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Math Success Deluxe is ideal for helping students at all learning levels find success. Inspire your child to keep learning while helping him or her build confidence in all areas of mathematics. This math software was created by educational experts to make the subject fun and easy to learn, from the basics all the way up to Algebra and Trigonometry. Featuring educator-endorsed and award-winning lessons including more than 1900 exercises and 300 fun activities, Math Success will improve comprehension in multiple subjects. Math Success Deluxe is a complete math learning system to help you get better grades fast - and it comes with free homework help from Tutor.com. Product Highlights Covers 80+ subjects 1,900+ exercises 300+ fun activities Easy-to-follow lessons For all learning levels Product Features Basic Math - More than 40 lessons cover math subjects to help prepare middle and high school students for more advanced concepts or help adult learners brush up on essentials Understand fractions and decimals Create factor trees How to get percentages Statistics explained Determine perimeter and area Pre-Algebra - Challenging problems are broken down in 66 simple lessons and more than 50 exercises, making pre-algebra subjects easy for every student to learn. How to reduce, multiply, compare fractions and more Figure out word problems Learn the Order of Operations When to use substitution Convert numbers to Scientific Notation Algebra I - Interactive quizzes, detailed explanations, and a helpful database of terms help make difficult subjects, including graphing, exponents, and more, easier for students to understand. Trigonometry - Students get help with more than 170 quiz questions, over 30 lessons, and 36 skill-building activities, plus useful resources give clear explanations on complex trigonometry subjects. How to graph sine and cosine Understand trigonometric functions and equations Learn polar and Cartesian coordinates The law of sines explained Master the trigonometric form of complex numbers Geometry - Build math skills for subjects that go beyond the classroom. Take the quizzes, use the animated exercises, and get helpful explanations of geometry subjects, from a circle to a quadrilateral. Non-Euclidean geometry explained Help with reasoning and equality Figure area, circumference and more Tips for space geometry Master angle measurements and vectors Probability and Statistics - Students will no longer be daunted by these advanced subjects with help from more than 30 lessons, over 165 quiz questions, and 25 skill-building activities.
Algebra 1, 1A, & 1B Algebra 1 is often called a gateway course since understanding of its content is fundamental to success in future math and science courses. The thinking processes that are found in Algebra 1 pave the way to clear thinking for all students and provide access to many career opportunities. California has placed an emphasis on this core curriculum and wants all 8th graders to have an algebra course. Teachers have found that it normally takes several years for students to completely master the content of a traditional Algebra 1 course, so many students will repeat their 8th grade algebra class. Much of the understanding and appreciation of the course content comes during subsequent years. It's often true that an Algebra 2 teacher spends time reteaching the Algebra 1 content that wasn't mastered fully. For most high school students algebra will be their most challenging course, and they should plan on spending quite a bit of time outside of class on it. For the large majority of students it is true that just spending more quality time on their mathematics work will pay dividends in understanding; there is no substitute for this focused time. Mathematics Content Standards for California Public Schools contains overviews of grade-level curriculum for Kindergarten through grade 12. All grade-level standards can be found here.
Current page is 5.5: Cauchy News Cauchy Augustin Louis Cauchy The Cauchy group is our newly-restructured upper high school group in its transitional year. This year, the Cauchy group targets 10th - 12th grade students; next year this focus will narrow on the 11th and 12th grades. Whatever a student's nominal grade, the Cauchy group is for students seeking problem solving challenges beyond the traditional high school mathmatics classroom. Cauchy topics will frequently expand broadly on core high school level mathematics, or use these core methods in more complex problem-solving strategies, or introduce students to advanced topics that build upon the high school foundation. Present-year 10th graders may legitimately choose to join the Cauchy class or the newly-formed early-high school Gauss class. This is a personal choice that may be guided by an interest in the topical mix of the Gauss class, or by an appetite for the higher level challenges of the Cauchy group. Students new to SDMC may find the Gauss group to be the more comfortable choice, while some students with past math circle experience be motiviated to try the Cauchy group. Cauchy students should be proficient with algebra and high-school geometry. Most Cauchy students will be proficient as well with common precalculus topics such as trigonometry, conic sections, and basic types of series. Many Cauchy students will be active in the study of calculus and some will have completed a year or more of calculus at the high school level. Cauchy instructors will not "teach" calculus, but some may draw connections with calculus concepts from time to time. Cauchy students tend to be very involved in mathematics competitions, so Cauchy topics are sometimes oriented toward this end. The Cauchy class is comprised of our most advanced, mature, and responsible students. Just one or two adult volunteers are needed in this class. Besides supervision, an important responsability of parent volunteers is to police the classroom at the end of each class session, to be sure the facilities are as clean and orderly as at the outset. The "Cauchy Coordinator" is a particular parent volunteer who assists SDMC in these matters.
Book Description: KEY BENEFIT: Ratti and McWaters have combined years of lecture notes and firsthand experience with students to bring professors a text series that teaches at the same level and in the style that they do. An extensive array of exercises and learning aids further complements your instruction in class and during office hours. KEY TOPICS: Trigonometric Functions; Right Triangle Trigonometry; Radian Measure and Circular Functions; Graphs of the Circular Functions; Trigonometric Identities; Inverse Functions and Trigonometric Equations; Applications of Trigonometric Functions; Vectors; Polar Coordinates and Complex Numbers MARKET: For all readers interested in trigonometry.
Mr. Mark Pierce Trig/College Math mcpierce@mpsaz.org (480) 472-5844 Room 616 Office Hours:Before School, B Lunch Course Description: This course is an accelerated course preparing students for enrollment in pre-calculus.Algebra 2 and Trigonometry are studied in-depth.Application of mathematics to the physical world will be stressed.Problem solving skills are also emphasizes throughout the course.Students will also continue to learn to use technology (TI-83 calculators) to aid them in problem solving. Textbook: Algebra and Trigonometry by Houghton Mifflin. 40% of the 1st quarter grade, 40% of the 2nd quarter grade, and 20
Prerequisite Study Sheet for MATH 1316 TRIGONOMETRY In MATH 1316, the student learns how to work with trigonometric functions, identities, equations, and applications of all of these. Students who wish to take scientific calculus must learn the material in MATH 1316 and MATH 2412 (Precalculus) to prepare for MATH 2413 (Calculus I). To begin the trigonometry course, it is necessary that you have completed the prerequisite for the course (one semester of high school trigonometry or precalculus, or College Algebra or the equivalent) and that you recall most of the high school geometry and algebraic techniques you have already studied. There is little or no review of algebra or geometry in the trigonometry course. The following problems provide a review of this algebra for students who have completed the prerequisite. The answers are listed at the end. If you find any of these that you do not know how to do correctly, you need to do one of two things before you enroll in MATH 1316: 1. Get an algebra book (at the Intermediate Algebra or College Algebra level) and review these topics until you can do all of these problems. If you do not have a book, you may check one out of a library, buy a non-current textbook at a used book store, buy an algebra revised book such as the Schaum's Outline Series, or buy a current textbook. 2. If you are unable (or don't have time) to learn these topics by reviewing on your own, you need to take an algebra course to refresh your algebra skills.
mathematics, some words are used in a more precise way than in English. It is important that a mathematical argument is unambiguous; therefore words that can be used in several contexts in English usually take only one meaning in mathematics. For instance, in English the word 'sum' might mean any calculation, but it has a precise mathematical meaning as exemplified by 'The sum of 456 and 789 is 1245'. Similarly, in English the word 'product' can have a variety of meanings lot of people use the equals sign wrongly in places where another word or phrase might actually make the meaning clearer. Sometimes a link word or phrase is useful at the beginning of a mathematical sentence: examples include 'So', 'This implies' or 'It follows that' or 'Hence'. Example 3 mentioned in the animation in Section 1.2 writing mathematics has a lot in common with writing English. When you write mathematics, you should write in the equivalent of sentences, with full stops at the end. As in English, each new statement should follow on logically from the previous one or it should contain an indication that a new idea is being introduced. However, laying out mathematics differs from laying out English: because mathematics is more condensed than written English way of testing whether or not you are conforming to the first guideline, is to read your solutions through aloud. Speaking aloud involves you in translating every symbol on the page into its verbal equivalent. If you find yourself needing to say more than is written on the page, you may need to expand your written account. To give you practice at this and at assessing the quality of some written mathematics, work through the animation below. The actual mathematics used is not important; jTimetables and distance-time graphs are different representations of scheduled train movements. They are both models which can be used to predict when trains will run, to analyse and compare different schedules when problems occur, and to design new operating schedules to meet new demands. Both models provide information which allows the company to operate safely and flexibly. The information is used by different groups of people show an application of distance-time graphs in the operation of a railway service. You will need graph paper for this section. This section uses the video 'Single track minders' to illustrate how distance-time graphs are drawn and interpreted by the timetable planners of a small railway company, and shows the role of this graphical technique in planning a flexible service. Graphical representations of journeys have been used for over a centur drawing a distance-time graph, Alice has predicted that she and Bob will pass on the stretch of road between Newcastle and Nottingham. Using the OU's computer system, she sends an email message to Bob suggesting that they meet at a roadside restaurant about 275 km north of Milton Keynes (for Bob this will be 510 − 275 = 235km south of Edinburgh). Bob acknowledges her email and the meeting is set up. Alice guesses they will probably stop for about 30 minutes. But what effect will should now be able to interpret distance-time graphs, and be able to use them to find information about the average speed, the distance travelled and the time taken for different sections of a journey. Given any two of these quantities you should be able to identify and use the appropriate formula to find the third. An important feature of a straight-line graph is its gradient. The gradient, or slope, of a graph expresses a relationship between a change measured along the horizontalDistance-time graphs are a means of replacing a description given in words by a mathematical description of the same event. What follows is a narrative account: that is, a description in the form of story about a bicycle ride. Read the story and then think about how you would use this account to produce a mathematical model of the ride in the form of a distance-time graph. Sunday started a bit cloudy. The temperatu three separate lines are combined into one overall distance-time graph representing the entire journey, as shown in Figure 44. The times for the sections are added together, so that the scale on the horizontal axis shows the total time that has elapsed since leaving Paris. Similarly, the distances of the sections are combine Eurostar train service that connects London and Paris via the tunnel under the English Channel (la Manche) covers a distance of about 380 km in three hours in 1996. Assuming a constant speed, what would the distance-time graph of this journey look like? Take the Gare du Nord (the Northern Station) in Paris as the start and measure time and distance from there. The vertical axis on formulas for speed, distance and time are all examples of mathematical models. Here, you should bear in mind that such models stress some aspects of travelling but ignore others. Building a mathematical model involves making some assumptions, and usually this involves disregarding those inconvenient aspects of real-world events which can not easily be fitted into a mathematical description. Take, for example, the model s = d/t used to calculate speed. Dividing introduce the distance-time graph as a mathematical model of a journey. Like any mathematical model, a distance-time graph stresses some features of the situation it claims to represent and ignores others. Bear this in mind as you work through this section, and note for yourself which aspects of a journey are described graphically, and which do not feature in the model. You will need graph paper for this section
Algebra is one of the building blocks of Mathematics in IIT JEE examination. While preparing for IIT JEE, it is this portion where an aspirant begins. Though Algebra begins with Sets and Relations but we seldom get any direct question from this portion. Functions can be said to be a prerequisite to Calculus and hence it is critical in IIT JEE preparation. Sequence and series is one other section which is mixed with other concepts and then asked in the examination. Quadratic equation fetches direct questions too and is also easy to grasp. Binomial Theorem is also a marks fetching topic as the questions on this topic is quite easy. Permutations and Combinations along with Probability is the most important section in Algebra. IIT JEE exam fetches a lot of questions on them. Those who get good IIT JEE rank always do well in this section. Complex Numbers are also important as this fetches question in the IIT JEE exam almost every year. Matrices and Determinant mostly give direct question and there are no twist and turns in the questions based on them. askIITians covers following topics in Algebra for IIT JEE, AIEEE and other engineering exams syllabus.
AcademicsDifferential Equations Course Description: In the sciences we often want to create a mathematical model of a process. We want this model to agree with our observations of the process and to be able to predict future behaviour. If the process we are modelling involves change over time, then our model will almost always need to consider the rate of change - so we need derivatives. Typically our model will be an equation involving derivatives; a differential equation. In this course we study how to solve differential equations, along with many of their applications. We study exact solutions where possible and power series and numerical solutions where not. The applications will come principally from mechanics and population dynamics, but there will be plenty of others too. The text for the course is Elementary Differential Equations by Boyce and Di Prima (7th or 8th ed.) Grades: Your grade will be calculated as follows: Final exam 40%, homeworks 40% and quizzes 20%. Class participation and prompt submission of homework are expected. Your overall grade may move up or down a small amount due to these factors. Homeworks: Homeworks will take two forms. You will be expected to attempt regular routine exercises from the text to make sure you stay on top of basic techniques, and to use the students' solution guide (on reserve in the library) to assess how you have done. Also, at the end of each of the six sections (see below) there will be a substantial set of questions to be handed in for marking. Office hours: TBA Tutoring: Julie Shumway (jshumway@marlboro.edu) Syllabus Outline. The following is an outline of the theoretical aspects of the course. Alongside this there will be applications dropped in, both from Elementary Differential Equations and other sources.
Mathematical Reasoning For Elementary Teachers - 6th edition Summary: Mathematical Reasoning for Elementary Teachers presents the mathematical knowledge needed for teaching, with an emphasis on why future teachers are learning the content as well as when and how they will use it in the classroom. the Sixth Edition has been streamlined to make it easier to focus on the most important concepts. the authors continue to make the course relevant for future teachers, including the new features like Examining School Book Pages, as well as the hallmark feature...show mores like Into the Classroom discussions and Responding to Students questions. Activities, classroom videos, and resources for professional development for future teachers are also available at ...show less 032169312439.76
You are talking about training in mathematics, not numerical analysis, so the answer is surely "yes". What is more, given that software packages exist, it should be taught in a more conceptual way than is done traditionally. I'm struck by how much of the "Moscow School" or Gel'fand way of looking at things depends on a good feel for the basics of linear algebra,
Place into MATT 133 with approved and documented math placement scores or by successfully completing MATT 132. NOTES: COURSE OBJECTIVES / GOALS: The student in this course must have facility in the fundamentals of Algebra. This course is designed to provide the student with the skill in the practical application of trigonometry in the industrial technology disciplines. Given radicals, students will learn to change them to a simple form so that basic arithmetic operations the group can be reduced to simplest form. The use of a personal electronic calculator in performing operations required in solving right triangles will be demonstrated so that students will develop the ability to substitute the calculator for the menial arithmetic tasks formerly required in fulfilling course objectives. Given second degree equations, students will solve by factoring or by quadratic formula. Given angles in any quadrant, the student will learn the trig functions and apply them in any polygon situation. Given any angle, the student will learn radian measurement and apply radians in linear, area, and velocity problems. Given vector components, the student will learn to solve for the resultants by trig. TOPICAL OUTLINE Use of electronic calculator in multiplying, dividing, and finding roots. Trig functions of any angle or number. Radians Vectors TEXTBOOK / SPECIAL MATERIALS: Technical Mathematics, John C. Peterson EVALUATION: (8)Hour Exams-(Competency based-must obtain a grade of "C" or better on each exam)
Year 9 Interactive Maths (2nd Ed) - Home Licence 5.01.02 (Windows) Year 9 Interactive Maths (Second Edition) by G S Rehill, an experienced mathematics author and teacher, helps students learn mathematics better and faster. The software has 337 interactive exercises spanning the following 18 chapters: The Distributive Law, Linear Equations and Inequalities, Pythagoras Theorem, Linear Graphs, Simultaneous Equations, Indices, Surds, Factors, Rational Expressions, Quadratic Equations and Graphs, Ratio and Proportion, Consumer Arithmetic, Geometry, Measurement, Trigonometry, Probability, Statistics and Revision. Questions use the metric system of measurement. Version 5.01.02 are a number of corrections for some errors either in the questions, solutions or support reading material. The software has an improved graphics engine. The software is now compatible with Windows Vista.
David Cohen's PRECALCULUS, WITH UNIT-CIRCLE TRIGONOMETRY, Fourth Edition, focuses on teaching mathematics, using a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. The author is known for his clear writing style and the numerous quality exercises and applications he includes in his respected texts. In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greater emphasis. Many sections now contain more examples and exercises involving applications and real-life data. While this edition takes the existence of the graphing calculator for granted, the material is arranged so that one can teach the course with as much or as little graphing utility work as he/she wishes. This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, ... Practitioners in the helping professions make life-affecting judgements and decisions. This new integrated learning package seeks to improve practice reasoning through principles of logical thinking ...
We are going to hold an introductory workshop about the statistics. The participants will be students who have just finished their 8th or 9th grade. The workshop consists of 10 two-hour sessions. The ... I can easily understand the advantage of multiple-choice questions for instance in grading and so. A drawback is that real life problem don't have multiple choice questions all the time for instance ... I'm in search of a mathematical analysis text that covers at least the same material as Walter Rudin's Principles of ... but does so in much more detail, without relegating the important results to ... We all know that when learning math, one has to do more than just simply read - one must try to solve problems and work actively with the material. Many books try to force the reader to participate ... I have just started teaching a very elementary class for 1st year students on introductory pure mathematics. ( classes at my institution are groups up to 20 students and supplement the lectures. The ... As a math educator, do you think it is appropriate to insist that students say "negative $0.8$" and not "minus $0.8$" to denote $-0.8$? The so called "textbook answer" regarding this question reads: ... Mat-1.1020 L2 course is a course usually taken by theoretical-physicist-dept students in Aalto University, here official site. It is a mass course that a massive amount of students fail every year. It ... Assuming we don't have a calculator that can do summation notation. My class is not up to summation yet, but I'm asking a question involving this concept because I'm not all that experienced using it. ... I have been asked to teach mathematics/physics to a few 8th grade/9th grade kids for a summer camp. I have been thinking about it and I realized that I could go about it in two ways: One of the ways ... It is a common practice to have students of elementary algebra infer the domain of a function as an exercise. I believe this is contrary to the spirit of the definition of a function as a collectionWith a few colleagues, we're trying to design an (intermediate) algebra course (US terminology) where we stress the interplay between algebra and geometry. The algebraic topics we would like to cover ... I am tutoring several talented students, middle school level and early high school level, in mathematics. I am always looking for new sources from which to draw questions. Can anyone recommend books, ... I like to use physical demonstrations when teaching mathematics (putting physics in the service of mathematics, for once, instead of the other way around), and it'd be great to get some more ideas to ...
Linear Algebra Labs with MATLAB 3rd Edition 0131432745 9780131432741 setting. The LABS and Projects are meant to supplement a standard sophomore level course in linear algebra. They follow the general outline for such a course, introducing instructional routines and appropriate MATLAB commands to solve problems related to each concept. Our primary goal is to use the laboratory experiences to aid in understanding the basic ideas of linear algebra. As such we use instructional M-files that provide a tool kit for working with linear algebra without the need for programming in the MATLAB command set. Although no programming background is assumed, those students with computing skills can further enhance their skills within MATLAB. We have found that students initially rely on the tool kit, but many quickly begin to use MATLAB commands directly, even though we provide little formal instruction in this area. We recommend an instructional approach that integrates the language and terminology of computing within the lecture format. In addition, when possible and appropriate, computer demonstrations and experiments should be used in lectures. Three of the LABS are different from the others. LAB 5 examines sets with addition and scalar multiplication and investigates the defining properties of a vector space in a pedagogical way. LAB 8 presents the defining properties of the determinant in such a way that a considerable amount of class time can be saved on this topic. Also, LAB 11 presents an independent supplement to the standard classroom coverage of linear transformations by examining the geometry of plane linear transformations. New Section 11.2 introduces homogeneous coordinates to incorporate translations. The LABS are not self contained. Except for LABS 8 and 11, they assume that the material has already been presented in the classroom. Sometimes, however, it is expedient to discuss a topic using a fresh, computational approach. New material has been added to this third addition, both in the LABS and in the accompanying instructional M-files. The modifications to the LABS provide a number of alternate approaches to topics some of which use more graphically oriented M-files to provide visualization of concepts. Many of the instructional M-files have been enhanced to take advantage of the graphical user interface (GUI) available in MATLAB . In addition we have included instructional files that use the Symbolic Math Toolbox. These sections can be omitted without loss of continuity if this toolbox is not available. A detailed list of new features is on page viii and a short description of all the instructional files is on page x. A full description of the instructional files is available by printing alldesc.txt that accompanies the tool kit of instructional files. We extend our sincere gratitude to the National Science Foundation (ILI #DMS-9051282) for providing the funds for implementing a mathematics laboratory at Temple University. This facility provided the educational arena necessary to develop the laboratory materials and extend our instructional M-files for MATLAB from 1990 to 1993. We thank the many students who were patient with and receptive to using the laboratory to aid in the development and understanding of the concepts of linear algebra. A special thanks to our colleague Dr. Nicholas Macri for his valuable assistance in designing and preparing this manual. David R. Hill David E. Zitarelh May, 2003 «Show less... Show more» Rent Linear Algebra Labs with MATLAB 3rd
This set accompanies Saxon Math's Saxon's Algebra 1 curriculum. Ideal for extra students, this set includes 30 test forms with full, step-by-step test solutions. The answer key features answers to all student textbook practices and problem sets Saxon Algebra 1, Answer Key Booklet & Test Forms Review 1 for Saxon Algebra 1, Answer Key Booklet & Test Forms Overall Rating: 5out of5 Date:November 4, 2011 jan123 Location:AZ Age:35-44 Gender:female Quality: 5out of5 Value: 5out of5 Meets Expectations: 5out of5 The only disadvantage in this booklet is not enough tests. For couple of chapters only one test. Even-though each chapter keeps repeating the questions fro previous chapter its just not enough practice. The test are very well made. They cover those chapters of the text book they specify. I like those test for my child. Share this review: 0points 0of0voted this as helpful. Review 2 for Saxon Algebra 1, Answer Key Booklet & Test Forms Overall Rating: 3out of5 This is included in the home study kit! Date:November 29, 2010 Juliana Lyon Age:25-34 Gender:female Quality: 3out of5 Value: 1out of5 Meets Expectations: 1out of5 I did not realize it was included in the home study kit. Just wanted to warn others ;)
Addition and subtraction within 5, 10, 20, 100, or 1000. Addition or subtraction of two whole numbers with whole number answers, and with sum or minuend in the range 0-5, 0-10, 0-20, or 0-100, respectively. Example: 8 + 2 = 10 is an addition within 10, 14 – 5 = 9 is a subtraction within 20, and 55 – 18 = 37 is a subtraction within 100. Bivariate data. Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team. Box plot. A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data.1 Commutative property. See Table 3 in this Glossary. Complex fraction. A fraction A/B where A and/or B are fractions (B nonzero). Computation algorithm. A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly. See also: computation strategy. Computation strategy. Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another. See also: computation algorithm. Congruent. Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations). Counting on. A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack all over again. One can find the total by counting on—pointing to the top book and saying "eight," following this with "nine, ten, eleven. There are eleven books now." Dot plot.See: line plot. Dilation. A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor. Expanded form. A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3. Expected value. For a random variable, the weighted average of its possible values, with weights given by their respective probabilities. First quartile. For a data set with median M, the first quartile is the median of the data values less than M. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the first quartile is 6.2See also: median, third quartile, interquartile range. Fraction. A number expressible in the form a/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number. Identity property of 0. See Table 3 in this Glossary. Independently combined probability models. Two probability models are said to be combined independently if the probability of each ordered pair in the combined model equals the product of the original probabilities of the two individual outcomes in the ordered pair. Integer. A number expressible in the form a or –a for some whole number a. Interquartile Range. A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 – 6 = 9. See also: first quartile, third quartile. Line plot. A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.3 Mathematics of Information Processing and the Internet (IA). The Internet is everywhere in modern life. To be informed consumers and citizens in the information-dense modern world permeated by the Internet, students should have a basic mathematical understanding of some of the issues of information processing on the Internet. For example, when making an online purchase, mathematics is used to help you find what you want, encrypt your credit card number so that you can safely buy it, send your order accurately to the vendor, and, if your order is immediately downloaded, as when purchasing software, music, or video, ensure that your download occurs quickly and error-free. Essential topics related to these aspects of information processing are basic set theory, logic, and modular arithmetic. These topics are not only fundamental to information processing on the Internet, but they are also important mathematical topics in their own right with applications in many other areas. Mathematics of Voting (IA). The instant-runoff voting (IRV), the Borda method (assigning points for preferences), and the Condorcet method (in which each pair of candidates is run off head to head) are all forms of preferential voting (rank according to your preferences, rather than just voting for your single favorite candidate). Mean. A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.4 Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. Mean absolute deviation. A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20. Median. A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list—or the mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11. Midline. In the graph of a trigonometric function, the horizontal line halfway between its maximum and minimum values. Multiplication and division within 100. Multiplication or division of two whole numbers with whole number answers, and with product or dividend in the range 0-100. Example: 72 ÷ 8 = 9. Multiplicative inverses. Two numbers whose product is 1 are multiplicative inverses of one another. Example: 3/4 and 4/3 are multiplicative inverses of one another because 3/4 × 4/3 = 4/3 × 3/4 = 1. Number line diagram. A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity. Percent rate of change. A rate of change expressed as a percent. Example: if a population grows from 50 to 55 in a year, it grows by 5/50 = 10% per year. Probability distribution. The set of possible values of a random variable with a probability assigned to each. Properties of operations. See Table 3 in this Glossary. Properties of equality. See Table 4 in this Glossary. Properties of inequality. See Table 5 in this Glossary. Properties of operations. See Table 3 in this Glossary. Probability. A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition). Probability model. A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model. Random variable. An assignment of a numerical value to each outcome in a sample space. Rational expression. A quotient of two polynomials with a non-zero denominator. Rational number. A number expressible in the form a/b or – a/b for some fraction a/b. The rational numbers include the integers. Rectilinear figure. A polygon all angles of which are right angles. Rigid motion. A transformation of points in space consisting of a sequence of one or more translations, reflections, and/or rotations. Rigid motions are here assumed to preserve distances and angle measures. Repeating decimal. The decimal form of a rational number. See also: terminating decimal. Sample space. In a probability model for a random process, a list of the individual outcomes that are to be considered. Scatter plot. A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people could be displayed on a scatter plot.5 Similarity transformation. A rigid motion followed by a dilation. Tape diagram. A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model. Terminating decimal. A decimal is called terminating if its repeating digit is 0. Third quartile. For a data set with median M, the third quartile is the median of the data values greater than M. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the third quartile is 15. See also: median, first quartile, interquartile range. Transitivity principle for indirect measurement. If the length of object A is greater than the length of object B, and the length of object B is greater than the length of object C, then the length of object A is greater than the length of object C. This principle applies to measurement of other quantities as well. Vector. A quantity with magnitude and direction in the plane or in space, defined by an ordered pair or triple of real numbers. Vertex-Edge Graphs (IA). Vertex-edge graphs are diagrams consisting of vertices (points) and edges (line segments or arcs) connecting some of the vertices. Vertex-edge graphs are also sometimes called networks, discrete graphs, or finite graphs. A vertex-edge graph shows relationships and connections among objects, such as in a road network, a telecommunications network, or a family tree. Within the context of school geometry, which is fundamentally the study of shape, vertex-edge graphs represent, in a sense, the situation of no shape. That is, vertex-edge graphs are geometric models consisting of vertices and edges in which shape is not essential, only the connections among vertices are essential. These graphs are widely used in business and industry to solve problems about networks, paths, and relationships among a finite number of objects – such as, analyzing a computer network; optimizing the route used for snowplowing, collecting garbage, or visiting business clients; scheduling committee meetings to avoid conflicts; or planning a large construction project to finish on time. Visual fraction model. A tape diagram, number line diagram, or area model. Whole numbers. The numbers 0, 1, 2, 3,.... Tables Table 1. Common addition and subtraction situations. 6 Result Unknown Change Unknown Start Unknown Add to Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now? 2 + 3 = ? Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two? 2 + ? = 5 Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before? ? + 3 = 5 Take from Five apples were on the table. I ate two apples. How many apples are on the table now? 5 – 2 = ? Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat? 5 – ? = 3 Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before? ? – 2 = 3 Total Unknown Addend Unknown Both Addends Unknown1 Put Together/ Take Apart2 Three red apples and two green apples are on the table. How many apples are on the table? 3 + 2 = ? Five apples are on the table. Three are red and the rest are green. How many apples are green? 3 + ? = 5, 5 – 3 = ? 1These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the left of the equal sign, help children understand that the = sign does not always mean makes or results in but always does mean is the same number as. 2Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation, especially for small numbers less than or equal to 10. 3For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for the smaller unknown). The other versions are more difficult. Table 2. Common multiplication and division situations.7 Unknown Product Group Size Unknown (How many in each group? Division) Number of Groups Unknown (How many groups? Division) 3 x ? = 18, and 18 ÷ 3 = ? ? x 6 = 18, and 18 ÷ 6 = ? Equal Groups There are 3 bags with 6 plums in each bag. How many plums are there in all? Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether? If 18 plums are shared equally into 3 bags, then how many plums will be in each bag? Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be? If 18 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have? Arrays,4 Area5 There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example. What is the area of a 3 cm by 6 cm rectangle? If 18 apples are arranged into 3 equal rows, how many apples will be in each row? Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it? If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it? Compare A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost? Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long? A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does a blue hat cost? Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first? A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue at? Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first? General a × b = ? a × ? = p, and p ÷ a = ? ? × b = p, and p ÷ b = ? 4The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable. 5Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations. Table 3. The properties of operations. Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system. Associative property of addition (a + b) + c = a + (b + c) Commutative property of addition a + b = b + a Additive identity property of 0 a + 0 = 0 + a = a Existence of additive inverses For every a there exists –a so that a + (–a) = (–a) + a = 0. Associative property of multiplication (a × b) × c = a × (b × c) Commutative property of multiplication a × b = b × a Multiplicative identity property of 1 a × 1 = 1 × a = a Existence of multiplicative inverses For every a ≠ 0 there exists 1/a so that a × 1/a = 1/a × a = 1. Distributive property of multiplication over addition a × (b + c) = a × b + a × c Table 4. The properties of equality. Here a, b and c stand for arbitrary numbers in the rational, real, or complex number systems. Reflexive property of equality a = a Symmetric property of equality If a = b, then b = a. Transitive property of equality If a = b and b = c, then a = c. Addition property of equality If a = b, then a + c = b + c. Subtraction property of equality If a = b, then a – c = b – c. Multiplication property of equality If a = b, then a × c = b × c. Division property of equality If a = b and c ≠ 0, then a ÷ c = b ÷ c. Substitution property of equality If a = b, then b may be substituted for a in any expression containing a. Table 5. The properties of inequality. Here a, b and c stand for arbitrary numbers in the rational or real number systems. Exactly one of the following is true: a < b, a = b, a > b. If a > b and b > c then a > c. If a > b, then b < a. If a > b, then –a < –b. If a > b, then a ± c > b ± c. If a > b and c > 0, then a × c > b × c. If a > b and c < 0, then a × c < b × c. If a > b and c > 0, then a ÷ c > b ÷ c. If a > b and c < 0, then a ÷ c < b ÷ c. 1Adapted from Wisconsin Department of Public Instruction, standards/mathglos.html, accessed March 2, 2010. 2Many different methods for computing quartiles are in use. The method defined here is sometimes called the Moore and McCabe method. See Langford, E., "Quartiles in Elementary Statistics," Journal of Statistics Education Volume 14, Number 3 (2006). 3Adapted from Wisconsin Department of Public Instruction, op. cit. 4To be more precise, this defines the arithmetic mean. 5Adapted from Wisconsin Department of Public Instruction, op. cit. 6Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33). 77The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples.
