic properties of characters and use them in examples; know the basic properties of a character table and be able to calculate character tables for certain small groups.
The books gives insights about the type of arithmetic question can be asked on the test day and are followed by the application of more difficult concepts with questions. Total questions in the book: 110+ (including examples and practice questions) The Good: 1. Each chapter in the book starts with giving explanation on the specific question types, and then in each chapter there are examples making life easy for test takers. Further, some questions are discussed as easy, medium and difficult level questions. After that there are sufficient challenging problems to practice on each question type. 2. Book not only gives concepts but also provides general information on the test i.e. how one should tackle this beast – GMAT. "Facts and formulas", "How your mind works", "Lazy genius" and "GMAT Insider" on the side-note make book worth going through. 3. Book gives insight on the common pitfalls and how to avoid them on test day. 4. Book covers all the topics, such as, Operations with real numbers, fractions, factors and multiples, ratios, percents, quotient/remainder, rate/distance and work/rate, Venn diagram and many more concepts. 5. I've never ever understood and have always confused the difference between LCM and GCF. The book really helped me to distinguish between these two and I hope I will never forget. The Bad: 1. More emphasis is given on PS questions; there are very few DS question. (Remember! There is separate Veritas guide for DS question. I will review that very soon.) 2. In the "Lesson Solution" section there are few misprints (check out solution of question no. 42 and 72 etc) also I think explanations can be made better. Final Note: Those who have read Veritas guide – 0 (Math Essentials) this Arithmetic guide reinforce the fundamentals and give strategies to attack the tougher problems. A must go through guide and I will mark this guide 4/
As part of a nationwide movement, the Mathematics Department has changed its approach to teaching mathematics to one which is "leaner, livelier, and more relevant to real-life problems." The main purpose of this fresh approach is to help you learn to think about mathematics. The text, as you will see, emphasizes understanding concepts and de-emphasizes rote memorization. Since our goal is to prepare you for further study in all mathematical subjects, there will be a strong emphasis on mathematics in everyday life and many of the applications will come from the physical and social sciences. In addition to the text, we will be using graphing calculators to help us better visualize the fundamental ideas, to do routine computations, and to make the course more interesting. You will find the graphing calculator very easy to learn and to use. Former students have consistently said that the use of calculators was a "big plus." In all of our department's introductory courses there is an emphasis on cooperative learning. Your instructor will be facilitating group activities and discussion rather than just repeating the content of the text to you at the blackboard. This means that we will be asking you to read the material and attempt the homework before it is "covered" in class. There will be times when you will have to learn topics which will not be formally discussed in the classroom. Along with your individual homework, another feature of the course will be team homework assignments. Each of the team problems will require considerable thought and a complete, well-written solution. You will often find that team homework problems are best solved in a cooperative environment. Your grade for each team homework assignment will be assigned to the team as a whole, so everyone in your group will be responsible for each other's learning of the material. Most students using homework teams in previous terms have found them helpful. Typical student comments include: "Discussing homework with other students makes the material easier and more understandable." "The group work lets us learn from each other instead of always from the instructor." "Doing homework in teams is effective - it provides a supportive environment." You will be cooperating with other students; not competing. Your course grade will depend on achievement and effort, and there is no limit to the number of students who can receive good grades in this course. We are excited about this new approach to teaching and learning mathematics, and we hope that you will join us in this excitement. Have a good semester! Students often ask, "Why do we have to do all this writing? Writing has nothing to do with mathematics!" The purpose of having you write explanations of your work is to improve your understanding. The more carefully and clearly you write your mathematics, the more likely it is to be correct, and the more likely you will be to remember it. Writing is a crucial part of the thinking process itself. As you are solving problems in this course, remember that getting the "answer" is only one of the steps. Don't think of what you write as just showing your instructor that you have done the homework. Think of writing as part of the process of learning. During this course you will have to do a significant amount of group work. It is a growing trend in professional schools and business to have teams work on various projects. For the team homework in this course, each member of the team has an important role. These roles are to be rotated each week so that everyone has the opportunity to try each role. The roles are the scribe, the clarifier, the reporter, and the manager. Scribe: The scribe is responsible for writing up the single final version of the homework to be handed in. This is the only set of solutions which will be accepted or graded. Each member of the group will receive the same grade as long as they work with the team. Students who do NOT participate will receive a zero. Whenever possible, your solutions should include symbolic, graphical and verbal explanations or interpretations. Diagrams and pictures should also be provided if possible. Clarifier: During the team meeting the clarifier assists the group by paraphrasing the ideas presented by other group members, e.g. "Let me make sure I understand, the graph goes up ...". The clarifier is responsible for making sure that everyone in the group understands the solutions to the problems and is prepared to present the problems to the class if the team is called on. Reporter: The reporter writes a record of how the homework sessions went, how long the team met, what difficulties or successes the team may have had (with math or otherwise). If there is disagreement about the solution of a problem, the reporter should present sketches of alternate solutions and explain the difference of opinion. The report should list the members of the team who attended the session and their roles. The report should be on a separate sheet of paper and the first page of the team's homework solutions. You may use a copy of the sample cover sheet for this purpose., if you like. Manager: The manager is responsible for arranging and running the meetings. If the team has only three members, or if one of the four members cannot attend, the manager should also take one of the other roles. When the homework is returned, the manager sees that it is photocopied and distributed so that each team member's portfolio contains a copy of the corrected problems. The goal of team homework is to ensure that everyone learns with and from the other members of the group. This means that when the work is completed and submitted, every member of the group should be able to explain how to solve all the problems. Here are some ideas that past students have come up with to help your group function at its full potential. Schedule enough meetings, and don't schedule them at the last minute. Go to every meeting and be on time. (Woody Allen says, 80% of life is just showing up.) Do the reading and work on each of the problems before the group meets. In this course, it is absolutely essential that you do the reading assignments. Your experience with previous math courses may make it seem unlikely, since it may have been possible to avoid reading the text, yet do adequately well by copying down examples the instructor did in class and then doing the homework exercises by just changing the numbers in those "pattern examples" and the pattern examples given in the text. Also, older-style texts subtly encouraged students to skip the reading assignments by putting procedures for doing exercises in boxes, thereby essentially telling the students that "everything you really need to know to do the exercises can be found inside the boxes; you might as well skip reading everything else." Unfortunately, this approach resulted in students being able to do the mechanical computations quite well, but having no real understanding of the material and no real ability to apply it in situations that are even a little bit different from that covered by the pattern examples. In essence, students were only being programmed like computers to do computations that computers can do faster and more accurately anyway. It is this deficiency in the old-style math courses that led to the national movement toward reformed courses, like this one, which stress understanding. This modern approach to learning requires new methods in the classroom emphasizing learning rather than lecturing, as well as new texts such as the one for this course. The difference between the text for this course and an old-style math text is apparent from even a cursory scanning of the first chapter. If you open the text and just begin turning pages, you will probably be struck by the following: The amount of text to be read outside of examples is much greater than in old-style books. Older books would typically have brief explanations, sometimes single paragraphs, followed by one or more pattern examples. This book has longer explanations that attempt to convey understanding of the concepts involved rather than just the mechanics of how to do computations. The examples tend to be much longer than those in an old-style text, and they often arise from actual real-world problems. The exercises, which also tend to be much longer than those in an old-style text, are often quite different from each other and from the examples in the text, and use real-world numbers that are not as "nice" as the made-up numbers in the shorter exercises typical of old-style texts. Doing the exercises requires an understanding of the material in the text, not just the ability to change numbers in pattern examples. Also, your instructor will be counting on you to read the text, since he or she will not be lecturing very much and will be relying on you to have seen the material before you work with it in class. Like other courses outside mathematics (but perhaps unlike other mathematics you have taken), not every small point on which you will be tested will be covered by in-class examples. Since the reading is so very important, some hints on how to it might be helpful. You may find that slight variations on the following scheme will work well for you. Plan to do the reading more than once, and do not make it an essential goal to understand everything in the reading the first time through it. The first reading should be devoted only to getting a general overview of the material in the section. After the first reading, stop for a few minutes and attempt to summarize to yourself, in your own words, what the section is all about. Then immediately re-read the section. During the second reading, make a serious effort to understand all of the material in the section. This does not mean to memorize it, but rather to understand all of the points before going on. If you do not understand something during the second reading, put the book aside awhile and return to it later when your mind is fresher. If you still do not understand it after returning to it, ask your instructor or your homework group members about it. Do make sure you eventually understand all of the material. You will probably get tripped up in later reading, in doing the homework, or on test if you treat material you don't quite understand as "probably not all that important." Do not get discouraged if some points require some time to understand. It is not uncommon to have to think about a point in a math test for a half hour (or more, for more complicated concepts) before it becomes clear what is really going on. Study Time. This course requires a solid effort. The faculty at the University of Michigan expects you to study a minimum of two hours outside class for each credit hour, which means that we expect you to spend at least eight hours a week outside of class working on mathematics. Math Lab. The Mathematics Department runs a free tutoring center for all introductory mathematics courses. The Math Lab, as it is called, is located in B860 East Hall and is staffed by course instructors and advanced undergraduate students. This is an excellent place for your homework team to meet or you to go when you need a little extra clarification. Lab hours and additional information are available on the Math Lab website or by calling (734) 936-0160. Calculator. You must have a high-end programmable graphing calculator; this is not optional. The TI-84 is strongly recommended. You may use another equivalent calculator, but you will be responsible for translating the supplied calculator programs into programs for your own calculator. Your instructor and the Math Lab will be most familiar with the TI-83 and may not be able to offer you help with other calculators. Attendance & Student Absences. Since much of the learning in this course occurs interactively during class time, attendance is essential. For that reason, the instructor is allowed to reduce the student's course grade if the absences become excessive; that is, if the student misses more than two or three classes during the course of the semester. Absences will usually be excused if due to a serious emergency. However, it is our policy that an emergency serious enough to cause an absence from a class activity or a test is also serious enough to require documentation. Students anticipating more than one or two absences due to athletic commitments (or any other type of predictable commitment) really should rearrange their class schedules to accommodate this, since frequent absences may not be excused. Absences will be dealt with on a case-by-case basis, however, two situations occur commonly enough to merit attention. Travel plans are never sufficient cause for an excused absence. In particular, the availability of cheap plane tickets for particular days near final exam time is not enough reason to reschedule a student's final exam. Also, an activity related to the social functions of a student's current of anticipated future residential organization, whether a university residence hall, apartment complex, sorority, or fraternity, is never sufficient excuse for an excused absence. Conflicts With Uniform Exams. The two uniform exams during the course of the semester are scheduled for 6:00 - 7:30 p.m. to make it possible for all students to attend, but we are aware that there can be conflicts with other scheduled academic activities such as a class or another evening test. If this happens, notify your instructor well in advance so that we can clear up the problem. Due to the nature of the final exam schedule, there are seldom conflicts between regularly scheduled final examinations. If a problem does occur, notify your instructor as early in the term as possible. Grades in this math course. All sections of this course use the same grading guidelines to ensure a fair, standardized evaluation process. Your grade in this course will be determined primarily by your work on the "uniform component," which is the same for all sections of the course. The majority of this component comes from your scores on the uniform exams. Your grade as determined by the uniform component may be influenced by the "section component" of the course, which includes your work in your class-section. In some cases, your section component may adjust your grade up or down (as explained below). In addition, there is a "gateway component" to your grade which may also adjust your grade downward. The details follow. 1. The uniform component. This includes two uniform midterm exams, a uniform final exam, and your scores on web homework. Each of the exams will be taken by all students in all sections at the same time, and are graded by all the instructors working together. Your uniform component score will be determined from your scores on each exam as follows: Midterm Exam 1 25% of uniform component score Midterm Exam 2 30% of uniform component score Final Exam 40% of uniform component score Web HW 5% of uniform component score After each exam, a letter grade will be assigned to your uniform component score using a scale determined by the course coordinator specifically for that exam. We do not use the "10-point scale" often seen in high school courses in which scores in the 90's get an A, in the 80's get a B, and so forth; the level of difficulty of the exams will be considered. The scale for the uniform component score will apply to all students in all sections. The scale for final course grades will be set by the coordinator based upon the above percents for each component. Most students will receive the course grade assigned by that scale. 2. The section component. To help you learn the material, you will be given a variety of reading assignments, team homework, quizzes and other in-class activities. Your instructor will decide how the section component is determined for your particular section and grade the section work. If, at the end of the term, your rankings on the section component and uniform component differ significantly from one another, your course grade will be examined to see if an adjustment should be made. If you have participated in section activities but your section component is significantly lower than your uniform grade, your course grade may be lowered by one third of a letter grade. Students who have not seriously attempted to contribute to the section component of the course (i.e., quizzes, team homework, etc.) may have their final course grade lowered by up to a full letter grade. If, on the other hand, you have struggled on an exam and your in-class performance is significantly higher than the uniform component grade, your instructor may in some cases adjust your grade upward by one-third of a letter grade. This raise is generally only given for students whose uniform component places them near the top (or at the "cusp") of a letter grade category. The majority of students will find that their in-class performance and their exam scores are quite reflective of one another. Thus, in the majority of cases, no adjustment is made to the uniform course grade. The best way to gauge your in-class performance is to keep an eye on the median grade in your section for each assignment and quiz. It is not useful to compare quiz and homework grades with students from other sections, because instructors write their own quizzes and determine the grading rubric for homework in a section. 3. The gateway component. There will be one or two (depending on the course you are taking) online basic skills gateway test(s) which you need to pass by the deadline announced in the course schedule. These tests may be taken multiple times, and cover skills that every student who passes the course should have. Therefore, students who are keeping up with the course work can and will pass the gateway---if they start taking it early enough! You may practice each test online as many times as you like, and you may take a test for a score as often as twice per day without penalty until the deadline. Because the gateway tests cover skills that every student must have, the gateway tests do not raise your baseline grade; instead, if they are not passed by the deadline, your final grade in the course will be automatically reduced. Opening dates, deadlines and grade penalties will be announced in your class. All sections of your course have the same open/closing dates and penalties assigned to the gateway component. Section averages. Course policy is that a section's average final letter grade cannot differ too much from that section's average baseline letter grades. This means that the better your entire section does on the uniform exams, the higher average letter grade your instructor can assign in your section. It is therefore in your best interest to help your fellow students in your section do well in this course. In other words, cooperation counts! Grades at the university. Many students who come to the University of Michigan have to adjust themselves to college grading standards. The mean high school grade point average (recalculated using only strictly academic classes) of our entering students is around 3.6, so many of you were accustomed to getting "straight A's" in high school. Students' first reaction to college grades is often, "I've never gotten grades like these." However, a grade of 15/20 on a team homework assignment (which you might previously have converted to 75% - a high school C) may well be a good score in a college math course. Your own instructor is your best source of information on your progress in the class. The classroom is place where all students need to be engaged in learning. This means that it cannot be a place for casual conversations, reading the newspaper, doing homework for other classes, etc. Be ready to concentrate on math and discuss the day's material. Be respectful and polite. Listen to your instructor and your fellow students when they are talking. In order to benefit from being in an interactive class, each student must come to class prepared. Come to class having done the assigned reading and attempted the homework problems. Contribute to your homework team. Work on the problems ahead of time. Go to every meeting promptly and do your share to make sure that the meeting is valuable to everyone. Be in your seat and ready to start when your class is scheduled to begin and remain until the class is dismissed. Students at the University of Michigan are expected to exhibit academic integrity. Each College has its own standards for treating cases of academic misconduct, but in all Colleges there can be serious consequences for violating the Code of Academic Conduct. Sanctions can include: suspension, disciplinary probation, and receiving a failing grade. Some examples of cheating, as stated in the LS&A Code of Academic Conduct, include: submitting work which has been previously submitted in another term or another section of the course. using information from another student or another student's paper or an examination which is supposed to be individual work. altering a test after it has been returned, and then resubmitting the work claiming that it was improperly graded.
Math Algebra 1 Algebra is the branch of mathematics concerned with representing numbers and ideas with symbols. Students have been using symbols for many years, but this is the first course that is entirely about algebra. All year, students will create and solve equations using many methods: trial-and-error, algebraic manipulation, tables, graphs and technology (computers and calculators). Students learn many new concepts but will focus on linear equations, quadratic equations, polynomials, systems of linear equations, exponential equations, and probability distributions. Many "real-world" examples are used, so that students can see how the math applies to jobs, science, and other academic subjects; this course starts to prepare students for these areas of study. Graphing calculators will be used in the classroom, but students are not expected to purchase one. Algebra 2 In Advanced Algebra, students become better at understanding the concepts of algebra. Mostly, students study functions: Linear equations in one variable; Systems of linear equations in several variables; Matrices; Quadratic functions; Power functions; Root functions; Exponential functions; Logarithms and logarithmic functions; Trigonometric functions; And polynomials. Conic sections (circles, ellipses, hyperbolas…) are also studied. Arithmetic and geometric series are introduced in this course, and statistics are studied in more detail than before. Technology is integrated throughout the curriculum. Graphing calculators are used extensively as visualization tools, and as symbolic manipulators to expedite algebraic computations, or to check answers arrived at by paper-and-pencil means. There will be many problems that students cannot solve without graphing calculators (like problems involving matrices). Students are required to own a graphing calculator because they are used so much. Applied Mathematics Applied Mathematics helps students to develop mathematically by engaging them in hands-on, open-ended, context-rich explorations that incorporate authentic data and the use of real-worlds tools, particularly the tools of technology. Through study mathematics from an applied perspective, students learn to see mathematics as a powerful set of processes, models and skills that can be used to solve non-routine problems, both in and out of the classroom. Students are asked to take the initiative and are given the latitude to explore. Geometry Graphing Calculators: Helpful, but not required in this course. (TI-84 plus Silver Edition is recommended.) In this course, we will use traditional methods and interactive, electronic resources like Geogebra to learn about the geometry of plane figures. Initial topics that will be covered will include parallel and perpendicular lines, triangles (congruent and otherwise), and other types of polygons. Students will be introduced to inductive reasoning using Geogebra, then they will learn to formalize their findings using deductive logic and formal proof. Geogebra will continue to be an especially powerful tool to help us examine the geometries of similarity and transformations – reflections, rotations, translations, dilations, and compositions. Lastly, we will learn about the geometry of 3-Dimensional figures (Surface Area and Volume), as well as the geometry of lines and angles in circles. Pre-Calculus Graphing Calculator: A graphing calculator is required for this course. (TI-84 plus Silver Edition is recommended.) Precalculus is a course designed to prepare students for the further study of calculus in general, and specifically for AP Calculus AB. About half of the course consists of a further study of functions, including polynomial, rational, power, and exponential functions, as well as their inverses, including logarithmic functions. The other half of the course will consist of a further study of trigonometry, including trigonometric identities, relationships, and graphs of the six trigonometric functions and their inverses. Graphing calculators, interactive Geogebra drawings, and other electronic resources will be used in most class sessions to deepen students' understandings of these topics, including function transformations, domain and range, end-behavior, asymptotic behavior, increasing and decreasing intervals, maxima and minima, and real-world problems applying these ideas. Other topics to be addressed are the Binomial Theorem, Synthetic Division & the Rational Root Theorem, elementary matrix and vector operations, parametric equations, and polar coordinates. Some calculus topics will be introduced throughout the year (but not mastered), including limits, continuity, and the average change function. AP Calculus Graphing Calculators: A graphing calculator is required for this course. (TI-84 plus Silver Edition is recommended.) AP Calculus is a course designed to introduce students to differential and integral calculus, and to prepare students for the culminating AP Calculus Exam given the following month of May. The course can be broken into three sections: Limits, Differential Calculus, and Integral Calculus. To begin, students will formally learn about limits, and limiting situations. This will culminate in several forms of the limit-definition of the derivative. In the Differential Calculus section of the course, students will learn about a multitude of differentiating techniques (including the product rule, quotient rule, chain rule, and implicit derivatives) for a multitude of familiar and unfamiliar functions (including polynomial, rational, power, trigonometric, exponential, and combination functions). Calculus techniques will be used to work on real-world applications, including kinematic problems (position, velocity, and acceleration), problems involving related rates, problems involving maxima and minima, and other applications. In the Integral Calculus section of the course, we will learn about a multitude of anti-differentiation techniques with, again, numerous familiar and unfamiliar functions. Applications of the integral will be introduced as well. Ideally, we will finish the AP Calculus AB syllabus near the end of March, so that we have 4-6 weeks to review topics before the AP Calculus Exam in early in the month of May. After the AP Calculus Exam, we will examine a few other topics and applications of calculus.
Center Square, PA SAT Math ...It introduces basic concepts like factoring, solving for "x", absolute values, and basic equations. I have used Algebra during my software development career to create equations, solve math problems, and create software using physics (distance, speed, etc.). Algebra is a critical skill one shoul...
Mathematics The Undergraduate Program The mathematics department offers a wide range of courses in pure and applied mathematics for its majors and for students in other disciplines. The department offers six majors leading to the B.A. degree: mathematics, applied mathematics, mathematics–applied science, mathematics–computer science, joint major in mathematics and economics, and mathematics– secondary education, and one leading to the B.S. Degree: mathematics–scientific computation. In addition, students can minor in mathematics. The department also has an Honors Program for exceptional students in any of the seven majors. See the sections on major programs and the other areas mentioned above as well as the course descriptions at the end of this section for more specific information about program requirements and the courses that are offered by the department. You may visit our Web site, math.ucsd.edu for more information including course Web pages, career advising, and research interests of our faculty. First-Year Courses Entering students must take the Mathematics Placement Exam prior to orientation unless they have either a passing score (3 or better) on a Calculus AP exam, or transferable credit in calculus. The purpose of the Mathematics Placement Exam is to assess the student's readiness to enter the department's calculus courses. Some students will be required to take precalculus courses before beginning a calculus sequence. Math. 3C is the department's preparatory course for the Math. 10 sequence, providing a review of algebraic skills, facility in graphing, and working with exponential and logarithmic functions. Math. 4C is the department's preparatory course for the Math. 20 sequence, providing a brief review of college algebra followed by an introduction to trigonometry and a more advanced treatment of graphing and functions. Math. 10A-B-C is one of two calculus sequences. The students in this sequence have completed a minimum of two years of high school mathematics. This sequence is intended for majors in liberal arts and the social and life sciences. It fulfills the mathematics requirements of Revelle College and the option of the general-education requirements of Muir College. Completion of two quarters fulfills the requirement of Marshall College and the option of Warren College and Eleanor Roosevelt College. The other first-year calculus sequence, Math. 20A-B-C, is taken mainly by students who have completed four years of high school mathematics or have taken a college level precalculus course such as Math. 4C. This sequence fulfills all college level requirements met by Math. 10A-B-C and is required of many majors, including chemistry and biochemistry, bioengineering, cognitive science, economics, mathematics, molecular biology, psychology, MAE, CSE, ECE, and physics. Students with adequate backgrounds in mathematics are strongly encouraged to take Math. 20 since it provides the foundation for Math. 20D-E-F which is required for some science and engineering majors. Note: As of summer 2003, Math. 21C and 21D have been renumbered to Math. 20C and 20D. Certain transfers between the Math. 10 and Math. 20 sequences are possible, but such transfers should be carefully discussed with an adviser. Able students who begin the Math. 10 sequence and who wish to transfer to the Math. 20 sequence, may follow one of three paths: Follow Math. 10A with Math. 20A, with two units of credit given for Math. 20A. This option is not available if the student has credit for Math. 10B or Math. 10C. This option is available only if the student obtains a grade of A in Math. 10A or by consent of the Math. 20A instructor. Follow Math. 10C with Math. 20B, receiving two units of credit for Math. 20B and two units of credit for Math. 20C. Credit will not be given for courses taken simultaneously from the Math. 10 and the Math. 20 sequence. Major Programs The department offers six different majors leading to the Bachelor of Arts degree: (1) mathematics, (2) applied mathematics, (3) mathematics–applied science, (4) mathematics–computer science, (5) joint major in mathematics and economics, (6) mathematics–secondary education; and one leading to a B.S. Degree: mathematics-scientific computation. The specific emphases and course requirements for these majors are described in the following sections. All majors must obtain a minimum 2.0 grade-point average in the upper-division courses used to satisfy the major requirements. Further, the student must receive a grade of C– or better in any course to be counted toward fulfillment of the major requirements. Any mathematics course numbered 100–194 may be used as an upper-division elective. (Note: 195, 196, 197, 198, 199, and 199H cannot be used towards any mathematics major.) All courses used to fulfill the major must be taken for a letter grade. It is strongly recommended that all mathematics majors review their programs at least annually with a departmental adviser, and that they consult with the Advising Office in AP&M 6016 before making any changes to their programs. Current course offering information for the entire academic year is maintained on the department's Web page at Special announcements are also emailed to all majors. Students who plan to go on to graduate school in mathematics should be advised that only the best and most motivated students are admitted. Many graduate schools expect that students will have completed a full sequence of abstract algebra (Math. 100A-B-C) as well as a full sequence of analysis (Math. 140A-B-C). he advanced Graduate Record Exam (GRE) often has questions that pertain to material covered in the last quarter of analysis or algebra. In addition, it is advisable that students consider Summer Research Experiences for Undergraduates. This is a program funded by the National Science Foundation to introduce students to math research while they are still undergraduates. In their senior year or earlier, students should consider taking some graduate courses so that they are exposed to material taught at a higher level. In their junior year, students should begin to think of obtaining letters of recommendation from professors who are familiar with their abilities. Education Abroad Students may be able to participate in the UC Education Abroad Program (EAP) and UCSD's Opportunities Abroad Program (OAP) while still making progress towards the major. Students interested in this option should contact the Programs Abroad Office in the International Center and discuss their plans with the mathematics advising officer before going abroad. The department must approve courses taken abroad. Information on EAP/OAP can be found in the Education Abroad Program section of the UCSD General Catalog and the Web site Major in Mathematics The upper-division curriculum provides programs for mathematics majors as well as courses for students who will use mathematics as a tool in the biological, physical and behavioral sciences, and the humanities. All students majoring in mathematics must complete the basic 20 sequence, Math. 20A-B-C-D-E-F. Math. 109 should be taken in the spring quarter of the sophomore year. All mathematics majors must complete at least twelve upper-division courses including: 109 140A-B or 142A-B and 120A 100A-B or 103A-B and 102 Upper-division electives to complete the thirteen courses required may be chosen from any mathematics course numbered 100–194. As with all departmental requirements, more advanced courses on the same material may be substituted with written approval from the departmental adviser. To be prepared for a strong major curriculum, students should complete the last three quarters of the 20 sequence and Math. 109 before the end of their sophomore year. Either Math. 140A-B or 100A-B should be taken during the junior year. Major in Applied Mathematics A major in applied mathematics is also offered. The program is intended for students planning to work on the interface between mathematics and other fields. All students majoring in applied mathematics are required to complete the following courses: One of the following: a. 180A-B-C-181A b. 180A-181A and any 2 from 181B-C-D-E c. (183 or 180A-181A) and any 3 from 170A-B-C-172-173. One additional sequence which may be chosen from the list (#6) above or the following list: 110-120A-130A, 120A-B, 130A-132A, 155A-B, 171A-B, 184A-B, 193A-B. At least thirteen upper-division courses must be completed in mathematics, except: Up to twelve units may be outside the department in an approved applied mathematical area. A petition specifying the courses to be used must be approved by an applied mathematics adviser. No such units may also be used for a minor or program of concentration. To be prepared for a strong major curriculum, students should complete the last three quarters of the 20 sequence and Math. 109 before the end of their sophomore year. Major in Mathematics–Scientific Computation This major is designed for students with a substantial interest in scientific computation. The program is a specialized applied mathematics program with a concentration in computer solutions of scientific problems. At least 15 upper-division mathematics courses are required for the major, except: Up to 3 upper-division courses may be taken outside the department in an approved scientific computation area in the sciences or engineering. A petition specifying the courses to be used must be approved by a mathematics-scientific computation adviser. No such units may also be used by a minor or program of concentration. Major in Mathematics–Applied Science This major is designed for students with a substantial interest in mathematics and its applications to a particular field such as physics, biology, chemistry, biochemistry, cognitive science, computer science, economics, management science, or engineering. Seven upper-division courses selected from one or two other departments At least three of these seven upper-division courses must require at least Math. 20C as a prerequisite Students must submit an individual plan for approval in advance by a mathematics department adviser, and all subsequent changes in the plan must be approved by a mathematics department adviser. Major in Mathematics–Computer Science The program provides for a major in computer science within the Department of Mathematics. Graduates of this program will be mathematically oriented computer scientists who have specialized in the mathematical aspects and foundations of computer science or in the computer applications of mathematics. As of fall 2000, a mathematics-computer science major is not allowed to also minor in computer science in the Computer Science and Engineering department. The detailed curriculum is given in the list below: Mathematics–Computer Science Pre-Major In October 2001, the Academic Senate approved a minimum GPA requirement of 2.5 in the lower-division mathematics courses required for the mathematics–computer science major. The 2.5 minimum GPA in the lower-division math courses reflects minimal preparation for the upper-division courses required for the major. Therefore, students entering UCSD as first- year students for the fall 2002 quarter and later and students entering as transfer students for the fall 2003 quarter and later will be held to this requirement. Applications from students entering UCSD on or after the effective dates above will be held until all lower-division math courses for the major are completed and the minimum GPA in those courses of 2.5 can be verified. Students meeting the 2.5 minimum GPA requirement will be accepted into the mathematics–computer science major. In order to graduate by the end of their senior year, students must complete Math. 103A-B by the end of their junior year. Joint Major in Mathematics and Economics Majors in mathematics and the natural sciences often feel the need for a more formal introduction to issues involving business applications of science and mathematics. Extending their studies into economics provides this application and can provide a bridge to successful careers or advanced study. Majors in economics generally recognize the importance of mathematics to their discipline. Undergraduate students who plan to pursue doctoral study in economics or business need the more advanced mathematics training prescribed in this major. This major is considered to be excellent preparation for Ph.D. study in economics and business administration, as well as for graduate studies for professional management degrees, including the MBA. The major provides a formal framework making it easier to combine study in the two fields. Course requirements of the Joint Major in Mathematics and Economics consist principally of the required courses of the pure mathematics major and the economics/management science major. Lower-Division Requirements: Calculus: Math. 20A-B-C-D-E-F Intro to Economics: Econ. 1A-B-C Upper-Division Requirements: Fifteen upper-division courses in mathematics and economics, with a minimum of seven courses in each department, chosen from the courses listed below (prerequisites are strictly enforced): One of the following: Macroeconomics: Econ. 110AB Mathematical Programming: Numerical Optimization: Math. 171AB or Two courses from the following: Decisions Under Uncertainty: Econ. 171 Introduction to Operations Research: Econ. 172A-B-C, (Note: 172A is a prerequisite for 172BC) Major in Mathematics–Secondary Education This major offers excellent preparation for teaching mathematics in secondary schools. Students interested in earning a California teaching credential from UCSD should contact the Teacher Education Program (TEP) for information regarding prerequisites and requirements. It is recommended you contact TEP as early as possible. Minor in Mathematics The minor in mathematics consists of seven or more courses. At least four of these courses must be upper-division courses taken from the UCSD Department of Mathematics. Acceptable lower-division courses are Math. 20D, 20E, and 20F. Math. 195, 196, 197, 198, 199, and 199H are not acceptable courses for the mathematics minor. A grade of C– or better (or P if the Pass/No Pass option is used) is required for all courses used to satisfy the requirements for a minor. There is no restriction on the number of classes taken with the P/NP option. Upper-division courses cannot overlap between major and minor programs. Mathematics Honors Program The Department of Mathematics offers an honors program for those students who have demonstrated excellence in the major. Successful completion of the honors program entitles the student to graduate with departmental honors (see Department Honors in the Academic Regulations section). Application to the program should be made the spring quarter before the student is at senior standing. Requirements for admission to the program are: Junior standing An overall GPA of 3.0 or higher A GPA in the major of 3.5 or higher Completion of Math. 109 (Mathematical Reasoning) and at least one of Math. 100A, 103A, 140A, or 142A. (Completion of additional major courses is strongly recommended.) Completion of the honors program requires the following: At least one quarter of the student colloquium, Math. 196 (Note: Math. 196 is only offered in the fall quarter.) The minimum 3.5 GPA in the major must be maintained An Honors Thesis. The research and writing of the thesis will be conducted over at least two quarters of the junior/senior years under the supervision of a faculty adviser. This research will be credited as eight to twelve units of Math. 199H. The completed thesis must be approved by the department's Honors Committee, and presented orally at the Undergraduate Research Conference or another appropriate occasion. The department's Honors Committee will determine the level of honors to be awarded, based on the student's GPA in the major and the quality of the honors work. Applications for the mathematics department's Honors Program can be obtained at the mathematics department Undergraduate Affairs Office (AP&M 7018) or the Mathematics Advising Office (AP&M 6016). Completed applications can be returned to the Mathematics Advising Office. Duplication of Credit In the circumstances listed below, a student will not receive full credit for a Department of Mathematics course. The notation "Math. 20A [2 if Math. 10A previously/0 if Math. 10A concurrently/0 if Math. 10B or 10C]" means that a student already having credit for Math. 10A will receive only two units of credit for Math. 20A, but will receive no units if he or she has credit for Math. 10B or 10C, and no credit will be awarded for Math. 20A if Math. 10A is being taken concurrently. Math. 183 [0 if Econ. 120A or Math. 180A or Math. 181A has been taken previously or concurrently. Full credit for Math. 183 will be given if taken previously to Math. 180A or Math. 181A.] For duplication or repeat of credit guidelines between the Math. 20 sequence and the Math. 10 sequence, refer to the section titled "First- Year Courses." Advisers Advisers change yearly. Contact the undergraduate office at (858) 534-3590 for current information. The Graduate Program The Department of Mathematics offers graduate programs leading to the M.A. (pure or applied mathematics), M.S. (statistics), and Ph.D. degrees. The application deadline for fall admission is January 15. Candidates should have a bachelor's or master's degree in mathematics or a related field from an accredited institution of higher education or the equivalent. A minimum scholastic average of B or better is required for course work completed in upper-division or prior graduate study. In addition, the department requires all applicants to submit scores no older than twelve months from both the GRE General Test and Advanced Subject Test in Mathematics. Completed files are judged on the candidate's mathematical background, qualifications, and goals. Departmental support is typically in the form of teaching assistantships, research assistantships, and fellowships. These are currently only awarded to students in the Ph.D. program. General Requirements All student course programs must be approved by a faculty adviser prior to registering for classes each quarter, as well as any changes throughout the quarter. Full-time students are required to register for a minimum of twelve (12) units every quarter, eight (8) of which must be graduate-level mathematics courses taken for a letter grade only. The remaining four (4) units can be approved upper-division or graduate-level courses in mathematics-related subjects (Math. 500 may not be used to satisfy any part of this requirement). After advancing to candidacy, Ph.D. candidates may take all course work on a Satisfactory/Unsatisfactory basis. Typically, students should not enroll in Math. 299 until they have satisfactorily passed both qualifying examinations (see Ph.D. in Mathematics) or obtained approval of their faculty adviser. Master of Arts in Pure Mathematics [Offered only under the Comprehensive Examination Plan.] The degree may be terminal or obtained on the way to the Ph.D. A total of forty-eight units of credit is required. Twenty-four of these units must be graduate-level mathematics courses approved in consultation with a faculty adviser. In the selection of course work to fulfill the remaining twenty-four units, the following restrictions must be followed: No more than eight units of upper-division mathematics courses. No more than twelve units of graduate courses in a related field outside the department (approved by the Department of Mathematics). No more than four units of Math. 295 (Special Topics) or Math. 500 (Apprentice Teaching). No units of Math. 299 (Reading and Research) may be used in satisfying the requirements for the master's degree. Comprehensive Examinations Seven written departmental examinations are offered in three areas (refer to "Ph.D. In Mathematics," Areas 1, 2, and 3, for list of exams). A student must complete two examinations, one from Area 1 and one from Area 2, both with an M.A. pass or better. Foreign Language Requirement A reading knowledge of one foreign language (French, German, or Russian) is required. In exceptional cases other languages may be substituted. Testing is administered by faculty in the department who select published mathematical material in one of these languages for a student to translate. Time Limits Full-time students are permitted seven quarters in which to complete all degree requirements. While there are no written time limits for part-time students, the department has the right to intervene and set individual deadlines if it becomes necessary. Master of Arts in Applied Mathematics [Offered only under the Comprehensive Examination Plan] The degree may be terminal or obtained on the way to the Ph.D. Out of the total forty-eight units of required credit, two applied mathematics sequences comprising twenty-four units must be chosen from the following list (not every course is offered each year): In choosing course work to fulfill the remaining twenty-four units, the following restrictions must be followed: At least eight units must be approved graduate courses in mathematics or other departments [a one-year sequence in a related area outside the department such as computer science, engineering, physics, or economics is strongly recommended]; A maximum of eight units can be approved upper-division courses in mathematics; and A maximum of eight units can be approved upper-division courses in other departments. A maximum of four units of Math. 500 (Apprentice Teaching). NO UNITS of Math. 295 (Special Topics) or Math. 299 (Reading and Research) may be used. Students are strongly encouraged to consult with a faculty adviser in their first quarter to prepare their course of study. Comprehensive Examinations Two written comprehensive examinations must be passed at the master's level in any of the required applied mathematics sequences listed above. The instructors of each course should be contacted for exam details. Foreign Language Requirement There is no foreign language requirement for the M.A. in applied mathematics. Time Limits Full-time M.A. students are permitted seven quarters in which to complete all requirements. While there are no written time limits for part-time students, the department has the right to intervene and set individual deadlines if it becomes necessary. Master of Science in Statistics [Offered only under the Comprehensive Examination Plan] The M.S. in statistics is designed to provide recipients with a strong mathematical background and experience in statistical computing with various applications. Out of the forty-eight units of credit needed, required core courses comprise twenty-four units, including: Upon the approval of the faculty adviser, all twenty-four units can be graduate-level courses in other departments. Comprehensive Examinations Two written comprehensive examinations must be passed at the master's level in related course work (approved by a faculty adviser). Instructors of the relevant courses should be consulted for exam dates as they vary on a yearly basis. Foreign Language Requirement There is no foreign language requirement for the M.S. in statistics. Time Limits Full-time M.S. students are permitted seven quarters in which to complete all requirements. While there are no written time limits for part-time students, the department has the right to intervene and set individual deadlines if it becomes necessary. Ph.D. In Mathematics Written Qualifying Examinations The department offers written qualifying examinations in seven subjects. These are grouped into three areas as follows: Three qualifying exams must be passed. At least one must be passed at the Ph.D. level, and a second must be passed at either the Ph.D. or Provisional Ph.D. Level The third exam must be passed at least at the master's level. Of the three qualifying exams, there must be at least one from each of Areas #1 and #2. Algebra and Applied Algebra do not count as distinct exams in Area #2. Students must pass a least two exams from distinct areas with a minimum grade of Provisional Ph.D. (For example, a Ph.D. pass in Real Analysis, Provisional Ph.D. Pass in Complex Analysis, M.A. pass in Algebra would NOT satisfy this requirement, but a Ph.D. Pass in Real Analysis, M.A. pass in Complex Analysis, Provisional Ph.D. Pass in Algebra would, as would a Ph.D. Pass in Numerical Analysis, Provisional Ph.D. Pass in Applied Algebra, and M.A. pass in Real Analysis.) All exams must be passed by the September exam session prior to the beginning of the third year of graduate studies. (Thus, there would be no limit on the number of attempts, encouraging new students to take exams when they arrive, without penalty.) Department policy stipulates that a least one of the exams must be completed with a Provisional Ph.D. Pass or better by September following the end of the first year. Anyone unable to comply with this schedule will be terminated from the doctoral program and transferred to one of our Master's programs. Any Master's student can submit for consideration a written request to transfer into the Ph.D. Program when the qualifying exam requirements for the Ph.D. Program have been met and a dissertation adviser is found. Approval by the Qualifying Exam and Appeals Committee (QEAC) is not automatic, however. Exams are typically offered twice a year, one scheduled late in the spring quarter and again in early September (prior to the start of fall quarter). Copies of past exams are made available for purchase in the Graduate Office. In choosing a program with an eye to future employment, students should seek the assistance of a faculty adviser and take a broad selection of courses including applied mathematics, such as those in Area #3. Foreign Language Requirement A reading knowledge of one foreign language (French, German, or Russian) is required prior to advancing to candidacy. In exceptional cases other languages may be substituted. Testing is administered within the department by faculty who select published mathematical material in one of these languages for a student to translate. Advancement to Candidacy It is expected that by the end of the third year (nine quarters), students should have a field of research chosen and a faculty member willing to direct and guide them. A student will advance to candidacy after successfully passing the oral qualifying examination, which deals primarily with the area of research proposed but may include the project itself. This examination is conducted by the student's appointed doctoral committee. Based on their recommendation, a student advances to candidacy and is awarded the C.Phil. Degree Dissertation and Final Defense Submission of a written dissertation and a final examination in which the thesis is publicly defended are the last steps before the Ph.D. Degree is awarded. When the dissertation is substantially completed, copies must be provided to all committee members at least four weeks in advance of the proposed defense date. Two weeks before the scheduled final defense, a copy of the dissertation must be made available in the department for public inspection. Time Limits The normative time for the Ph.D. In mathematics is five years. Students must be advanced to candidacy by the end of eleven quarters. Total university support cannot exceed six years. Total registered time at UCSD cannot exceed seven years.