For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and pro... For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately. This text is designed to provide instructors with a convenient single text...
Book Description"...a valuable addition to the resources of any teacher preparing high school students for mathematics contests. ...an ideal addition to high school libraries." CRUX with Mayhem Book Description This book contains almost 600 unusual and challenging multiple-choice problems designed for. The first part consists of past papers (1988–93) for the annual UK Schools Mathematical Challenge.The second part contains forty-two short papers (10 questions each) in the same style. The book consists of question papers of the UKMT junior maths challenge for the years 1988 to 1993. In addition to this there are 42 question papers of 10 questions each. The book has 570 questions in total which is a good value for money. The second book in this series More Mathematical Challenges has slightly more challenging problems and is designed for junior maths olympiad preparation. 4.0 out of 5 starsBritish mathematics competition problems for middle school students.15 April 2007 By N. F. Taussig - Published on Amazon.com Format:Paperback This text contains papers from the U. K. School Mathematics Challenge for the years 1989 - 1994, each of which contains 25 multiple choice problems meant to be done without a calculator by middle school students, and 42 additional 10 problems papers in the same format provided for additional practice. The problems, which are succinctly stated and sometimes humorous, require good arithmetic skills, number sense, a rudimentary knowledge of algebra and geometry, and the willingness to think through a multi-step problem. The problems range from routine calculations to problems that require considerable ingenuity to solve. The U. K. School Mathematical Challenge papers consist of 25 problems. The 15 problems in part A of the examination are relatively routine; the 10 problems in part B are not. Given the difficulty of the problems in part B and the time limit of one hour to complete the examination, students are encouraged to check that their answers to the problems in part A are correct before they delve into the more difficult problems in part B. The second part of the book consists of miniature examinations. Each paper has 10 problems that increase in difficulty. The papers themselves also increase in difficulty. Some problems are more challenging than those that appeared in the competitions. Answers to all problems are provided; solutions are not. This is the chief limitation of the book, because it is not always possible to discern a solution to a problem even when you know the correct answer. Even with this limitation, working through this text is a great way for students of this age to prepare for mathematics competitions. Their teachers could use this text as a source of enrichment, whether in class or in mathematics clubs. The companion volume, More Mathematical Challenges, to this text consists of the open-ended problems given to students who scored well enough on the U. K. School Mathematics Challenge to qualify for the U. K. Junior Mathematical Olympiad.
School Search Mathematics JUNIOR INSTITUTE Students learn mathematics by focusing on real world applications and exploring key concepts from the New York State math standards in depth. Units are based around hands on projects. Students learn how to use math concepts to become critical thinkers. The curriculum content follows the 6th, 7th, and 8th grade New York State Content Standards. SENIOR INSTITUTE Students study Algebra, Geometry, and Algebra 2 consecutively for grades 9-11. Students learn math by focusing on real world applications and exploring in depth key concepts from the New York State math standards. Units are based around hands on projects, while learning how to use math concepts to become critical thinkers. The curriculum content follows the New York State Content Standards.
This course will emphasize the study of linear functions. Student will use functions to represent, model, analyze, and interpret relationships in problem situations. Topics include graphing, solving equations and inequalities, and systems of linear equations. Quadratic and nonlinear functions will be introduced.
Wednesday, April 11, 2012 April 11, 2012 1st3rd4th Hour Algebra II: Today we started with a Daily Routine that reviewed concepts from lessons 6.1 and 6.2. We worked through each of them together, as there were many questions. Next, we checked and went over questions 1-25, on Practice Worksheet 6.1, that the students completed in class before Spring Break. We went over several of those questions as well to ensure understanding. Finally, we completed the Notetaking Guide for lesson 6.2, discussing the method for rationalizing the denominators. For homework, the students should do problems 5-17, on Practice Worksheet 6.2. 6th Hour Algebra II: Today the students worked through a factoring worksheet in order to review these skills. We then checked and went over problems 1-4, 8-13, and 14-16, on page 407. We went over several of these problems to ensure understanding. For homework, the students should do problem 19, on page 407, and problem 35, on page 405, and problems 28 and 32, on page 404.
Product Description From the Inside Flap Preface The mere thought of taking a math course causes most people to clench their teeth, break out in a cold sweat, and start biting their fingernails. Relax! This course is different. This course uses practical applications to help you understand the tools of the trade. The approach is geared to help you interpret industry words and thoughts and then use your calculators (or computers) to translate your needs into clear mathematical answers. You will approach this course in a very logical manner, with a step-by-step approach, one that parallels your career path in the merchandising industry. From the start in Chapter 1, you will discover, with the help of the text, which uses a worktext format, that your calculator is a key tool for solving problems effectively. Chapter 2 teaches you the fundamentals of working with numbers. You look at the relationship of whole numbers to parts so you can calculate sales figures, commission statements, taxes, and discounts. With the numbers serving as the foundation, you can then look at how the numbers reflect the consumer, economic, fashion, and lifestyle trends that businesses address daily. Once you grasp working with numbers, the work will flow, just as though you were on the job, to more responsible tasks. In Chapter 3 you will look at some of the forms you may be asked to complete in a clerical position or as an assistant buyer. Along with the forms, you will learn what you will be filling in, and why. The information on these forms comes from a buyer's purchases at market. You'll take an inside look at the buyer's role in the marketplace, as he or she must negotiate prices with the wholesalers to arrive at the sharpest terms and conditions of sale, including product price, payment arrangements, and shipping charges. The text then takes you to the retail end of merchandising, pricing and reprising products. In Chapters 4 and S you will apply the basic math skills you learned in Chapter 2 to determine individual, initial, average, cumulative, and maintained markups. Through the exercises in Chapter 5, you will continue to develop strong critical thinking skills that reinforce pricing decisions. Markdowns, a very strong component in the competitive retailing world, are covered in Chapter 6. As you move on in the text, you will see how job responsibilities expand and provide further challenges. Part IV of the workbook is designed to help merchandising majors learn the financial planning methods used in the industry. This section covers six-month plans, open to buy, and classification planning. Chapter 7 introduces you to the elements of six-month plans and explains why they are important to a merchandising operation. From there you move on to Chapter 8, where you will learn how to analyze and interpret what the numbers mean and how a merchant can use these figures to judge the overall "healthiness" of an operation. Chapters 9 and 10 will carry you to a different level, that of the planner. With a solid foundation in analyzing numbers, adding on markup, and applying markdown pricing, as a merchandiser you now plan stocks, balance the flow of new merchandise and maintain balanced stocks, first by using last year's figures as a guide in Chapter 9 and, then, in Chapter 10, by designing a plan from scratch, just as you would do for a new business. Chapter 11 helps you prepare buying plans for market, which are then reinforced in Chapter 12 as you learn how to build strong merchandise assortments through classification planning. Part V shows you how numbers serve as tools to use in determining if a company's objectives and goals have been met. Here you take a look at how buying, pricing, and planning decisions are measured and evaluated. Again, using the skills from Chapter 2, you will apply basic math skills to profit-and-loss statements and income statements in Chapter 13. Sales per square foot, a key factor in profitability, is introduced in Chapter 14. Part VI briefly introduces the basics of corporate buying offices. With an increase in national brand products and private labeling growing worldwide, merchandisers faced with increasing competition now have to be able to calculate the cost of goods sold and determine if it is feasible to develop a product for a company. In this chapter you will learn how to prepare cost sheets and apply the pricing concepts you learned in Part III to determine if a product is competitive. Here you get a glimpse of how merchandising strategies are developing for the 21st century. The final section provides a check-in point for students. Often students want to make sure they are doing the calculations correctly, but if they are working outside the classroom, they don't have anyone with whom to check. Basic formulas and the solutions to the odd-numbered problems are given. So, relax! You will take this course step by step, just like your career in the industry. This text will give you the big picture, serving as a "reality check" for what really goes on behind the store windows. Hands-on experience is always the first step in on-the-job training, and this is a great place for all of you to start. The skills you learn here will lead you to the next step, coordinating this skill set with technology. Merchants today depend on the speed and accuracy of information provided by computer software programs. However, you first have to learn What is entered into the programs What the data means How to interpret and develop effective strategies based on the direction the numbers target Math for Merchandising: A Step-by-Step Approach guides you through the common-sense steps needed as you develop visionary ideas, forecast trends, and end up with financial success in the ever-changing fashion merchandising world. Acknowledgments Completion of this project was due in great part to my students, who, for many years, have challenged me to find better and easier ways to teach them the merchandising math skills needed for success in the job market. I am grateful for their insistence and their one constantly repeated question, What do I do first? I thank all of you for reading and improving the materials in this manuscript over the years, but, most importantly, for the confidence you've placed in me. Many people at Prentice Hall have played significant roles in the completion of this project, and I wish to extend my special thanks to Mark Cohen for his ongoing encouragement and to Stephen Helba and Elizabeth Sugg for their support and confidence. To Kelli Jauron and Michael Jennings with Carlisle Publishing, I truly appreciate your efforts to design a very user friendly book for students of all ages. I would also like to thank the experts who critiqued this work and provided such good advice and direction for the second edition: Leslie Evans Bush, Phoenix College (AZ); Gary M. Donnelly, Caspar College (WY); Farrell D. Doss, Ph.D., Radford University (VA); Fran Huey, ICM School of Business (PA); Dr. Gwendolyn Jones, University of Akron (OH); and Jerry W. Lancio, Daytona Beach Community College (FL). Along with the help of my peers, the meticulous attention shown to me by Michelle Churma, associate editor, has been truly appreciated. And, most importantly I would like to say to copyeditor Linda Thompson: Your advice, suggestions and expertise through both the first and second editions of this text, have been invaluable to me, and I honestly cannot begin to thank you enough! Evelyn Moore --This text refers to an out of print or unavailable edition of this title. From the Back CoverAs a newcomer to merchandising, I found this book's explanations of key terminology and tips on merchandise planning to be very helpful. The math, however, was entirely too simplistic to be of much use. This book contains an entire chapter on how to use a calculator. If you're looking for a good general overview of the field, this is a good book. But anyone with an elementary education should already know the math. 16 of 17 people found the following review helpful 5.0 out of 5 starsI finally understand math!Oct 7 1999 By A Customer - Published on Amazon.com I finally understand math! This is the first time I ever enjoyed a math class. I learned one step at a time how to solve problems easily. There are problems, with business definitions explained, examples, the forms you really use on the job, and helpful hints on how to solve the problems successfully. The book is easy to follow, and really helps you with the work,instead of frustrating you. I'm working in a retail store while I attend school, and I finally understand the paperwork I have to complete. The book shows you how to understand and calculate all the retail math skills you'll ever need to know! 9 of 9 people found the following review helpful 5.0 out of 5 starsA step by step approach, anyone can learn and understand!Oct 6 1999 By A Customer - Published on Amazon.com This book is unlike any math book I have ever studied, in all my years of education. It is not only a book to study from, but it is a work book that you should write all over! The "helpful hints" in each chapter help any student understand and it gives them something to go back to and review, when questioning one self. When most students think of a math course they are usually afraid. This text makes a student want to try and excel. The step by step approach is none threatening and is easy to follow,even for the math student who continually struggles!
More About This Textbook Overview This is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at
MTH101 Calculus 1 Lecturer: Duration :1 semester 39 lectures Aim: This course aims to introduce gently the rigour of mathematical analysis to first year undergraduate students with some background of A-Level calculus. The concentration is on motivating results and concepts geometrically rather than on providing rigorous proofs. Concepts are defined carefully and results stated precisely, but illustrated by way of vivid, concrete examples. INTEGRATION. Finding areas, volumes, distances travelled, etc.; the definite integral: definition from first principles using upper and lower sums; properties of the definite integral; the Fundamental Theorem of Calculus (geometrical proof); the indefinite integral as an "anti-derivative'', examples and a few integration formulae; some integration techniques (e.g. integration by parts, use of partial fractions, substitutions, inspection, numerical methods); analysis of the elementary functions and their inverses; applications of integration to include areas and volumes of revolution. 6 Recommended Texts: M R Spiegel, Advanced Calculus (Schaum's Outline Series). J C Burkill, A First Course In Mathematical Analysis (Cambridge University Press, 1970).
Math Dictionary Confusion with mathematical terminology is a constant problem for some students. Our math dictionary covers math terms and explains the definition in detail describing how and where it is used. There is a complete A to Z of mathematical terms and explanations. These terms are required both by teachers and students and can also help parents understand what a question is actually asking. The dictionary terms and explanations can be printed out if required
Self-Taught Calculus Self-Taught Calculus"The Calculus Lifesaver" by Adrian Banner is way better, I used it for Calculus 1 and Calculus 2, and i even refer to it if I need to look something up, it even has online videos. Why aren't you doing Mathematics SL? I can't imagine it being very hard (I was in HL for a while, then switched to A-Levels), especially for someone who intends on going into physics. Studies SL is fluffy. Too fluffy. Oh, now I get it. You want an easy 7? Self-Taught Calculus What about Calculus by Gilbert Strang Spivak's Calculus or Paul's Online Math Notes? Are those good for self study compared to The Calculus Lifesaver and A First Course In Calculus? I really want something that contains proofs and really give me a good understanding and masterI spent 11 years in the Navy and had a 12 year break in math. I had to reteach myself College Algebra and PreCalc. For PreCalc I found out what book they were using at the college I wanted to go to and ordered it from Amazon. If I had questions about it the internet has so many resources to answers those questions. WolframsAlpha is a great tool, also YouTube. Just some food for thought!
Meshoppen AlgebraOnce these rules are learned, the equations become a jigsaw puzzle and can be quite fun to solve. Pre-algebra is the first step on the path to higher mathematics for most students. Pre-algebra courses introduce students to mathematical concepts beyond that of basic arithmetic.
College Prep: Math College Prep: Math is designed to help students build the knowledge and skills they need for college-level math courses. With successful completion of College Prep: Math, students can meet entrance requirements, successfully complete college placement tests, and transition to college-level math without remediation. The course includes an academic year of content, and the following six units of content are covered: Basic Operations and Applications: Number Concepts and Properties; Expressions, Equations, and Inequalities; Functions; Graphs and Measurement; Probability, Statistics, and Data Analysis. Interactive components throughout the course serve to engage students and enhance learning.
The Geometer's Sketchpad 5.04 description The Geometer's Sketchpad 5.04 is considered as the world's leading software which is capable of teaching mathematics. Sketchpad® gives students at all levels—from third grade through college—a tangible, visual way to learn mathematics that increases their engagement, understanding, and achievement. Make math more meaningful and memorable using Sketchpad. Elementary students can manipulate dynamic models of fractions, number lines, and geometric patterns. Middle school students can build their readiness for algebra by exploring ratio and proportion, rate of change, and functional relationships through numeric, tabular, and graphical representations. And high school students can use Sketchpad to construct and transform geometric shapes and functions—from linear to trigonometric—promoting deep understanding. Sketchpad is the optimal tool for interactive whiteboards. Teachers can use it daily to illustrate and illuminate mathematical ideas. Classroom-tested activities are accompanied by presentation sketches and detailed teacher notes, which provide suggestions for use by teachers as a demonstration tool or for use by students in a computer lab or on laptops. Enhancements: Rounding errors no longer occur when measuring right angles in degrees. The Geometer\s Sketchpad Updater brings you an advanced and convenient to use tool which spans the mathematics curriculum from middle school to college, The Geometer\s Sketchpad brings a powerful dimension to the study of mathematics. Free Download Soccer Sketchpad is released as a high quality and smart sketch program that could produce and print a professional looking drawing in 4 minutes. It is designed for soccer coaches who teach the game. Free Download
This classic Algebra textbook by G.A. Wentworth set the standard by which later textbooks in mathematics were judged. It became known within academic circles for its emphasis on problem solving and the development of practical mathematical thinking. The text takes students from simple equations to more complex arithmetical and geometrical progressions.
MATH 104: Introduction to Mathematical Problem Solving Introduction to problem solving with emphasis on strategies applied to algebra, geometry, and data analysis. Every semester. MAY NOT BE USED TO SATISFY THE REQUIREMENTS FOR A MAJOR OR MINOR IN MATHEMATICS. MAY BE USED TO FULFULL CORE SKILL 3. Credits:3 Overall Rating:2.5 Stars N/A Thanks, enjoy the course! Come back and let us know how you like it by writing a review.