Rent Textbook Used Textbook eTextbook New Textbook We're Sorry Sold Out Related Products Fundamental Mathematics Through Applications Fundamental Mathematics Through Applications Fundamental Mathematics through Applications Summary The second edition of Akst/Bragg's Fundamental Mathematics through Applications brings you even more of a good thing! Throughout the text, motivating real-world applications, examples, and exercises demonstrate how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive side-by-side format, pairing each example with a corresponding practice exercise, encourages students to get actively involved in the mathematical content from the start. Unique Mindstretchers target different levels and types of student understanding in one comprehensive section problem set per section. Mindstretchers incorporate related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and historical connections. Compelling Historical Notes give students more evidence that mathematics grew out of a universal need to find efficient solutions to everyday problems. Plenty of practice exercises provide ample opportunity for students to thoroughly master basic mathematics skills and develop confidence in their understanding. Finally, new MyMathLab icons in the margins of the text indicate to students that there is a video clip, animated example, or practice exercise for them to explore on-line if you take advantage of the package deal.
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Tag Archives: Success Learning how to solve problems in mathematics is simply to know what to look for. Math problems often require established procedures and one must know What & When to apply them. To identify procedures, you have to be familiar with the different problem situations, and be able to collect the appropriate information, identify a strategy or strategies and use the strategy/strategies appropriately. But exercise is must for problem solving. It needs practice!! The more you practice, the better you get. The great mathematical wizard G Polya wrote a book titled How to Solve It in 1957. Many of the ideas that worked then, do still continue to work for us. Given below are the four essential steps of problem solving based on the central ideas of Polya.
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... Show More manual. Detailed solutions at the back of the book help students over obstacles to their learning and the operation of the menus and submenus are absorbed with minimal effort as the mathematics is learned. Deeper investigations are included to challenge the more capable student, and historical vignettes are introduced to add a human dimension to the mathematical excursions. This new publication has been expanded to include a more detailed treatment of linear and quadratic functions and the law of sines and cosines found in most state and provincial guidelines. The topics include finding zeros, domain and range, extrema, and singularities of polynomial and rational functions. Properties of the trigonometric, exponential and logarithmic functions are also explored. Topics also include the study of limits and asymptotic behavior, polar coordinates, parametric equations and conics
Problem Solving George Polya Suggestions For Problem Solving (from Mathematician George Polya's book: "How To Solve It", 1945) Mr. Dave Clausen La Cañada High School How To Solve It  George Polya has four steps for solving problems: – 1. Understand The Problem – 2. Devise A Plan – 3. Carry Out The Plan – 4. Look Back 5/30/2012 Mr. Dave Clausen 2 Understand The Problem  Is it possible to do this?  Can I verbalize what I need to do? 5/30/2012 Mr. Dave Clausen 3 Devise A Plan  Have I seen this before?  Have I seen it in a slightly different form?  Do I know a related problem?  Here is a problem related to mine that is solved. Can I use it?  Can I restate this problem?  If I can't solve this problem, can I first solve some related problem?  Can I solve part of the problem? 5/30/2012 Mr. Dave Clausen 4 Carry Out The Plan  Carry out the plan, checking each step as you work to see if it makes sense. 5/30/2012 Mr. Dave Clausen 5 Look Back  Is the result what I expected?  Can I get this same result in a different way?  Can I use this result in some other problem?  Can I use my method in a different problem? 5/30/2012 Mr. Dave Clausen 6
View From The Top: Analysis, Combinatorics And Number Theory (Student Mathematical Library) A View From The Top: Analysis, Combinatorics And Number Theory (Student Mathematical Library) (Paperback) by Alex Iosevich48 Our Price Rs.1756 Discount Rs.92 A View From The Top: Analysis, Combinatorics And N... Book Summary of A View From The Top: Analysis, Combinatorics And Number Theory (Student Mathematical Library) This book is based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another. In teaching his readers a variety of problem solving techniques as well, the author succeeds in enhancing the readers' hands-on knowledge of mathematics and provides glimpses into the world of research and discovery. The connections between different techniques and areas of mathematics are emphasized throughout and constitute one of the most important lessons this book attempts to impart. This book is interesting and accessible to anyone with a basic knowledge of high school mathematics and a curiosity about research mathematics. The author is a professor at the University of Missouri and has maintained a keen interest in teaching at different levels since his undergraduate days at the University of Chicago. He has run numerous summer programs in mathematics for local high school students and undergraduate students at his university. The author gets much of his research inspiration from his teaching activities and looks forward to exploring this wonderful and rewarding symbiosis for years to come. Books Similar to : A View From The Top: Analysis, Combinatorics And N
I for Dummies One of the most commonly asked questions in a mathematics classroom is, "Will I ever use this stuff in real life?" Some teachers can give a good, ...Show synopsisOne of the most commonly asked questions in a mathematics classroom is, "Will I ever use this stuff in real life?" Some teachers can give a good, convincing answer; others hem and haw and stare at the floor. The real response to the question should be, "Yes, you will, because algebra gives you "power"" - the power to help your children with their math homework, the power to manage your finances, the power to be successful in your career (especially if you have to manage the company budget). The list goes on. Algebra is a system of mathematical symbols and rules that are universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end to solve complex problems. There's no doubt that algebra can be easy to some while extremely challenging to others. For those of you who are challenged by working with numbers, "Algebra I For Dummies" can provide the help you need. This easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems. But rest assured, this book is not about memorizing a bunch of meaningless steps; you find out the whys behind algebra to increase your understanding of how algebra works. In "Algebra I For Dummies," you'll discover the following topics and more: All about numbers - rational and irrational, variables, and positive and negativeFiguring out fractions and decimalsExplaining exponents and radicalsSolving linear and quadratic equationsUnderstanding formulas and solving story problemsHaving fun with graphsTop Ten lists on common algebraic errors, factoring tips, and divisibility rules. No matter if you're 16 years old or 60 years old; no matter if you're learning algebra for the first time or need a quick refresher course; no matter if you're cramming for an algebra test, helping your kid with his or her homework, or coming up with next year's company budget, "Algebra I For Dummies" can give you the tools you need to succeed.Hide synopsis Reviews of Algebra I for Dummies Simple explanations to problems. I needed a book that would explain formulas in simple terms without insulting my intellegence or I wouldn't bother to continue to read it. Excellent choice for first time learners at any age
Bell Schedule School Hours After School Block Schedule Office Hours Mon - Fri: 7:30am - 4:30pm Mathematics MATHEMATICS 7 36 weeks (year) Grade: 7 Students examine algebra- and geometry-preparatory concepts and skills; strategies for collecting, analyzing, and interpreting data; and number concepts and skills especially proportional reasoning. Reasoning, problem solving, communication, concept representation, and connections among mathematical ideas are emphasized in a hands-on learning environment. Graphing calculators and computers are integrated with instruction. This course provides students the opportun ity to acquire the concepts and skills necessary for success in Algebra I or Algebra I Honors. Students are required to take the Standards of Learning End of Course Test. MATHEMATICS 7 HN 36 weeks (year) Grade: 7 The depth and level of understanding in Mathematics 7 Honors is beyond the scope of Mathematics 7. This course is based on Mathematics 8 curriculum and includes extensions and enrichment. Emphasis is placed on mathematical reasoning, non-routine problem solving, and algebraic connections among mathematical ideas. This course provides students the opportunity to acquire the concepts and skills necessary for success in Algebra I or Algebra I Honors. Students are required to take the Standards of Learning End of Course Test. MATHEMATICS 8 36 weeks (year) Grade: 8 Prerequisite: Mathematics 7 Students extend their study of algebra- and geometry-preparatory concepts and skills; strategies for collecting, analyzing, and interpreting data; and number concepts and skills especially proportional reasoning. Reasoning, problem solving, communication, concept representation, and connections among mathematical ideas are emphasized in a hands -on learning environment. Graphing calculators and computers are integrated with instruction. This course provides students the opportunity to acquire the concepts and skills necessary for success in Algebra I or Algebra I Honors. Students are required to take the Standards of Learning End of Course Test. ALGEBRA 1 36 weeks (year) Grade: 8 Credit: one Prerequisite: Middle School Mathematics This course extends students' knowledge and understanding of the real number system and its properties through the study of v ariables, expressions, equations, inequalities, and analysis of data derived from real-world phenomena. Emphasis is placed on making connections in algebra to geometry and statistics. Calculator and computer technologies will be used as tools wherever appropriate. Use of a graphing calculator is considered essential to provide a graphical and numerica l approach to topics in addition to a symbolic approach. Topics include linear equations and inequalities, systems of linear equations, relations, functions, polynomials, and statistics. Students are required to take the Standards of Learning End of Course Test. When Algebra 1 is taken in middle school, it becomes part of the high school transcript record and is included in the determin ation of the high s chool grade point average (GPA) and counts as one of the required mathematics credits for high school graduation. Parents may request that the Algebra 1 grade be omitted from the student's transcript and not earn high school credit for the course. Note: Admission to the Thomas Jefferson High School of Science and Technology requires the compl etion of Algebra 1 prior to grade 9. Rising 7 th grade students will be placed in Algebra I Honors by meeting the following division-wide requirements: 1. Participation in sixth grade Compacted Mathematics or a full year' s advanced mathematics program in grade 6. 2. A score at the 92nd percentile or better on the Iowa Algebra Aptitude Test (IATT) in grade 6. 3. A score of 500 or better (pass advanced) on the Virginia Standards of Learning Grade 7 mathematics test at the end of grade 6. ALGEBRA 1 HONORS 36 weeks (year) Grade: 7, 8 Credit: one/weighted +.5 Prerequisite: Mathematics 7 and/or Mathematics 8 The depth and level of understanding expected in Algebra I Honors is beyond the scope of Algebra I. Students are expected to master algebraic mechanics and understand the underlying theory, as well as apply the concepts to real -world situations in a meaningful way. Students extend knowledge and understanding of the real number system and its properties through the study of variables, expressions, equations, inequ alities, and the analysis of data fro m real world phenomena. Emphasis is placed on algebraic connections to arithmetic, geometry, and statistics. Calculators and computer technologies are integral tools. Graphing calculators are an essential tool for every student to explore graphical, numerical, and symbolic relationships. Students are required to take the Standards of Learning End of Course Test. GEOMETRY HONORS 36 weeks (year) Grade: 8 Credit: one/weighted +.5 Prerequisite: Algebra 1 The depth and level of understanding expected in Geometry Honors is beyond the scope of Geometry. This course emphasizes two - and three-dimensional reasoning skills, coordinate and transformational geometry, and the use o f geometric models to solve problems. A variety of applications and some general problem-solving techniques, including algebraic skills, will be used to explore geometric relationships. Conjectures about properties and relationships are developed inductively an d then verified deductively. Students investigate non- Euclidean geometries, formal logic, and use deductive proofs to verify theorems. Calculators, computers, graphing utilities, dynamic geometry software, and other appropriate technology tools will be used to assist in teaching and learning. Students are required to take the Standards of Learning End of Course Test. Mathematics Department Chair: Dana Scabis This web page contains links to one or more web pages that are outside the FCPS network. FCPS does not control the content or relevancy of these pages.
Certificate in Senior Secondary Mathematics - Arithmetic and Algebra is a well organized, accessible and in-depth course book designed to teach the fundamental aspects of elementary mathematics that are indispensable in building interest, confidence and competence in mathematical reasoning and problem solving. This reader-friendly course book is presented in a format that encourages the average student and challenges the more able student, starting with the basic aspects and progressing to the more advanced aspects of secondary level mathematics. With well over 1000 worked-through examples, more than 840 exercises (answers provided), 20 chapters and 4 appendices; numerous graphs, diagrams and tables, this comprehensive course book is a necessary text for students who desire to do well in secondary or high school mathematics. Emphasis has been laid on detailed presentation and communication through out the course book with the intention of engaging to a greater extent, the attention of the reader. From fractions, logarithms, number system to graphs, equations (literal, simultaneous, quadratic), inequalities, sets and probability, this comprehensive course book furnishes detailed theories, practice and formulae that will ultimately benefit the reader. Certificate in Senior Secondary Mathematics is a valuable course book created to tutor students studying privately to earn good grades in mathematics in certificate and matriculation examinations. Teachers and students in normal classroom studies will also find this book quite helpful. Preview coming soon. Dili Okay Nwabueze at various times taught mathematics at both Ordinary and Advanced (Pure and Applied) Levels. He was formally a Polytechnic/University lecturer in mechanical engineering. He has written publishable books and papers in diverse areas including but not limited to Mathematics, Mechanical Engineering, Petroleum Engineering, Petroleum Refining, and Materials Management. Dili Okay Nwabueze is a registered Engineer. Add a review Name (Required) Email (Required, never displayed) Rating 12345 Comments Please enter the text from the above text box exactly as is (case sensitive)
Fundamentals of Elementary Calculus The Real Number System Continuous Functions Extensions of the Law of the Mean Functions of Several Variables The Elements of Partial Differentiation General Theorems of Partial Differentiation Implicit-Function Theorems The Inverse Function Theorem with Applications Vectors and Vector Fields Linear Transformations Differential Calculus of Functions from Rn to Rm Double and Triple Integrals Curves and Surfaces Line and Surface Integrals Point-Set Theory Fundamental Theorems on Continuous Functions The Theory of Integration Infinite Series Uniform Convergence Power Series Improper Integrals Answers to Selected Exercises
A First Course in Complex Analysis With Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manor. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and su... MOREpported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis. Previous Edition 9780763746582
Saxon Teacher, Algebra 2 is designed to supplement the 3rd edition homeschool kit for Algebra 2. Using this set of CDs without the textbook will lead to an incomplete understanding of the concepts. The program is written with the assumption that the textbook is being used while working on the computer CDs. This program consists of 5 CDs and works on both Windows and Mac computer systems. The grade level is 8th to Adult and the cost including the textbook is reasonable. This set includes over 110 hours of Algebra 2 content, including instruction for every part of every lesson, as well as complete solutions for every example problem, practice problem, problem set, and test problem. There are two types of CDs included in this program. Lessons which include practice and problems sets, then the instruction CD which includes tutorials of each lesson and the answer key for teachers. Some of the following lessons are taught by a professional teacher and the teacher works through each set of problems. The practice sets are on one CD and are continuous videos; however, at the end of each set there are references given at the end of each lesson for students or teachers needing additional help. I found this to be a very helpful feature in returning to the text for help. The CDs cover a wide range of problems from Polygons, Trinomials, Negative Exponents, Geometry, Trigonometry, Rounding, Factoring, and Formatting. All the problems and practice sets are equivalent to one full semester of Algebra 2 and the student has enough information and training to be able to do Pre-Calculus work when the CDs have been completed. The mastery aim is for 80% at completion. The CD format offers students helpful navigation tools that are easy to access and are within a customized player and is compatible with both Windows and Mac. The CDs are very well planned and have a general understanding of Algebra 2. One can easily follow the step-by-step instructions of the teacher. This program along with the text would take a student through to a successful completion of the Algebra 2 course.
Academic level (A-D) Subject area Grade scale Learning outcomes The course will give the basic understanding and knowledge of electrical networks and mathematical methods for analysis of linear models. The course is an essential base for further studies in many different areas where piecewise linear or linear models are used. Aim After the completed course the student will have the ability to: describe properties of passive and active components explain concepts in the mathematical model used for description of the circuits identify the most common passive and active circuits and describe their properties apply the solution methods such as nodal analysis and mesh analysis use superposition and two-terminal equivalents solve transient problems in switching circuits master AC steady state analysis using phasors be acquainted with graphical solution techniques for nonlinear components
Math Solver 0.00 (0 votes) Document Description To Math problems made Easy One Solving Math problems is not easy! A lot of students have difficulty with Math questions but employing some of these techniques will help you to solve Math problems easily : Read it carefully - Math problem solving involves reading the problem slowly and carefully in order to understand what is it that you need to solve. At times you miss out important information when you give it a quick reading. The following steps are genrally followed to solve Math problems: Break Change it into an equation - It is important to convert what you read in words into an equation you can solve. So basically you need to change the English into numbers! Always cross check - Once you get the answer to your Math problem you should always go back and recheck. Sometimes you might miss out on small details and going over the problem and solution again helps. Ask new topic is introduced you should write it down, review it and in case of any doubts bring it up with your tutor. This process of continuously revising what you learn will gear you up to solve math problems online. Add New Comment To solve Math problems quickly and accurately you need an understanding of various math concepts and solving math problems is not an easy task. TutorVista has a team of expert online Math tutors to ... Before talking about linear programming, I would like to tell you the meaning of "linear". Linear is a Latin word which means pertaining to or resembling a line. In mathematics, linear equation means ... Before talking about linear programming, I would like to tell you the meaning of "linear". Linear is a Latin word which means pertaining to or resembling a line. In mathematics, linear equation means ... To Math solve problems quickly and accurately you need an understanding of various math concepts and solving math problems is not an easy task. TutorVista has a team of expert online Math tutors toDifferential Equation is a type of equation which contains derivatives in it. The derivative may de partial deerivative or a ordinary derivative.The eqution may contain derivative of any order. It ... Content Preview Math Solver To Math problems made Easy One Solving Math problems is not easy! A lot of students have difficulty with Math questions but employing some of these techniques will help you to solve Math problems easily : Read it carefully - Math problem solving involves reading the problem slowly and carefully in order to understand what is it that you need to solve. At times you miss out important information when you give it a quick reading. The following steps are genrally fol owed to solve Math problems: Break Change it into an equation - It is important to convert what you read in words into an equation you can solve. So basical y you need to change the English into numbers! Always cross check - Once you get the answer to your Math problem you should always go back and recheck. Sometimes you might miss out on small details and going over the problem and solution again helps. Ask new topic is introduced you should write it down, review it and in case of any doubts bring it up with your tutor. This process of continuously revising what you learn will gear you up to solve math problems online. Help with Math Topics TutorVista's expert tutors will make solving Math Solver very easy. Our expert tutors will work with you in a personalized one-on-one environment to help you understand Math questions better thereby ensuring that you are able to solve the problems. Solve problems in topics like: * Algebra * Geometry * Calculus * Pre-Algebra * Trigonometry * Discrete Mathematics Students frequently need help with fractions, solving algebra expressions, geometry problems, equations, ratios, probability and statistics measurements and calculus. Each of these topics has its own approach for solving problems. TutorVista's online tutoring in math can help students understand the methods for solving Math Solver in each of these categories.
As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues. In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis that help readers to understand and evaluate the computed solutions • many examples that illustrate the techniques and algorithms Least Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering. This book aims to illustrate with practical examples the applications of linear optimization techniques. It is written in simple and easy to understand language and has put together a useful and comprehensive set of worked examples based on real life problems. Mel Gibson teaching Euclidean geometry, Meg Ryan and Tim Robbins acting out Zeno's paradox, Michael Jackson proving in three different ways that 7 x 13 = 28. These are just a few of the intriguing mathematical snippets that occur in hundreds of movies. Burkard Polster and Marty Ross have pored through the cinematic calculus and here offer a thorough and entertaining survey of the quirky, fun, and beautiful mathematics to be found on the big screen. Math Goes to the Movies is based on the authors' own collection of more than 700 mathematical movies and their many years using movie clips to inject moments of fun into their courses. With more than 200 illustrations, many of them screenshots from the movies themselves, this book provides an inviting way to explore math, featuring such movies as • Good Will Hunting • A Beautiful Mind • Stand and Deliver • Pi • Die Hard • The Mirror Has Two Faces The authors use these iconic movies to introduce and explain important and famous mathematical ideas: higher dimensions, the golden ratio, infinity, and much more. Not all math in movies makes sense, however, and Polster and Ross talk about Hollywood's most absurd blunders and outrageous mathematical scenes. They round out this engaging journey into the realm of mathematics by conducting interviews with mathematical consultants to movies. This fascinating behind-the-scenes look at movie math shows how fun and illuminating equations can be. This magisterial annotated bibliography of the earliest mathematical works to be printed in the New World challenges long-held assumptions about the earliest examples of American mathematical endeavor. Bruce Stanley Burdick brings together mathematical writings from Mexico, Lima, and the English colonies of Massachusetts, Pennsylvania, and New York. The book provides important information such as author, printer, place of publication, and location of original copies of each of the works discussed. Burdick's exhaustive research has unearthed numerous examples of books not previously cataloged as mathematical. While it was thought that no mathematical writings in English were printed in the Americas before 1703, Burdick gives scholars one of their first chances to discover Jacob Taylor's 1697 Tenebrae, a treatise on solving triangles and other figures using basic trigonometry. He also goes beyond the English language to discuss works in Spanish and Latin, such as Alonso de la Vera Cruz's 1554 logic text, the Recognitio Summularum; a book on astrology by Enrico Martínez; books on the nature of comets by Carlos de Sigüenza y Góngora and Eusebio Francisco Kino; and a 1676 almanac by Feliciana Ruiz, the first woman to produce a mathematical work in the Americas. Those fascinated by mathematics, its history, and its culture will note with interest that many of these works, including all of the earliest ones, are from Mexico, not from what is now the United States. As such, the book will challenge us to rethink the history of mathematics on the American continents. In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration. What makes mathematicians tick? How do their minds process formulas and concepts that, for most of the rest of the world's population, remain mysterious and beyond comprehension? Is there a connection between mathematical creativity and mental illness? In The Mind of the Mathematician, internationally famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind. Together they explore the behavior and personality traits that tend to fit the profile of a mathematician. They discuss mathematics and the arts, savants, gender and mathematical ability, and the impact of autism, personality disorders, and mood disorders. These topics, together with a succinct analysis of some of the great mathematical personalities of the past three centuries, combine to form an eclectic and fascinating blend of story and scientific inquiry
These programs allow students to use TI-83 Plus calculators to investigate the mathematics they are learning. Please be sure to download the appropriate file for your platform. After downloading, consult your TI-83 Plus user's manual for instructions on how to transfer the file to your calculator using a TI GraphLink cable and software. If you need additional assistance, please access the Texas Instruments Calculator site. PC users can directly download the file to the desktop. Macintosh users should download the associated *.sea file to the desktop and double-click to Unstuff it. Chapter 1 (page 10) Description: plots points in a relation Special Instructions: The program will prompt you to enter the x- and y- values you wish to graph. It will then ask if you wish to graph more points or to quit. PC - MAC Chapter 3 (page 133) Description: determines whether a function is even, odd, or neither Special Instructions: Enter the function you are testing as Y1 in the Y= menu before running the program. The program will prompt you to enter an x-coordinate that lies on the graph of the function and then will calculate whether the function is odd, even, or neither. PC - MAC Chapter 4 (page 226) Description: computes the value of a function Special Instructions: Enter the function you are testing as Y1 in the Y= menu before running the program. The program automatically repeats itself until you quit. PC - MAC Chapter 5 (page 331) Description: determines the area of a triangle, given the lengths of all sides of the triangle Special Instructions: The program will prompt you to enter the measure of each side of the triangle. PC - MAC Chapter 5 (page 333) Description: determines the lengths of the sides and the angle measures of a triangle, given the coordinates of the vertices of the triangle Special Instructions: Make sure the calculator is set in DEGREE mode. The program will prompt you to enter each vertex. Enter each coordinate separately followed by pressing ENTER. PC - MAC Chapter 7 (page 470) Description: computes the distance from a point to a line Special Instructions: Make sure the equation of the line is written in standard form before beginning the program. Enter the information from each prompt in the program. Chapter 8 (page 512) Description: determines the components of the cross product of two vectors Special Instructions: The program will ask you to identify the two vectors as (A, B, C) and (X, Y, Z). Enter each coordinate separately followed by ENTER. The result will appear as three values in order of their appearance in the ordered triple. PC - MAC Chapter 9 (page 582) Description: performs complex iteration Special Instructions: Make sure the calculator is in complex (a + bi) mode before beginning the program. When entering the number, enter it in a + bi form. PC - MAC Chapter 9 (page 604) Description: draws Julia sets Special Instructions: Make sure the calculator is in complex (a + bi) mode. Set the calculator window for [0, 100] scl:1 by [0, 100] scl:1. CX and CY correspond to a and b, respectively, in a + bi. Select values from -1.5 to 1 for CX and CY to make the program run more efficiently. This program takes 35-60 minutes to run. PC - MAC Chapter 10 (page 620) Description: determines the distance and midpoint between two points Special Instructions: The two points are entered as (X1, Y1) and (X2, Y2). Each coordinate is entered separately followed by ENTER. The coordinates of the midpoint are displayed on two separate lines. PC - MAC Chapter 10 (page 628) Description: determines the radius and the coordinates of the center of a circle from an equation written in general form Special Instructions: Write the equation of the circle in standard form before beginning the program. Enter the values of D, E, and F when prompted. PC - MAC Chapter 12 (page 780) Description: calculates the value of the nth term of a continued fraction sequence Special Instructions: Each term of this sequence equals the sum of A and the reciprocal of the previous term. When prompted, enter any value for A, the initial term of the sequence. PC - MAC Chapter 14 (page 961) Description: uses rectangles to approximate the area under a curve Special Instructions: The program approximates the area between the graphs of two functions by dividing the region into rectangles. Store the two functions as Y1 and Y2 in the Y= list before beginning the program. It is a good idea to look at the graphs of the two functions to help you determine the lower and upper bounds from which the rectangles are to be made. PC - MAC
1800 118 002 [Toll Free] Download CBSE Important Questions Class 10: Mathematics Table Of Contents Number Systems CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Euclid's Division Lemma, The Fundamental Theorem of Arithmetic, Revisiting Irrational Numbers, Revisiting Rational Numbers and Their Decimal Expansions. Polynomials CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Geometrical Meaning of the Zeroes of a Polynomial, Relationship between Zeroes and Coefficients of a Polynomial, Division Algorithm for Polynomials. Pair of Linear Equations in Two Variables CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Pair of Linear Equations in TwVariables, Graphical Method of Solution of a Pair of Linear Equations, Algebraic Methods of Solving a Pair of Linear Equations, Substitution Method, Elimination Method, Cross-Multiplication Method, Equations Reducible ta Pair of Linear Equations in TwVariables. Quadratic Equations CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Quadratic Equations, Solution of a Quadratic Equation by Factorisation, Solution of a Quadratic Equation by Completing the Square, Nature of Roots. Arithmetic Progressions CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Arithmetic Progressions, nth Term of an AP, Sum of First n Terms of an AP. Trigonometry CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Trigonometric Ratios, Trigonometric Ratios of Some Specific Angles, Trigonometric Ratios of Complementary Angles, Trigonometric Identities. Heights and Distances CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Heights and Distances. Co-Ordinate Geometry CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Distance Formula, Section Formula, Area of a Triangle. Similar Triangles CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Similar Figures, Similarity of Triangles, Criteria for Similarity of Triangles, Areas of Similar Triangles, Pythagoras Theorem. Circles CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Tangent ta Circle, Number of Tangents from a Point on a Circle. Constructions CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Division of a Line Segment, Construction of Tangents ta Circle. Areas Related tCircles CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Perimeter and Area of a Circle A Review, Areas of Sector and Segment of a Circle, Areas of Combinations of Plane Figures. Surface Areas and Volumes CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Surface Area of a Combination of Solids, Volume of a Combination of Solids, Conversion of Solid from One Shape tAnother, Frustum of a Cone. Statistics CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Mean of Grouped Data, Mode of Grouped Data, Median of Grouped Data, Graphical Representation of Cumulative Frequency Distribution. Probability CBSE Important Questions for class 10 Mathematics. The following topics and points are given for download Introduction, Probability A Theoretical Approach.
mathematics Mathematics Tools is a tools that help people in solving Mathematical problems such as: - Solving quadratic equation and cubic equation - Solving System of equations (2 or 3 unknowns) - Working in the Base Numbe The applications are many and reach from education over science to productive use in your company: in exampleCur One thing is to study and try to solve problems on Plane Analytic... Icons are carefully created pixel by pixel by the hand of a professional artist. They shine with a bright palette of colors, smooth and well-rounded edges. Superb in their quality, icons will help a developer to... Field-level Online Help is included as well as an effective variety of Themes.... by less intricate equations. The problems presented are... This bilingual problem-solving mathematics software allows you to work through 36319 arithmetic and pre-algebra problems with guided solutions, and encourages to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. Each solution step is provided with its objective, related definition, rule and underlying math formula or theorem. A translation option offers a way to learn math lexicon in a foreign language. Test preparation options... Test authoring mathematics software offers 53809 hyperbolic equations with answers and solutions and easy-to-use test authoring options. Hyperbolic equations from basic to advanced are arranged by complexity and solution method; all the hyperbolic functions are included. The software enables users to prepare math tests, homeworks, quizzes and exams of varied complexity literally in a minute, and generates three variants around each prepared test. Tests with or without the solutions can beThis educational software is great for children and even adults wanting to... Most people find this to be easier and faster.Mathpad has some... Calculate tedious and difficult Statistics and Discrete Mathematics formulas accurately, quickly, and with ease! Combinatorics (permutations and combinations, etc.), probabilities, expected values, confidence intervals, data analysis, hypothesis testing and more.Statistics Pro does more than simply give you the correct answer! It helps to ensure your understanding of the formulas and concepts involved by showing, and explaining, the actual formula you're using, all with a simple click of the... Size: 2.2 MB License: Demo Price: $9.95 For searches similar to mathematics see "Related Downloads" under the categories listing.
Wavelets: A Tutorial in Theory and Applications is the second volume in the new series WAVELET ANALYSIS AND ITS APPLICATIONS. As a companion to the first volume in this series, this volume covers several of the most important areas in wavelets, ranging from the development of the basic theory such as construction and analysis of wavelet bases to An accessible and practical introduction to wavelets With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents... more... Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and... more... Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are... more...
As atudents progress in thier educational pathway, more knowledge and skills will be required. This course will foster a development and understanding of mathematics in the real world. Students will acquire skills in adding, subtracting, multiplyuing and diving signed numbers which will include integers. Students will solve multi-step equations involving the real number system and algebraic thinking. Problems solving in this course includes applications of ratios, proportion, fractions, and percents. It continues to develop other important mathematics topics including patterns, functions, gemoetry, measurement, probability, and statistics. It provides hands-on, visuals for students who are below grade level as well as renrichment for advanced students. Algebra I is intended to build a foundation for all higher math classes. It is the brige from the concrete to the abstract study of mathematics. This course will review algebraic expressions, integers, and mathematical proporties that will lead into working with variables and linear equations. There will be an in-depth study of graphing, polynomials, quadratic equations, data analysis, and systems of equations through direct class instruction, group work, homework, and Fuse (I-pads).
Book Description: Now you can combine a highly effective, practical approach to mathematics with the latest procedures, technologies, and practices in today's welding industry with PRACTICAL PROBLEMS IN MATHEMATICS FOR WELDERS, 6E. Readers clearly see how welders rely on mathematical skills to solve both everyday and more challenging problems, from measuring materials for cutting and assembling to effectively and economically ordering materials. Highly readable explanations, numerous real-world examples, and practice problems emphasize math skills most important in welding today, from basic procedures to more advanced math formulas and technologies. Readers leave equipped with the strong math tools they need for success in today's welding careers. Buyback (Sell directly to one of these merchants and get cash immediately) Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it
9780321279224Introductory and Intermediate Algebra (3rd Edition) Lial/Hornsby/McGinnis s Introductory and Intermediate Algebra, 3e gives students the necessary tools to succeed in developmental math courses and prepares them for future math courses and the rest of their lives. The Lial developmental team creates a pattern for success by emphasizing problem solving
Introduction to Analysis This book developed slowly through notes starting around 1975. It's meant as a first introduction to proofs in analysis, drawing upon the reader's background in one-variable calculus; it's not a technical reference work. It has a lot of unnecessary explanations and cautionary warnings, based on what I've seen on students' problem sets. It has some attempts to smooth over some standard early bumps in the path to understanding. It emphasizes estimation and approximation as the basic tools of analysis, rather than concepts from algebra or point-set topology. Students who think they might need some analysis for their work but don't like mathematics have been able to read it (without complaints), and it has even converted a few. Some stick close to their desks and never go to class -- they read the book, hand in the frequent homework, take the tests and do OK. It has been used at small colleges and state universities. To get the flavor in a few minutes, I suggest looking at these links in order, to get an idea of what reading it will be like. These are a few sections, totalling about 15 pages in all, showing text material, Questions, Exercises, and Problems, to give you a sample of the writing style and level. They are selected from the first three chapters: PRINTING: There is only one edition so far, but several printings. The printing is identified by a number sequence like 10 9 8 7 6 5 4 on the left-hand page facing the dedication page; the sequence shown identifies the fourth printing, for example. CORRECTIONS: I would be grateful to hear about any needed mathematical corrections not listed below, as well as your experience with the book, as teacher or student. Write to: mattuck@mit.edu Thanks. Mathematical corrections to the Third through the Seventh Printing ( pdf file ) Mathematical corrections to the Second Printing (check also the corrections to printings 3-7) ( pdf file ) Mathematical corrections to the First Printing (check also the corrections to printings 3-7) ( pdf file )
"A Framework for Adult Numeracy Standards" is based upon a study by the Adult Numeracy Network (ANN). In this study, instructors and learners identified the mathematical skills and abilities adults need to fulfill their life roles. These topics are similar to the subjects that will be emphasized in the 2002 GED Math test. For a more in depth examination of the study and description of the frameworks, see: A Framework for Adult Numeracy Students, The Mathematical Skills and Abilities Adults Need to Be Equipped for the Future, by Donna Curry, Mary Jane Schmitt, and Sally Waldron at: Number and Number Sense This skill (being able to handle numbers comfortably and competently) needs to be explored using whole numbers, fractions, decimals, percents, ratio, money, and estimation. Estimation, mental math, computation, and calculators are all tools that develop number and number sense. Problem Solving: Reasoning and Decision Making Problem solving includes seeking to understand the problem then figuring out what information and math skills are important to use and solve the problem. While problem solving is embedded in mathematics, there are specific skills and strategies that help greatly. Data Analysis, Probability and Statistics, and Graphing Reading charts and graphs, interpreting data, and making decisions based on information are key skills to being a successful worker and informed citizen. Geometry: Spatial Sense andMeasurement Measurement, a foundation skill for geometry, is an essential life skill. Awareness of acceptable tolerances, margins, and upper and lower limits critical to measurement competence. Today, much is computerized, but the results are only as good as the information inputted. Visualization and concrete models help reasoning in this area. Algebra: Patterns and Functions Algebra includes more than formal methods of equation solving, age problems, and lots of X's and Y's. Conceptual understanding, algebra as a means of representation, and algebraic methods are all problem solving tools. Algebraic reasoning allows us to think about and express patterns, relations, and functions which ultimately give us access to technology.