Listed below are most of the courses that mathematics majors take either as required courses or electives in mathematics. The variety of courses offered allows students to design programs to meet their individual needs. The department also teaches a number of additional courses students in the liberal arts or business take to meet general requirements. The department also offers courses at the graduate level, which mathematics majors may take in their senior year as electives. In some cases, mathematics seniors obtain dual enrollment with the MU Graduate School and receive graduate credit for some courses taken in their final undergraduate year. All prerequisite courses listed must be passed with a C- or better (whether specifically indicated or not). MATH _0110-Intermediate Algebra (3). Mathematics [MATH] 0110 is a preparatory course for college algebra that carries no credit towards any baccalaureate degree. However, the grade received in Mathematics [MATH] 0110 does count towards a student's overall GPA. The course covers operations with real numbers, graphs of functions, domain and range of functions, linear equations and inequalities, quadratic equations; operations with polynomials, rational expressions, exponents and radicals; equations of lines. Emphasis is also put on problem-solving. Prerequisites: Elementary College Algebra or equivalent. Placement in Mathematics [MATH] 0110 based on the student's ACT math score or equivalent, in addition to other criteria. MATH 1100-College Algebra (3). A review of exponents, order of operations, factoring, and simplifying polynomial, rational, and radical expres sions. Topics include: linear, quadratic, polyno mial, rational, inverse, exponential, and logarithmic functions and their applications. Students will solve equations involving these functions, and systems of linear equations in two variables, as well as inequali ties. Prerequisite: Mathematics [MATH] 0110 or a sufficient score on the ALEKS exam. This course is offered in both 3 day and 5 day versions. See the math placement website for specific requirements. A student may receive at most 5.0 credit hours among the Mathematics courses 1100, 1120, 1140, and 1160. MATH 1300-Finite Mathematics (3). A selections of topics in finite mathematics such as: basic financial mathematics, counting methods and basic prob ability and statistics, systems of linear equations and matrices. Prerequisites: Math [MATH] 1100, or Math [MATH] 1160, or both a College Algebra exemp tion and sufficient ALEKS score. Warning: without a College Algebra exemption, a sufficient ALEKS score will not suffice unless it is a proctored exam (for Math [MATH] 1100 credit). MATH 1320-Elements of Calculus (3). Introduc tory analytic geometry, derivatives, definite integrals. Primarily for Computer Science BA candidates, Economics majors, and students preparing to enter the College of BUS. No credit for students who have completed a calculus course. Prerequisite: Math [MATH] 1100, or Math [MATH] 1160, or sufficient ALEKS score. A student may receive credit for Math [MATH] 1320 or 1400, but not both. A student may receive at most 5 credit hours among the Mathemat ics courses 1320 or 1400 and 1500. MATH 1400-Calculus for Social and Life Sci ences I (3). The real number system, functions, analytic geometry, derivatives, integrals, maximum- minimum problems. No credit for students who have completed a calculus course. Prerequisite: grade of C- or better in Mathematics [MATH] 1100 or 1160, or sufficient ALEKS score. A student may receive credit for Mathematics [MATH] 1320 or 1400 but not both. A student may receive at most 5 units of credit among the Mathematics [MATH] 1320 or 1400 and 1500. Math Reasoning Proficiency Course. MATH 1800-Introduction to Analysis I (5). This course will cover the material taught in a traditional first semester calculus course at a more rigorous level. The focus of this course will be on proofs of basic theorems of differential and integral calculus. The topics to be covered include axioms of arithmetic, mathematical induction, functions, graphs, limits, continuous functions, derivatives and their applications, integrals, the fundamental theorem of calculus and trigonometric functions. Students in this class will be expected to learn to write clear proofs of mathematical assertions. Some previous exposure to calculus is helpful but not required. No credit for Mathematics [MATH] 1800 and 1320, 1400 or 1500. Prerequisites: ACT mathematics score of at least 31 and ACT composite of at least 30 or instructor's consent. Graded on A/F basis only. MATH 1900-Introduction to Analysis II (5). This course is a continuation of Mathematics [MATH] 1800. In this course we shall cover uniform convergence and uniform continuity, integration, and sequences and series. The topics will be covered in a mathematically rigourous manner. No credit for Mathematics [MATH] 1900 and 1700 or 2100. Prerequisite: Mathematics [MATH] 1800 or instructor's consent. Graded on A/F basis only. MATH 2100-Calculus for Social and Life Sciences II (3). Riemann integral, transcendental functions, techniques of integration, improper integrals and functions of several variables. No credit for students who have completed two calculus courses. Prerequisites: Mathematics [MATH] 1320 or 1400 or 1500. Math Reasoning Proficiency Course. MATH 4150-History of Mathematics (3). This is a history course with mathematics as its subject. Includes topics in the history of mathematics from early civilizations onwards. The growth of mathematics, both as an abstract discipline and as a subject which interacts with others and with practical concerns, is explored. Pre- or Co-requisite: Mathematics [MATH] 2300 or 2340. MATH 4335-College Geometry (3). Euclidean geometry from an advanced viewpoint. Synthetic and coordinate methods will be used. The Euclidean group of transformations will be studied. Prerequisite: Mathematics [MATH] 2300. MATH 4340-Projective Geometry (3). Basic ideas and methods of projective geometry built around the concept of geometry as the study of invariants of a group. Extensive treatment of collineations. Prerequisite: Mathematics [MATH] 2300. MATH 4370-Actuarial Modeling I (3). This course covers the concepts underlying the theory of interest and their applications to valuation of various cash flows, annuities certain, bonds, and loan repayment. This course is designed to help students prepare for Society of Actuaries exam FM (Financial Mathematics). It is oriented towards problem solving techniques applied to real-life situations and illustrated with previous exam problems. Prerequisites: grade of C-or better in Mathematics [MATH] 2300. MATH 4371-Actuarial Modeling II (3). This course covers the actuarial models and their applications to insurance and other business decisions. It is a helpful tool in preparing for the Society of Actuaries exam M (Actuarial Models), and it is oriented towards problem solving techniques illustrated with previous exam problems. Prerequisites: Mathematics [MATH] 2300 and 4320 or Statistics [STAT] 4750. Students are encouraged to take Mathematics [MATH] 4355 prior to this course. MATH 4540-Mathematical Modeling I (3). Solution of problems from industry, physical, social and life sciences, economics, and engineering using mathematical models. Prerequisites: 3 semesters of calculus and some exposure to ordinary differential equations or instructor's consent. MATH 4580-Mathematical Modeling II (3). Solution of problems from industry, physical, social and life sciences, economics, and engineering using mathematical models. More general classes of problems than in Mathematics 4540 will be considered. Prerequisites: 3 semesters of calculus and some exposure to ordinary differential equations or instructor's consent. Mathematics [MATH] 4540 is not a prerequisite. MATH 4800-Advanced Calculus for One Real Variable II (4). Continuation of Advanced Calculus for functions of a single real variable. Topics include sequences and series of functions, power series and real analytic functions, Fourier series. Prerequisites: Mathematics [MATH] 4700/7700 or permission of the instructor. MATH 4900-Advanced Multivariable Calculus (3). This is a course in calculus in several variables. The following is core material: Basic topology of n-dimensional Euclidian space; limits and continuity of functions; the derivative as a linear transformation; Taylor's formula with remainder; the Inverse and Implicit Function Theorems, change of coordinates; integration (including transformation of integrals under changes of coordinates); Green's Theorem. Additional material from the calculus of several variables may be included, such as Lagrange multipliers, differential forms, etc. Prerequisite: Mathematics [MATH] 4700. MATH 4970-Senior Seminar in Mathematics (3). Seminar with student presentations, written projects, and problem solving. May be used for the capstone requirement. Prerequisite: 12 hours of mathematics courses numbered 4000 or above.
Work at the biology bench requires an ever-increasing knowledge of mathematical methods and formulae. In Lab Math, Dany Spencer Adams has compiled the most common mathematical concepts and methods in molecular biology, and provided clear, straightforward guidance on their application to research investigations. Subjects range from basics such as scientific notation and measuring and making solutions, to more complex activities like quantifying and designing nucleic acids and analyzing protein activity. Tips on how to present mathematical data and statistical analysis are included. A reference section features useful tables, conversion charts and "plug and chug" equations for experimental procedures. This volume is an excellent, structured source of information that in many laboratories is often scattered and informally organized. "This is a practical text for the lab. It covers the basics about numbers and generic types of measurements, numbers used in chemistry, calibration and the use of lab equipment, methods and short cuts for making solutions, methods used in molecular biology, an introduction to statistics and reports and the communication of numerical data, and reference tables and equations. The book is spiral–bound." —PBS Teacher Source "This volume is a handy reference for anyone who has kept equations and reagent recipe calculations plastered in strategic locations around their laboratory. Seasoned bench researchers will spend less time coaching collaborators and students stalled over elusive calculation details. Its tone is that of a clear and patient teacher who carefully explains essential mathematical details so almost anyone can understand how and why the calculations are done....Lab Math will certainly save time researchers might otherwise spend explaining how to find reference tables, make measurements, do laboratory calculations, make solutions, work with proteins and nucleotide calculations, or perform basic statistics to undergraduates, graduate students, or visiting fellows." —The Quarterly Review of Biology
Mathematics is the foundation of the sciences and is at the core of a liberal arts education. Many great ideas in human history are mathematical in nature or are easily understood by viewing them mathematically. The idea of infinity was first explained by mathematicians, for example, although originated by philosophers and theologians. While mathematics has practical applications to many academic disciplines, including business, computer science, psychology, political science, music, chemistry and physics, most mathematicians do not study mathematics because it is useful. Instead, they study mathematics for the same reason that other people study art, music or literature – because it interests them. The math major Berry's broad-based mathematics major is designed to prepare you for graduate study or a professional career. You also can earn a degree to teach mathematics in grades 6-12. In your first two years as a math major you'll get a solid foundation of calculus, differential equations and linear algebra, as well as an introduction to proof. Then you'll study abstract algebra, real and complex analysis, and other electives. Faculty members also teach "special topics" courses. Subjects that have been offered or are under consideration include topology, combinatorics, knot theory, differential geometry, chaos theory, fractal geometry, graph theory and functional analysis. In addition, you'll have the opportunity to take directed-readings courses in areas that are of particular interest to you. Students have studied partial differential equations, number theory and topology. They also have prepared to take the mathematics GRE subject test and the first actuarial exam. Students who are declaring a major in mathematics should use the documents to the right of the screen to work with their advisor to build an appropriate plan of study. The information represents tentative degree plans for students majoring in mathematics. It presupposes that the students decide to be mathematics majors at the beginning of their academic careers. Working with faculty members on research projects. Recent subject areas have included number theory, dynamical systems, geometry and complex analysis. Working in the mathematics tutoring lab, earning extra money as you explain mathematics to others. Helping to plan and implement regional mathematics competitions for middle-school and high-school students. Joining mathematics professional organizations and honor societies, including a chapter of the Kappa Mu Epsilon mathematics honor society and a student chapter of the Mathematical Association of America. Joining the Georgia Council of Teachers of Mathematics, if you are a mathematics-education major. Attending annual professional meetings with members of the faculty. Scholarships are available Outstanding upper-class students are eligible for special mathematics scholarships, including the: Barton Mathematics Award. Hubert McCaleb Memorial Scholarship. Mary Alta Sproull Scholarship. The faculty Berry College's mathematics faculty members have a diverse range of teaching and research interests. In addition, they simply enjoy working with students – inside and outside of the classroom. You'll find that it is common to see students talking with their professors. You'll also discover that there is a real sense of community among the mathematics faculty and students. Graduate study Berry College mathematics students have gone on to graduate school at such places as Duke University, the University of Virginia, the University of North Carolina at Chapel Hill, Georgia Tech, Georgia State, the University of Georgia, Auburn University, Syracuse University, Tulane, Clemson and Harvard.
Quick Overview M Details A child with a strong foundation takes much less time to understand a subject as compared to other students. M The book covers a very broad syllabus so as to build a strong base. The USP of the book is its style and format. The book is supplemented with Do You Know, Knowledge Enhancer, Checkpoints and Idea Box. Another unique feature is the Exercise Part which is divided into 2 levels. The broad variety of questions covered are Short, Very Short, Long, Fill in the Blanks, True/ False, Matching, HOTS, Chart/ Picture/ Activity Based, MCQ's - one option correct, multiple options correct, Passage based, Assertion-Reason, Multiple Matching etc. Solutions to selected questions has been provided at the end of each chapter. Why Buy AIETS IIT Foundation MATHEMATICS Class IIT Foundation MATHEMATICS Class 10 at KOOLSKOOL. Get unmatched deals and discounts when you buy AIETS IIT Foundation MATHEMATICS Class IIT Foundation MATHEMATICS Class
Linear Algebra 56 Lectures The Span of a Set of Vectors. In this video, I look at the notion of a span of a vector set. I work in R2 just to keep things simple, but the results can be generalized! I show how to justify that two vectors do in fact span all of R2. Row Reducing a Matrix - Systems of Linear Equations - Part 1. Basic notation and procedure as well as a full example are shown. The last part of the second part got cut off, but is finished in another video!!! An Introduction to the Dot Product. In this video, I give the formula for the dot product of two vectors, discuss the geometric meaning of the dot product, and find the dot product between some vectors. Word Problems Involving Velocity or Other Forces (Vectors), Ex 2. In this problem we are given the bearing and velocity of a plane and the bearing and velocity of the wind; we want to find out the actual velocity of the plane after taking the wind into consideration. (a nice little problem!) Vector Addition and Scalar Multiplication, Example 1. In this video, we look at vector addition and scalar multiplication algebraically using the component form of the vector. I do not graph the vectors in this video (but do in others). Vector Basics - Drawing Vectors/ Vector Addition. In this video, I discuss the basic notion of a vector, and how to add vectors together graphically as well as what it means graphically to multiply a vector by a scalar. Linear Independence and Linear Dependence, Ex 1. In this video, I explore the idea of what it means for a set of vectors to be linearly independent or dependent. I then work an example showing that a set of vectors is linearly dependent. Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1. In this video, I show what a homogeneous system of linear equations is, and show what it means to have only trivial solutions. In the next video, I work out an example that has nontrivial solutions. Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2. In this video, I show how to find solutions to a homogeneous system of linear equations that has nontrivial solutions. Basis for a Set of Vectors. In this video, I give the definition for a apos; basis apos; of a set of vectors. I think proceed to work an example that shows three vectors that I picked form a basis for R_3. Linear Transformations , Example 1, Part 1 of 2. In this video, I introduce the idea of a linear transformation of vectors from one space to another. I then proceed to show an example of whether or not a particular transformation is linear or not. Linear Transformations , Example 1, Part 2 of 2. In this video, I introduce the idea of a linear transformation of vectors from one space to another. I then proceed to finish an example of whether or not a particular transformation is linear or not
ELEMENTARY STATISTICS: A BRIEF VERSION is for introductory statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. In recent editions, Al Bluman has placed more emphasis on conceptual understanding and understanding results, along with increased focus on Excel, MINITAB, and the TI-83 Plus and TI-84 Plus graphing calculators; computing technologies commonly used in such courses. The 6th edition of Bluman, Elementary Statistics: A Brief Version provides a significant leap forward in terms of online course management with McGraw-Hill?s homework platform, Connect Statistics ? Hosted by ALEKS. Statistic instructors served as digital contributors to choose the problems that will be available, authoring each algorithm and providing stepped out solutions that go into great detail and are focused on areas where students commonly make mistakes. From there, the ALEKS Corporation reviewed each algorithm to ensure accuracy. The result is an online homework platform that provides superior content and feedback, allowing students to effectively learn the material being taught. Over 200 new or updated exercises have been incorporated into the text. Over 30 new or updated examples have been incorporated into the text. Benefit: The new and updated exercises ensure that the text stays current and incorporates examples students will recognize and relate to. Chapter Summaries were updated into bulleted paragraphs representing each section from the chapter. At the end of appropriate sections, Technology Step by Step Boxes show students how to use MINITAB, the TI-83 Plus and TI-84 Plus graphing calculators, and Excel to solve the types of problems covered in the section. Critical Thinking Challenges - These problems extend the material in the chapter and are subsequently solved using the statistical techniques presented in the chapter. Procedure Tables - These boxes embody the text?s step by step approach and summarize methods for solving various types of common problems. Worked examples include every step. Speaking of Statistics - These sections invite students to think about poll results and other statistics-related news stories and apply what they have learned. Statistics Today - The outline and learning objectives of each chapter are followed by Statistics Today, a real-life problem that shows students the relevance of the chapter?s topic. Applying the Concepts ? These exercises are found at the end of each section to reinforce concepts explained in the section. Most contain open-ended questions that require critical thinking and interpretation and may have more than one correct answer. Data Projects ? Appear at the end of each chapter and often require students to gather, analyze and report on real data. They are specific to the areas of Business and Finance, Sports and Leisure, Technology, Health and Wellness, Politics and Economics, and the classroom. Technology Answers - The answers in the answer appendix now include solutions based on the use of tables as well as solutions with answers derived from technology (calculator, Minitab, Excel, etc.) when there are discrepancies.
Summary: In what follows we investigate some simple examples of how Maple can help you to solve basic mathematical problems, allowing you to concentrate on the formulation and analysis aspects, which are closer to the real engineering parts. For a more thorough introduction to Maple for scientific and engineering programmers, I can recommend the book by R. M. Corless, "Essential Maple", Springer (1995; Zbl 0813.68069).
Learn about Mathematical Modeling The solution to a mathematical equation can be feasible or infeasible. There can be mathematical models with boundaries as well. Such models are termed as optimization models where the solution resides within a set of values. Usually such models are expressed with a set of constraints. For example, the classical functions of pricing the supply and demand for products, both these functions together create a fixed value for the price. Here is a sample mathematical model Objective: Maximize Profits from selling two products P1 and P2 at Price $3 and $4 respectively. If you carefully notice the system of equations above, the first equation constantly increases for any value of P1 and P2. But the increase is restricted by equation number 2 which enforces a boundary on the system. Hence the solution set returns feasible values. Equations can be both deterministic as well as stochastic. Stochastic systems are systems that do not have fixed values such as USD 3 as cost of product or labor hours as 2 hours per product. The expected values can be specified as a probability distribution. An Example of a probability distribution is the arrival rate of automobiles in a junction. One cannot determine the exact rate as the source would be dependant upon a lot of factors. Simulation is an extended technique of analyzing variations of input and output using expected values for a large number of trials. Many contrasting system conditions can be specified and the simulation can be run for a large number of trials. Math models are common place and are used to describe physical phenomena, astronomical phenomena and population growth. They are also used in production planning, manufacturing etc. In synopsis a mathematical model can create unbounded values or bounded values. A system with boundaries can be used to study extreme objectives such as profit maximization, time minimization etc., Related Posts This entry was posted on Sunday, February 7th, 2010 at 10:24 am and is filed under Science. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
Combinatorics & Discrete MathematicsContaining exercises and materials that engage students at all levels, Discrete Mathematics with Ducks presents a gentle introduction for students who find the proofs and abstractions of mathematics challenging. This classroom-tested text uses discrete mathematics as the context for introducing … Easily Accessible to Students with Nontechnical Backgrounds In a clear, nontechnical manner, Cryptology: Classical and Modern with Maplets explains how fundamental mathematical concepts are the bases of cryptographic algorithms. Designed for students with no background in college-level mathematics,Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective … Reflecting many of the recent advances and trends in this area, Discrete Structures with Contemporary Applications covers the core topics in discrete structures as well as an assortment of novel applications-oriented topics. The applications described include simulations, genetic algorithms, … Accessible to undergraduate students, Introduction to Combinatorics presents approaches for solving counting and structural questions. It looks at how many ways a selection or arrangement can be chosen with a specific set of properties and determines if a selection or arrangement of objects exists … Emphasizes a Problem Solving ApproachA first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces … From the exciting history of its development in ancient times to the present day, Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than present an encyclopedic treatment of topics in …
Discrete and Combinatorial Mathematics An Applied Introduction 9780201726343 ISBN: 0201726343 Edition: 5 Pub Date: 2003 Publisher: Addison-Wesley Summary: This text is organised into 4 main parts - discrete mathematics, graph theory, modern algebra and combinatorics (flexible modular structuring). It includes a large variety of elementary problems allowing students to establish skills as they practice. Ships From:Multiple LocationsShipping:Standard, ExpeditedComments:RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks). 075 Item may show signs of shelf wear. Pages may include limited notes and highlighting. Includes... [more]RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks). 075 Item may show signs of shelf wear. Pages may include limited notes and highlighting. Includes supplemental or companion materials if applicable. Access codes may or may not work. Connecting readers since 1972.[
Article Databases - AlsoeJournalsSIAM has a comprehensive publishing program in applied and computational mathematics. n addition to SIAM News, SIAM Review, and Theory of Probability and Its Applications, SIAM publishes ten peer-reviewed research journals.
Lecturethe short run and the long run the relationship between a firms output and labor employed in the short run the relationship between a firms output and costs in the short run a firms short-run cost curves the relationship between a firm The Financial SystemSaving, Investment, and the Financial SystemThe financial system consists of the group of institutions in the economy that help to match one person's saving with another person's investment. It moves the economy's scarce resou The Finite Element Method on Domains with Conical or Angular PointsHengguang Li and Victor Nistor Department of Mathematics, The Pennsylvania State University, USAIntroductionThe Finite Element Method (FEM) is an important method for the numerica MAT 514 - SPRING 2009 - EXAM I REVIEW You should be able to recognize the order of a differential equation, and identify the special types of linear, separable, and exact differential equations. You should understand how to graph direction fields ( MAT 285 FALL 2007 (TTh) CALCULUS FOR THE LIFE SCIENCES ICourse Description: This is the first course in a two-course, terminal calculus sequence. It is designed to introduce students to the beauty and power of calculus. Topics include functions, lim MAT 221: Elementary Probability and Statistics I (MWF Sections) Fall 2008 Course Description: The primary objective of MAT 221 is to provide students with knowledge of elementary probability and statistics. Students will learn the basic concepts of d MAT 514 FALL 2008 EXAM I REVIEW You should be able to recognize the order of a dierential equation, and identify the special types of linear, separable, and exact dierential equations. You should understand how to graph direction elds (slope elds) MAT 221 Fall 2008 Quiz 3 (1.3, 2.1, 2.2, 2.3)Name1. Using either Table A or your calculator or software, nd the proportion of observations from a standard Normal distribution that satises each of the following statements. In each case, sketch a 2.2 Correlation A scatterplot displays the form, direction, and strength ofthe relationship between two quantitative variables. The form can be clusters or linear. A linear relationship is particularly important because it issimple and quite 2.2 Correlation A scatterplot displays the form, direction, and strength ofthe relationship between two quantitative variables. The form can be clusters or linear. A linear relationship is particularly important because it issimple and quite Looking at Data-Relationships Recall the rst basic strategy in the data analysis:Begin by examining each variable by itself. Then move on to study the relationships among variables. In Chapter 1, we studied how to draw graphs and computenumeri ECS 104Lecture 7 Solving a Nonlinear EquationProblem Solving analyze the problem develop an algorithm write out the steps in words make a flowchart write the program test the program analyze the resultIterative Calculation?Iterative Ca LECTURE 2 BASIC DATA TYPES AND EXPRESSIONSIDENTIFIERSThe identifiers are names given to various program elements such as variables, functions and arrays. Identifiers consist of letters and digits in any order, except that: The First character mus CPS 196 Introduction to Computer Programming: Cfiles FileA File is a collection of related data and that resides on secondary storage, e.g. on disks. The C stdio (standard input/output) library contains a large number of routines for mani Question 1Yes, I predicted the results correctly. Val1+ means val1 is increased by 1 after the operation. So During the operation "val2=(val1=3)val1+", the value of val1 is 3. val2=33=9. After that, val1 becomes 3+1=4. Question 2val1: +val2 Q1.I was alble to predict the results.With the sentence (val1=3), the initial value of val1 is set as 3.For val2 =(val1=3)val1+, the initial value of val1 is used, then it is added on one. So val2=33=9. val1 became 3+1=4 after that.So the outp Economics 621 Handout #4Extensive Form Games: UncertaintyExample without uncertaintyExogenous uncertainty611.04 - 1Information Sets611.04 - 2Two more examples:611.04 - 3A system of beliefs for an extensive form game ' is a mapping : X CSE382 Algorithms and Data StructuresFall 2008Lab #7 Map<K,V> classversion 2Prologue:This lab is concerned with building a map class, Map<K,V>, using an instance of a Pair<K,V> class as the type held by an instance of the BTree<T>. That Design of a HashTable and its IteratorsJim Fawcett CSE687 Object Oriented Design Spring 2007Iterators as Smart PointersIterators are "smart" pointers: They provide part, or in some cases, all of the standard pointer interface: *it, i Why C+? Why not C#?Jim Fawcett CSE687 Object Oriented Design Spring 2003Both are ImportantC+ has a huge installed base. Your next employer is very likely to be a C+ house.C# is gaining popularity very quickly. But, your next employer CSE687 Object Oriented DesignMidterm#3 Spring 2004Midterm #3 Instructor's SolutionName:_ SUID:_This is a closed book examination. Please place all your books on the floor beside you. You may keep one page of not CSE687 Object Oriented DesignMidterm #1 Spring 2004Midterm #1 Instructor's SolutionName:_ SUID:_This is a closed book examination. Please place all your books on the floor beside you. You may keep one page of no CSE687 Object Oriented DesignMidterm #4 Spring 2006Instructor's Solution for CSE687 Midterm #4 Jim FawcettThis is a closed book examination. Please place all your books on the floor beside you. You may keep one page of note CSE687 Object Oriented DesignMidTerm Makeup Spring 2004Midterm MakeupThis is a takehome examination, which you are expected to prepare entirely yourself. You may, however, ask the instructor or any TA any questio
If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?" First principle: Understand the problem "Understand the problem" is often neglected as being obvious and is not even mentioned in many mathematics classes. Yet students are often stymied in their efforts to solve it, simply because they don't understand it fully, or even in part. In order to remedy this oversight, Pólya taught teachers how to prompt each student with appropriate questions, depending on the situation, such as: What are you asked to find or show? Can you restate the problem in your own words? Can you think of a picture or a diagram that might help you understand the problem? Is there enough information to enable you to find a solution? Do you understand all the words used in stating the problem? Do you need to ask a question to get the answer? The teacher is to select the question with the appropriate level of difficulty for each student to ascertain if each student understands at their own level, moving up or down the list to prompt each student, until each one can respond with something constructive. Second principle: Devise a plan Pólya mentions that there are many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included: Guess and check Make an orderly list Eliminate possibilities Use symmetry Consider special cases Use direct reasoning Solve an equation Also suggested: Look for a pattern Draw a picture Solve a simpler problem Use a model Work backward Use a formula Be creative Use your head/noggin Third principle: Carry out the plan This step is usually easier than devising the plan. In general, all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work discard it and choose another. Don't be misled; this is how mathematics is done, even by professionals. Fourth principle: Review/extend Pólya mentions that much can be gained by taking the time to reflect and look back at what you have done, what worked and what didn't. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem. The book contains a dictionary-style set of heuristics, many of which have to do with generating a more accessible problem. For example: The technique "have I used everything" is perhaps most applicable to formal educational examinations (e.g., n men digging m ditches) problems. The book has achieved "classic" status because of its considerable influence (see the next section). Russian inventor Genrich Altshuller developed an elaborate set of methods for problem solving known as TRIZ, which in many aspects reproduces or parallels Pólya's work. From Yahoo Answers Question:I am searching the WWW but I can't find what I need. I need a site that breaks down how to slove this arithmetic reasoning problems found on the Officer Aptitude Rating exam given by the navy to Qualify for OCS. I'm math eliterate!!!!! Answers:Well, I was unable to find a site as well. I do have a suggestion.... In doing research, I came across the description of the math portion of the exam.... "The math skills assessed by the ASTB subtests include arithmetic and algebra, with some geometry. The assessments include both equations and word problems. Some items require solving for variables, others are time and distance problems, and some require the estimation of simple probabilities. Skills assessed include basic arithmetic operations, solving for variables, fractions, roots, exponents, and the calculation of angles, areas, and perimeters of geometric shapes." Given each of these topics, maybe will be a good place to start, looking under algebra and geometry primarily. From browsing the site, it looks like it provides enough information necessary to help you learn the steps needed to work most problems on the exam. Hope this was of some help to you. Best wishes on your exam. Question:I've been trying to convince my parents to let me do online high school and they just wont give in! I have solid reasons as to why I want to study at home and I'm wondering why they're so stubborn about it. If you were a parent, would you think that these are good reasons to let your child do online schooling? - I'm originally from California but my family moved to Switzerland. The school system is so different here and they focus on shoving French down my throat before any other subject. I've studied at the public school here for a year and counting, and they teach me things that I already know. I don't feel like I'm up-to-par with the things the kids my age are studying back in the US. For example: Before I left, I was in the 8th grade and in Algebra. I actually felt challenged in all of my classes. When I got here, the teacher was teaching our class how to add fractions. - I also don't want to end up like my brother, who was told that he can't go to "college" (the high school here) if he doesn't perfect his French by June. My brother is supposed to be in his senior year of high school in the US, yet they won't even let him start the first year of "college" here because he can't speak French. I feel like I'm cracking under the pressure to learn this language and not have to repeat grades. - I'm harassed at school on a daily basis to the point where I can't even go through the same hallways anymore. I've changed my routes to all my classes just to avoid being bullied. I feel THAT threatened at school. Because of the bullying, I constantly feel stressed and scared. I can't defend myself either because I still have a ton of French to learn and I'll end up looking like even more of an idiot. I'm being reasonable, right? It's not like I want to do online schooling just to sit at home and rot. I feel like it's the best thing to do if I want to stay sane. The only problem is that my mom is extremely old-fashioned and thinks that anything out of the ordinary should be shunned by society! She doesn't realize how bad of an influence public school has on me because I'm so good at controlling myself at home. Answers:You can easily compare info about these schools in this site - schools.iblogger.org Question:how does it benefit us to know other peoples learning styles? Answers:Numero Uno: If I know your preferred way of learning, then I can adjust my training/teaching in such a way to make it easier for you to learn Question:Scientists can now determine the complete DNA sequences of organisms, including humans. Now that this milestone has been reached, is there a reason to continue to learning about Mendel, alleles, and inheritance patterns. Answers:Just because you have a few million base pairs of code doesn't mean you have a clue about how the genes are regulated and interact in order to fashion an organism. When you selectively breed and make crosses you can study the interactions of combinations of alleles. Basic introduction to mendelian genetics shows you a maximum of three or four gene interactions with no linkage but an organism is the cascading series of interactions of thousands of genes. Looking at restricted breeding experiments can give insight in how the the allelic combinations respond. This is done to link a variation in phenotype with actual genotypes. This often how specific desirable alleles that influence predisposition to disease resistance are found. More Reasons NOT to Believe in God - 2 :More Reasons NOT to Believe in God: Reason #2: Arrogance To quote douglas adams: Space... is big. Really big. You just won't believe how vastly hugely mindboggingly big it is... -We, are just one species of many on this tiny planet. -There are 9 planets, (give of take pluto) orbiting this average star we call the sun. -there are over 200 billion stars in our average galaxy we call the milky way. -traveling at 186000 miles per second it would take 100000 years to travel from one side of our galaxy to the other. -There are hundreds of BILLIONS of galaxies in the universe. -the Universe existed 9.1 billion years before earth was ever even formed. -The earth existed for almost 1 billion years before primitive life even began to emerge -microbes didn't even exist on land until 2.7 billion years ago. -245 million years ago the earth was populated by giant dinosaurs and prehistoric beasts (Dinosaurs lived on earth for 180 million years, homosapiens have lived on Earth for less than 1 million years) -over the course of 2.5 million years our primate species evolved from the genus: homo into the homosapiens we are now. -for hundreds of thousands of years mankind told stories and developed folklore. only recently, within the past ten thousand years have we learned to sustain our culture through written language. And to be certain, based on nothing but personal intuition, that in this TINY TINY TINY fragment of a blink in time, on this TINY TINY spec of dust we call home, and out of ...