Tag Info At least for me, starting by trying to solve the homework questions, even if I hadn't fully grasped some proofs (or even full grasped the concepts involved) usually worked out better than trying to understand everything first and only then starting with the homework problems. As long as I found a solution (where found means found it myself, though. I tried ... I will second Serge Lang's book "Basic Mathematics". It is definitely challenging though for those used to traditional high-school textbooks. But as originally asked, AOPS has something called the "Alcumus" which you might find useful. As mentioned on the website : Art of Problem Solving's Alcumus offers students a ... I don't know anything about programming but you mentioned "3D" and to me that screams Linear Algebra. However, you only mention doing Gr.7 level math so you have lots of work to do. When growing up I learned a lot from the site Purple Math. It seems to have a lot more topics now then when I used to use it but I remember it being quite good. Recently I have ... If you've enjoyed the Khan Academy for coding, then check out it offerings with respect to math! That's my "starting point" recommendation. (Math:...that's where Sal Khan got going, before branching off into other areas.) See also Paul's Notes: Click on course notes: you'll see a drop down menu: Algebra, Calculus I, II, III, Linear Algebra, etc. Many ... The obvious answer is the math section of Khan Academy! More advanced courses can be found here and here, a couple of nice ones on analysis and functional analysis by Joel Feinstein here and some brilliant ones on linear algebra/systems/optimisation by Stephen Boyd here. It is also worthwhile to check for courses here and (in the future) here. See also ... I find this interesting myself as I also have messy writing. For me I always try to keep equal signs aligned and leave equal spacing. I also prefer using paper landscape as opposed to portrait but this is all just personal preference. As for speed vs. neatness, I think it really is just about finding a fine line between them, neatness is important but you ... It may just be my fanatical opinion, but I think that clarity is one of the most important attributes of performing mathematics, regardless of level. For your purposes, let me present an example: Regardless of what course I am teaching, whether it be first year calculus or fourth year topology, I always have students who submit messy, poorly structured, ... My handwriting is pretty bad, I love $\LaTeX$, I've lectured on chalkboards/blackboards a couple of times, and given computerized presentations. My general feeling is that you should make the general direction of everything you write in exams crystal clear, and keep letters/symbols distinct, but otherwise don't waste too much time on lovely handwriting. ... I.M Gelfand's books on trigonometry,algebra,functions and graphs and calculus of variations(and much more) are comparable to Feynman Lectures. He has even stated his effort to write a book like feynman's in the book's preface. I strongly recommend the books. You can search the books in amazon for user reviews. Search by web for how to understand mathematics. Read for instance: - many topics of mathematics - this is about Serge Lang Good Luck! I posted this first in a comment, but it is really worth status as an answer.: A middle school teacher gifted me an old book: "How to Lie with Statistics" by Darrell Huff: "Darrell Huff runs the gamut of every popularly used type of statistic, probes such things as the sample study, the tabulation method, the interview technique, or the way results are ... It is a common misconception in regard to math, but this kind of misconception is common everywhere. It's caused by the recursive properties of knowledge. The more you learn, the more you realize how little you know.; i.e: Since it is known that less informed individuals see fields as more finite than informed individuals; While laymen may relate to the ... Probability with dice and coin tosses seems like a standard starting point. Discussion of normal distributions (percentiles, standard deviation) also is pretty fundamental. The great thing about both of those is that they're easy to illustrate. Probability is great to discuss in terms of games of chance (and while talking about dice and coin tosses is great ... Maybe you can look into: Share My Lesson High School Statistics Resources Statistics and Probability Books Activities and Projects for High School Statistics Courses by Ron Millard, John C. Turner See this list of books on Google Teaching Stats in High School Search out other such books and resources You might also want to try some of the ... The number looks small enough to be brute-forced on a computer. Just try every possible factor, starting with 2, 3, 4, ... and keep dividing them out as long as the division comes out even. Then continue looking for factors of the quotient. You don't even need to explicitly restrict to primes, because any composite number you try simply won't divide the ... The thing with Project Euler is that there is usually an obvious brute-force method to do the problem, which will take just about forever. As the questions become more difficult, you will need to implement clever solutions. One way you can solve this problem is to use a loop that always finds the smallest (positive integer) factor of a number. When the ... Project Euler problems (at least the ones that I have done) tend to deal with a lot of number theory topics. So, reading an introductory number theory book could be helpful. With regards to your particular situation, I suggest finding primes first, then testing the primes for divisibility. That is, to find prime factors of $25$, don't test $1, 2, 3, 4, 5, ... The important aspect in these kinds of permutations and combinations questioins is the direction with which you are approaching the problem. For some questions, starting from the left most digit and then moving towards right may be a good strategy. Ex-- How many numbers are greater than 500 or less than 800 kind of questions, where hundred's digit has a lot ... On the wiki page I noticed this appeared: Lisa Glendenning (May 2005). Mastering Quoridor (B.Sc. thesis). University of New Mexico. The link to it does not work, but if you can get to it, it probably at least contains references to published work done on the game. I agree with the author of the question that inferring the domain from the definition of the function is backward. There are a couple of points that I think would be worth adding to the previous answers. Firstly, it is not quite clear to me that the one right setup in which all of mathematics is happening is $\mathbb{R}$. There seems to be no particular ... We have a museum at our university, with an installation of morenaments, an application I wrote myself. We find visitors of all ages spending hours drawing wallpaper ornaments with these. For iOS devices like the iPad, there is a newer development called iOrnament. These applications can be great to use an aesthetic faszination and turn it into curiosity ... My two cents: if you are not sure about where exactly in mathematics you want to go, then vector calculus is a pretty good way to make more paths viable. If you do any sort of analysis, chances are you'll need to know vector calculus forwards and backwards; this is especially true if you want to work in PDEs. If you want to do anything on manifolds ... Yes. "Studying math is as much about specific examples as it is about general theorems." My teacher Mike Artin used to expound on this concept (and then assign ridiculous and tedious homework assignments) and I would not get what he was saying. But the more I read math, the more I've come to realize that understanding specific examples is what allows you ... The answer depends on your interests, and on the place you continue your education. In some areas in the world, PhD's are very specialized so any course that is not directly related to the subject matter is not necessary. One could complete a pure math PhD and not know vector or multivariate calculus. However, this is increasingly rare; more and more PhD ... I second the notion of Intuiton and Instincts, though in a different context. Many hard research problems are hard simply because there is no cookie cutter method for solving them. After trudging though core curriculum like Calculus, Algebra, Analysis, PDE's, etc, you acquire a vast array of problem solving techniques albeit for specific classes of problems. ... A controversial and easy answer is "intuition". I know you don't like it, but sadly it is true. All that we know about Calculus started with Newton and Leibnitz's intuition about limits,continuity and derivatives and integrals. And for many decades Calculus stuck to be an "intuitively correct" idea, and along came Augustin-Louis Cauchy who defined it ... Note first that the derivative of the quadratic in the denominator is $-2x+2$. It would be great if the numerator were $4x-4$, because then we could set $u=3+2x-x^2$, $du=(-2x+2)dx$, and write the indefinite integral as $$\int\frac{-2}{\sqrt u}du=-2\int u^{-1/2}du\;.$$ Unfortunately, the numerator is actually $4x-5=-2(-2x+2)-1$. The trick is to split the ... My first think of infinity was square diagonal vs. orthogonal stepping. Start with route (0,0) -- (0,1) -- (1,1), then take (0,0) -- (0,½) -- (½,½) -- (1,½) -- (1,1) and so on. Form of later will come closer to diagonal, but lenght will not. I have been going back to review my calculus and differential equations for myself. I was using Lyx and LaTex for a while but it is slow and tedious to learn(for me). I will say that if you are willing use Microsoft OneNote install the math plugin which you can download from MS(free) also install the Microsoft Graphing Calculator software (also free) where ... If you're writing a children's book on mathematics, please start by reading some excellent children's books dealing with mathematics. Here are some books I have fond memories of: The Man Who Counted The Phantom Tollbooth Flatland Alice in Wonderland / Through the Looking Glass Everything by Martin Gardner Godel, Escher, Bach: An Eternal Golden Thread For me it was Monty Hall problem: ... The fact that you can't divide by zero always amazed me. I once read the following analogy: Imagine you go to a shop with 100 dollars in your pocket, and imagine that everything in the shop costs 1 dollar. How many things can you buy? 100. What if instead of 1 dollar, each thing costed $0.5? How many things can you buy? 200. Now imagine that ... Rosenlicht's Intro to Analsysis was an awesome read, but the real learning took place in the excersises. It was cheap, and just as rigorous as the introductory analysis course I took the following semester! To be able to solve the problem I think a student would need to know basic algebra some trigonometry some geometry, including the concept of circles, triangles, and equidistance At what education level... Education level is a strange concept, but I think a bright student in an advanced secondary mathematics class should be able to solve this. It's ... I might be being silly but it appears to me that the question is not written very well and it is mathematically inaccurate. My main issue is that Dana might not be able to stand anywhere. How do we know that there is a place that is one rod away from both Bob and Carl? They might be at a distance of more than two rods away from each other, in which case ... By the way, just to give a much simpler answer (which indeed does not really explain the issue but might help if you're not studying calculus yet): The problem here is that, in reality, $\infty$ is not a number. It is used to represent an unimaginably big number, but you obviously can't tell which. Therefore, infinity itself is not a defined number. That's ... When your teacher talks about $0/0$ or $\infty/\infty$ or $1^\infty$ he/she's not talking about numbers, but about functions, more precisely about limits of functions. It's just a convenient expression, but it should not be confused with computations on simple numbers (which $\infty$ isn't, by the way). When $1^\infty$ is referred to, it is to mean the ... What $1^\infty$ is, or is not, is merely a matter of definition. Normally, one would only define $a^b$ for some specific class of pairs of $a,b$ - say $b$ - positive integer, $a$ - real number. When extending the definition of exponentiation to more general pairs, the key thing people keep in mind is that various nice properties are preserved. For ... The Sieve of Eratosthenes code on Wikipedia is intended to generate a list of all primes up to $n$. Suppose $k\le n$ is not prime, so we have two factors $a,b$. We can't have $a,b$ both larger than $\sqrt{n}$, as then $k=ab$ would be larger than $n$. Thus in order to show that $k$ is prime, we only need to check that it is not divisible by a number up to ... I was always good at maths as a child, and took to reading extension maths books for fun (other kids thought I was weird). When I was about 10 I was completely hooked when I saw Euclid's proof for an infinity of primes. I had been given it as a question in one of the books I was reading. I spent about an hour desperately trying to prove it . . . then I ... As a high-school student, who studies Euclidean Geometry for the purpose of Mathematics Olymnpiads, I would recommend the following, not as high-powered as Coxeter, books. The Geometry of the Triangle - Gerry Leversha Plane Euclidean Geometry - AD Gardiner and CJ Bradley Introduction to Geometry (2 book set) - Richard Rusczyk These are all fairly basic, ... I'm not sure I like the subspace topology for this. I think the torus bit is good, though; perhaps expand that to flipping over two cards, one for the space and one for the topology, where the space is given by an identification diagram, which would yield the cylinder, moebius strip, torus, klein bottle, sphere, and the real projective space on R2 (that I ... To add my 2 cents-part of what's hindering and scaring a lot of people who have to teach "college geometry" these days is the utter collapse of the American high school system. As a result,it's no longer a given that your students are comfortable with what used to be "high school" geometry-something that used to be a given for any student at any university. ... I was hooked on math by a small side note in a kid's book of mathematics about perfect numbers, numbers that are twice the sum of their factors. For example, 6 is the smallest perfect number because 1 + 2 + 3 + 6 = 2 × 6 and 28 is the next one because 1 + 2 + 4 + 7 + 14 + 28 = 2 × 28. The next perfect numbers are 496, 8,128, 33,550,336, and 8,589,869,056. I ... I have my students play almost exactly this game at the start of a course in College Geometry, through GeoGebra. Of course, it lacks the video game style interface you're describing (and which, I agree, would be awesome), so I would be excited to see something like this polished up nicely. I'll tell you briefly what I do in class and a little about how ...
Synopsis This textbook emphasises the fundamentals and the mathematics underlying computer graphics. The minimal prerequisites, a basic knowledge of calculus and vectors plus some programming experience in C or C++, make the book suitable for self study or for use as an advanced undergraduate or introductory graduate text. The author gives a thorough treatment of transformations and viewing, lighting and shading models, interpolation and averaging, BÈzier curves and B-splines, ray tracing and radiosity, and intersection testing with rays. Additional topics, covered in less depth, include texture mapping and colour theory. The book covers some aspects of animation, including quaternions, orientation, and inverse kinematics, and includes source code for a Ray Tracing software package. The book is intended for use along with any OpenGL programming book, but the crucial features of OpenGL are briefly covered to help readers get up to speed. Accompanying software is available freely from the book's web site. Found In eBook Information ISBN: 9780511075
books.google.com - This... and combinatorial mathematics Discrete and combinatorial mathematics: This were added, creating a greater variety of level in problem sets, which allows students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making this the ideal text for preparing students for advanced study. From inside the book Review: Discrete and Combinatorial Mathematics User Review - Joecolelife - Goodreads The book is very well-written, clear and precise. I have read a couple of other books for discrete math courses, but found nothing exciting there; mostly frustrating errors, bad examples and confusion ...Read full review Review: Discrete and Combinatorial Mathematics User Review - Bart - Goodreads This book is amazing. It aroused in me a love of discrete mathematics. It has great coverage of combinatorics, set theory, graph theory, finite state machines. The examples are great although they ...Read full review
She Does Math! edited by Marla Parker The range of applications is broad. The examples are easy to understand and are generally supported by interesting problems. The book is carefully edited and the graphic and text style are consistent from chapter to chapter—the hallmark of attention to detail in a book with numerous authors. — Mathematical Reviews Finally—a practical, innovative, well-written book that will also inspire its readers. The wonder is...it is a mathematics text and a biography! The idea of women telling their own career stories, emphasizing the mathematics they use in their jobs is extremely creative. This book makes me wish that I could go through school all over again! — Anne Bryant, Executive Director, American Association of University Women She Does Math! presents the career histories of 38 professional women and math problems written by them. Each history describes how much math the author took in high school and college; how she chose her field of study; and how she ended up in her current job. Each of the women present several problems typical of those she had to solve on the job using mathematics. There are many good reasons to buy this book: It contains real-life problems. Any student who asks the question, "Why do I have to learn algebra (or trigonometry or geometery)?" will find many answers in its pages. Students will welcome seeing solutions from real-world jobs where the math skills they are learning in class are actually used. It provides strong female role models. It supplies practical information about the job market. Students learn that they can only compete for these interesting, well-paying jobs by taking mathematics throughout theur high school and college years. It demonstrates the surprising variety of fields in which mathematics is used. Who should have this book? Your daughter or granddaughter, your sister, your former math teacher, your students — and young men, too. They want to know how the math they study is applied — and this book will show them.
Read this article hotklixed More than a Year Ago! Free Algebra worksheets and Pre-Algebra worksheets for people in 6th grade, 7th grade, 8th grade and 9th grade. Math problems, quizzes, tests and exams included.
Courses 120. Appreciation of Mathematics An exploration of topics which illustrate the power and beauty of mathematics, with a focus on the role mathematics has played in the development of Western culture. Topics differ by instructor but may include: Fibonacci numbers, mathematical logic, credit card security, or the butterfly effect. This course is designed for students who are not required to take statistics or calculus as part of their studies. 140. Statistics An introduction to statistical thinking and the analysis of data using such methods as graphical descriptions, correlation and regression, estimation, hypothesis testing, and statistical models. A graphing calculator is required. 160. Calculus for the Social Sciences A graphical, numerical and symbolic introduction to the theory and applications of derivatives and integrals of algebraic, exponential, and logarithmic functions, with an emphasis on applications in the social sciences. A student may not receive credit for both Mathematics 160 and 181. 181. Calculus I A graphical, numerical, and symbolic study of the theory and application of the derivative of algebraic, trigonometric, exponential, and logarithmic functions, and an introduction to the theory and applications of the integral. Suitable for students of both the natural and the social sciences. A graphing calculator is required. A student may not receive credit for both Mathematics 160 and 181. 182. Calculus II A graphical, numerical, and symbolic study of the theory, techniques, and applications of integration, and an introduction to infinite series and/or differential equations. A graphing calculator is required. Prerequisite: Mathematics 181 or the equivalent. 201. Modeling and Simulation for the Sciences A course in scientific programming, part of the interdisciplinary field of computational science. Large, open-ended, scientific problems often require the algorithms and techniques of discrete and continuous computational modeling and Monte Carlo simulation. Students learn fundamental concepts and implementation of algorithms in various scientific programming environments. Throughout, applications in the sciences are emphasized. Cross-listed as Computer Science 201. Prerequisite: Mathematics 181. 210. Multivariable Calculus A study of the geometry of three-dimensional space and the calculus of functions of several variables. Prerequisite: Mathematics 182. 212. Vector Calculus A study of vectors and the calculus of vector fields, highlighting applications relevant to engineering such as fluid dynamics and electrostatics. Prerequisite: MATH 182. 220. Linear Algebra The theoretical and numerical aspects of finite dimensional vector spaces, linear transformations, and matrices, with applications to such problems as systems of linear equations, difference and differential equations, and linear regression. A graphing calculator is required. Prerequisite: Mathematics 182. 235. Discrete Mathematical Models An introduction to some of the important models, techniques, and modes of reasoning of non-calculus mathematics. Emphasis on graph theory and combinatorics. Applications to computing, statistics, operations research, and the physical and behavioral sciences. 240. Differential Equations The theory and application of first- and second-order differential equations including both analytical and numerical techniques. Prerequisite: Mathematics 182. 250. Introduction to Technical Writing An introduction to technical writing in mathematics and the sciences with the markup language LaTeX, which is used to typeset mathematical and scientific papers, especially those with significant symbolic content. 260. Introduction to Mathematical Proof An introduction to rigorous mathematical argument with an emphasis on the writing of clear, concise mathematical proofs. Topics will include logic, sets, relations, functions, and mathematical induction. Additional topics may be chosen by the instructor. Prerequisite: Math 182 280. Selected Topics in Mathematics Selected topics in mathematics at the introductory or intermediate level. 310. History of Mathematics A survey of the history and development of mathematics from antiquity to the twentieth century. Prerequisite: Math 260. 410. Geometry A study of the foundations of Euclidean geometry with emphasis on the role of the parallel postulate. An introduction to non-Euclidean (hyperbolic) geometry and its intellectual implications. Prerequisite: Mathematics 260 421 - 422. Probability and Statistics A study of probability models, random variables, estimation, hypothesis testing, and linear models, with applications to problems in the physical and social sciences. Prerequisite: Mathematics 210 and 260. 435. Cryptology An introduction to cryptology and modern applications. Students will study various historical and modern ciphers and implement select schemes using mathematical software. Cross-listed with COSC 435. Prerequisites: MATH 220 and either MATH 235 or 260. 439. Elementary Number Theory A study of the oldest branch of mathematics, this course focuses on mathematical properties of the integers and prime numbers. Topics include divisibility, congruences, diophantine equations, arithmetic functions, primitive roots, and quadratic residues. Prerequisite: MATH 260. 441 - 442. Mathematical Analysis A rigorous study of the fundamental concepts of analysis, including limits, continuity, the derivative, the Riemann integral, and sequences and series. Prerequisites: Mathematics 210 and 260. 445. Advanced Differential Equations This course is a continuation of a first course on differential equations. It will extend previous concepts to higher dimensions and include a geometric perspective. Topics will include linear systems of equations, bifurcations, chaos theory, and partial differential equations. Prerequisite: Math 240. 448. Functions of a Complex Variable An introduction to the analysis of functions of a complex variable. Topics will include differentiation, contour integration, power series, Laurent series, and applications. Prerequisite: MATH 260.
Find a Hammond, IN Precalculus ...The Complex Number System Topics may include performing arithmetic operations with complex numbers, representing complex numbers and their operations on the complex plane, and using complex numbers in polynomial identities and equations. Algebra Seeing Structure in Expressions Topics may inclu...
The guiding principles of the Mathematics syllabus direct that Mathematics as taught in Caribbean schools should be: relevant to the existing and anticipated needs of Caribbean society; related to the ability and interest of Caribbean students; aligned to the philosophy of the educational system. These principles focus attention on the use of Mathematics as a problem solving tool, as well as on some of the functional concepts which help to unify Mathematics as a body of knowledge. The syllabus explains general and unifying concepts that facilitate the study of Mathematics as a coherent rather than as a set of unrelated topics.
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MATHEMATICS PROGRAM MODELS FOR OHIO HIGH SCHOOLS The ODE Mathematics Program Models offer six (6) different sequences of courses that take an applications, blended, or connected approach to the high school mathematics curriculum. The ORC Pacing Guides (upper left navigation bar) feature a schedule of topics, links to best practice lessons, teaching tips, and rich problems to engage students in exploration, analysis, and application of big ideas in mathematics. (Below is condensed from Ohio Department of Education draft, June 2006) The State Board of Education adopted the Ohio Academic Content Standards for K-12 Mathematics in December 2001. The Standards set high learning expectations for every student, recognizing that in the 21st century, every student will need a strong preparation in mathematics. In Ohio, the assumption is that all students can learn significant mathematics, and the commitment is that all students will be successful in learning mathematics and will graduate from high school fully prepared for the demands of the workplace and further study. Many factors influence how secondary mathematics programs can best be designed and delivered at this time. Day-to-day decision making, as well as the expectations for today's workforce, require a greater emphasis on data analysis, probability, and statistics in the secondary curriculum. The tools of technology make some mathematical concepts accessible to students at an earlier stage. The curriculum of the middle grades now includes many of the basic concepts of algebra, geometry, measurement, and data analysis. Consequently, what is needed in many Ohio districts is not a simple adjustment on the margin of an old curriculum, but rather a full rethinking of the secondary school mathematics program. There are many ways a curriculum can be configured to respond to the requirements of the Content Standards. In the area of secondary mathematics, the Department of Education is providing districts with three different models for mathematics programs in grades 9-12. Descriptions of the Mathematics Program Models The three models were drafted by a panel of Ohio teachers, mathematicians, and mathematics educators in the summer of 2005. They were reviewed and discussed by professional groups, practitioners, and others during the school year 2005-2006, and after revision, are now available to schools. The models are presented in terms of years of study (Year 1 through Year 5) rather than in terms of grade levels (grade 9 through grade 12), recognizing that some students will start the secondary mathematics curriculum in grade 8, others in grade 9, and that there can be years when some students take more than one mathematics course. The models emphasize the importance of every student taking mathematics in each of the four years of high school, and they provide appropriate courses for all students in grade 12. Characteristics Common to All Three Program Models Although the models presented here offer distinctive ways of approaching the mathematics described in the Ohio Academic Content Standards, they share several basic characteristics: Each demonstrates how the Standards can be implemented through a curriculum and how instruction can be organized to improve student learning; Each prepares students to achieve or exceed the proficiency level on the mathematics portion of the Ohio Graduation Test in grade 10 and to achieve or exceed the requirements to enter Ohio college and university mathematics and logical reasoning; Each displays the connectedness and coherence of the mathematics studied within each course and across the courses in a sequence. Distinctive Characteristics of the Three Models Each model also has distinctive characteristics: Model A. This model uses the applications of mathematics to motivate the need to master mathematical topics in algebra and geometry. By using applications to motivate the mathematics, students can become more engaged in algebraic and geometric topics, and motivated to work hard on meaningful problems. Mathematics developed in this way is intended to encourage problem solving and reasoning skills, thus preparing students well for the workplace or for further education. Model B. This model blends the mathematics of the various content strands (algebra/number, geometry/measurement, data/statistics), weaving them together in each course and providing a sequence of courses that build on one another to form a coherent curriculum. Data topics are woven throughout the model with a focus on a data project in Year 3. Model C. This model features a classic sequence of courses that emphasizes connections across content strands. Data analysis topics have been added to the familiar high school mathematics curriculum. Year 1 focuses on algebraic thinking and skills, augmented with data analysis. Year 2 focuses on geometric topics, both synthetic and analytic, and includes formal geometric argument. Year 3 extends the algebra topics from Year 1 and introduces traditional topics of Algebra II. Year 4 includes trigonometric functions and other topics from pre-calculus mathematics. Each of the Models A, B, and C prepares students to take a calculus course in their first year of college. The Program Models presume that all Ohio graduates will enter postsecondary education at some time, but that not every student's academic program will include calculus. Consequently, Models A, B, and C are followed by Model A', Model B', and Model C', respectively, which adjust the original models to provide an appropriate curriculum for students whose postsecondary program will not include the study of calculus. Success for All Students A program model is a guide to assist in organizing mathematical ideas and student experiences for effective learning. However, different students learn in different ways. The amount of time, practice, and assistance students require to learn mathematics varies from student to student. These differences must be accommodated in a district's plan for delivering the curriculum. In this section, we offer suggestions for organizing programs to accommodate student differences. We offer suggestions for three specific groups of students: Students entering grade 9 without the mathematical skills and understanding needed to be successful in a Year 1 course; Students who have completed grade 10 but not achieved or exceeded the proficiency level on the mathematics portion of the Ohio Graduation Test; Students with the background and abilities to be accelerated in the regular mathematics curriculum. Preparation for the Year 1 Mathematics Course A mathematics curriculum that reflects the Ohio Content Standards will build mathematical skills and dispositions that enable all students to understand the fundamentals of algebra. As early as pre-kindergarten, algebraic thinking activities such as finding patterns, identifying missing pieces in sequences, and acquiring informal number sense will be central parts of students' experiences. The middle school curriculum moves students from numerical arithmetic to generalized arithmetic where symbols can represent numbers. This curriculum gives students experience with numeric, geometric, and algebraic representations of relationships. Students develop proportional reasoning skills; they investigate more complex problem settings and move from concrete experiences in mathematics to the formulation of more abstract concepts. The Year 1 mathematics course in any secondary curriculum model is expected to be the foundation for future learning of mathematics. Formal algebra will be a focus of this course. Whether students enter the workforce directly after graduation or enter postsecondary education, success in Year 1 mathematics will be critical to their futures. There are several strategies districts should consider for students who complete grade 8 without the mathematics background needed to succeed in Year 1. These strategies assure that all students study Year 1 mathematics no later than grade 9. Summer Sessions During the summer prior to their Year 1 course, students could attend: A focused summer course that strengthens pre-algebra methods and terminology, provides a review of basic mathematical procedures, and uses some topics of discrete mathematics to help students move from concrete thinking to generalization, or A computer-based program with a teacher or coach to individualize students' instruction and correct misunderstandings. During the Standard School Year In addition to summer opportunities, districts may consider the following options: Provide some Year 1 mathematics classes in grade 9 that meet 8 or 10 periods a week for students who need more time to learn the mathematics in this course. Alternatively, all Year 1 mathematics classes can be taught for 8 or 10 periods a week so teachers have time to differentiate instruction and engage in extended, supervised problem solving. Create a program of peer tutoring that includes training, supervision, and time for students to work with other students. Create Mathematics Labs associated with specific mathematics courses (similar to labs that are linked to science courses) and to which students are assigned on a regular basis. Create parent/community help teams that work under the direction of teachers and assist students with mathematics after school or during study halls. A common feature of these strategies is that each one recognizes some students will need more time and more assistance to be successful in learning the mathematics of the Year 1 course. There are, of course, costs to each of these interventions. However, the costs of providing timely help to students is significantly less than the cost of teaching remedial courses or allowing students to enter the workforce with deficiencies in mathematics. Reaching Proficiency Level on the OGT Students who do not achieve or exceed the proficiency level on the mathematics portion of the Ohio Graduation Test in grade 10 can benefit from the following options: Require students to attend a summer program between grades 10 and 11 in which basic concepts are reviewed and problem solving is emphasized. These students should re-take the OGT when it is offered again later in the summer. Offer before school, after school, or Saturday sessions to review core mathematics topics and work with students individually; study hall periods may be used in this way for some students. Develop peer-tutoring programs to help students who did not succeed on the OGT, giving peer tutors sufficient training and supervision. Develop a 9-week OGT preparation course to be taken concurrently with the Year 3 mathematics course during the first grading period in grade 11. This course could also be taught during the second semester in preparation for the spring administration of the OGT. (Because the content of this short course will repeat content from earlier courses, credit for this course should not count toward the mathematics credits required for graduation.) Students Who Are Accelerated in the Curriculum Some students are able to move successfully through a standard mathematics curriculum at a quicker pace than the majority of students. Commitment to accelerated students must be as great as the commitment to other students to assure that they are challenged in each year of study and persist in mathematics through their senior year. Two strategies are suggested: A district may designate some sections of a regular course as honors or enriched and in these sections deal with topics in greater depth, assign students more complex problems, and develop more team projects for students. Differentiating instruction in this way, rather than having a student skip a course in order to move ahead, will assure students do not miss critical material covered in each of the grade level curricula. Some students may have the ability to study the Year 1 course in 8th grade if the curriculum has been modified to assure they have studied all topics of the middle school curriculum before grade 8. Because the Ohio Academic Content Standards in Mathematics identify new topics to be introduced in each of the middle grades, no mathematics course can simply be skipped. Students with the potential to be accelerated will need to be identified by the teaching staff and by readiness tests, and have their curriculum appropriately modified in the grades prior to grade 8. Students who study the Year 1 course in 8th grade should move ahead to the Year 2 course in 9th grade, continue in an enriched curriculum through grade 11, and study an advanced level mathematics course in grade 12 so they are well positioned for further study or for workplace opportunities. Advanced Courses for Accelerated Students The models present several options for accelerated students after they have completed the mathematics in the standard curriculum. The models include a course called Modeling and Quantitative Reasoning that provides mathematics accessible and of interest to high school students, but not always included in the high school curriculum. Another option for students who have strong backgrounds in algebra, geometry, coordinate geometry, trigonometry, and pre-calculus mathematics is a course in calculus. When a calculus course is offered for high school students, the course should be taught at the college level and students should expect it to replace a first-year calculus course in college. This can be assured by using a College Board Advanced Placement calculus course and requiring students to take the AP exam at the end of the course. In some locations, accelerated students are able to enroll in a mathematics course at an area college or take a college level course through distance education, concurrent with their high school studies. The models also prepare accelerated students to take an Advanced Placement statistics course, which can be an exciting and appropriate option. Mathematical Processes The content in the mathematics Program Models is specified in the Ohio Academic Content Standards: Number, Number Sense and Operations; Measurement; Geometry and Spatial Sense; Patterns, Functions and Algebra; Data Analysis and Probability. The sixth standard, Mathematical Processes, is the thread that ties the five content standards together to make a meaningful and cohesive curriculum. Mathematical processes can be divided into five strands: problem solving, reasoning, communication, representation, and connections. Authentic problem solving requires students not simply to get an answer but to develop strategies to analyze and investigate problem contexts. The National Council of Teachers of Mathematics publication, Principles and Standards for School Mathematics, states that "solving problems is not only a goal of learning mathematics but also a major means of doing so. Students should have frequent opportunities to formulate, grapple with and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking." Indeed, this is how students come to understand deeply the mathematical topics in their courses. "Reasoning involves examining patterns, making conjectures about generalizations, and evaluating those conjectures" (Ohio Academic Content Standards, K-12 Mathematics, p. 196). In mathematics, reasoning includes creating arguments using inductive and deductive techniques. Students need opportunities to make and test their conjectures, explain their reasoning, and evaluate the arguments of other students as well as their own. Oral and written communication skills give students tools for sharing ideas and clarifying their understanding of mathematical ideas. Mathematics has its own language, and this language becomes increasingly more precise as students move through their studies. Developing skill in using this language requires students to read, write, and talk about mathematics. Understanding mathematical terminology is essential to understanding mathematical concepts. Mathematics uses many different forms of representation to embody mathematical concepts and relationships. Some are numerical (e.g., tables); some are algebraic (e.g., expressions, equations); some are geometric (e.g., sketches, graphs); some are physical models. Students need to be comfortable using multiple representations for a single concept. This skill will help them develop problem-solving strategies and communicate mathematical ideas effectively to others. Appropriate use of technology is an essential tool for increasing students' access to different kinds of representation in mathematics. A coherent curriculum will help students make connections between the mathematical concepts they learned in earlier grades and the concepts they study later on. Students need to appreciate that the five content strands are not independent blocks of mathematics and that the process standard is part of learning within each content strand. Without this appreciation, students may view the content of their courses as little more than a checklist of topics. Students also need to experience the connections between mathematics and the other subjects they study. Their mathematics courses should include frequent applications drawn from the life sciences, physical sciences, social studies, and other fields. If students are to understand the importance and power of mathematics, these connections need to be explicitly discussed. In the Program Models, these mathematical processes are developed through course design and through experiences students have when they work with rich contextual problems. Successful learning of mathematics requires that students struggle with complex problems, communicate mathematics clearly, represent mathematics accurately and in various forms, make conjectures and reason effectively, and connect mathematical concepts across the various areas of mathematics and to applications in other fields. There is no shortcut. Each of the processes must be developed in every course, in every sequence, and in every year of study. Technology Assumptions Appropriate use of technology in the mathematics classroom is an issue that must be addressed in the development of a new curriculum. In this area, there are dual goals: (1) student proficiency with foundational skills and basic mathematical concepts using basic manual algorithms, and (2) student competence in using appropriate technology to encourage mathematical exploration and enhance understanding. With respect to the first goal, the Program Models presume that students will enter the Year 1 course with an understanding of basic mathematical concepts and with proficiency in performing accurate pencil and paper numerical procedures. Even so, the secondary program should be designed to strengthen numerical skills and build additional skills in algebraic computation, estimation, and mental mathematics. The study of algebra, measurement, geometry, and data analysis provides useful contexts for students to continue to develop written and mental computational skills that deepen their understanding of mathematics and strengthen their abilities in problem solving. With respect to the second goal, the Program Models presume that students will use technology as a tool in learning the mathematical concepts and working the complex problems in the secondary school curriculum. For example, technology can assist students in investigating applications of mathematics, testing mathematical conjectures, visualizing transformations of geometric shapes, and handling large data sets. Technology appropriately used can enhance students' understanding and use of numbers and operations, as well as facilitate the learning of new concepts. Students will need to be alerted to the possibility of serious round-off error when technology is used for complex computations in real-world applications. At this time, the Ohio Graduation Test allows students to use a state-specified scientific calculator. This calculator is primarily a computational tool, and students will need adequate time and practice using it prior to the OGT. A scientific calculator alone does not provide all the features needed to study the topics described in the Program Models. Implementing the Program Models requires decisions about the kinds of technology that students will use at different stages of their learning to assure a balanced program that results in students' knowing when to use technology and when not to, when to use pencil and paper, and when to do mathematics in their heads. The goal, always, is to develop a program that focuses on mathematical understanding and proficiency.
GaussianReadership Graduate students and research mathematicians interested in random matrix theory.
Forest Park, IL GeTopics include simplifying expressions, evaluating and solving equations and inequalities, and graphing linear and quadratic functions and relations. Real world applications are presented within the course content and a function's approach is emphasized. This course builds on algebraic and geometric concepts
Books by W. Michael Kelley The best way to learn calculus is to work through tons and tons of problems. The Humongous Book of Calculus Problems contains 1,000 problems, each with ridiculously detailed explanations and hand-written notes in the margins that clarify the most difficult steps. Click here to see a sample page. All of the major players are here: limits, continuity, derivatives, integrals, tangent lines, velocity, acceleration, area, volume, infinite series--even the really tough stuff like epsilon-delta proofs and formal Riemann sums. So dig in to your heart's content, with completely worked-out examples for just about every problem you'll see in calculus! There aren't many math books, let alone calculus books, out there that are very fun to read. In fact, a recent survey showed that 9 out of 10 people would rather be trampled to death by wild stallions than have to read even one sentence of a math textbook. That is a shocking statustic, even if I did just make it up. The Complete Idiot's Guide to Calculus will teach you everything you need to know about Calculus and keep a smile on your face. In addition to straightforward explanations, studying tips, memory techniques, and practice problems with complete and understandable explanations for every step, the book will keep you entertained with its wry sense of humor. Believe it or not, it's a math book you'll actually enjoy reading! Remember how excited Dorothy was when she landed in Oz? She was in a new place, filled with color and tiny people who could sing and dance perfectly choreographed routines without even rehearsing! Even better, she had a mission. Simply follow the yellow brick road and everything would be wonderful. This is powerful magic indeed. Remember, all of this frolicking is going on not twenty feet from a recently-crushed witch corpse, but no one seems to mind. Do you feel like Dorothy, ready to step out onto the long, magical road of math, full of excitment, dread, and also pigtails and/or a tiny dog? Are you someone lost along the way to Oz and starting to wonder whether it was really worth stopping to help that scarecrow down? I mean, he can't even add fractions for the love of corn. The Humongous Book of Basic Math and Pre-Algebra Problems will take you through the poppy fields, away from the flying monkeys, and right up to the front door of Oz, all oiled up and ready to go. Feel like you need a new brain when you're in a math class? Are your computational skills all rusty, Tin Man? Maybe a big boost of courage is all you really need to be toto-ly prepared. If you are about to take an algebra class (or have a friend that desperately needs your help), don't wait! Click this link to BUY TODAY! When I launched the Humongous Book of Calculus Problems, I hoped that students would find value in a massive vat of practice problems with very detailed descriptions, but I had no idea how overwhelmingly positive the response would be. As soon as the book was released, I immediately started working to give Algebra the same treatment. This book will take students through all the topics of Algebra I and Algebra II, including: solving equations and inequalities, functions, factoring, logarithmic and exponential functions, radical expressions, conic sections, and work problems. Bring me your scared, your coonfused, your bewildered students yearning to pass Algebra! It's true, most people hate algebra, and I'm talking about heavy duty hate here—the "I hate that pack of wolves that devoured my family" kind of hate, not the "I hate carrot cake" kind. Algebra represents some sort of mysterious conglomeration of topics that makes no sense, and for some reason, the only people allowed to teach it are the most boring (and nerdiest) people on the planet! Let me be your translator and guide to the world of math. I know my way around, and can explain things to you so that you understand. I know the sort of things that confuse people, and can steer you around the quicksand and jagged rocks that loom in your path. But wait! there's more! You also get a full trigonometry course as well, including: the unit circle; sine, cosine, tangent, secant, cosecant, and cotangent; right triangle trigonometry; graphing trig functions; proving identities; solving trig equations, the Laws of Sine and Cosine, and much, much more! Finally there's a book that will cover all the important topics of precalculus. In the past, you'd have to buy Algebra I, Algebra II, and Trigonometry review books in a desperate attempt to get the help you'd need in Precalculus. Even more frustrating, there was no guarantee that those books would even contain everything you were expected to understand in class (can you say "Gauss-Jordan elimination"?). CliffsQuickReview Precalculus is written in the same style as other titles in the famous series: You get right to the point with all the topics, with no fluff, and just the right amount of practice. Keep in mind that even though Mike's characteristic humor is absent (a requirement of the series), his crystal clear explanations remain. They said it couldn't be done. They said it shouldn't be done. They said I should own more then two pairs of pants for "hygiene reasons." But who are they anyway? Honestly, I am not sure who they are, but I am sure they'd want 1,000 geometry problems in every shape, size, area, and volume. Everything you need to get from Point A to Point B is right here, including these topics: logic and proof, parallel and perpendicular lines, polygons, congruent and similar triangles, quadrilaterals and parallelograms, right triangles, circles, area, perimeter, volume, surface area, gometric constructions, coordinate geometry, vectors, transformations, symmetry, and even truth tables! The best guidebook for new, or rookie, teachers that will really prepare you for your first few years in the classroom. It's a hilarious but practical book full of tips, advice, and real-life scenarios that you can put into practice starting on the first day of school. Find out what life will be like as a teacherLearn how to deal with administrators, students, parents, and coworkers Establish and maintain firm control of your class beginning the first day of school Avoid the rookie mistakes most veteran teachers made when they were new Get advice from people who have already been there and fought the battles A guide for all teachers, from elementary to high school, that will prepare you, entertain you, and turn good teachers into great ones! If you're preparing for the AP Calculus AB or BC Exam, there's no better resource than this hulking workbook. Not only does it contain detailed review information about every topic on the exams, it also includes four, full-length exams you can use to prepare yourself for test day. Want more? You got it. Each chapter also includes detailed tutorials to help you use your Texas Instruments calculator to help you understand and score higher!