Tabula Bookmark Publisher Description Tabula is a new software program for math instruction that joins the conveniences of a presentation program with the tools specific to teaching geometry. Tabula also excels at modeling math concepts with geometry. A novel set of manipulation and transformation tools facilitates and extends activities that use paper, scissors, straight edge, and other hands-on items. Students can use Tabula to apply concepts in projects involving tiling patterns, tessellation, perspective drawing, and more. Tabula can be used in 5th grade through high school geometry. Soft-Files is not responsible for the content of "Tabula" software description. We encourage you to determine whether this product or your intended use is legal. We do not encourage or condone the use of any software in violation of applicable laws.
Take the Parent Guide with You! Math Lab The goal of the Math Lab is to offer the highest quality service to students requiring assistance in lower-level mathematics classes up to and including differential equations. We promote an atmosphere that is conducive to learning, which makes the lab an ideal place for those wanting to work on a homework assignment or study for an upcoming exam. We also have solution manuals for many of the courses with which we assist. Past results have shown that regular attendance of the Math Lab can make a difference in gaining a higher grade, so we strongly recommend that students take advantage of the resources available.
ENEE 759F: Mathematical Foundations for Computer Systems Course Goals: Mathematical modeling, design, analysis, and proof techniques related to computer systems. Probability, logic, combinatorics, set theory, and graph theory, as they pertain to the design and performance of computer systems. Techniques for the design and analysis of algorithms and data structures. Study of efficient algorithms from areas such as graph theory and networks. Translation from mathematical theory to actual programming. Understanding of the inherent complexity of problems: polynomial time, NP-completeness and approximation algorithms. The course emphasizes mathematical rigor.
No-Nonsense Algebra Review There's a reason that I became a writing teacher and not a math teacher: algebra. If I could think about math in small, systematic bites like I can with the writing process, I'd be the perfect homeschooling mother. Thankfully, Richard Fisher's No-Nonsense Algebra will bring any math-challenged mother of 8th graders and older into the realm of near perfection. My 16 year old worked through a variety of lessons in the following recommended fashion: Watch the lesson video. Work along with Mr. Fisher, copying and working through the examples on paper. Read the lesson Introduction and Helpful Hints section. Complete the exercises by writing out each step of the equation on paper. Complete the review exercises, writing out each step on paper. Check the answers in the solutions key. Rework any exercises and/or review the video where needed. My daughter is a diligent self-starter and eager independent learner, and the program worked well for her. Here are her remarks: It's straightforward math. No stories, no bunny trails. Just examples and practice. Short and sweet lessons. Mr. Fisher's voice on the videos is pleasant. The whiteboard/screen gives clear examples. Mr. Fisher explains things well. I liked using pretty colors for the graphs. When I pressed her for any dislikes, all she could say was, "If I hadn't already bonded with the other math program that I'm already doing, I would do this one." My only regret is that we didn't know about No-Nonsense Algebra before I spent what I did to find a program for her to bond with! HA! No-Nonsense Algebra is the most affordable and effective algebra program I have ever seen. Math Essentials sells No-Nonsense Algebra for $27.95, and that INCLUDES access to all the online videos! I must say I like the idea of videos that are conveniently stored online – no media discs to keep track of! Even if your student is not necessarily an eager self-starter, No-Nonsense Algebra would work well with parental oversight. The lessons take only about 20 minutes to complete. A parent would check that the student is diligently writing out all the steps to each practice question. Mr. Fisher emphasizes the importance of this step repeatedly throughout the program. Reminders like this one are peppered throughout the text. Along with No-Nonsense Algebra, I had the opportunity to look through Mastering Essential Math Skills: Geometry, a supplemental text in a series of others such as Fractions, Decimals and Percents, Integers, and more. Although much shorter (80 pages), this book is laid out well like the algebra book. Each practice page is also designed to take about 20 minutes to work through. However, there are no companion video lessons, so a parent/teacher must read through and discuss the lesson with the student as he writes out the work on paper. Math Essentials Geometry You can find sample pages of Geometry and other Math Essential books here. Unconditionally guaranteed! My daughter and I truly enjoyed working with and reviewing Math Essentials' No-Nonsense Algebra. I highly recommend it for anyone looking for a solid algebra program. Math Essentials offers an unconditional guarantee with their products. You really can't go wrong with this one. Disclaimer: As a member of the Schoolhouse Review Crew, I received this product at no cost to me in exchange for my honest review. All opinions are mine alone.
Matrices - Enter The Matrix In order to put Miss Loi's new found freedom into good use, it's about time the Matrix is loaded onto this website … hohoho. Do take particular note on the second question of Part 1. Recently Miss Loi's been seeing that more and more school papers are testing students' understanding of concepts like these (which is the right thing to do). From experience, many students don't pay enough attention to mundane little things like the conditions for inverses to exist. Even Miss Loi is sometimes guilty of that in her uni days . Given that A = and B = , find AB. State, with reason, whether A-1 and (AB)-1 exist. Yes there can be many answers to N in Part 2 but one thing that wasn't stated is that Part 2 only carries 2 marks in the actual question. So in the interest of grabbing this puny 2 marks in the quickest of time under stressful exam conditions, it's not really advisable to go through that lengthy 長氣workings of yours (even though your final answer is correct). A simple recall of the Identity Matrix (which is in this case) that satisfies the conditions of N ought to do the trick a F9, E8 person for maths ... But after attending lessons for a month (4 sessions, 8 hours!), I jumped to A1! ... [read more]
Jae Ki Lee Assistant Professor Mathematics Courses Taught This course is a combination of arithmetic and elementary algebra. It includes the arithmetic of integers, fractions, decimals, and percent. In addition, such topics as signed numbers, algebraic representation, operations with polynomials, factoring, the solution of simultaneous linear equations of two variables, and graphing are covered. This developmental course provides an alternative and accelerated pathway to the college-level liberal arts mathematics courses. The course will focus on applications of numerical reason to make sense of the world around us. Applications of arithmetic, proportional reasoning and algebra are emphasized. This course cannot be used as a prerequisite for MAT 056 and is not suited for Science, Technology, Engineering or Mathematics (STEM) students. This course is the second algebra course offered at the college. It is open to students who have completed elementary algebra or its equivalent. It includes such topics as: factoring, solutions of linear and quadratic equations, trigonometric relationships, exponents, logarithms, and the graphs of quadratic equations. A New Approach to Factoring Trinomial ax^2+bx+c, The New Jersey Mathematics Teacher Current Interests Alternative Teaching and Leanring Algorithm Common Core State Standard and School Curriculum Teaching Mathematics using Techonlogy Reform Based Instruction (Group Discussion Method) Honors & Awards PSC-CUNY (2013) Research Award Current Projects Exploring mathematical reasoning of the Order of Operations: Rearranging the procedural component PEMDAS and students' discoveries PEMDAS is one of the mnemonic devices to memorize the prior order to calculate if an expression contains more than one operation. However, students frequently make miscalculation with the expression which has either multiplication and division, or addition and subtraction are next to each other. This project explores the mathematical reasoning of the Order of Operation, and the effectiveness of a new approach. In addition, it observes students' discoveries
An investigation into the extent and nature of the understanding first year college of education students have of aspects of arithematic and elementary number theory Oliphant, Vincent George (1996) An investigation into the extent and nature of the understanding first year college of education students have of aspects of arithematic and elementary number theory. Masters thesis, Rhodes University. Abstract First Year College of Education students who have done and/or passed mathematics at matric level, often lack adequate understanding of basic mathematical concepts and principles. This is due to the fact that formal tests and examinations often fail to assess understanding at anything but a basic level. It is against this background that this study uses alternative and more direct means of assessing the level and nature of the understanding such students have of aspects of basic arithmetic and number theory. More specifically, the goals of the study are: 1. To determine the students' levels of understanding of the following number concepts: Rational numbers; Irrational numbers Real numbers and Imaginary numbers. 2. To determine whether the students understand the rules governing operations with negative numbers and with zero as principles rather than conventions. 3. To determine whether the students understand the rule governing the order of operations as a matter of convention rather than as a matter of principle. A survey of the literature concerning the nature of understanding as well as the nature of assessment is given. The students' understanding in the above areas was assessed by means of a written test followid by interviews. A sample of 50 students participated in the study while a sub-sample of 6 were interviewed. Some of the significant findings of the study were : 1. The students largely failed to draw clear distinctions between Real and Rational numbers as well as between Irrational and Imaginary numbers. 2. Very few of the students could explain the rationale behind the rules governing the. operations with negative numbers and zero. 3. Only half of the students had any knowledge of the rule governing the order of operations. Only one student demonstrated an understanding of the rule as a convention
Representations of finite groups. Characters, orthogonality of the characters of irreducible representations, a ring of representations. Induced representations, Artin's theorem, Brauer's theorem. Representations of compact groups and the Peter-Weyl theorem. Lie groups, examples of Lie groups, representations and characters of Lie group. Lie algebras associated with Lie groups. Applications of the group representations in algebra and physics. Elements of algebraic geometry. Number Theory Introduction to elementary methods of number theory. Topics: arithmetic functions, congruences, the prime number theorem, primes in arithmetic progression, quadratic reciprocity, the arithmetic of number fields, approximations and transcendence theory, p-adic numbers, diophantine equations of degree 2 and 3. Cryptography The primary focus of this course is on definitions and constructions of various cryptographic objects, such as pseudorandom generators, encryption schemes, digital signature schemes, message authentication codes, block ciphers, and others time permitting. The class tries to understand what security properties are desirable in such objects, how to properly define these properties, and how to design objects that satisfy them. Once a good definition is established for a particular object, the emphasis will be on constructing examples that provably satisfy the definition. Thus, a main prerequisite of this course is mathematical maturity and a certain comfort level with proofs. Secondary topics, covered only briefly, are current cryptographic practice and the history of cryptography and cryptanalysis. Topology After introducing metric and general topological spaces, the emphasis will be on the algebraic topology of manifolds and cell complexes. Elements of algebraic topology to be covered include fundamental groups and covering spaces, homotopy and the degree of maps and its applications. Some differential topology will be introduced including transversality and intersection theory. Some examples will be taken from knot theory. Homology and cohomology from simplicial, singular, cellular, axiomatic and differential form viewpoints. Axiomatic characterizations and applications to geometrical problems of embedding and fixed points. Manifolds and Poincare duality. Products and ring structures. Vector bundles, tangent bundles, De Rham cohomology and differential forms. Advanced Topics in Geometry Asymptotic geometry is concerned with properties of metric spaces which are insensitive to small-scale structure. It is a well-known theme in many areas of mathematics, such as the geometry of Riemannian manifolds or singular spaces, geometric group theory, the theory of discrete subgroups of Lie groups, geometric topology (especially 3-manifolds), graph theory, and recently in theoretical computer science. The course will begin with asymptotic invariants such as growth rates, isoperimetric inequalities, coarse topology, and boundaries, followed by a discussion of Mostow rigidity and variants. Subsequent topics will chosen according to the interests of the audience. Analysis Functions of one variable: rigorous treatment of limits and continuity. Derivatives. Riemann integral. Taylor series. Convergence of infinite series and integrals. Absolute and uniform convergence. Infinite series of functions. Fourier series. Functions of several variables and their derivatives. Topology of Euclidean spaces. The implicit function theorem, optimization and Lagrange multipliers. Line integrals, multiple integrals, theorems of Gauss, Stokes, and Green. Functional Analysis The course will concentrate on concrete aspects of the subject and on the spaces most commonly used in practice such as Lp(1<= p <= ?), C, C?, and their duals. Working knowledge of Lebesgue measure and integral is expected. Special attention to Hilbert space (L2, Hardy spaces, Sobolev spaces, etc.), to the general spectral theorem there, and to its application to ordinary and partial differential equations. Fourier series and integrals in that setting. Compact operators and Fredholm determinants with an application or two. Introduction to measure/volume in infinite-dimensional spaces (Brownian motion). Some indications about non-linear analysis in an infinite-dimensional setting. General theme: How does ordinary linear algebra and calculus extend to d=? dimensions? This course will cover fundamental methods that are essential for numerical solution of differential equations. It is intended for students familiar with ODE and PDE and interested in numerical computing; computer programming assignments form an essential part of the course. The course will introduce students to numerical methods for (1) nonlinear equations, Newton's method; (2) ordinary differential equations, Runge-Kutta and multistep methods, convergence and stability; (3) finite difference and ;finite element methods; (4) fast solvers, multigrid method; (5) parabolic and hyperbolic partial differential equations. System Optimization Methods Formulations of System Optimization problems; Elements of Functional Analysis Applied to System Optimization; Local and Global system optimization with and without constraints; Variational methods, calculus of variations, and linear, nonlinear and dynamic programming iterative methods; Examples and applications; Newton and Lagrange multiplier algorithms, convergence analysis. Mechatronics Introduction to Theoretical and Applied Mechatronics, design and operation of Mechatronics systems; Mechanical, Electrical, Electronic, and Opto-electronic components; Sensors and Actuators including signal conditioning and Power Electronics; Microcontrollers--fundamentals, Programming, and Interfacing; and Feedback control. Includes structured and term projects in the design and development of proto-type integrated Mechatronic systems.
Basic Mathematics: A Text/Workbook, 7th Edition Pat McKeague's seventh edition of BASIC MATHEMATICS is the book for the modern student like you. Like its predecessors, the seventh edition is clear, concise, and patient in explaining the concepts. This new edition contains hundreds of new and updated examples and applications, a redesign that includes cleaner graphics and images (some from Google Earth) that allow you to see the connection between mathematics and your world. This includes references to contemporary topics like gas prices and some of today's most forward thinking companies like Google
Algebra Formulas when you need them... Algebra formulas are an important part of any Algebra class. They apply to all Algebra classes from pre-algebra, Algebra I, Algebra II, all the way to College Algebra. There are a lot of basic formulas you will need to use during your journey to understand algebra. No matter the level of algebra course you are taking you will need some of these important formulas: Purpose of College Algebra! College Algebra is here to help students in an efficient manner with college algebra. Paying for a college algebra math tutor can be costly and time consuming. It is the intent of College Algebra to provide a more efficient college algebra help service than typical math tutoring. College Algebra is not here to help any student or students cheat on homework or tests. Our purpose is to help students obtain a better understanding of college algebra by seeing worked out solutions to difficult problems.
Our Price$53.13Reg.$62.50Algebra 1 Teachers Edition 9 By: Kathy Pilger Present algebra topics in a logical order. The text develops an understanding of algebra by justifying methods and by explaining how to do the problems. It introduces graphing, solving systems of equations, operations with... more Our Price$13.69Reg.$16.11Precalculus Tests 12 For One Student By: Kathy Pilger
...Robert Moses calls math and algebra the ticket to 21st century citizenship, and I would agree. It is the foundation upon which all other secondary and college math and science success will be built, so it is of strategic importance to every student. I focus on working with students to understand the "why" not just the "how", so the "how" will stick. ...But the simple fact of the matter is that algebra is NOTHING but arithmetic without the numbers. If you can add, subtract, multiply, and divide numbers, then there is very little in public school algebra that one doesn't already know. It really is a shame that Algebra 1 is the topic that turns so many students off to math, when it ought to be a cakewalk
The first edition was highly regarded for the manner and the extent in which it covered the basic concepts and procedures of linear analysis of frameworks by matrix methods, underlying theories of elasticity and the principles of virtual work, and application issues such as the solution of linear equations and the treatment of constraints. These features have been retained and strengthened by editing to improve clarity and elimination of a few topics that have proved to be of minor interest. In addition, this edition accounts for changes in the use and the teaching of matrix structural analysis that have taken place in the past twenty years. It incorporates advances in the art of analysis that are regarded as suitable for use in structural engineering design practice now and of increasing importance in the years just ahead. Chief among these are an introduction to nonlinear analysis and an interactive computer graphics computer program.
Functional Maths - Maths in A selection of 10 Functional Maths worksheets from Axis Education's brand new maths series Maths in. Full of practical Functional Maths tasks with students required to collect, present and analyse their own data, Maths in helps to engage students by demonstrating how mathematics can be applied to everyday life.
Author Abstract During the last decade a lot of emphasis has been placed in the understanding of the concepts in the teaching of calculus de-emphasizing the computational part. The use of technology has increased tremendously to help the student understand the basics ideas behind crucial concepts such as the derivative and integral. Animation of these concepts is one way to use technology as a pedagogical tool to help the students gain insight and understanding of them. From the stand point of teachers' preparation it will have a very positive repercussion, since the teachers will be teaching concepts which they understand better, and are more meaningful for them than just a simple formula or expression. In this paper I am reporting on the use of animations as a pedagogical tool, and possible effects in the teachers preparation. All these animations were created with Mathematica, a computer algebra system (CAS).
Milwaukee, WI AlgebraThe, or in combination with college level algebra. ...It can offer insight into less than informative news articles, medical research, internet polls and more. Once a student understands statistics, he or she is capable of critically evaluating those things people take for granted. Even statistics knowledge is power.
To create mathematically, scientifically and technologically literate and functional learners who will be successful in a business world that relies on calculators, computers, scientific and mathematical procedures, rapidly growing and extensively applied in diverse situations.
Based on Saxon's proven methods of incremental development and continual review strategies, the Saxon Advanced Math Homeschool Kit builds on intermediate algebraic concepts and trigonometry concepts introduced in Algebra 2 and prepares students for future success in calculus, chemistry, physics and social sciences. Kit includes Student Textbook with 125 lessons, Homeschool Packet with test forms and answer key to all tests and Student Textbook problem sets, and Solutions Manual with worked solutions to every problem in the textbook. This helped my first two children to be ready for calculus in college--they were able to test out of college algebra. My youngest child needed to go at a slower rate and had to take college Math in college. So it is great for those who have a bent for math and science. Our daughter had difficulty with math when we started using Saxon math curriculum. The spiral organization of the curriculum never gave her the opportunity to 'forget' previously learned concepts, but challenged her to continually progress in each concept. Math is now her top subject.
Search Academics at Champion MATHEMATICS - Algebra ll The purpose of this course is to develop thinking and reasoning skills, provide general knowledge of basic mathematical concepts including number systems, operations, geometry, and functions, to develop problem-solving abilities as well as speed and accuracy in computation and to promote an interest in and an enjoyment of mathematics. The importance of this course is the development of the reasoning and problem-solving skills essential throughout life. Also important is the general knowledge and computational skills necessary for placement and aptitude testing. Such general goals require both content and process. Certain content topics must be covered to prepare students for standardized tests but all the goals require teachers to employ appropriate processes. Skill development requires the process of regular review. Developing reasoning ability requires regular challenges to students' thinking processes. It is the purpose of this course to meet the needs of various teachers and students. Since every class is unique and students have varying abilities, the course will adapt the materials to the students. The teacher is the key to the students' learning with an attitude that will set the tone for the class. This fact will be considered when assigning homework with three alternatives available: (1) minimum, (2) standard, and (3) extended. Efforts to improve student attitudes will bring greater success. A sense of success in solving challenging problems, a recognition of the power of mathematics, and an interest in further development of mathematical skills will impart students with attitudes for success. This discipline complements and expands the mathematical content and concepts of algebra I and geometry. Students who master algebra II will gain experience with algebraic solutions of problems in various content areas. Students will solve problems in these areas which include: operations of number systems (real and complex), linear equations and inequalities, (functions and graphing), solving quadratic equations by factoring, completing the square, and by use of the Quadratic Formula. Students add, subtract, multiply, divide, and evaluate radical and exponential expressions, graph functions, and solve equations. Students solve systems of equations and inequalities using various methods and simplify rational expressions and equations. Trigonometry is introduced by right, special, and reciprocal triangular ratios along with functions, radian measure, amplitude, and period. Students prove simple laws of logarithms and understand and use the properties of logarithms to simplify logarithmic expressions. Students use fundamental counting principles to compute combinations and permutations and use these principles to compute probabilities. They know the binomial theorem and demonstrate and explain how geometry of the graph of a conic section depends on the coefficients of the quadratic equation representing it. ALGEBRA II (1 year - 10 credits - grades 9-12) PREREQUISITE: Successful Completion of Algebra 1 PURPOSE: To develop a student's problem solving ability. To provide a background and preparation for Trigonometry and Pre-calculus.
Virtual Nerd - Virtual Nerd, LLC This online tutorial service for secondary math and science students supplements its video instruction with the interactive Dynamic Whiteboard™, which takes notes for you during lessons, and lets you find definitions of terms mid-stream and write ...more>> Virtual Polyhedra - George W. Hart A growing collection of over 1000 virtual reality polyhedra to explore, complementing Hart's Pavilion of Polyhedreality. Includes instructions for building paper models of polyhedra including modular origami, with ideas for classroom use. Each of the ...more>> Virtual Tutor - Calculus An Internet service that delivers a tutor containing over 700 calculus problems and their solutions. Topics covered match those presented in most first year calculus textbooks. Each solution contains solution hints and hyperlinks to the relevant theory ...more>> Walpha Wiki - Derek Bruff and others As collaborative site to record how secondary and undergraduate math educators use Wolfram\|Alpha, or Walpha as it's called here, in the classroom. In particular, the authors are interested in how students might use Walpha themselves, as well as how teachers ...more>>
Tour of Symmetry Groups This document is being developed to provide a guided tour of symmetry groups using the Kali program. Currently, only frieze groups are covered by the tour. How to use this document The pages in this document may be viewed with a WWW browser but may be more useful if printed out in PostScript from a WWW browser. A PostScript version of each section will eventually be provided to avoid the hassle of having to save or print each page as PostScript from the WWW browser. The first two sections, Types of Symmetry and Symmetry in Frieze Groups, cover information that students should be familiar with before they come into the Geometry Center for a tour. Teachers may use the materials provided here or other equivalent material in their classrooms before bringing the students into the Geometry Center, so that the visit will be more productive. The third section, Using Kali to Explore Frieze Groups, contains a bunch of exercises that students may do while using the Kali program at the Geometry Center. The exercises are divided into groups based on their level of difficulty: beginner, intermediate and advanced. The last set of exercises, the Pattern Gallery, contains exercises in all ranges of difficulty. The fourth section contains a very brief mention of symmetries in the plane. This section may or may not be developed into exercises at a later date.