College Mathematics CLEP test Ebook College Mathematics CLEP test The College Mathematics CLEP test is a great review of basic math. Most of you will already know the main concepts. We will give you detailed examples and exercises to teach and test your skills. You don't need a separate textbook with this or any other CLEP study guide we offer. This ebook will teach you everything you need to know to pass this test! Here's what you'll learn: What Your Score Means Venn Diagrams The Pythagorean Theorem Test Taking Strategies Sets Sample Questions Real Number System Probability and Statistics Perimeter and Area of Plane Figures Parallel and Perpendicular Lines Open and Closed Intervals Logic Logarithms and Exponents Functions and Their Graphs Factors and Divisibility Example of Determination of Necessary and Sufficient Conditions Basic Properties of Numbers Answer Key Algebraic Inequalities Algebraic Equations Additional Topics From Algebra And Geometry Absolute Value and Order
The physics of hot plasmas is of great importance for describing many phenomena in the Universe and is fundamental for the prospect of future fusion energy production on Earth. Non-trivial results of nonlinear electromagnetic effects in plasmas include the self-organization an self-formation in the plasma of structures compact in time and space. These... more... This book is a text on mathematical analysis suitable for graduate students and advanced undergraduates. It provides an extensive introduction to proof and to rigorous mathematical thinking. It contains many remarks and examples and 500 exercises designed to provide motivation, test understanding, help practice mathematical writing and explore additional... more... Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific... more... The International Mathematical Olympiad (IMO) is a prestigious competition for high-school students interested in mathematics. It offers high school students a chance to measure up with students from the rest of the world. This book contains problems and solutions that appeared on the IMO over the years. It presents a grand total of 1900 problems. more... Most colleges and universities now require their non-science majors to take a one- or two-semester course in mathematics. Taken by 300,000 students annually, finite mathematics is the most popular. Updated and revised to match the structures and syllabuses of contemporary course offerings, Schaum's Outline of Beginning Finite Mathematics provides a... more... A renowned mathematician who considers himself both applied and theoretical in his approach, the author has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several published works and has received numerous honors. more...
Transformations This course will focus on transformations, taken broadly to include functions, algebraic operations and geometrical changes such as rotations and expansions, and will build on the various representations introduced in Course 1. For example, a quadratic equation can be solved by factoring, completing the square, or using the quadratic formula. The relationship among these three algebraic approaches becomes clear when graphing the corresponding parabola and noticing how the solutions are related to intersection of the graph with the x-axis. Particular attention will be paid to transformations among physical quantities (such as distance and time, pressure and volume, and temperature). Research about middle-school children's approaches to transformations (e.g. "building-up" strategies) will be examined in light of the distinction between input-output and differential approaches to functions that are congenial to closed-form and recursive descriptions, respectively.
Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Calculus, students will enjoy the same clear, concise... $ 9.49 In its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems... $ 11.99 Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern... $ 14.79Tough Test Questions? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's.More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is... $ 13.99 Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students...
From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience. Description For introductory sophomore-level courses in Linear Algebra or Matrix Theory. This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof. Table of contents 1 - Linear Equations And Matrices 2 - Solving Linear Systems 3 - Determinants 4 - Real Vector Spaces 5 - Inner Product Spaces 6 - Linear Transformations and Matrices 7 - Eigenvalues and Eigenvectors 8 - Applications of Eigenvalues and Eigenvectors (Optional) 9 - MATLAB for Linear Algebra 10 - MATLAB Exercises A P P E N D I X A Preliminaries A P P E N D I X B Complex Numbers A P P E N D I X C Introduction to Proofs New to this edition Applications of Eigen value and Eigenvectors (Chapter 8) - new to the edition in this form. It consists of old sections 7.3, 7.5-7.9, 8.1, 8.2 Organizational Changes Section 1.7, Computer Graphics, has been expanded Old section 2.1 has been split in two sections: 2.1 Echelon Form of a Matrix and 2.2 Solving Linear Systems. This will provided improved pedagogy for covering this important material. Old section 3.4 Span and Linear Independence has been split into two sections 3.3 Span and 3.4 Linear Independence. Since students often have difficulties with these more abstract topics, this revision presents this material at a somewhat slower pace and has more examples. Old Chapter 6 Determinants, has now become Chapter 3 to permit earlier coverage of the material. Exercises involving real world data have been updated to include more recent data sets Varied examples of vector spaces have been introduced. More exercises at all levels have been added More MATLAB exercises have been added. MATLAB M-files have been upgraded to more modern versions Discussion has been added to the Chapter Review material. Many of these are suitable for writing projects or group activities. More geometric material illustrating the discussions of diagonalization of symmetric matrices and singular value decompositions. More applications have been added (including application to networks and chemical balance equations) More material on recurrence relations More material discussing the four fundamental subspaces of linear algebra Features & benefits Strong pedagogical framework. Provides students with a strong understanding by gradually introducing topics that connect abstract ideas to concrete foundations. General level of applications–Presents applications that are suited to a more general audience, rather than for a strongly science-oriented one. Enables instructors to use this text for a greater variety of class levels.
"Algebra" is a loose translation from Arabic meaning "reunion of broken parts." In Algebra II we utilize tools from Algebra I to make connections between more advanced concepts in Algebra. Students will be deriving much of their own knowledge through group explorations and should be willing to approach unfamiliar problems. Topics in Algebra II will include sequences, statistics, functions, complex numbers, logarithms and trigonometry
Pre-Algebra 0 v1.0 Version: 1.0 Very simple review of some topics in pre-algebra. Basic review and introduction about fractions and their manipliulations. Basic review and introduction about decimals. Relative sizes. Basic review and introduction about indices. Standard form (scientific notation). Approximation. Range of values of corrected numbers.
This course is designed to demonstrate to students the necessity and importance of mathematics in their everyday lives. Practical application of mathematics will be emphasized. Skills such as making change, balancing ones checkbook and account, computing sales tax, figuring interest, developing a personal budget, and learning to achieve and maintain an excellent credit rating will be explored.
Mathematics Wright Dunbar Math Course The Wright Dunbar Math Unit was developed via collaboration with DECA, University of Dayton, and Wright State University. This inquiry driven unit provides reinforcement of critical middle school Ohio recommended curriculum as well as introduces many of the mathematical strands tested on the OGT. This is an engaging course of study for the students as they design and build a model home. The students go through all phases of the building process from engineering to accounting. Geometrical Optics and Algebra This course is designed to cover the remaining critical algebra I standards from their first year of study and the critical geometry content standards. Students learn the curriculum in the real world setting of geometrical optics. This course was developed with a partnership between the Engineering Department of the University of Dayton (UD) and the Sensors Directorate of the Air Force Research Laboratory (AFRL). This inquiry based course introduces the students to light and optics and includes the topics optical illusions, simple lenses, light waves, diffraction, and natural optical phenomena such as rainbows, shadows, and mirages. Many laboratory activities are embedded in this course and are completed in DECA's optical laboratory comprising equipment donated by UD and AFRL. Algebra II This course provides instruction and assessment in the critical algebra indicators mandated by the Ohio Department of Education for grades ten and eleven as well as those recommended by The National Council of Teachers of Mathematics. Students also are introduced to basic trigonometry during this course. Students significantly utilize graphing calculators and the teacher aligns the curriculum to the chemistry course. This course is also designed to improve ACT and SAT performance as well as begin the transition from secondary class setting to a more college setting. Precalculus This is an advanced course of study to prepare students for a college calculus course. It encompasses the National Council of Teachers of Mathematics suggested curriculum including an intense study of trigonometry, with additional topics of complex numbers, vectors, polar coordinates, higher-order polynomial functions, and a brief introduction to limits. This is the last math course for most of our current DECA students and is aligned with the physics class. However, once the 7th grade students matriculate they will all have the opportunity to take calculus. Students who were placed in the Geometrical Optics and Algebra Class during their 9th grade year will complete calculus in addition to this course. Calculus This course provides an introduction to differential and integral calculus. Topics include limits, derivatives, related rates, Newton's method, the Mean-Value Theorem, Max-Min problems, the integral, the Fundamental Theorem of Integral Calculus, areas, volumes, and average values. This course is coordinated with the physics course. Science FYA Science First year academy science is a yearlong course that covers a semester of physical science including measurement, forces, energy and introductory chemistry. The second semester covers introductory biology including cell theory, genetics, life processes, and introductory botany. Students apply their science skills in these areas by studying the river system of Dayton using a variety of modern sensor equipment. Earth Science This course is an introduction to earth science and addresses the earth science curriculum recommended by the Ohio Department of Education including earth processes, rocks, earth changes, and weather. Students also learn about the ecology of the earth including adaptation, competition, predation, tropic structure and energy cycles, populations, and ecosystems. This course is taken simultaneously with Forces and Motion and Genetics, DECA students enroll in two sciences second year. Forces and Motion This semester long course is designed to equip the students with problem solving skills and analytical reasoning skills as well as Newtonian mechanics. The students learn about motion, energy, forces, vectors, equilibrium torque, rotating systems, uniform acceleration, work and simple machines. Genetics This semester long course covers the topics of DNA, transcription, translation, protein synthesis, mutations, sex linked gene, heredity, and associated laboratory techniques. The course follows the recommended curriculum put forth by the National Science Foundation for a course in genetic studies as well as that recommend by the Ohio Department of Education for the tenth and twelfth grade years. This course follows FYA science and completes the life science requirement for DECA students. Chemistry This is a rigorous laboratory course covering the chemistry content recommended by the NSTA and the American Chemical Society. Topics include atomic structure, the periodic table, chemical reactions, stoichiometry, aqueous solutions, the gas laws, thermochemistry, chemical bonding theory, intermolecular forces, and kinetics. The students learn the content in four real world settings including Alchemy, material science, consumer chemistry, and energy. This course was developed with the help of the Materials and Engineering Department at the University of Dayton. Physics This mathematical based course covers the critical academic content standards recommended by the NSTA and the American Physics Association and includes Newtonian mechanics, electricity and magnetism, thermal physics, light and optics, the Theory of Relativity, and astronomy. This is a laboratory based course and is coordinated with the precalculus and calculus courses. All DECA students conclude their study of science with the completion of this course. Social Studies World History This introductory course studies world history from the Age of Enlightenment to present day. This course is coordinated with the first year language arts course with thematic units covering the Enlightenment, the Industrial Revolution, Imperialism, World War I, World War II, the Cold War, and Current Events. American History Using the variable method TCI approach that brings history alive, students learn their American history from the Reconstruction to the present. Students work in cooperative learning groups to utilize primary source material to focus on the five founding ideals in our history. Students study in depth the Declaration of Independence, equality, rights, liberty, opportunity, and democracy. Government This course will explore the basic foundations of US government and how they are still applied today. We will take an in-depth look at the US Constitution in almost every unit that is covered. Major topics that will be covered during this course include: 1 st Amendment, origins of US government, the Constitution and individual rights, legislative branch, executive branch, judicial branch, federalism, economic policy, foreign policy, and elections. Mock Trial This course is designed to prepare students to compete at a high level in the Ohio Mock Trial Competition. The competition is a state wide educational program created by the Ohio Center for Law-Related Education. The program teaches students about their constitutional rights as they learn about court proceedings and the judicial system. Most importantly, students greatly enhance their critical thinking and public speaking skills. Language Arts Language Arts I This course provides introductory instruction to the writing process and writing conventions at the high school. The course also studies and practices reading comprehension skills including critical thinking, literary analysis, and genre comparisons. Students will also study genres of literature including fiction, nonfiction, poetry and drama. Language Arts II This course's primary goal is to reinforce the reading and writing skills learned in Language Arts I. Being able to draw meaning from texts of diverse genres and cultural and historical origins is a vital academic and life skill. Of equal importance is being able to create meaning through various forms of writing. To those ends, students will be examining a wide variety of literature in complete or excerpted form. Students will be writing analytical essays of many sorts, developing themselves as writers. Students will begin with the standard five paragraph essay, but expand into writing comparative, persuasive, literary analysis, cultural/historical pieces, and beyond. Students will frequently be given the opportunity to workshop their writing in class, fine-tuning their work in conjunction with their peers and their teacher. Language Arts III/IV Junior and Senior Literature is a two-year sequence that helps to transition students from high school-level to college-level reading and writing. The intention of this course is to encourage critical-thinking, improve analytical writing and extended response skills, as well as familiarize students with college-level literature and the historical significance of certain texts. Units include African American Literature, Gothic Literature, Norse Mythology, Protest Fiction, Greek Mythology, and Shakespeare's Tragedies
Courses MATH-099 College Mathematics Prep Topics may include sets, radicals, polynomials, factoring, inequalities, linear and quadratic equations, functions, exponents, and simple descriptive statistics. Intended for students not ready for college credit math; placement in this course is determined by the Department of Mathematics. MATH-101 Precalculus Mathematics MATH-105 Introductory Topics This is a two-credit course meant to help education majors satisfy the Pennsylvania state requirement for six credits of college mathematics. Each course will cover a topic of the instructor's choice at an introductory level. Topics so far have included Symmetry, Counting, and Math and Music. This course does not count toward a math major or minor, and particular topics may overlap enough with other math courses to bar a student from taking both. Education majors will be given priority. MATH-108 Introduction to Statistics A basic introduction to data analysis, descriptive statistics, probability, Bayes' Theorem, distributions of random variables, and topics in statistical inference. (Students may earn credit for only one of the introductory statistics courses offered by the departments of Management, Psychology or Mathematics.) MATH-203 Math and Music This course will explore the interplay of mathematics and music. Topics such as the Fourier theory of sound, consonance and dissonance, scales, temperament, digital signal processing, sound synthesis, twelve tone music theory and algorithmic composition will be covered in the course. Some knowledge of music theory and computer programming would be helpful but not required. MATH-231 Foundations of Analysis A rigorous study of the theoretical basis of (single-variable) differntial and integral calculus: limits, continuity, differentiation, and integration. MATH-321 Abstract Algebra A more detailed study of algebraic structures. Introduces fundamental concepts of groups, rings and fields. MATH-331 Geometry A concentrated study of elementary geometry. Includes Euclidean and non-Euclidean geometries and selected topics such as symmetry, Penrose tilings, fractals, knots, mapmaking, and the shape of the universe. MATH-351 Numerical Computing An introduction to the computational techniques for solving mathematical problems. Topics include roots of non-linear equations, interpolation, numerical differentiation and integration, and numerical solutions of differential equations. MATH-353 Differential Equations MATH-355 Operations Research Mathematical models and optimization techniques useful in decision making. Includes linear programming, game theory, integer programming, queuing theory, inventory theory, networks and reliability. Further topics, such as non-linear programming and Markov chains, as time permits. MATH-370 Cryptology & Number Theory Cryptology is the study of hiding the meaning of messages. Cryptology is an interesting venue for the study of its mathematical underpinnings {number theory, matrix algebra, probability and statistics} and as an opportunity to implement techniques by means of computer programs. We will consider monoalphabetic and polyalphabetic encryptions, public key cryptography, security, and anonymity. MATH-411 Real Analysis A deeper look at the fundamentals of calculus. Real numbers, point set theory, limits and the theory of continuity, differentiation and integration. MATH-415 Complex Analysis MATH-434 Artificial Life Science and mathematics describe natural phenomena so well that lines between real world events and the corresponding theoretical world events have become blurred. Proponents of strong artificial intelligence and artificial life believe that computers will eventually serve not only to model thinking and life processes but will actually think and be alive. These contentions will be compared and contrasted with an emphasis on the current status and future implications of strong artificial life. MATH-482 Theory of Computation An introduction to the classical and contemporary theory of computation. Topics include the theory of automata and formal languages, computability by Turing machines and recursive functions, computational complexity and quantum computers. MATH-500 Senior Colloquium Experience in individual research and presentation of topics in mathematics. The one-hour version culminates in a presentation to an audience of faculty and students. The two-hour version also includes a paper. MATH-501 Topics in Mathematics Subject depends on students' and instructor's interests. Possibilities include: number theory, set theoretic foundations of mathematics, topology, graph theory, differential geometry and applied mathematics. Whether the course counts as a 400-level course for majors will be announced along with the course description. MATH-502 Independent Study Individual work for capable students under faculty supervision. MATH-503 Independent Research A research project leading to a substantive paper on a selected topic in mathematics. By arrangement with a department instructor. MATH-599 Mathematics Internship Full-time mathematics-related employment at an industrial firm or a public service organization.