Pages Monday, April 1, 2013 When I look back on my own mathematical education, I have many people to thank for helping me develop productive mathematical habits of mind. I remember walking to the car with my dad on a bitter cold day on the way home from kindergarten, and I just had to understand how you could do subtraction with regrouping. Instead of brushing off my pesky questioning (and I was pesky), he explained it to me, writing in the frost on the car window to illustrate the ideas. Some years later, Linda Agreen, my Advanced Placement calculus teacher, made sure that I understood why the fundamental theorem of calculus was fundamental, even though that was not going to be on the AP test. These habits of seeking real understanding were solidified in the mathematics department at Spelman College, under Etta Z. Falconer and her colleagues. Building on the foundation laid by my father and my other mathematics teachers, I learned the mathematical habit of doggedly pursuing a complete understanding of ideas. I also learned how to recognize when my understanding was not complete and the reasoning skills to address the situation. Unfortunately, too many students of mathematics, whether in college algebra or abstract algebra, do not possess these productive mathematical habits of mind. Instead, they have picked up some bad habits along the way: a tendency to look for the quick answer, a lack of persistence when the answer is not obvious, memorization over understanding. Why do I keep referring to reasoning skills as "mathematical habits of mind"? Because I believe that if we start thinking about these unproductive practices as habits of mind, it opens up a different set of strategies for addressing the problem. When Al Cuoco, Paul Goldenberg, and June Mark introduced the concept of mathematical habits of mind (The Journal of Mathematical Behavior 15, no. 4 [1996]), it was a powerful concept for rethinking K-12 students' learning of mathematics. Habits are behaviors we engage in unconsciously, but they are the result of a long evolution of choices we make at a young age. Habits of mind evolve from the choices that we make about how to think about ideas. Thus, my dad's early intervention was important. At 5 years old, I was still making choices about how to learn. So were my teachers—in elementary school, high school, and beyond. But too few students develop the habits of mind needed for more advanced mathematical learning. Presented with a problem with no obvious example to follow, a poorly trained student might start writing things down or try some calculations with no real strategy in mind. Faced with the task of learning to write proofs, a person without sound mathematical habits usually attempts to memorize various arguments instead of re-creating them from their internal logic. These habits may have served them well previously, but no longer. Habits reflect what a person is likely to do in a given situation, especially a stressful one such as taking a test, and habits are notoriously hard to break. Smokers know that continuing to smoke has a high likelihood of leading to cancer and other diseases, but that knowledge alone is rarely sufficient for those who are trying to quit. With this in mind, we need to ask whether the way mathematics is currently taught reinforces bad habits of mind. Is it too easy to get by for too long using bad mathematical habits? And where did these bad habits come from in the first place? The likely answer is that there are some entrenched teaching habits in need of attention. Thinking in terms of habitual behaviors conjures up powerful analogies. How might we change our approach to learning—and teaching—math if we labeled as "unproductive habits of mind" those methods that serve us poorly? Just like the person who finally replaces smoking with a healthier habit—or better yet, who never starts in the first place—we will all be better served with healthier mathematical habits of mind. Karen King is the former director of research for the National Council of Teachers of Mathematics. She has been a member of the mathematics education faculty at New York University, Michigan State University, and San Diego State University. This article was published in the April 2013 issue of Math Horizons. Friday, February 1, 2013 When the national election finally came to a merciful end in November, there was one universally recognized winner whose name did not appear on any ballot. In a stunning denouement, political blogger Nate Silver may have permanently altered the way elections are reported—and run for that matter—and he did so by staking his claim to the veracity of Bayesian statistics. Like everything else in an election year, Silver's story is nearly impossible to separate from its heated political overtones, but in this case it is worth a try. Not only was mathematics well served, but its objectivity emerged as a potential means for making headway into the political storms that lie ahead. Nate Silver's first statistical love was analyzing baseball, which he did successfully for a sports media company after college, but in the run-up to the 2008 presidential election Silver began applying his mathematical tools to political forecasting. In March of that year he started a blog called FiveThirtyEight and made a name for himself by correctly predicting the outcome of every state except for Indiana in the Obama-McCain race. With its star on the rise, FiveThirtyEight was picked up by The New York Times, just before the 2010 midterm elections. In anticipation of 2012, the Times signed Silver to a multiyear contract. And this is where the plot thickens. In addition to being a first-rate statistician, Silver is also a self-professed progressive with ties to the Obama campaign. Thus, when Silver's blog showed Obama with a comfortable polling edge going into the final weeks of the election, attacks from conservative pundits began to fly. Denigrating the messenger is standard procedure in elections, but Silver's methods—i.e., his mathematics—also became fair game. An L.A. Times editorial characterized the FiveThirtyEight model as a "numbers racket." Referring to Silver, MSNBC's Joe Scarborough proclaimed that "anybody that thinks that this race is anything but a toss-up right now is such an ideologue [that] they should be kept away from typewriters, computers, laptops, and microphones for the next ten days, because they're jokes." Silver's series of responses make for some pedagogically compelling reading. "There were twenty-two poles of swing states published Friday," he wrote in a November 2, 2012, post. "Of these, Mr. Obama led in nineteen polls, and two showed a tie. Mitt Romney led in just one . . . a 'toss-up' race isn't likely to produce [these results] any more than a fair coin is likely to come up heads nineteen times and tails just once in twenty tosses. Instead, Mr. Romney will have to hope that the coin isn't fair." Silver then goes on to give a razor-sharp explanation of the difference between statistical bias and sampling error and how one accounts for each in assessing uncertainty. The FiveThirtyEight author's mathematical rejoinders only agitated his antagonists, who vowed to make him a "one-term political blogger." But on Election Day Silver's model was correct for all 49 state results that were announced that evening. And what about Florida, which was too close to call for several days? Silver had rated it a virtual tie. Predictably, this "victory for arithmetic" was quickly employed as weaponry in the red versus blue debate. This is as unfortunate as it is counterproductive, and here is why. If we can agree on anything in today's political climate, it is the need for a more productive means of public discourse. If we ignore Silver's political orientation for a moment, what we have is an illustration of how mathematics, in the proper hands, can provide an objective foothold when the partisan winds start to blow. What could mathematics, and a mathematical approach that prioritized proof over punditry, contribute to our ongoing debates about climate change? The national debt? The relationship of gun laws to violent crime? What are the chances that some disciplined mathematical analysis might provide an objective first step in bridging at least some of our philosophical differences? I'd rate it a toss-up. Stephen Abbott is a professor of mathematics at Middlebury College and coeditor of Math Horizons. This article was published in the February 2013 issue of Math Horizons. Image by Randall Munroe ( Thursday, November 1, 2012 Paul Zorn—Saint Olaf College I remember vividly the moment—and the room decor, the time of night, and the LP on the stereo—when my cousin Jon taught me algebra. He and I, then seventh-graders, enjoyed those hoary old story problems (Al is twice as old as Betty; in seven years . . .) that once appeared in magazines such as Life and Look. I had concocted a simple strategy that one might charitably call iterative: Make any old integer guesses and tweak them as the errors suggest. What Jon first saw, and memorably pointed out, was that an unknown, say A, for Al's age, can be manipulated as though it were a known quantity like one of my guesses. What thrilled me then was the prospect of zipping through an entire genre of contrived puzzles. What amazes me still is the power of one simple idea: You can manipulate unknowns and knowns to solve equations. That prescription seems a decent nine-word summary of what algebra does, even beyond the seventh grade. Jon and I got a preview, however dim, of an idea bigger and better than we could have suspected. Every student should encounter, and eventually own, an idea so simple and powerful. I'm convinced that almost every student has a fighting chance. Is algebra necessary? So asked a provocative New York Times op-ed last July. In fact, the title is slightly misleading. Author Andrew Hacker, professor emeritus of political science at Queens College, doesn't question algebra's larger importance. He notes cheerfully that "mathematics, both pure and applied, is integral [Hacker's good word] to our civilization, whether the realm is aesthetic or electronic." Hacker's different but equally provocative question is how much "algebra," that "onerous stumbling block for all kinds of students," should be required in high school and college. His answer: Much less. And less of other mathematics, too. Here "algebra" is in quotes because Hacker's beef is not really with that subject in particular. Indeed, Hacker sees both "algebra" and existing curricula idiosyncratically. His examples of supposedly superfluous material—"vectorial angles" and "discontinuous functions"—are unlikely examples of "algebra" and even less representative of what is typically taught. And Hacker's en passant endorsement of teaching long division (right up there with reading and writing) surprised me. He doesn't acknowledge, or seem aware of, creative efforts to improve school teaching of "algebra" by teachers like those supported and mentored by, say, Math for America. Hacker's real curricular concern is broader than algebra: It's the curricular complement of quantitative literacy (QL). He refers generally to "the toll mathematics takes" (my emphasis), not just to difficulties posed by algebra. In this sense Hacker's three Rs proposal—require QR, but not "mathematics"—is more radical, and Philistine, than the article's title suggests. But let's concentrate on algebra. Where he's right, and wrong. Some of Hacker's rhetorical targets are legitimate. Algebra can indeed be taught rigidly and applied ineffectively. (I remember the joy of solving algebra puzzles but also tedious hours of FOIL-ing quadratics.) Hustling high school students toward calculus sometimes pushes them too rapidly for effective mastery through prerequisite courses—including algebra. And Hacker, keen to avoid "dumbing down," suggests some interesting applications of QL methods to such topics as the Affordable Care Act, cost/benefit analysis of environmental regulation, and climate change. (Whether such topics can really be approached without algebra is another question.) As Hacker observes, few workers use algebra explicitly in daily life. (We all use it implicitly.) To infer that algebra can therefore vanish from required curricula is mistaken. Similar arguments might be made against history, the humanities, and the sciences generally, none of which is widely practiced in daily life. More important in curricular design than eventual daily use are broader intellectual values, which algebra clearly serves: learning to learn, detecting and exploiting structure, exposure to the best human ideas, and—the educational Holy Grail—transferability to novel contexts. Transferability is undeniably difficult, as Hacker duly notes. The National Research Council agrees (see Education for Life and Work Report (pdf))and indeed stresses the value of "deeper learning," of which a key element is the detection of structure. "Transfer is supported," says the NRC, when learners master general principles that underlie techniques and operations. Algebra is a poster child for deeper instruction. We should teach it. Students can learn it. Paul Zorn is a professor of mathematics at Saint Olaf College and currently serving as president of the Mathematical Association of America. This article was published in the November 2012 issue of Math Horizons. Saturday, September 1, 2012 Linda Becerra and Ron Barnes—University of Houston–Downtown Many believe that residual effects of past hindrances and discrimination against women in mathematics are being overcome. Studies by the American Mathematical Society and National Science Foundation on women in mathematics appear to reinforce this belief. Conventional wisdom suggests it is only a matter of time before women achieve parity. Julia Robinson (instrumental in the solution of Hilbert's tenth problem) suggested that one measure of parity would be when male mathematicians no longer consider female mathematicians to be unusual. Unfortunately, a close reading of AMS and NSF data suggests that significant progress is not being made. One can be deceived by looking only at raw numbers without considering the related percentages. Among entering students at U.S. institutions, data for the years 2000 to 2008 indicate the number of female and male freshmen expressing interest in a major in mathematics went from 44,500 and 49,500 in 2000, to 66,000 and 66,600 in 2008. These figures indicate the gap between female and male interest in majoring in math narrowed from 5,000 in the year 2000 to 600 in 2008. However, among all undergraduates, the percentage of females and males interested in a math major went from 0.6 percent (female) and 0.8 percent (male) in 2000, to 0.7 percent and 1 percent, respectively, in 2008. Hence, the percentage gap between the sexes increased during this time. This is because there was considerably higher growth in the overall female undergraduate population during this period. Total graduate enrollment in the mathematical sciences increased from about 9,600 in 2000 to 22,200 in 2009 (131 percent), while female graduate enrollment increased from 3,670 to 7,979 (117 percent). However, the percentage of female graduate enrollment in the mathematical sciences remained relatively static in the decade—38 percent in 2000 and 36 percent in 2009. AMS mathematics data noted that the number of Ph.D.s awarded to U.S. citizens in the mathematical sciences increased from 494 in 2000 to 669 in 2008, and the number of Ph.D.s awarded to women grew from 148 to 200. However, the percentage of Ph.D.s earned by women in 2000 and 2008 were both approximately 30 percent, with some variation in the intervening years. Also, the percentage of bachelor's degrees awarded to females during this time varied little from 41 percent. The NSF used a different data set, and the conclusions are even less encouraging. It indicates that women's percentage of bachelor's degrees in mathematics from 2002 to 2009 steadily decreased from 48 percent to 43 percent. In mathematics, the number of doctoral full-time tenure/tenure-track (T/TT) positions held by women at U.S. institutions increased from about 2,850 in 2001 to 4,000 in 2009 (a 40 percent increase). However, the percentage of T/TT positions held by females increased only from 18 percent to 23 percent during this time. This smaller difference is explained by the fact that significantly more males also obtained T/TT positions in this period. There are reasons to believe that women's progress in mathematics should be much better by now. Since 1982, considering all fields, women have annually earned more bachelor's degrees than men. By 2011, more women than men had earned advanced degrees. Yet, the statistics cited show that in mathematics, women's participation at advanced levels is still unusually low and either improving slowly or, in some cases, making no progress whatsoever. The real question is: How can meaningful progress be effected? Evidently the present strategies are not working. A few ideas for consideration: • Engage in a rigorous, sustained intervention with girls throughout school-level mathematics and in universities—not a few small programs, but a broad, concentrated, and sustained effort to integrate girls into mathematics, its culture, and its relevance. This effort must involve all the professional mathematical societies. • Reengineer the culture in the mathematics professoriate with an eye toward more flexibility in the tenure and promotion process. The standards need not be watered down in any way, but the process should allow for a variety of pathways to meet them. As Julia Robinson observed, "If we don't change anything, then nothing will change." Linda Becerra and Ron Barnes are professors of mathematics at the University of Houston–Downtown. Monday, April 2, 2012 Stephen Abbott—Middlebury College, Math Horizons Co-Editor There was no identifiable moment when I said, yes, I believe. My conversion must have come on silently and unexpectedly. I do, however, remember the moment when I realized something had inalterably changed... Wednesday, February 1, 2012 Tommy Ratliff—Wheaton College When I opened the MathFest program in Lexington last summer, I took one look at the first page and nearly yelled out loud "NO! NO! NO!" The inside cover to the program contained an advertisement for an online homework system with the following example: Find the derivative of y = 2 cos(3x − π) with respect to x. The assertion is that a competing system marked this answer as wrong, but the advertised system identified the expression as correct, demonstrating its superiority. I assume that the intent is to show that the system can recognize equivalent, but not identical, algebraic expressions. What caused me to react so strongly, however, is that I would have also marked the given answer as wrong. The answer should have been The parentheses matter! The expression sin(x) represents a function! I should be clear: My irritation is not directed at this particular homework system as much as at the entire mathematics community for the sloppiness in notation that we tolerate, and even encourage, when dealing with trigonometric functions. You can pick up almost any calculus text, peek into almost any math classroom, or attend any number of talks at various MAA events to find a plethora of examples of trig functions lacking their parentheses. Why do I think the parentheses matter so much? This is not just a pedantic preference on my part. The lack of parentheses represents an irregularity in notation that obscures the meaning of the mathematics. We often use a space to indicate multiplication, as in or 3 sin(x), so leaving off the parentheses hides the fact that we are using a trigonometric function. The confusion is compounded when we say that the derivative of "sine" is "cosine." If we were to be consistent, this would lead to applying a distorted product rule to get I have seen students struggle with this, even when they understand the intent of the original notation. They correctly apply the chain rule only to confuse the order of operations at the end because they did not put the constant multiple of 3 at the beginning of the expression: After all, why should you apply the cosine function to the first 3 in the 3x but not to the trailing 3? If we always used parentheses to enclose a function's argument, then there would be no confusion. An even worse abuse of notation occurs in the location of the exponent when a trig function is raised to a power. I will never write sin2(x) for sin(x)2 because the first notation leads to ambiguity when discussing the inverse trig functions. Since f− 1 (x) is the standard, consistent notation for the inverse function of f(x) , we also use sin− 1(x) for arcsin(x). If we were consistent with notation, a perfectly reasonable calculation would be Notice that I had to make a choice about the meaning of sin−2 (x) in simplifying the expression—an impossible task! Should it be sin2(x)-1 = 1/sin2(x) or sin -1(x)2 = arcsin (x)2? The point is that we should never have to make this choice! We should be taking the derivative of the inverse sine function. This is horrific. The bad notation allows at least three different interpretations of the expression We in the mathematics community pride ourselves on the consistency and deterministic nature of our discipline. I think we do ourselves a genuine disservice when we use sloppy notation that requires another layer of interpretation to understand the intended meaning. The purpose of mathematical notation is to provide clarity and, ideally, to provide insight into the mathematics being notated. Therefore, I implore you: The next time you use a trig function, please remember the parentheses, put the exponent on the outside, and never, ever write anything like sin3x2 cos-25x. Tommy Ratliff is a professor of mathematics at Wheaton College in Massachusetts where he enjoys thinking about voting theory, building new science centers, and being precise in his notation. Tuesday, November 1, 2011 The last time I taught introductory probability and statistics, I turned in my grades and asked my department chair to take me off the course permanently. I'd spent some time working on a committee to update the course and we'd modernized it roughly to my taste, so my chair was puzzled. The best I could offer by way of explanation was, "I just hate it." Then I went to France and taught their version of the same course. My stint in France lasted three weeks. Essentially, I was substitute teaching and not looking for more than an excuse to be in the country for a while. My students were second-year engineering students, pretty much like my students at home. And like my students, the French students were a few notches below elite. While the similarities between my home university and my French university were comforting, the contrasts in the probability/statistics courses could not have been more jarring. Anyone who has taught or learned in a U.S. mathematics department recently knows the typical introductory probability and statistics course. It involves an expensive, gassy textbook with lots of color pictures, word problems involving industrial applications, and charts to help students navigate problems. American students purchase the textbook and far too often, the ancillaries the bookstore peddles alongside the text. At my home university, the chair has some difficulty finding mathematics faculty willing to teach the course. While I can't speak for my colleagues, to me the course seems oddly estranged from mathematics. There is a section on probability, and we love that: the probability laws, the counting. It's possible to trick out that section and get a chewier piece of mathematics into the act, but, by and large, the course is a hodgepodge of recipes, motivated by problems involving IQ testing, rhesus monkeys, salamanders, and the like. Regardless of the text, there is almost invariably a peculiar pair of caveats presented as from on high: Never accept the alternative hypothesis, and never say the probability is 0.95 that the mean lies in a 95% confidence interval for the mean. I dreaded teaching it in France. The French course, though, was a different kettle of fish. No one expects French students to shell out money for books, so the course was based on notes produced by the instructor of record. The notes were spare and lacked attribution. They started with simple examples involving coins, dice, and lifetimes of electronic gadgets, what one would expect. The definition of sample space appeared on page one. (That was fast.) The definitions of sigma-algebra (Gasp! Are they joking?) and probability space (Is this a grad course?) appeared on page two. The course spooled out from there. Yes, it assumed more calculus than we do but mostly in the more interesting problems, and it treated testing and interval estimates in much the same way we do. No one was joking, and this was not a grad course: it was introductory prob/stats, in an unapologetically mathematical setting. Statistics is possibly the most important course we teach in mathematics: for life and for cultural literacy, a basic understanding of it is essential. The high schools teach it, yet I've heard excellent high school math teachers express fear, if not loathing, of the subject. An introductory probability and statistics course based on mathematics is missing, not just from the math education curricula, but from American soil altogether, as far as I can tell. While we teach these courses from bloated texts that avoid mathematics, we might seize the opportunity to teach a critical life skill—understanding statistics—through an exposition that glorifies its foundation in mathematics. A big chunk of statistics courses in the United States are taught by non-mathematicians, outside math and statistics departments. By the looks of things, students can often get by on facility with software and a foggy understanding of principles. We still see many of these students in the introductory course, though. Could we do better there? Could we rope these students in with mathematical ideas, and could this happen anytime soon? I don't know, but I'm hoping to go back to teach in France next year. About the author: Meg Dillon is a professor of mathematics at Southern Polytechnic State University in Marietta, Georgia. Aftermath essays are intended to be editorials and do not necessarily reflect the views of the MAA.
Search Find a Video Math Resources This link leads to a freely available on-line book, "Algebra Real-World (It's easier to understand than you think!)," written by Edward J. Farkas, Sc.D. This on-line book takes algebra out of the abstract and places it in a context that is readily understandable. In the high school curriculum, physics is the subject most relevant for providing this context. Teaching video lectures of prerequisite materials in arithmetic and algebra, presented by esteemed math teacher, Professor Herb Gross. This site is recommended both for students and for teachers—who want to see how to explain difficult concepts in crystal clear ways. In Zona Land Education, you will find educational and entertaining items pertaining to physics, to the mathematical sciences, and to mathematics in general. Use the search tools to find resources, which teach core math and science standards, integrate calculator and computer-based technologies, and introduce 21st Century concepts in the areas of fractal geometry, nanotechnology, and engineering. MathBits.com is devoted to offering fun, yet challenging, lessons and activities in secondary (and college level) mathematics and computer programming for students and teachers. Created by two mathematics teachers The Math Forum, developed by the Drexel University School of Education, is a leading online resource for improving math learning, teaching, and communication since. It is run by teachers, mathematicians, researchers, students, and parents using the power of the Web to learn math and improve math education. The Millennium Mathematics Project (MMP) is a maths education initiative for ages 5 to 19 and the general public, based at the University of Cambridge in England and active nationally and internationally. The program aims to support maths education and promote the development of mathematical skills and understanding, particularly through enrichment activities MathWorld is an extensive mathematical resource, provided as a free service to the world's mathematics and Internet communities as part of a commitment to education and educationa outreach by Wolfram Research, makers of Mathematica. This site, sponsored by +Plus Magazine: Living Mathematics, provides articles from the top mathematicians and science writers on topics as diverse as art, medicine, cosmology and sport. Shodor is a nonprofit organization serving students and educators by providing materials and instruction relating to computational science (scientific, interactive computing). Shodor Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. These pages have been provided by Professor David Eppstein of the Computer Science Department at the University of California in Irvine. They contain usenet clippings, web pointers, lecture notes, research excerpts, papers, abstracts, programs, problems, and other content related to discrete and computational geometry. Professor Eppstein writes that "while some of it is quite serious, I hope much of it is also entertaining This is a second site provided by Professor Eppstein. It collects various areas in which ideas from discrete and computational geometry (meaning mainly low-dimensional Euclidean geometry) meet some real world applications. It contains brief descriptions of those applications and the geometric questions arising from them, as well as pointers to web pages on the applications themselves and on their geometric connections. This site is for teachers, parents and students who seek engaging mathematics. Many of the topics are accompanied by Java illustrations. There are more than 900 Java applets. The applets can be licensed by teachers for inclusion in their own pages. The Math Nexus website brings experiences into mathematics classrooms each day as a collective resource for challenging problems, responses to teacher questions, and real-world uses of mathematics. It also includes announcements of conferences and workshops, humor, and mathematics history tidbits.
Excel HSC General Mathematics covers all the HSC topics for the current syllabus. It also features an explanation of the HSC course, a checklist of the topics in the Preliminary course, all the theory for each of the HSC topics with many fully worked examples, Practice questions, Challenge questions and a Topic Test at the end of each chapter, as well as Unit Tests and two sample HSC-style exam papers, all with Quick Answers and Worked Solutions, a comprehensive index and a Formulae Sheet. Features: - Anultra-compact summary of the preliminary course — a fast way of finding any gaps in your knowledge! - Aunique format where each worked example in every chapter has a matched question in its corresponding Further Practice section — this means there's an almost identical question for you to practise for each question in the chapter! - Hundreds of questions to practise on your own in the Further Practice section — what you need to get up to speed! - AChallenge section for each chapter with harder questions — questions that will get you top marks in the HSC! - AKey point Summary and Checklist for each chapter — the most important points summarised for you! - Two types of tests: Topic Tests, which contain HSC-type questions that test each chapter; and Unit Tests, which also feature HSC-type questions, but test all the chapters in each unit. - AFeedback Improvement System that clearly shows you a revision method once you get feedback from your test results — turn your feedback into even better results! - AQuick Answer section with answers for every question — the fastest way to mark your work! - AWorked Solution answer section with a worked solution to every question in the book — all the solutions at your fingertips! -Ticks in the worked solution answer section to show you the distribution of marks — know the breakdown of marks in each question! - Two examination papers — not one but two papers to practise before tackling the HSC exam! - 383 pages packed with notes, questions, worked examples and exam papers — what you need to succeed in the HSC!