This graduate-level textbook introduces fundamental concepts and methods in machine learning. It describes several important modern algorithms, provides the theoretical underpinnings of these algorithms, and illustrates key aspects for their application. The authors aim to present novel theoretical tools and concepts while giving concise proofs even for relatively advanced topics. Foundations of Machine Learning fills the need for a general textbook that also offers theoretical details and an emphasis on proofs. Certain topics that are often treated with insufficient attention are discussed in more detail here; for example, entire chapters are devoted to regression, multi-class classification, and ranking. The first three chapters lay the theoretical foundation for what follows, but each remaining chapter is mostly self-contained. The appendix offers a concise probability review, a short introduction to convex optimization, tools for concentration bounds, and several basic properties of matrices and norms used in the book. The book is intended for graduate students and researchers in machine learning, statistics, and related areas; it can be used either as a textbook or as a reference text for a research seminar
Description For freshman/sophomore, 2 semester/2-3 quarter courses covering finite mathematics and calculus for students in business, economics, social sciences, or life sciences departments. This accessible text is designed to help students help themselves excel in the course. The content is organized into three parts: (1) A Library of Elementary Functions (Chapters 1—2), (2) Finite Mathematics (Chapters 3—9), and (3) Calculus (Chapters 10—15). The book's overall approach, refined by the authors' experience with large sections of college freshmen, addresses CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book 6-3 The Dual; Minimization with Problem Constraints of the form ≥ 6-4 Maximization and Minimization with Mixed Problem Constraints Chapter 6 Review Review Exercise Chapter 7: Logic, Sets, and Counting 7-1 Logic 7-2 Sets 7-3 Basic Counting Principles 7-4 Permutations and Combinations Chapter 7 Review Review Exercise Chapter 8: Probability 8-1 Sample Spaces, Events, and Probability 8-2 Union, Intersection, and Complement of Events; Odds 8-3 Conditional Probability, Intersection, and Independence 8-4 Bayes' Formula 8-5 Random Variables, Probability Distribution, and Expected Value Chapter 8 Review Review Exercise Chapter 9: Markov Chains 9-1 Properties of Markov Chains 9-2 Regular Markov Chains 9-3 Absorbing Markov Chains Chapter 9 Review Review Exercise Part Three: Calculus Chapter 10: Limits and the Derivative 10-1 Introduction to Limits 10-2 Infinite Limits and Limits at Infinity 10-3 Continuity 10-4 The Derivative 10-5 Basic Differentiation Properties 10-6 Differentials 10-7 Marginal Analysis in Business and Economics Chapter 10 Review Review Exercise Chapter 11: Additional Derivative Topics 11-1 The Constant e and Continuous Compound Interest 11-2 Derivatives of Logarithmic and Exponential Functions 11-3 Derivatives of Products and Quotients 11-4 The Chain Rule 11-4 Implicit Differentiation 11-5 Related Rates 11-7 Elasticity of Demand Chapter 11 Review Review Exercise Chapter 12: Graphing and Optimization 12-1 First Derivative and Graphs 12-2 Second Derivative and Graphs 12-3 L'Hopitals's Rule 12-4 Curve Sketching Techniques 12-5 Absolute Maxima and Minima 12-6 Optimization Chapter 12 Review Review Exercise Chapter 13: Integration 13-1 Antiderivatives and Indefinite Integrals 13-2 Integration by Substitution 13-3 Differential Equations; Growth and Decay 13-4 The Definite Integral 13-5 The Fundamental Theorem of Calculus Chapter 13 Review Review Exercise Chapter 14: Additional Integration Topics 14-1 Area Between Curves 14-2 Applications in Business and Economics 14-3 Integration by Parts 14-4 Integration Using Tables Chapter 14 Review Review Exercise Chapter 15: Multivariable Calculus 15-1 Functions of Several Variables 15-2 Partial Derivatives 15-3 Maxima and Minima 15-4 Maxima and Minima Using Lagrange Multipliers 15-5 Method of Least Squares 15-6 Double Integrals Over Rectangular Regions 15-7 Double Integrals Over More General Regions Chapter 15 Review Review Exercise Appendixes Appendix A: Basic Algebra Review Self-Test on Basic Algebra A-1 Algebra and Real Numbers A-2 Operations on Polynomials A-3 Factoring Polynomials A-4 Operations on Rational Expressions A-5 Integer Exponents and Scientific Notation A-6 Rational Exponents and Radicals A-7 Quadratic Equations Appendix B: Special Topics B-1 Sequences, Series, and Summation Notation B-2 Arithmetic and Geometric Sequences B-3 Binomial Theorem Appendix C: Tables Table I Area Under the Standard Normal Curve Table II Basic Geometric Formulas Answers Index Applications Index A Library of Elementary Functions
0534407617 9780534407612 Numerical Methods: This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are essentially the same as those covered in the authors' top-selling Numerical Analysis text, but in this text, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally. «Show less Numerical Methods: This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what type of errors to expect,... Show more» Rent Numerical Methods 3rd Edition today, or search our site for other Faires
Thinkwell s Calculus with Edward Burger lays the foundation for success because, unlike a traditional textbook, students actually like using it. Thinkwell works with the learning styles of students who have found that traditional textbooks are not effective. Watch one Thinkwell video lecture and you ll understand why Thinkwell works better.
Elementary and Intermediate Algebra: A Unified Approach with WindowsElementary and Intermediate Algebra w/ MacStudent's Smart CD-ROM for Windows for use with Beginning Algebra (bundle version) Editorial review This interactive CD-ROM is a self-paced tutorial specifically linked to the text and reinforces topics through unlimited opportunities to review concepts and practice problem solving. The CD-ROM contains chapter-and section-specific tutor Math Fundamentals Editorial review The first manual in a series of three for developmental students, this booklet contains numerous exercises and review material, and complements any core text for Basic Math. Mandatory Package College Algebra with Smart CD (Windows) Editorial review Smart CD is packaged with the seventh edition of the book. This CD tutorial reinforces important concepts, and provides students with extra practice problems. Reviewed by Christina Francis, (Kansas City, MO) r (or suppliment) before tackling this text. It will be well worth the extra [money] spent! Reviewed by Fred Matthews, (Colorado) College Algebra is well written. The concepts of algebra are thoroughly explained and illustrated with examples. Answers to half the problems are included in the back of the book. Reviewed by Fred Matthews, (Colorado) College Algebra is well written. The concepts of algebra are thoroughly explained and illustrated with examples. Answers to half the problems are included in the back of the book. Reviewed by a reader I am currently enrolled In a distanced learning college and was sent this book.The book Is hard to figure out and the problems give you no pretense on who to solve them go with a different book
Combinations & Permut lesson was written for a Pre-Calculus class to review combinations and permutations that were learned in Algebra 2. It was also as a review of the two concepts for my Algebra 2 classes after they had worked individual lessons on combinations and permutations. Presentation (Powerpoint) File Be sure that you have an application to open this file type before downloading and/or purchasing. 860
The Academic Foundations Mathematics area is responsible for helping students master basic math skills so that they can take their academic courses with a solid foundation. Offered in this area are the following three courses: DEV084 - Basic Mathematics I Provides instruction in basic arithmetic for whole numbers, fractions and decimals with the goal of developing computational skills, number-sense, and problem-solving skills. Prepares students for further study in mathematics by employing effective study strategies and a variety of teaching/learning experiences. DEV085 - Basic Mathematics II Review of basic arithmetic skills in whole numbers, decimals, and fractions with emphasis on problem solving situations. Instruction into the meaning and use of percentages, ratios, proportions, and measurements. Brief introduction into signed numbers. DEV108 - Introduction to Algebra Introduction to beginning algebra concepts including operations with rational numbers, identifying and combining like terms, solving one-variable linear equations/inequalities, and laws of exponents. Additional topics include the recognition of simple algebraic patterns and the study and use of some basic geometric formulas. Faculty use a variety of instructional methods including individualized instruction, self-paced approach, lecture format, and the utilization of technology such as calculators, computers, and instructional DVDs. All of these are well integrated throughout the courses to maximize students' learning ability.
You might want to check to see if your school's algorithms course uses CLRS. If they use the book (which wouldn't be completely out of the ordinary), well then you're going to have to buy it eventually anyway, right? CLRS doesn't really require much beyond the algebra you get in high school. There's some stuff on series and sets that you may or may not have gotten in high school, but I found it very readable even if you weren't a math geek (Disclosure: I am a math geek, so perhaps that isn't accurate). If you have a proofs class in college that might be helpful before reading it, but very little other college math is required.
Diophantine Equations Diophantine equations is the branch of number theory which studies solutions of polynomial equations in several unknowns in the ring of integers, rational numbers or in a given finite extension. Of course the most famous one is Fermat's equation x^n+y^n=z^n in integers x,y,z. In these lectures we give an overview of some of the main results and an insight in some of the techniques used. In the study of diophantine equations one uses a large variety of techniques from algebraic number theory, p-adic numbers and algebraic curves. The course will contain several very brief introductions into these subjects, so as to understand how they are used in diophantine equations. The discussion of diophantine equations themselves will then be based on two fundamental theorems by A.Thue and W.M.Schmidt. These theorems have a large number of applications in the area of diophantine equations. Organization The format of every session is two hours of lecture followed by a one hour exercise class.
Question on the Boas Math Methods book. I'm going to pick up a math methods book to beef up my more physicsy math, as it were, since the math program at my school is less geared to physics and engineering and more towards education, business, and computer science (and the physics program itself is falling apart). All the rage seems to be around the Boas book. So I looked it up on Amazon and found that in the used and new section I can get 2e for about fifteen bucks, while I can't get the 3e for less than seventy. Is there a significant difference between these two editions that would warrant the investment in the third edition when I'm just going to use it for some casual self-study?
0321279220 and Intermediate Algebra (3rd Edition) Lial/Hornsby/McGinnis s Introductory and Intermediate Algebra, 3e gives students the necessary tools to succeed in developmental math courses and prepares them for future math courses and the rest of their lives. The Lial developmental team creates a pattern for success by emphasizing problem solving skills, vocabulary comprehension, real-world applications, and strong exercise sets. In keeping with its proven track record, this revision includes an effective new design, many new exercises and applications, and increased Summary Exercises to enhance comprehension and challenge students' knowledge of the subject matter
Book Description--This text refers to an out of print or unavailable edition of this title. book when my eldest was 9 and 3 years on it's still proving to be an invaluable guide for reference, explanation and revision. It provides a good level of depth for all levels within core and key areas succinctly and clearly. I've recommended this book to a number of friends with children who've all found it really helpful (especially when your child has a maths exam the following week and you can't remember how to do long division!). I would expect this book to continue to be indispensable when my children sit GCSE. I can't praise it enough! I bought this because my own school maths wasnt brilliant.. of course much was forgotten when I didnt use it and now I have children Im being asked to help! My daughter (11) constantly dips into it. Its not like a 'textbook'which you might find in school, its informative and clear with steo by step explainations and diagrams which are very easy to follow and useful. I really wish this had existed when I was in school! I can see it being useful when shes sitting her GCSE maths! This is the first review I have done as it is the first book I have felt strongly enough to recommend! I bought this book two years ago when my daughter started in Year 7. I don't always have the time to help with homework, and it has clear instructions for each topic. This book has consistently helped her with both homework and revision. The sections are clear and there are samples laid out for you to follow. I have now started using it with my other children and so far it has not let us down! Brilliant buy.
More About This Textbook Overview With a clear writing style and matter-of-fact approach, this rigorous yet accessible introduction to quantum computing is designed for readers with a solid mathematical background but limited knowledge of physics and quantum mechanics. Using a methodical approach and an abundance of worked examples, this handbook delivers a thorough introduction to the quantum circuit model, including the mathematical formalism required for quantum computing. Concentrates on the quantum circuit model to make complex subject matter more accessible. Provides a phenomenological introduction to quantum computing, encouraging readers to view the subject as a fundamentally new approach to computing. Detailed presentation of quantum algorithms demonstrates the logic behind the development of Deutsch's problem, quantum Fourier transform, Shor's factoring algorithm, Simon's algorithm for phase estimation, and discrete logarithms evaluation problems. For anyone interested in learning more about quantum computing. Related Subjects Read an Excerpt dataPreface data 2, 2005 a new topic in cs and math In planning a course on quantum computing, an instructor would want to cover the significant highpoints in the subject: Shor¿s factoring algorithm, Grover¿s search algorithm, Deutsch¿s problem, the hidden subgroup problem. I for one found that this book does precisely that. Students will want an accessible and attractive presentation. This book is beautifully presented, nicely organized, and pedagogically presented with motivation, clear explanations, and well chosen exercises. While the subject has a variety of facets, physics, math, computer science, this book emphasizes the last two. In a highly interdisciplinary subject, each author (or team of authors) must make selections. In selecting what to cover, the authors had the classroom and students in mind. More precisely the subject here is presented in the form of quantum gates, channels, and circuits. Yet, quantum physics and the foundations are not neglected. The graphic presentation (figures and diagrams) is done in a way to aid learning, and I expect that this book will be the preferred text in courses in the subject for some time to come. Advanced undergraduates will be able to follow the logical progression of subjects. Several special features in the book help: Exercises, an extensive and instructive glossary, historical insight, motivation, appendices (including key math topics, e.g., modular arithmetic and Hadamard transforms which perhaps may not be widely known), and circuit diagrams illustrating at the same time matrix factorization and the complexity of circuits. Contents: 1. History and background, 2. Rudiments of quantum physics as it is needed, 3. Qubits and computer science rewritten in the form of quantum gates, 4. The key quantum algorithms (Shor, Grover, Simon) and the highpoints in the subject, 5. Entanglement, decoherence, error-correcting codes, Bell, dense coding, EPR, reversible computation, thermodynamic entropy, and more. Highly recommended! Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Lecture 1: How to solve inequalities. Chris Tisdell UNSW Sydney Embed Lecture Details : I present a simple example of how to solve a basic inequality arising in calculus and the theory of functions. Such ideas are seen in first-year university or high school mathematics. Inequalities are used in virtually all areas of mathematics and its applications. A good understanding of inequality techniques empower us to solve more difficult problems where inequalities arise (eg: in optimization; in linear programming; in error bounds for numerical approximation etc).
infocobuild Math 210 - Calculus I (UMKC) This is a collection of video lectures for Math 210 - Calculus I taught by Professor Richard Delaware, from UMKC (University of Missouri-Kansas city). Math 210 - Calculus I (UMKC) consists of 31 video lectures, and introduces the concepts and techniques of differential calculus and integral calculus. The topics include a review of precalculus, limits of functions, the derivative of a function, applications of differential calculus, the integral of a function, and applications of integral calculus. Unit 2 - The Derivative of a Function Lecture 10 - What is a Derivative? Definition of the Derived Function: The "Derivative", & Slopes of Tangent Lines. Instantaneous Velocity. Functions Differentiable (or not!) at a Single Point. Functions Differentiable on an Interval Lecture 25 - Area Defined as a Limit The Sigma Shorthand for Sums. Summation Properties & Handy Formulas. Definition of Area "Under a Curve". Net "Area". Approximating Area Numerically Lecture 26 - The Definite Integral The Definite Integral Defined. The Definite Integral of a Continuous Function = Net "Area" Under a Curve. Finding Definite Integrals. A Note on the Definite Integral of a Discontinuous Function
Contains notes and answers for each chapter, together with worksheets and tests intended for further practice, extension and assessment.. < Essential Mental Maths Practice Tests Editorial review A way to improve your pupils' performance in mental maths in preparation for the National Tests. This photocopiable resource includes 200 practice tests from NC levels 2/3 to 7/8. Maths in Action (Maths in Action) Editorial review The content follows the order of the Higher Still Unit specifications. Full explanatory text with worked examples allows an element of self-study. Graded exercises develop the questions beyond minimum competence level. End of chapter revi Maths for Advanced Physics Editorial review Maths for Advanced Physics is a practical handbook for students following Advanced or Higher courses in Physics. It contains essential information on the use of mathematics to solve physics problems and includes useful hints and worked ex Algebraic and Diagrammatic Methods in Many-Fermion Theory Editorial review The importance of electron correlation effects for the accurate description of the electronic structure of atoms, molecules and crystals is now widely recognized. In this text, modern theories of electronic structure and methods of incorp
Product Description sets. Each problem set focuses like a laser beam on a particular algebra skill, then offers ample practice problems. Answers are conveniently displayed in the back. This book is for parents of schooled students, homeschooling parents and teachers. Parents of schooled children find that the problems give their children a "leg up" for mastering all skills presented in the classroom. Homeschoolers use the Workbook - in conjunction with the Guide - as a complete Algebra 1 curriculum. Teachers use the workbook's problem sets to help children sharpen specific skills - or they can use the reproducible pages as tests or quizzes on specific topics. Like the Algebra Survival Guide, the Workbook is adorned with beautiful art and sports a stylish, teen-friendly design. Product Description ideas in this book will increase the learning effectiveness of any online program."--Marc J. Rosenberg, consultant, and author of Beyond E-Learning"Patti Shank has collected great ideas about online learning and teaching from all over the globe. If you are an online instructor or instructional designer looking for new ways to involve and engage your learners, you'll be inspired by this book!"--Terry Morris, associate professor, William Rainey Harper CollegesFilled with techniques, tools, tips, examples, resources, and dozens of "great ideas,? this invaluable resource helps people who are looking to build online instructional materials -- or improve existing materials -- discover and implement what the best and brightest in industry and education are doing to make online learning more engaging and compelling. Increase your know-how in the following areas: Look and Feel: how to increase ease-of-use Graphics and Multimedia: how to make instructional graphics engaging and compelling Activities: how to make instruction itself engaging and compelling Tools: how to use a variety of online tools Instructional Design: how to design better and faster
This is a translation of the second Czech edition of a book whose title translates as Methods for Solving Mathematical Problems, vol. II. It is a rich compendium of problems (310 worked examples, plus 650 exercises having hints or solutions at the back of the book), covering a wide range of topics in enumeration: binomial coefficients, inclusion/exclusion, the pigeon-hole principle, the orbit-counting formula, permutations, the combinatorics of elementary number theory (including M\"{o}bius inversion), the use of mathematical induction and of recursion relations, etc. Combinatorial problems in plane geometry are also considered, including some involving the coloring of points or regions, and some involving tilings. Despite the title Counting and Configurations, there is no discussion of combinatorial designs. This book is aimed at the level of bright high school students or beginning college students. The problems were taken from a multiplicity of sources, including Mathematical Olympiads and other competitions, especially from Eastern Europe. The sources of individual problems are not acknowledged. For example, this reviewer's book Polyominoes is "Reference 1", and is specially recommended to those interested in further study of certain types of tiling questions; but individual results and problems taken from it are not identified as such. The translation is generally excellent, although "fields" is not the best word to refer to the cells, or squares, of a chessboard or other rectangular array. This book would be ideal for preparing high school students for competitions such as the Mathematical Olympiads, and is an outstanding source of classroom and homework problems for college students taking a course in combinatorics. This book could be used as an auxiliary text, but probably not as the main text, in such a course.
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