Combo Class The Combo Class at Foothill HS in the Shasta Union HSD has a unique class structure. It was created by Mr. L with support from the Math Dept chair, Ms. Sheena McCloud. It has been operating with great success since the school year 2005-06. Many 8th grade students take algebra, understand quite a bit of the material, but are not as proficient as they could be with more exposure to the curriculum. At FHS we identify a core group of incoming 9th graders and place these students in the two-year Combo Class program. Some key facts about the Combo Class: All 25 CA Algebra 1 standards are covered in the freshman year A smooth transition to Algebra 2 curriculum is made in the second half of 9th grade Geometrical concepts critical to future success are covered in the first half of the 10th grade The remaining parts of the Algebra 2 curriculum (all 25 CA standards) are completed in the second half of the 10th grade The large majority of students leaving the Combo Class are ready for Trigonometry/Pre-Calculus their junior year 98% of the 06-07 and 07-08 freshmen scored Proficient on the CA STAR Algebra 1 test. 53% of the 06-07 freshmen and 70% of the 07-08 freshmen scored Advanced on the CA STAR Algebra 1 test; the state average is 2% Students learn how to use GeoGebra, a powerful problem-solving Algebra/Geometry/Calculus software The Combo Class is a rewarding course to teach, since it requires the teacher to stimulate and challenge high caliber students. It's exciting to watch the mathematical growth of these students over the course of two years.
Students write their names and birthdays on cupcake patterns, and use them for a classroom picture graph. Patterns for eye color picture graph. Each student colors their own. — "Math Worksheets - Graphing", Demonstrates how to solve quadratics by graphing, and explains why this is a poor method to use. — "Solving Quadratic Equations: Solving by Graphing", This section will help you better understand the coordinate plane and how to graph points on the plane. When graphing, the coordinate plane will be labeled with "tick marks" denoting the scale. — "Pre-Algebra: Basic Graphing - Math for Morons Like UsLearn about Graphing on . Find info and videos including: How to Plot a Graph With a Graphing Calculator, How to Perform 3D Graphs With a Graphing Calculator, How to Graph a Line Graph in Excel 2007 and much more. — "Graphing - ", Definition of graphing in the Online Dictionary. Meaning of graphing. Pronunciation of graphing. Translations of graphing. graphing synonyms, graphing antonyms. Information about graphing in the free online English dictionary and encyclopedia. — "graphing - definition of graphing by the Free Online", The Graphing module is used in conjunction with the viewing and printing modules to obtain a complete presentation of image motion data for biomechanical *ysis. First, individual data curves are specified and the data values are read and saved by the Graphing module. — "Graphing", Graphing calculators present a challenging task for mathematics teachers in the classroom. This digest offers four distinct methods for using graphing calculators in mathematics classrooms. — "Graphing Calculators in the Mathematics Classroom. ERIC Digest", Graphing. In this section we need to review some of the basic ideas in graphing. It is assumed that you've seen some graphing to this point and so we aren't going to go into great depth here. We will only be reviewing some of the basic ideas. — "Pauls Online Notes : Algebra - Graphing", tutorial.math.lamar.edu Major Steps of Graphing. This lesson has two major parts, easy and advanced. Whenever you need to draw a graph, you always need to follow the following guidelines. How to plot a nice graph with sweaty shaky hands. Determine what kind of function you are going to plot. — "Lesson on graphing functions", Recommended graphing calculators for advanced placement (AP) statistics and calculus. All of the recommended calculators received above-average ratings by users. — "Graphing calculators: Approved for AP Statistics and Calculus", TI Graphing Calculators for students of all levels of math, science, physics, engineering, calculus, applied studies and more. Many TI calculators are certified for use in standardized tests and college entrance exams that require a graphing. — "Graphing Calculators by Texas Instruments - US and Canada", There are six easy steps to creating graphs and tables on a graphing calculator. This list takes a look at 3 different graphing calculators that are the standard for any college or high school student. — "Graphing - Topic - Associated Content from Yahoo!", The intersection of X and Y is zero (which is not typically written on the graph) Both axes of the graph are given verbal labels and the total graph is given a clear concise title. — "Psych. Statistics: Graphing", uwsp.edu The following problems illustrate detailed graphing of functions of one variable using the first and second derivatives. If possible, determine the values of A and B so that the graph of y has a maximum value at x= -1 and an inflection point at x=1. — "Graphing Using First and Second Derivatives", math.ucdavis.edu To graph a linear equation, we can use the slope and y-intercept. Locate the y-intercept on the graph and plot the point. From this point, use the slope to find a second point and plot it. Draw the line that connects the two points. Homework. — "Graphing Equations and Inequalities - Graphing linear", Images related images for graphing Return to Top The IDE interface The Data Collection Interface When one or more test cases are selected the Coverage ysis function calculates the selected test cases percentage of weak and strong functiona l coverage Fewer Tests Dialog This feature allows you to enter in a number less than or equal to the number of total tests and have RBT determine which is the optimal subset of graphing d7 jpg the points the student is placing in this instance are not intended to be mathematical objects Since they are just there to help the student place the line properly WebAssign ignores them Also did you know there are short videos inside the Graphing Help for students who might be having trouble understanding how to use the graphing tool Many students missed those as well We different searches You specify the search with a regular expression and the title for the graph Each search created creates a graph which is displayed on a site like the picture below The search sends a request to a log server where I ve created an interface which then parses the log files and sends back the granulated information from the log file I then create a graph software this makes DeltaDash truly invaluable During live data capture 4 selectable graphs can be displayed However all ogue input channels can be logged for later ysis As an example the following ogue data may be retrieved from a 2002 Impreza WRX Stef leaning against a massive black metal thing No you can t take my picture I think I made something on a graphing calculator that looked like this once I judge modern sculpture by the ease it could be grabbed during a superhero fight and used as a weapon So this of their source To design test cases RBT first generates the list of Functional Variations These are the primitive combinations of data that must be tested RBT s Functional Variation Report Errors in the requirements logical consistency will show up in this report Graphing jpg Click button to the left to enlarge the graph You can also go into a high speed graphing mode by clicking the RED button at the lower right A scaling with Min Max can also be seen in black Here we can see Channel 3 in the enlarged mode By clicking the BLUE channel button to the left again you then go back into the 8 channels mode Is that simple x z2 x z3 After the graph is created you can change the line type marker type axis characteristics and figure charactreistics by using various menus as shown in the Figure below Want to know what load average has looked like for the last week No problem And add to this the ability to custom create graphs which can combine multiple keys into a single view If you see a screenshot with pretty graphs all over it on the Zabbix front page thats a Screen A screen is a page custom layed out with several custom graphs So you might want a graph Graphing Instructions AMIRGraphingCalc gif that everyone has weaknesses and that is why it is so important for everyone to work toghether in the classroom as a community to help each other learn and grow To see a sample graph click here The categories across the bottom can be adapted to suit your preferences Reading Writing Surveys Interviews Many To see a sample Reading Survey I developed to use with in two and three dimensions The following figure shows a sample of each type of chart Note In two dimensions bar and cylinder charts appear the same as do cone and pyramid charts CLIPSGraphing gif Więcej tylni tożsamość grzech 3x =3sin x 4sin3 x Students can use the graphing calculator in Microsoft Math View larger image Graphing Videos related videos for graphing Graphs of Quadratic Functions Introduction to Graphing in Excel 2010 (Win 7).mov In this video I show you the basics of creating a graph in Microsoft Excel 2010. You can find a collection of my iWork and MS Office tutorials at iws.collin.edu Graphing Linear Functions by Finding X,Y Intercept For more FREE math videos, visit !! Graphing Linear Functions by Finding the X-Intercept and Y-Intercept of the Function. The basic idea and two full examples are shown! Graphing the Trigonometric Functions Graphing the Trigonometric Functions - I do a quick sketch of the 6 trigonometric functions. For more free math videos, visit Graphing Quadratic Functions - - Algebra Help OUR LESSONS MATCHED TO YOUR TEXTBOOK/ STANDARDIZED TEST: Students are introduced to the parent graph for quadratic functions y = x^2. Students then learn how to graph quadratic functions, such as y = x^2 + 2, and how to identify the vertex, minimum, x- and y-intercepts, axis of symmetry, one pair of symmetric points, and the domain and range of the graph. Finally, students are asked to compare their graph with the parent graph for quadratic functions. Graphing Quadratic Functions - Example 1 Graphing Quadratic Functions - Example 1. In this video, I outline a little recipe of things to examine when graphing a quadratic function by hand. I then proceed to do one example of graphing a quadraticSolving a Linear System of Equations by Graphing Solving a Linear System of Equations by Graphing. In this video, I solve a relatively simple simple of linear equations by graphingMore trig graphs Determining the equations of trig functions by inspecting their graphs. Graphing Linear Inequalities - - Algebra Help For a complete lesson on graphing linear inequalities, go to - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to graph inequalities in two variables. For example, to graph y is less than x + 2, the first step is to graph the boundary line y = x + 2, using the chart method from lesson 4B. Note that greater than or less than means that the boundary line will be dotted, and greater than or equal to or less than or equal to means that the boundary line will be solid. To determine which side of the boundary line to shade, substitute a test point, such as (0, 0), into the original inequality, y is less than x + 2. Since (0) is less than (0) + 2, or 0 is less than 2, is a true statement, the side of the line that contains the point (0, 0) is shaded. Converting to Slope-Intercept Form and Graphing - Subscribe now to the Channel or go to for access to 1000+ online math lessons featuring a personal math teacher inside every lesson! Follow us at Facebook Follow us at MySpace: In this lesson, students learn to convert a linear equation to slope-intercept, or y = mx + b form, by getting y by itself on the left side of the equation. For example, to convert the equation x -- 3y = -12 to y = mx + b form, the first step is to subtract x from both sides to get --3y = -x -- 12. Notice that the x term is positioned before the number on the right side of the equation so that the equation will eventually match up with y = mx + b form. Next, divide both sides by --3 to get y = 1/3 x + 4. Now the problem is in y = mx + b form, with m = 1/3 and b = 4, and the line can be graphed using the slope and y-intercept. Graphing Systems of Equations - - Algebra Help For a complete lesson on graphing systems of equations, go to - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students the equation of that line. The Graphing Calculator Story Google TechTalks August 1, 2006 Ron Avitzur ABSTRACT It's midnight. I've been working six* hours a day, seven days a week. I'm not being paid. In fact, my project was canceled six months ago, so I'm evading security, sneaking into Apple Computer's main offices in the heart of Silicon Valley, doing clandestine volunteer work for an eight-billion-dollar corporation. For more info visit: Introduction to Graphing in Excel 2011 (Mac).mov In this video I give you the basic concepts and instructions for creating a graph in excel. In this way you can easily take your enzyme data and convert it into a variety of graphs that look clean and elegant. You can find a collection of my iWork and MS Office tutorials at iws.collin.edu Graphing a Rational Function - Example 1 Graphing a Polar Curve - Part 1 Graphing a Polar Curve. In this video, I discuss how to graph the polar curve r = 3cos(2theta). For more free math videos, visit Graphing trig functions *yzing the amplitude and periods of the sine and cosine functions. Math Made Easy: Creating Line Graphs In this video, I show you how easy it can be to create a line graph. Graphing a Polar Curve - Part 2 Graphing a Polar Curve. In this video, I discuss how to graph the polar curve r = 3cos(2theta). For more free math videos, visit Graphing a Trig Function MORE AT Graphing Trig functions: Phase ShiftVideoExcel - How to create graphs or charts in Excel 2010 (Charts 101) This tutorial shows how to add a chart in Microsoft Excel 2010. The tutorial walks you through an example of a creating a bar chart but you can choose the chart that suits your needs. It also shows how to change the chart design, layout and format. You will learn to add or edit the chart legends, add or remove gridlines, change the style of information displayed on the horizontal and vertical axis. This tutorial also covers the placement of data labels within the chart. An example of adding a trend line is also shown in this Excel 2010 tutorial. A14.9 Graphing Linear Equations From /Graphing-Linear-Equations the following video shows how to graph a linear equation using the slope and y-intercept. For more math help check out On Twitter twitter about graphing Blogs & Forum blogs and forums about graphing "Graphing Forum Cop. Re: Graphing " Reply #2 on: February 07, 2009, 01:14:20 PM " It is definitely possible to graph the data in real time. You need to validate the PIDs, and use the "record" button (not the "monitor" button). I asked Palmer Performance to reply with more details" — Graphing, "Langwitches Blog " We Need More Examples from the Classrooms! one of my latest blog post describing a SmartBoard lesson "Graphing on the Smartboard for" — Langwitches Blog " Graphing on the SmartBoard for the Little Ones, "Blog. About Us. The ROI Revolution Blog. Main. New Graphing Options. April 4, 2008. Today Google released new These graphing features are found right below the date selection tool, above the timeline, and can be found on all reports within" — New Graphing Options, "The graph used the open source PHPlot graphing class in order to draw a line graph definately be considered if you want graphing in your application" — - Entries tagged as Graphing, "Live Blog: Graphing Social Patterns, Day 3, Opening the Social Graph Live Blog: Graphing Social Patterns, Day 3, FB Apps with , Silverlight, and Popfly" — geek!daily: Graphing.Social, "less helpful Graphing Stories, Vol. 1 [zipped iso, 755mb] The Love. If you're all about the love, be a friend and link this post from your blog. I'll send out 20 DVDs to the first 20 bloggers who link this up and send a mailing address to dan at mrmeyer dot com" — dy/dan " Blog Archive " Graphing Stories,
Mathematics and Statistics Recommended Tracks Through College Algebra, Pre-calculus, and Calculus There are several different programs on campus that require students to take a series of pre-calculus and calculus courses. Sometimes students switch programs midway through the typical course sequence and need to be advised how to finish. Here are some possible tracks to calculus for students who must start in one of the courses that precede calculus. All course descriptions may be found together here. Students must get a C or higher in each course in order to go on to the next course listed. Routes to Math 1260, Basic Calculus 1300 - 1260 for students who have had trigonometry and place into Math 1300. 1280 - 1260 for students who have had trigonometry and place into Math 1280 1220 - 1260 for students who have not had trigonometry but have fairly good algebra skills 1210 - 1220 - 1260 for students who need more time with basic algebra skills 95 - 1210 - 1220 - 1260 for students with weak algebra backgrounds Recommended routes to Math 1310 or (1340 and 1350), Calculus and Analytic Geometry I 1300 - 1310 for the well-prepared student who places into Math 1300 1280 - 1310 for the well-prepared, motivated, and mature student (these are both five-hour courses) 1280 - 1340 - 1350 for the well-prepared student who needs a less intense calculus course spread over two semesters 1220 - 1300 - 1340 - 1350 for a student who does extremely well in 1220 and is anxious to make an agressive run through precalculus (Math 1300). 1220 - 1280 - 1340 - 1350 for the typical student who places into Math 1220. Math 1280 is a five-hour course, but only three of those hours count toward graduation because of the overlap with 1220. For most students in Math 1220, Math 1280 will be a better choice than Math 1300 because it covers roughly the same topics but meets two additional times per week. It contributes the same number of hours toward graduation as 1300. 1210 - 1220 - 1280 - 1340 - 1350 for students who place into Math 1210. This is a long sequence of courses, but our experience has shown that skipping any course in the sequence works poorly. Students who want to shorten this sequence of courses may choose to study independently or with a private tutor and re-take the placement test to try to skip over a course.
[Protip] Watch the answer video for unit 2-21 4 1 I know sometimes folks skip answer videos after quizzes when they got them right on the first try. In general, you should make sure to watch the answer videos, because they sometimes have extra content in them. For example, in unit 2-28, there is an interesting digression into the history of computing. Very true - I learned a lot about how the instructors think from seeing how they solved the problems in the quizzes - this helped me anticipate the approaches they were looking for in the homework (test other values for the variables, test other values for the variables became my mantra, but only because of how the instructor delivered the answer videos.)
Ace the MAT and prepare for the next phase in your education! McGraw-Hill's MAT Miller Analogies Test, Second Edition , gives you the names and terms you need to know to solve Miller Analogies. It provides lists, definitions, and descriptions of the names and terms in fields such as literature, art, music, mathematics, and the natural and social... more... Peterson's Graduate Programs in the Physical Sciences, Mathematics, Agricultural Sciences, the Environment & Natural Resources contains a wealth of information on colleges and universities that offer graduate work in these exciting fields. The institutions listed include those in the United States and Canada, as well international institutions that... more... This new edition of The SAT For Dummies gives you the information you need to focus on those areas that are most problematic and to ensure that you achieve the best possible score. Whether you're struggling with math, reading, or writing essays, this updated guide offers advice for tackling the toughest questions, as well as hints and tips for making Praise for previous edition: 'Reader-friendly format and wide-ranging coverage of material... this will be useful as a pre-course reader to new students and as a companion during the course' - Journal of Advanced Nursing The new edition of Study Skills for Nurses will help students develop the skills and techniques needed for stress-free... more... Watch Tom Burns introduce his book Essential Study Skills - Second Edition. Watch Sandra Sinfield discuss one of her favourite chapters - how to make the best notes. Praise for the first edition: The effect on our students was like star dust!". Anne Schofield, Ruskin College, Oxford. Student feedback from Study Skills sessions at London Metropolitan... more...
What is Basic Algebra? That is my question! So many students and parents ask for instruction on basic Algebra. But... Algebra is NOT Basic! It can actually be very complex. There are a few basic skills that you must MASTER before diving into the heart of Algebra. Most of these skills you learned in your Pre-Algebra course, but I'll review them here. If you're not sure if you need to review the basic skills, take the Algebra Readiness Test! It's only 30 questions and it won't take you long! Remember... math has a spiral effect. Each new skill builds on a previously learned skill. So, at least review these topics if you need to freshen up on your Algebra skills. Below you will find the lessons and practice problems for the unit. Click on the topic that you need help with or follow along in order for a complete study of skills that you will need to be successful in Algebra 1. If you find that you need more practice or more in-depth instruction on these topics, then don't miss out on my FREE e-course and video tutorials on Algebraic Expressions. You will find video tutorials and a lot of practice problems for integers, algebraic expressions, the distributive property, matrices, and formulas.
books.google.co.nz - This... interactive introduction to mathematical analysis An interactive introduction to mathematical analysis This study of real analysis. The companion onscreen version of this text contains hundreds of links to alternative approaches, more complete explanations and solutions to exercises; links that make it more friendly than any printed book could be. In addition, there are links to a wealth of optional material that an instructor can select for a more advanced course, and that students can use as a reference long after their first course has ended. The CD provides exercises that can be worked interactively with the help of the computer algebra systems that are bundled with Scientific Notebook. Great book. Mathematicians should use a language that is simple enough to comprehend the complexity in this field, usually in math books we see the opposite, i.e. writers use complicated language to present simplicity and leave the readers lost. This books grabs your interest, keeps you wanting for more. The smartness lies in making people understand what you know or atleast what they should know. Then, we have a great teacher. Finding an analysis book that speaks to me mind to mind really makes me happy. I unfortunately, cannot speak for all the chapters but certain topics that I looked up on this online book were the boundedness of sets, and I am looking forward for the rest.
Description Now with offline access functionality, CourseSmart offers instructors and students the freedom and convenience of online, offline, and mobile access using a single platform. CourseSmart eTextbooks do not include media or supplements that are packaged with the bound textbook. Table of Contents 1. Variables, Real Numbers, and Mathematical Models 1.1 Introduction to Algebra: Variables and Mathematical Models 1.2 Fractions in Algebra 1.3 The Real Numbers 1.4 Basic Rules of Algebra Mid-Chapter Check Point Section 1.1–Section 1.4 1.5 Addition of Real Numbers 1.6 Subtraction of Real Numbers 1.7 Multiplication and Division of Real Numbers 1.8 Exponents and Order of Operations Chapter 1 Group Project Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Test 2. Linear Equations and Inequalities in One Variable 2.1 The Addition Property of Equality 2.2 The Multiplication Property of Equality 2.3 Solving Linear Equations 2.4 Formulas and Percents Mid-Chapter Check Point Section 2.1–Section 2.4 2.5 An Introduction to Problem Solving 2.6 Problem Solving in Geometry 2.7 Solving Linear Inequalities Chapter 2 Group Project Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Test Cumulative Review Exercises (Chapters 1–2) 3. Linear Equations and Inequalities in Two Variables 3.1 Graphing Linear Equations in Two Variables 3.2 Graphing Linear Equations Using Intercepts 3.3 Slope 3.4 The Slope-Intercept Form of the Equation of a Line Mid-Chapter Check Point Section 3.1–Section 3.4 3.5 The Point-Slope Form of the Equation of a Line 3.6 Linear Inequalities in Two Variables Chapter 3 Group Project Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Test Cumulative Review Exercises (Chapters 1–3) 4. Systems of Linear Equations and Inequalities 4.1 Solving Systems of Linear Equations by Graphing 4.2 Solving Systems of Linear Equations by the Substitution Method 4.3 Solving Systems of Linear Equations by the Addition Method Mid-Chapter Check Point Section 4.1–Section 4.3 4.4 Problem Solving Using Systems of Equations 4.5 Systems of Linear Inequalities Chapter 4 Group Project Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Test Cumulative Review Exercises (Chapters 1–4) 5. Exponents and Polynomials 5.1 Adding and Subtracting Polynomials 5.2 Multiplying Polynomials 5.3 Special Products 5.4 Polynomials in Several Variables Mid-Chapter Check Point Section 5.1–Section 5.4 5.5 Dividing Polynomials 5.6 Dividing Polynomials by Binomials 5.7 Negative Exponents and Scientific Notation Chapter 5 Group Project Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Test Cumulative Review Exercises (Chapters 1–5) 6. Factoring Polynomials 6.1 The Greatest Common Factor and Factoring By Grouping 6.2 Factoring Trinomials Whose Leading Coefficient Is 1 6.3 Factoring Trinomials Whose Leading Coefficient Is Not 1 Mid-Chapter Check Point Section 6.1–Section 6.3 6.4 Factoring Special Forms 6.5 A General Factoring Strategy 6.6 Solving Quadratic Equations By Factoring Chapter 6 Group Project Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Test Cumulative Review Exercises (Chapters 1–6) 7. Rational Expressions 7.1 Rational Expressions and Their Simplification 7.2 Multiplying and Dividing Rational Expressions
Algebra, Part 1 The goal of this first course in the Algebra series is to enable students to develop the mathematical skills they need to solve problems in algebra. Topics Course MTH-401. Media: LP, (B coming soon). Lessons: 6 chapters, 10 assignments. Algebra, Part 1 Course ID: MTH-401 Audience Adult Continuing Education Program and High School Program Course Description The goal of the Algebra series is to enable students to develop the mathematical skills they need to solve problems in algebra. Topics in this first course Media large print Organization Six chapters, ten assignments Credit Students who successfully complete both "Algebra, Part 1" and "Algebra, Part 2" earn 1 high school credit or Carnegie Unit. Prerequisites To enroll in this class, a student needs one of the following prerequisites: - successful completion of the "Pre-Algebra" series - instructor's approval based on placement test Overview Students submit ten assignments to the instructor. Grading letter grades Objectives and Content Chapter 1: Solving Equations After completing this chapter, the student will be able to a. tell whether a given number is the solution of an equation b. show that two equations are equivalent c. use the properties of equality to make equivalent equations d. use inverse operations to solve equations e. solve equations using subtraction f. solve equations using addition g. solve equations using multiplication h. solve equations using division i. solve equations using more than one operation j. solve equations containing parentheses k. solve equations with the variable on both sides Chapter 2: Introducing Functions After completing this chapter, the student will be able to a. give the location of a point on the coordinate plane b. graph ordered pairs on the coordinate plane c. write and graph ordered pairs from a table d. find at least three ordered pairs for a given equation e. tell without graphing whether each group of ordered pairs is a function f. find the value of a function g. use a bar graph or table to answer questions Chapter 3: Linear Equations and Functions After completing this chapter, the student will be able to a. tell whether an ordered pair is the solution to an equation b. graph linear equations c. find the slope of a line from two points on the line d. find the slope of a line from its graph e. use a pair of points to tell if the lines are parallel or perpendicular f. find the x-intercept and y-intercept of a line g. use the slope-intercept form to find the slope and y-intercept of a line h. write an equation in slope-intercept form Chapter 4: Writing Linear Equations After completing this chapter, the student will be able to a. find the equation of a line by using the slope and y-intercept b. find the equation of a line by using a point and the slope c. find the equation of a line by using two points on the line Chapter 5: Inequalities After completing this chapter, the student will be able to a. graph the solution of an inequality on a number line b. solve inequalities using addition or subtraction c. solve inequalities using multiplication or division d. solve inequalities using more than one step e. tell whether a point on the number line belongs to the graph of an inequality Chapter 6: Systems of Equations After completing this chapter, the student will be able to a. tell whether a given ordered pair is the solution to a given equation b. solve a system of linear equations using substitution c. solve a system of linear equations using addition or subtraction d. solve a system of linear equations using multiplication or division e. solve a system of linear equations using more than one equation
Contemporary's Number Power 9: Measurement Book Description: Number Power is the first choice for those who want to develop and improve their math skills. Every Number Power book targets a particular set of math skills with straightforward explanations, easy-to-follow, step-by-step instruction, real-life examples, and extensive reinforcement exercises. Use these texts across the full scope of the basic math curriculum, from whole numbers to pre-algebra and geometry. Number Power 9: Measurement topics include length, angles, weight, temperature, capacity, volume, time, and velocity. Both English and metric units are covered.
This course is a comprehensive study of mathematical skills which should provide a strong mathematical foundation to pursue further study. Topics include principles and applications of decimals, fractions, percents, ratio and proportion, order of operations, geometry, measurement and elements of algebra and statistics. Upon completion, students should be able to perform basic computations and solve relevant, multi-step mathematical problems using technology where appropriate. This course covers skills and strategies designed to improve study behaviors. Topics include time management, note taking, test taking, memory techniques, active reading strategies, critical thinking, communication skills, learning styles and other strategies for effective learning. Upon completion, students should be able to apply appropriate study strategies and techniques to the development of an effective study plan. CORE 4 Competency: Personal Growth and Responsibility: the ability to understand and manage self, to function effectively in social and professional environments and to make reasoned judgments based on an understanding of the diversity of the world community.
by Virtual Dynamics Org Visual Mathematics, is a Mathematical Visualizer (containing -at least- 67 modules) to learn more and better in less time. Enjoy learning!!! . Get to really Understand what you Study !!! by Virtual Dynamics Org Panageos is oriented to the intensive solution of problems on Plane Analytic Geometry. The main feature of Panagoes is its power to read the user's equations and interpret them, for this reason the data input is exclusively through the keyboard. by Virtual Dynamics Org Curvilinear: Easy Learning Plane Analytic Geometry An Intuitively-Easy-To-Use visual interactive software, oriented to overcome the abstraction that exists in the Plane Analytic Geometry (PAG), this is a tool that makes it easy to master PAG. by SolidLearning, Inc. mBasics makes math worksheets for addition, subtraction, multiplication and division. Generate worksheets and assign them to students for testing. Automatic grading and customizable by RomanLab Software Powerful yet easy-to-use graph plotting and data visualization software. You can plot and animate 2D and 3D equation and table-based graphs. The unlimited number of graphs can be plotted in one coordinate system using different colors and lighting.
Keeping it R.E.A.L.: Research Experiences for all Learners Carla Martin and Anthony Tongen Keeping it R.E.A.L.: Research Experiences for All Learners is a collection of computational classroom projects carefully designed to inspire critical thinking and mathematical inquiry. This book also contains background subject information for each project, grading rubrics, and directions for further research. Instructors can use these materials inside or outside the classroom to inspire creativity and encourage undergraduate research. R.E.A.L. projects are suitable for a wide-range of college students, from those with minimal computational exposure and precalculus background to upper-level students in a numerical analysis course. Each project is class tested, and most were presented as posters at regional conferences. Note: Teachers may copy or print out the activities or projects to use as handouts for their students. Print-on-Demand (POD) books are not returnable because they are printed at your request. Damaged books will, of course, be replaced (customer support information is on your receipt). Please note that all Print-on-Demand books are paperbound.
Mathematics The career of a mathematician in all of its various forms has been rated as one of the top five jobs by The Jobs Rated Almanac. Mathematicians are typically held in high regard on the basis of their demonstrated proficiency with numbers and formulas, and with logical problem-solving skills. Careers for mathematics majors cover a wide range of opportunities. Mathematicians are employed by banks, investment companies, and insurance companies where quantitative skills are essential. Mathematics teachers continue to be in demand. Computer Applications Computers are utilized in a mathematics classroom. Mathematical software allows mathematics to be studied in three representations: numeric, symbolic, and graphic. Equipment/Facilities Students currently have access to the college's network of interconnected computers and a large mathematics classroom. The new computer-equipped classroom gives students access to a large lab which uses mathematics software. While a great deal of work in mathematics still uses pencil and paper, students are no longer restricted to those tools. Calculators and computers provide efficient means of solving a wide range of problems, giving students the chance to concentrate on underlying principles. Students are encouraged to take advantage of these whenever possible. Off-Campus Programs Students who choose to do so may apply to participate in the Oak Ridge Science Semester at the Oak Ridge National Laboratory in Tennessee. Students spend part of their time during the semester taking mathematics and science courses, and part of their time working with ongoing research projects at the National Laboratory. Summer internships and research opportunities are often available for undergraduate mathematics students. These are typically sponsored by the National Science Foundation and other government research agencies, and give students the chance to engage in hands-on research activities at a large university. Usually housing and meals are provided, and students are paid a stipend for their summer work. Graduate School Opportunities Graduate school programs in mathematics actively seek qualified students. Assistantships and fellowships are available which waive tuition, and pay the graduate student a stipend. Mathematics graduates area also recruited by other graduate programs. Students with good quantitative and problem-solving skills are well suited for graduate studies in business administration (the M.B.A. degree) and law, as well as graduate programs in engineering and computer science. Teacher Certification Those preparing for secondary level Mathematics teaching must complete the major as specified above and MATH 324. The additional requirements for certification are described in the Education Department section of the catalog.
Book Description: Get a good grade in your precalculus course with Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH and it's accompanying CD-ROM! Written in a clear, student-friendly style and providing a graphical perspective so you can develop a visual understanding of college algebra and trigonometry, this text provides you with the tools you need to be successful in this course. Preparing for exams is made easy with iLrn, an online tutorial resource, that gives you access to text-specific tutorials, step-by-step explanations, exercises, quizzes, and one-on-one online help from a tutor. Examples, exercises, applications, and real-life data found throughout the text will help you become a successful mathematics student!
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 Designed to give undergraduate engineering students a practical and rigorous introduction to the fundamentals of numerical computation. This book is a thoroughly modern exposition of classic numerical methods using MATLAB. The fundamental theory of each method is briefly developed. Rather than providing a detailed numerical analysis, the behavior of the methods is exposed by carefully designed numerical experiments. The methods are then exercised on several nontrivial example problems from engineering practice. The material in each chapter is organized as a progression from the simple to the complex. This leads the student to an understanding of the sophisticated numerical methods that are part of MATLAB. An integral part of the book is the Numerical Methods with MATLAB (NMM) Toolbox, which provides 150 programs and over forty data sets. The NMM Toolbox is a library of numerical techniques implemented in structured and clearly written code. Features & benefits Clarity—Development of the numerical methods is self-contained, complete, and uncluttered. Each chapter begins with the simplest routine for a particular class of problems, and then develops progressively more sophisticated routines. The goal is not necessarily to be exhaustive, but rather to introduce more powerful methods as enhancements to simpler methods. At the end of the chapter the student is prepared to use the built-in MATLAB routines correctly and with confidence. Ex.___ Emphasis Of Application Over Theory—The mathematical foundation of each method is developed, but the emphasis of the presentation is on the application of numerical methods. The text is well-suited to engineering students who need a rigorous presentation of the numerical algorithms, without getting bogged down in a theoretical treatment of each method. Ex.___ Companion Website—With many support resources. Numerical Experiments—Behavior of the numerical methods is demonstrated by numerical experiments instead of by mathematical proof. The theoretical performance (e.g. convergence rate, truncation error) of a method is stated and then verified by solving a well-defined problem with known solution. MATLAB Reference—The book contains an extensive reference to using MATLAB. This includes interactive (command line) use of MATLAB, MATLAB programming, plotting, file input and output. NMM Toolbox—The code supplied with the book is organized into a library of reusable components. All programs in the NMM Toolbox are structured, concise, efficient, and use the MATLAB idiom. The Toolbox contains almost 150 programs and over forty data sets from a variety of applications. Once the NMM Toolbox is installed readers can execute all of the examples in the book and apply the NMM Toolbox code to problems of their own choosing. Ex.___ Over 130 Examples—Each chapter contains a large number of examples of two basic types. One type of example demonstrates a principle or numerical method in the simplest possible terms. Another type of example demonstrates how a particular method can be used to solve a more complex practical problem. Over 300 Problems—End-of-Chapter problems cover all aspects of the methods presented in the book. Each problem is rated on a difficulty/effort scale. Flexibility—The book provides more material than would usually be covered in a one-semester course. The text is heavily cross-referenced so that supporting material from other chapters can be easily located. Supplemental Material—Study guides, lecture slides, and in-class worksheets are available via the web. This extensive supplemental material makes it easy to adopt and adapt the text according to the interests of an individual instructor. Ex.___ Author biography GERALD RECKTENWALD is an Associate Professor of Mechanical Engineering at Portland State University, and regularly teaches courses in Numerical Methods.
Lessons and Resources Core Math Tools is a downloadable suite of interactive software tools for algebra and functions, geometry and trigonometry, and statistics and probability. The tools are appropriate for use with any high school mathematics curriculum and compatible with the Common Core State Standards for Mathematics in terms of content and mathematical practices. Java required. The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
Calculus definition, a method of calculation, esp. one of several highly systematic methods of treating problems by a special system of algebraic notations, as d See more. — "Calculus \| Define Calculus at ", Calculus is the BEST thing ever created by man or beast. Invented sometime in the 18th century, it represents a culmination of love toward high school students. There are ten types of Calculus so far: Pre Calculus, Fun Calculus, I Love My Math. — "Calculus - Uncyclopedia, the content-free encyclopedia", Historically, it was sometimes referred to as "the calculus", but that usage is seldom seen today. Calculus has widespread applications in science and engineering and is used to solve complicated problems for which algebra alone is insufficient. — "Calculus", schools- Calculus is a central branch of mathematics, developed from algebra and geometry. The word stems from the nascent development of mathematics: the early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, and the Latin. — "Calculus - Psychology Wiki", Calculus on the Web. The COW Library - Click on a button below to open a book. General in for a recorded session, click on the Login button. Login help. Calculus on the Web was. — "Calculus on the Web", math.temple.edu For other uses of the term calculus see calculus (disambiguation) The first idea, called differential calculus, is about a vast generalization of the slope of a line. — "Calculus - Definition", e-Calculus is a Calculus I tutorial written in TeX and converted to the Adobe PDF format. Features include typeset quality mathematics, verbose discussion of topics, user interactivity, and pop-up graphics. — "e-Calculus", math.uakron.edu Calculus. A printable version of Calculus is available. (edit it) This wikibook aims to be a quality calculus textbook through which users may master the discipline. Standard topics such as limits, differentiation and integration are covered as well as several others. — "Calculus - Wikibooks, collection of open-content textbooks", Images Mail Phone Fax Marketing Math Club Mathematics calculus jpg Calculus 2d jpg 2006 12 14 第三次小考考卷 Mudkip Card Art My favorite of the Kids WB contest entries and pretty much everyone else s favorite out of everyone who s seen it I kind of want to redo it someday Calculus In my old high school math class we used to complain about how hard calculus would be once we got around to learning it Our teacher would tell us Oh you can teach a monkey to Calculus Placement Test Sample Questions and Solutions for students majoring in mathematics or engineering Here is the kind of stuff I had fun with in college well before we got on to more of the electrical stuff calculus jpg Table of Contents \|\| As a kid my dad would bring me back a new Tintin album each time he went away on a business trip I loved Tintin then and I still do today and now as a professional designer I have an Calculus jpg Page 1 Page 2 Sammy proves the h cobordism theorem February 2002 A lot has happened since last time It s been quite a while Ruminating pondering thinking reflecting taking a break maybe being a bit lazy and all that I ve had it with Calculus I couldn t take it anymore I didn t want And here is the integration to find the cross sectional area of the FVA screw in the powertube The area marked a1 is half of the cross sectional area that the FVA screw takes up when the contact area with the PT is wider than or equal to the width of the FVA screw itself The striped Videos Calculus: Maximum and minimum values on an interval 2 examples of finding the maximum and minimum points on an interval. Calculus: Derivatives 1 (new HD version) Calculus-Derivative: Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line) This Is Calculus Chorus: One: This is Calculus I'm always integratin' Calc is the subject To which I'm masturbatin' Integration of The number known as e For e to the u du dx It's e to the u plus c If you gotta problem That you cannot do Take it to John Rogers And he'll solve it just for you Whether he's at home Or riding on the bus He'll get his pen and paper out And solve that Calculus So if you have no life And study just like me For indefinite integrals You always add ac If you have a cusp It never differentiates What...When...Knowing? Is chillin' wit related rates First derivative test You can find a min or max These critical numbers come out o' me Just like I took Ex-Lax People say it's hard and they start to whine They ask me how I do it and simply I reply... Two: I took the AP test On the ninth of May Opened up Part II And said "Man this *** is gay" I thought I'd make a run for it And book it out the door But I'd probably get arrested And tortured by College Board So I looked down at the booklet It said find the change in y Time for the Titanium ...TI-89 On to derivatives Or slopes of the tangent lines The rules for derivin' products ... Calculus - Infinite Limits Calculus - Infinite Limits. In this video I calculate a few limits where the solutions are either +/- infinity or the limits do not exist. For more free math videos, visit Stand and Deliver - What's calculus? The best line in the movie. Calculus Help: Integrals I in 20 Minutes (The Original) by Thinkwell Want to see the ENTIRE Calculus in 20 Minutes for FREE? Click on this link to see all 20 minutes in the full multimedia environment. Calculus 1.1: Functions The first section in the Calculus I sequence. We cover the definition of a function, its domain and range, and how functions might be used in calculus. Calculus: Derivatives 2 More intuition of what a derivative is. Using the derivative to find the slope at any point along f(x)=x^2U + Me = Us (Calculus) 2gether Fundamental Theorem of Calculus Part 1 Fundamental Theorem of Calculus Part 1 - Derivatives of Integrals. In this video I show the FTC part 1 and show 4 examples involving derivatives of integrals. For more free math videos, visit Optimization with Calculus 1 Find two numbers whose products is -16 and the sum of whose squares is a minimum. What is Calculus? This clip provides an introduction to Calculus. More information can be found at . Calculus: Derivatives 0.5Jacob Barnett teaches us Calculus 2. Techniques of Integration Jake talks about Trig integrals on a "back of the house" calculation Big Picture of Calculus Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations, such as: * driving a car * climbing a mountain * growing to full adult height View the complete course at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu Dancing Honeybee Using Vector Calculus to Communicate How honeybees communicate with each other. Waggle dance of bees Calculus: Implicit Differentiation Help: LimitsOptimization with Calculus 2 Find the volume of the largest open box that can be made from a piece of cardboard 24 inches square by cutting equal squares from the corners and turning up the sides. Calculus: Related Rates 0 YMoreI Will Derive! I parody of "I Will Survive" that I did with a couple of my friends for our Calculus and Physics classes. Lyrics: At first I was afraid, what could the answer be? It said given this position find velocity. So I tried to work it out, but I knew that I was wrong. I struggled; I cried, "A problem shouldn't take this long!" I tried to think, control my nerve. It's evident that speed's tangential to that time-position curve. This problem would be mine if I just knew that tangent line. But what to do? Show me a sign! derive. Find the derivative of x position with respect to time. It's as easy as can be, just have to take dx/dt. I will derive, I will derive. Hey, hey! And then I went ahead to the second part. But as I looked at it I wasn't sure quite how to start. It was asking for the time at which velocity Was at a maximum, and I was thinking "Woe is me." But then I thought, this much I know. I've gotta find acceleration, set it equal to zero. Now if I only knew what the function was for a. I guess I'm gonna have to solve for it someway. ... Calculus: Fundamental Theorem of Calculus, Part II for a bundle of videos on the Fundamental Theorem of Calculus. For an even broader bundle of videos that cover the Fundamental Theorem of Calculus and Integration Basics Or, for access to this single video, go to: The Second part of the Fundamental Theorem of Calculus provides the link between velocity and area. It states that the sum of the area under the curve between two points (A and B) is equal to the difference of the antiderivatives of A and B. Thus, to find the area under a curve between two points, you will take the difference of the derivatives calculated at the end points, A and B. This theorem enables you to evaluate definite integrals by finding the area between the function described and the X axis. The lesson will also cover proper notation that shoud be used to denote what you're evaluating over which interval. You will also work problems that involve trigonometric functions (like finding the area under a portion of the sine curve or cosine curve) This lesson explains the second half of the Fundamental Theorem of Calculus. To see the fist half of the explanation, check out: Taught by Professor Edward Burger, this lesson was ... Calculus: Logarithmic Differentiation Finding the slope of a tangent line to a curve (the derivative). Introduction to Calculus. Optimization with Calculus 3 A wire of length 100 centimeters is cut into two pieces; one is bent to form a square, and the other is bent to form an equilateral triangle. Where should the cut be made if (a) the sum of the two areas is to be a minimum; (b) a maximum? (Allow the possibility of no cut.) Calculus Rhapsody Calculus Rhapsody By Phil Kirk & Mike Gospel Is this x defined? Is f continuous? How do you find out? You can use the limit process. Approach from both sides, The left and the right and meet. Im a just a limit, defined ***ytically Functions continuous, Theres no holes, No sharp points, Or asymptotes. Any way this graph goes It is differentiable for me for me. All year, in Calculus Weve learned so many things About which we are going to sing We can find derivatives And integrals And the area enclosed between two curves. Y prime oooh Is the derivative of y Y equals x to the n, dy/dx Equals n times x To the n-1. Other applications Of derivatives apply If y is divided or multiplied You use the quotient And product rules And dont you forget To do the dance Also oooh (dont forget the chain rule) Before you are done, You gotta remember to multiply by the chain (Instrumental solo) I need to find the area under a curve Integrate! Integrate! You can use the integration Raise exponent by one multiply the reciprocal Plus a constant Plus a constant Add a constant Add a constant Add a constant labeled C (Labeled C-ee-ee-ee-ee) Im just a constant Nobody loves me. Hes just a constant Might as well just call it C Never forget to add the constant C Can you find the area between f and g In-te-grate f and then integrate g (then subtract) To revolve around the y-axis (integrate) outer radius squared minus inner radius squared (multiplied) multiplied by pi (multiply) Multiply the integral by ... The Two Questions of Calculus Do you wish that Professor Burger was your teacher? Click the link to learn more about Thinkwell's Online Video Calculus Course. AP CALCULUS: Third Period Don LaFontaine and Broken Vacuum present "AP Calculus: Third Period" Where will you be when it's test time? View all of Broken Vacuum's movies at A huge thanks to Don LaFontaine who is the coolest person to ever exist. "Calculus Made Easy (Free book) OK, it looks old and dusty, but Calculus Made Easy [PDF] is an excellent book and I strongly recommend it to those of you who are struggling with calculus concepts. It's also great for teachers, to give you ideas" — Calculus Made Easy (Free book) :: squareCircleZ, "The fun part for Calculus is that, because the given continuous function is positive forum/t-163369/calculus-ii#post- Help \| Terms of Service \| Privacy" — Per page discussions: Calculus II, "Views expressed in these public forums are not endorsed by Drexel University or The Math Forum. Read-only archive of The College Board's Advanced Placement Calculus mailing list" — Math Forum Discussions - ap-calculus,
The goal of this series is to provide readers with a strong foundation in Algebra. Each book is designed to develop readers' critical thinking and problem-solving capabilities and prepare readers for subsequent Algebra courses as well as "service" math courses. Topics are presented in an interesting and inviting format, incorporating real world sourced data and encouraging modeling and problem-solving. The Real Number System. Linear Equations and Inequalities in One Variable. Problem Solving. Linear Equations and Inequalities in Two Variables. Systems of Linear Equations and Inequalities. Exponents and Polynomials. Factoring Polynomials. Rational Expressions. Roots and Radicals. Quadratic Equations and Functions. For anyone interested in introductory and intermediate algebra and for the combined introductory and intermediate algebra.
How do you have projects in math? X.x I never had projects in math. Just a bunch of homework to do Dx
Gambrills CalculusIt has amazing plotting capabilities with both 2-D and 3-D plots. It also provides a vast array of statistical functions including means, variances, medians, and modes of data sets. It can also generate random data from uniformly distributed and normally distributed random variables for use in monte carlo simulations. ...My method of tutoring is mostly "hands on" with the use of a personal-sized white board. With the white board, the students are able to display to me their knowledge of the concept and topic in order for me to assist if they understand. I am also able to display the mathematical concept and topic pictorial to them.
Course Outline Rationale: This course line was developed in response to the changing mathematical requirements in the work place. The increased use of technology and the way information is communicated has changed significantly in the last 20 years. This course was developed to give students practical hands on mathematics that they will use in the jobs that they work at after high school. Units: Unit A: Systems of Inequalities Unit B: Quadratic Functions Unit C: Scale Unit D Trigonometry Unit E: Statistics Unit F: Proofs Unit G: Problem Solving Unit H: Personal Finacne The units may not be taught in the order listed above. Each unit will be allotted approximately two weeks. This means there will be a test about every two weeks.
Algebra Placement Exam - Study Guide 1 Purpose of this document There are currently four ways to become eligible to enroll in any of th 100 level math classes at The University of Montana Western 1. Pass MATH 007 with a C- or better. 2. Earn a score of 520 or higher on the math section of the SAT or 22 or higher on the math section of the ACT. 3. Earn a C- or better on a transferrable course from another university. This course must be equivalent to MATH 007 or any of the 100 level math classes offered at the University of Montana Western. 4. Pass the math placement exam with a score of 70% or higher. The primary purpose of this document is to provide you with an inventory of the skills you should become proficient in in order to pass the placement exam. However, it also should serve as a reasonable study guide for MATH 007. With this in mind, pages from Prealgebra and Algebra, by Daniel D. Benice (the MATH 007 textbook) will be cited in this document. A broad description of the skills you should posess before taking a 100 level math class follows. 1. You should be able to state what an algebraic expression is, know the mathematical operations you may apply to it without changing its value, and demonstrate skills at simplifying or manipulating algebraic expressions that involve monomials, polynomials, fractions, exponents, and roots and various combinations of these. 2. You should be able to solve single linear equations for an unknown variable (or root). This includes equations that are obviously linear and equations that must be transformed or simplified first. 3. you should be able to solve a system of two linear equations in two independent variables by employing either the method of elimination or the method of substitution . In addition, you should be able to demonstrate the connection between the solution of a system of linear equations and the graphs of the lines described by the two equations. 4. You should be able to take an equation for a line, interpret its slope and x and y intercepts , and graph the line. Similarly, you should be able to look at the graph of a line and be able to come up with its equation. Finally, you should be able to write down the equation of a line if you are given two points on the line or one point on the line and the slope of the line. 5. You should be able to solve quadratic equations by factoring them or by employing either "completing the square" or the quadratic formula. 3 Course of study for preparing for the placement exam If you are looking for a more general course of study that should cover the topics you will need to master in order to pass the placement exam, or, if you simply want to have an overview of what you will most likely be studying in Math 007, then read on. 1. Expressions are introduced in section 11.1 of Prealgebra and Algebra, pages 134 and 135. 2. Elementary simplification problems first appear in sections 11.1–11.4 of Prealgebra and Algebra, pages 135–153. These problems involve, combining like terms, elementary manipulation of expressions involving exponents, use of the FOIL method, and division of polynomials and monomials . 3. Linear equations are first introduced and defined in section 12.1 of Prealgebra and Algebra, on page 154. 5. A strategy for solving slightly more general linear equations appears in sectin 12.6, pages 165–169. These are mostly just linear equations that ought to be simplified before you solve them, but they are good practice. 6. You can learn what it means to graph a straight line in chapter 14. The basic idea of how to graph anything in a two-dimensional, Cartesian coordinate system is intoduced in 14.1, pages 197–201. 7. Techniques for graphing straight lines appear in sections 14.2–14.4, pages 201–221. You need to be familiar with how to graph lines by plotting points, and using slope intercept method. In addition, you need to be able to write down the equation for a line if you are given (1) two points on the line, or (2) a point on the line and the slope of the line. 8. Be sure that you can explain the relationship between the x-intercept of a line and the solution to the equation of the line. 9. Systems of linear equations are first introduced and defined in section 15.1 on pages 222 and 223. 10. You need to demonstrate an ability to solve a system of two linear equations (in two independent variables) using both the method of elimination and the method of substitution. These appear in sections 15.2 and 15.3, respectively (pages 223–230.) 11. You should be able to explain the relationship between the graphs of the two equations in the system and the solution to the system. 12. The skill of factoring simple mathematical expressions is first developed in section 17.1, pages 248–251. 14. Once you can factor simple quadratic expressions that have rational roots, use this skill to solve simple quadratic equations. This skill is developed in section 17.4, pages 251–268. 15. You need to be able to manipulate and simplify expressions involving fractions. Fractional expressions are introduced in section 18.1, pages 269–271. However, there are some very specific skills you need to develop. In particular, (a) you can learn how to apply your factoring and elementary simplification skills in order to simplify fractions that involvemonomials and polynomials in the numerator and denomenator in section 18.2, pages 271–276; (b) you can learn how to simplify expressions that involve products and quotients of fractional expressions in sections 18.3 and 18.4, respectively (pages 276–281); (c) you can learn how to simplify expression involving sums and differences of fractions in section 18.5, pages 281–285. This requires you to develop an ability to find a common denomenator between two fractions; (d) you can learn how to mix and match some of these skills and apply them to some slightly more complex fractional expressions in section 18.6, pages 286–289. 16. Once you have mastered the skills for manipulating and simplifying fractional expressions, you can apply these to solving equations that involve fractional expressions. Generally this means simplifying the equations until you have reduced them to either linear or quadratic equations. Once you've done that, you can solve them as before. Section 18.7, pages 289-294, addresses this. 17. Many expressions involve exponents. The laws of exponents are reviewed in section 20.1, pages 313–317. You should be able to use these laws to simplify and manipulate expressions that involve exponents when appropriate. 18. Exponents need not be positive numbers (or even integers!). You can find out an interpretation of what negative and fractional exponents mean in sections 20.2 and 20.5. (Section 20.4 tells you what it means to raise a quantity to the power of 0). Be sure that you understand the relationship between fractional exponents and radicals! 19. Since radicals are intimitely related to exponents, your ability to manipulate and simplify expressions that involve radicals will depend on your ability to work with exponents. Some basic skills are developed in sections 21.1–21.2, pages 336–341. 20. You can learn how to combine two or more like radicals in section 21.3, pages 341–342. 21. You can learn how to take a fractional expression that involves radicals in both the numerator and denomenator and simplify it in a way that leaves the radicals only in one position (but not both). This is called rationalization, and it can be found in section 21.4, pages 342–346. 22. Once you have mastered the skills for manipulating and simplifying expressions that involve radicals, you can apply these to solving equations that involve radicals. Generally this means simplifying the equations until you have reduced them to either linear or quadratic equations. Once you've done that, you can solve them as before. Section 21.5, pages 346–351, provides instruction on this subject. 23. Finally, it is important that you recognize that not all quadratic equations have integer or rational roots. Many have irrational roots. It is not easy to factor these equations "by inspection," so a more general technique is needed. One is called completing the square and the other is called the quadratic equation. Both methods are related and knowing either one will do. You can learn about them in sections 22.1–22.3, pages 353–362. 4 Practice exam Have you studied the concepts in the previous section hard? Do you feel like you are ready for the placement exam? If so, read on. There is a practice exam (with a key) immediately fol lowing this document . You should take it under conditions similar to the ones you will find on the the test day. In particular take it in during a quiet, fifty minute period, use only a pencil or something else to write with, and put away all books, notes, calculators, and other mathematical aids. You can miss no more than 6 out of the 20 problems on the practice exam in order to earn a pass. Please note that this exam should be representative of the actual placement exams, but it is not the same exam you will see. Actual placement exams may seem harder (or easier), but they will address similar topics. IMPORTANT: The test consists of 20 problems. You will have 50 minutes to complete the problems. You are not allowed to use calculators, books or any other aids during the test. Calculations may be done on provided scratch paper, but you must turn this scratch paper in with your test. All answers must be complete, legible and simplified to lowest terms. Record only final answers in the blanks after the problems. 1. Simplify: 3(2x + 1) − 5 2. Find the equation of the line through point (1, 2) and (3, 8). (The equation should be in a slope-intercept form y = mx + b.) 3. Solve the equation for x. Express your answer as a common fraction. 4. Solve an equation for x. Express your answer as a common fraction. 5. Solve the equation: 2x + 1 = 3x + 7 6. Solve the following system of equations for x and y: 7. Solve the following system of equations for x and y: 8. Simplify: 9. Simplify: 10. Simplify: 11. Solve the equation: 12. Solve the equation: 13. Solve the equation: 14. Solve the equation for x. Express your answer as a common fraction.
A video that focuses on the TI-Nspire graphing calculator in the context of teaching algebra. In this program the TI-Nspire is used to explore the nature of linear functions. Examples ranging from ...How do you get started at mathematical modeling? Here is an easy, quick, and engaging activity and a "just add data" interactive Excel spreadsheet to accomplish that first modeling task. The task ... More: lessons, discussions, ratings, reviews,... This activity is perfect for grade 7 and 8 students who are just learning about slope. The tutorial applet allows students to drag collinear points on a plane. As they move the points, the students wi... More: lessons, discussions, ratings, reviews,... Guided activities with the Graph Explorer applet, in which students explore how the graph of a linear function relates to its formula, and learn to graph and edit functions in the applet, including on... More: lessons, discussions, ratings, reviews,... How does changing the slope of a line affect the equation of that line? How might changing a part of an equation cause the related line to move? Explore these challenges using the Linear Transformer t... More: lessons, discussions, ratings, reviews,... The Marabyn problem requires students to recommend a distance for someone to travel on a bus and a walking time to complete the journey home. The complicating factor is that there is a given window of... More: lessons, discussions, ratings, reviews,... In conjunction with the simulation, a graph is generated by the applet that illustrates the relationship between number of people and time. Students are asked to investigate how the shape of the graph... More: lessons, discussions, ratings, reviews,... Compare different representations of motion: a story, a position graph, and the motion itself. Create a graph that matches a story, or write a story to match a graph, and check either by watching Mell... More: lessons, discussions, ratings, reviews,... This is a computer activity using Sketchpad and specially selected pictures located online (SlopePix web page) to help students understand the concept of slope. Following the instructions, students... More: lessons, discussions, ratings, reviews,... Students use a two-player game to develop and refine their sense of the slopes of lines. The link to the activity itself is to a zip file that contains both the activity in pdf format and the corrThis activity focuses on: * graphing an ordered pair, (a, f(a)), for a function f * the connection between a function, its table, and its graph * the interpretation of the horizontal coordinate o
The library of Math Tutorials is a comprehensive collection of worked-out solutions to common math problems. This overcomes a common limitation of most textbooks: the handful of worked-out examples for a given concept. We provide the full array of examples and solutions, allowing students to identify patterns among the solutions, in order to aid concept retention. We also have quizzes for many of these topics.
Solutions and Dosage ABSTRACT An understanding of simple arithmetic, through "percentage" and "ratio and proportion," is essential to the accurate preparation and administration of drugs. This textbook provides a clear presentation of simple mathematical relations, explained in terms of both the apothecary and metric systems of units. It contains chapters on arithmetic review, on the preparation of solutions and on dosage, with many exercises and experiments designed to develop facility in accurate calculation. The problems deal with drugs used in modern therapy. This book should prove useful to student nurses, pharmacy students and physicians who wish to review simple arithmetic
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Mathematics Courses College Core Courses Algebra 1 Enriched Grade Level: 9-10-11-12 Semester Offered: Full year Course Numbers: MTH111, MTH112 Prerequisite: Placement exam and approval of Director Description: Students in this course will meet for two consecutive periods so that by the end of this course, students will have completed a year of algebra as well as developed readiness skills necessary for success in future mathematics. The course is designed to emphasize the development of skills, techniques, and applications that deal with algebra, number relations, linear equations, formulas, polynomials, graphing, systems of equations, factoring, quadratic and exponential equations. Completion of this course prepares a student for further work in mathematics, usually in Geometry (MTH231/232). Upon successful completion of this course, students will receive two credits in mathematics. Algebra 1 Grade Level: 9-10-11-12 Semester Offered: Full year Course Numbers: MTH131, MTH132 Prerequisite: Successful completion of Algebra Enriched or approval of Director Description: This sequence is designed for students who desire a year of algebra while strengthening mathematical skills. The course is designed to emphasize the development of skills, techniques and applications that deal with algebra, number relations, linear equations, formulas, polynomials, graphing, systems of equations, factoring, quadratic and exponential equations. Completion of Algebra (MTH131/132) prepares a student for further work in mathematics, usually in Geometry (MTH231/232). Geometry Grade Level: 10-11-12 Semester Offered: Full year Course Numbers: MTH231, MTH232 Prerequisite: Successful completion of Algebra (MTH131/132) or Approval of Director Description: This course integrates the basic principles of geometry and algebra. This sequence is for students who would like a complete year of geometry while strengthening algebraic skills. Students study such topics as triangle congruence, similarity, parallelism, quadrilaterals, circles and use of dynamic geometry software. Logic is studied without the use of formal proof. Completion of this course prepares a student for further work in Advanced Algebra. College Prep Courses Algebra I Grade Level: 9-10 Semester Offered: Full year Course Numbers: MTH151, MTH152 Prerequisite: Approval of Director; Recommended for Freshmen Description: This course emphasizes the development of skills, techniques and applications that deal with number relations, linear equations, formulas, polynomials, graphing, systems of equations, factoring, rational expressions, data analysis, quadratic, exponential functions and probability. Successful completion of this sequence will prepare students for entry into a geometry sequence. Geometry Grade Level: 10-11-12 Semester Offered: Full year Course Numbers: MTH251, MTH252 Prerequisite: Algebra I or equivalent Description: This course deals with sets of points and related properties. Sets studied include lines, angles, polygons, with emphasis on circles, planes and surfaces of geometric solids such as pyramids, cones, cylinders and spheres. This sequence emphasizes systematic approaches to and processes for proving and applying theorems. Algebra is utilized extensively during the course. Successful completion of this course prepares the students for further work in Advanced Algebra. Advanced Algebra Grade Level: 11-12 Semester Offered: Full year Course Numbers: MTH351, MTH352 Prerequisite: Geometry or Geometry C Description: This course blends the theory and skills of advanced algebra. Polynomial, logarithmic, and exponential functions are studied. Additional topics include the complex number system, sequences and series, matrices, systems of equations, and the binomial theorem. Students with a six-week grade less than "C-" must attend Advanced Algebra Support for the next six-week grading period. Completion of this sequence prepares the student for entry into Precalculus. Advanced Mathematical Decision Making Grade Level: 12 Semester Offered: Full year Course Numbers: MTH441, MTH442 Prerequisite: Successful completion of Advanced Algebra Description: This course is designed for students who are college bound non-mathemathics majors. Specific emphasis will be given to data analysis, probability, statistical analysis, matrix algebra, graph theory, combinatorics, graph theory, Markov chains, finance, and elementary trigonometry. Students with credit in Precalculus or Statistics may not take this course for credit. Advanced Algebra-Accelerated Grade Level: 9-10 Semester Offered: Full year Course Numbers: MTH171, MTH172 Prerequisite: Approval of Director; Recommended for Freshmen Description: This course deals with an in-depth study of the complex number system, the techniques of evaluating and simplifying algebraic expressions, the solving of linear and quadratic open sentences, the techniques of graphing, the methods of factoring, ratio and proportion, series, and probability. Successful completion of this sequence prepares the student for entry into the Geometry Accelerated sequence. Geometry-Accelerated Grade Level: 10-11-12 Semester Offered: Full year Course Numbers: MTH271, MTH272 Prerequisite: Advanced Algebra Accelerated; Recommended for Sophomores Description: This course requires the students to complete an in-depth study of Euclidian Geometry. Properties of some conic sections are included during the second semester. Successful completion of this course prepares a student for Precalculus Accelerated. Precalculus-Accelerated Grade Level: 11-12 Semester Offered: Full year Course Numbers: MTH371, MTH372 Prerequisite: Advanced Algebra Accelerated and Geometry Accelerated or Approval of Director Description: This course provides an in-depth study of precalculus mathematics. Topics include polynomial, rational, algebraic, exponential, logarithmic and trigonometric functions and relations, conics and their properties, the complex number system, inequalities, probability and statistics and matrices. Successful completion of this course provides the student with the necessary prerequisites for Advanced Placement Calculus AB. AP Statistics Grade Level: 12 Semester Offered: Full year Course Numbers: MTH461, MTH462 Prerequisite: Precalculus or Precalculus Accelerated examination. AP Calculus AB Grade Level: 12 Semester Offered: Full year Course Numbers: MTH471, MTH472 Prerequisite: Precalculus Accelerated Description: This course deals with the study of limits and the limiting processes. The topics of differentiation, integration, continuity, limits, indeterminate forms, and improper integrals are included. Students enrolled in this course are expected to write the Advanced Placement AB Calculus examination. Honors Courses Advanced Algebra-Honors Grade Level: 9 Semester Offered: Full year Course Numbers: MTH191, MTH192 Prerequisite: Approval of Director Description: This course deals with an in-depth study of the topics covered in the Advanced Algebra Accelerated sequence. Additional content includes the study of permutations and combinations, probability, sequences, and series. Successful completion of this sequence prepares the student for entry into the Geometry Honors sequence. Since the student will cover content normally taught in the Advanced Algebra course, students successfully completing Advanced Algebra Honors may not register for credit in Advanced Algebra. Precalculus-Honors Grade Level: 10-11 Semester Offered: Full year Course Numbers: MTH391, MTH392 Prerequisite: Advanced Algebra Honors and Geometry Honors or Approval of Director Description: This course is a continuation of the mathematics studied in Advanced Algebra Honors and Geometry Honors. The content includes that of Precalculus as well as topics related to limits, matrix algebra, discrete mathematics, polar coordinates, proof by induction, and conic sections. Successful completion of this sequence prepares the student for entry into Advanced Placement Calculus BC. AP Calculus BC Grade Level: 11-12 Semester Offered: Full year Course Numbers: MTH491, MTH492 Prerequisite: Precalculus Honors or Approval of Director Description: This course deals with the BC content of the Advanced Placement curriculum beyond that of the Calculus AB sequence. Additional topics include sequences, infinite series, solutions of differential equations, advanced techniques of integration, as well as parametric and polar equations. Students enrolled in this course are expected to write the Advanced Placement Calculus BC examination. AP Statistics Honors Grade Level: 12 Semester Offered: Full year Course Numbers: MTH57C, MTH58C Prerequisite: Concurrent enrollment or credit in Advanced Placement Calculus AB, BC or Approval of Director Examination. Advanced Linear Algebra-Honors Grade Level: 12 Semester Offered: Semester 2 only Course Number: MTH592 Prerequisite: Advanced Placement Calculus BC or Approval of Director Description: This course provides detailed work in the study of vectors and vector spaces. Topics include solving n by n systems of equations, operating within a vector space, performing linear transformations of vector spaces and locating eigen vectors and eigen values. This course is equivalent to a one semester college linear algebra course. Calculus III - Honors Grade Level: 12 Semester Offered: Semester 1 only Course Number: MTH591 Prerequisite: Advanced Placement Calculus BC or Approval of Director Description: This course is the last of a three-course sequence in calculus and analytic geometry and includes the essential elements of multi-variable calculus as well as the analytic geometry of space. Students perform operations with vectors, lines and planes, understand and apply curves and surfaces, understand and apply concepts involving differentiation for functions of several variables, and compute double and triple integrals. In addition, students will perform operations of polar coordinates and parametric equations. Computer Science Courses Computer Programming (College Prep) Grade Level: 9-10-11-12 Course Numbers: Semester 1 - CSC151, Semester 2 - CSC152 Prerequisite Concurrent enrollment or credit in Algebra I: Description: Students will learn to program computers using both Java and C++. The course will begin with introductory programs in C++. Students learn Java to write graphics-related programs which can run as applets on web pages. Students will also investigate the graphics features of Java applets. Java and C++ are both used to write simple text-based and graphics related computer games. Successful completion of this course prepares the student to continue into Advanced Placement Computer Science A. Students cannot earn credit in CSC 151/152 and Computer Programming (Accelerated). Computer Programming Accelerated Grade Level: 9-10-11-12 Course Numbers: Semester 1 - CSC171, Semester 2 - CSC172 Prerequisite: Freshmen enrolled in Algebra 1 Description: This course introduces students to computer programming using both Java and C++. Students use Java to write several simple game applications as well as learn how to include buttons and pop-up menus within Java applets (which can be run as a web-page). Students use Java applets to write programs with both random and student-designed graphics/animations. C++ will be used for the first several weeks to introduce the general programming concepts that are needed in both C++ and Java. Introductory topics include using data files, translating formulas, using loops to get the computer to automate steps, etc. Successful completion of this one semester course prepares the student for Advanced Placement Computer Science A. AP Computer Science A (Honors) Grade Level: 10-11-12 Course Numbers: Semester 1 - CSC271, Semester 2 - CSC272 Prerequisite: Computer Programming College Prep or Accelerated or approval of Director Description: In the first semester, students learn abbot arrays, Array Lists, sorting/searching techniques, class (object-oriented) design and stacks, and queues. Several graphics-oriented projects are used to illustrated and practice key concepts. During second semester students learn more advanced data structures such as linked lists, trees, sets and maps. Students learn and focus on object-oriented programs. This AP course will prepare the student for the Ap Computer Science exam.. Students may earn one semester of college credit in Data Structures/Algorithms.
MATLAB excels at numerical computations, especially when dealing with vectors or matrices of data. Symbolic math is available through an add-on toolbox that uses a Maple kernel. An optional toolbox uses the symbolic engine, allowing access to symbolic computing capabilities. An additional package, Simulink, adds graphical multi-domain simulation and Model-Based Design for dynamic and embedded systems.There are many add-on toolboxes that extend MATLAB to specific areas of functionality, such as statistics, finance, signal processing, image processing, bioinformatics, etc.
Many objects of study in mathematics have an underlying algebra that could be worth a better understanding. Linear algebra, in particular, is worth knowing very well. If this wasn't a requirement or an elective it's probably worth taking over an abstract algebra course; it crops up in a lot of interesting places. I'm not sure of any direct applications of algebra (groups, rings, and fields specifically) to analysis or probability (anyone who could chime in on this point would be great!). If you want something more pertinent, topology might be more illuminating for your focus. Study of metric spaces (a special kind of topological space) is closely related to real/complex analysis. That said, learning more mathematics never hurts! Even seemingly unrelated topics often have an important bridge. So take algebra if it interests you. Maybe you'll come over to the dark side! Linear Algebra. It took me a few years, but I'm still amazed at how applicable this subject is. The former Dean of Mathematics from my alma mater said: "Mathematics is, in some respects, the study of linear operators." My high school calculus teacher was the only teacher clever enough to get homework out of me. Somehow, he earned my respect and actually taught me a few things. While I didn't start out as a math major when I began college, I eventually made the switch and I attribute a good portion of that decision to him. I start a PhD in pure mathematics in the Fall. I had trouble with algebra until I read four or five books on the subject. I've come to the conclusion that books are often a good way to get into the headspace of someone who understands. You definitely need to read actively though. Math is learned through applications. If I had known this, I wouldn't have responded as I did; you had more context than I did. Your response seemed narrowly focused on a single point so I (poorly) tried to bring in more perspective by, ironically, giving the flipside. My mistake. Removal is really, really strong in Modern. I can't think of a tier 1 deck that doesn't use one of the spells mentioned above. While we're at it: Maelstom Pulse, Oblivion Stone, Pyroclasm. Also, Jund and the Rock both sport enough discard that, even assuming they don't kill your tokens, it probably won't matter because they'll pluck the Polymorph out of your hand. The first thing I notice is that you probably want more creatures. You only have 13 (15 if you include Selesnya Charm) and you probably want more in such a creature focused deck. I would add more that generate tokens (Doomed Traveler, Voice of Resurgence). Your deck also has a lot of distinct cards. Read the article on the right about the rule of 9. Analyzing your card list, I came up with the following for your top cards: Your list has 10 primary cards and then 4 other 2-ofs. That's probably way too many. Looking at the showing above, your deck doesn't have anything very scary and has only basic synergy. Your best case scenario is a T2: Centaur's Herald, T3: Rancor, Attack, Giant Growth x 2, hit for 11. That's, of course, an unlikely scenario requires 7 cards (including land and a T1 guildgate) and every other line of play is going to be slower by at least 2 turns. Since you have so few token generators, early disruption will likely put you too far behind to recover. Selesnya Charm is your only real interaction with your opponent as well. And finally, your game changing cards are all expensive and you only run 18 land. You should probably be running 24. To fix this, you need to figure out exactly what your angle of attack is. The strength of some of the token generation is that the good ones give you undercosted bodies: Call of the Conclave and Advent of the Wurm. Populate lets you get cheap copies of these. Creatures like Doomed Traveler and Voice of Resurgence let you get in early pressure and eventually leave a few token bodies for you to populate with. You probably don't need Burst of Strength or Giant Growth; you'd rather just populate and have more creatures. Rancor, though, helps you get through blockers and is hard to deal -- so it's worth keeping that. Heroes' Reunion can be dropped too; life gain does not contribute to you winning, only not losing. Slime Molding and Centaur's Healer are both overcosted. The importance of seeing sine curves everywhere is that it gives you a reason to study the concept. I think the more important concern though is, "Why are they learning about sine curves?" A sine curve represents a relationship between angle measure and side length ratios. This is a terrible starting point as another poster pointed out. In isolation, the definition of the sine of an angle is trivia. However, there is a good reason the sine curve has been studied: it is useful. Motivate the definition of the sine function via its applications. When they understand why they need it, they'll take to the finer points of it much easier. Unfortunately, I can't think of anyway to motivate the sine function without a good grasp of both algebra and geometry. If they aren't sufficiently well-read in those, I wouldn't move to trigonometry. Algebra and geometry are arguably more useful and are probably more pertinent to the topics someone that young will be exposed to. That's not to say that going beyond the typical curriculum is bad, but there's a reason trigonometry is usually part of a pre-calculus course. You don't want to rush through topics either. Algebra and geometry are basic to higher mathematics. If you are interested in fostering a love for the subject and want your child to excel, have them really learn and get comfortable with new ideas before moving on. As von Neumann said, "Young man, in mathematics you don't understand things. You just get used to them." I've been bitten by this a lot. A basic concept in linear algebra is that of an "eigenvalue." Embarrassingly, I "got" this concept in my second year of graduate studies. Linear algebra is a junior level undergraduate course. When I finally got to differential equations, I could not for the life of me understand why I needed an eigenvalue to find a solution! I had to go back and learn enough linear algebra to realize that I was still doing linear algebra! If I had taken more time and "paid my dues" the first time around, I would have saved myself a lot of time and frustration. I would have, ironically, been further ahead had I slowed down. I mention this because it sounds almost like you are going through topics too quickly: linear functions, triangles, and the Pythagorean theorem is a topic hodgepodge. Rather than try to get to difficult and impressive sounding subjects quickly, just try to find new ways to apply what is already known and keep the material fresh. Strangely enough, this might lead you to trigonometry faster than you expect. I always just use a legal pad. Nothing beats the speed and freedom of writing by hand. If your priority is being less wasteful, then there are other options but, if you are in it for the long haul, just get used to reams of paper; other methods will just slow you down. On tests, you don't get other options anyway, so doing it with paper and pencil prepares you for those situations. The correct answer is not 25%. If it were, there would be a 50% chance of getting it correct by randomly choosing. However, that would mean that the correct answer is actually c) 50%... but then this only appears one out of 4 times so the correct answer is actually 25%... but then, again, this leads the correct answer to be 50%... and so on. Interesting. I don't think comet storm works since each target must be different (rulings at gatherer). Pyromatics is a good replacement though. Replicate makes it nearly uncounterable... and it can still target multiple things. I like the idea of clones. It might help get around all the removal in modern. You, however, only have vapor snag to interact with an opponent which might not be nearly enough. Have you done any testing against other modern decks? I know my version of the deck has a really difficult Jund match up. In fact, when piloting both decks myself, my deck has yet to win. Granted, I know exactly what both decks are capable of at any given moment, but it seems that you have to vastly outplay a Jund player to even stand a chance. I'd disagree with skill planning based solely on training time. Ideally, you remap to Perception and Willpower, train all the skills for which that gives you good times (perception-willpower and willpower-perception and anything with charisma-willpower, willpower-charisma, and mutatis mutandis for perception). Then remap Intelligence-Memory and do basically the same thing. However, this likely means you are mediocre at nearly everything until you finish your plan. Instead, I'd suggest ordering roles you want to do. For example, focus on building up your core skills, then work on missile/gunnery skills. Train to be an interceptor pilot (t2 guns/missiles, t2 propulsion, t2 frigates, t2 webs/disruptors). Then maybe move onto light dictors and heavy dictors. Once you get there change to focus on recons; then maybe command ships. Doing it that way means your training is actively giving you stuff to do. That will make the game much more fun and engaging rather than having a ton of skills that may not complement each other. If anything, I'd drop the hinterland harbors for islands or forests. With only 4 Island/Forests (Breeding Pool) they are often not going to meet the condition to come in untapped. Extra forests and islands will always ETB untapped, even if they don't tap for both colors. They also make your Misty Rainforests more useful. And, finally, they make Path to Exile hurt less (without basic lands, there is no upside to path for you). It seems crackling perimeter and hold the gates are his alternate win cons. The first lets him do direct damage to his opponent while the latter makes his creatures rather difficult to take out with straight damage and gives them vigilance to boot. There are also Azor's Elocutors which, with Hold the Gates, seems like a fairly good way to win assuming it avoids removal or bouncing. This is a principle of inclusion-exclusion problem. Each bullet points corresponds to the size of a set. Let T, P, and H stand for the sets as in the problem. Note that \|T\| means "the size of T". I'll use the "&" symbol to represent set intersection. (I still don't know how to get Latex to work!) \|T\| = 60, \|P\| = 85, \|H\| = 82 \|T&H\| = 20 \|T&P\| = 43 \|H&P\| = 25 \|T&H&P\| = 13 Once you have this, then the Inclusion-Exclusion principle gives you the important equations. Let U represent all the people surveyed, the universal set. We know that \|U\| = 160. i) \|U\| - \|T\| - \|P\| - \|H\| + \|T&H\| + \|T&P\| + \|H&P\| - \|T&H&P\| ii) \|T\| - \|T&P\| - \|T&H\| + \|T&H&P\| The first equation considers all of the people surveyed (U), minus all the people who read each newspaper (T, P, H). We have double counted those people who read two newspapers (T&H, T&P, H&P) and need to add those people back in. Again, however, we've double counted those who read all three newspapers (T&H&P) and have overcompensated. We remove the counts for those who read all three. What remains is the number of people who read no newspapers. The second equation proceeds similarly. We know how many people read the Times so we need to remove those people who read the Times and another magazine (T&P, T&H). Some of the people removed however actually read all three (T&P&H) and were counted in both groups. We need to add them back in since they were double counted. Disrupting their tron lands is really all you can do to slow down Tron. A Naya deck could run Blood Moon. That shuts them down pretty well until they can get out an Oblivion Stone. Aside from that, try to speed your deck up. Tron has a very strong late game and will usually win if it gets that far. Do your best to make sure the game doesn't last that long. Pyroclasm is probably your biggest impediment to a quick win for both decks (assuming Naya is some Zoo variant). I'm not sure what to do about it in the tokens deck, but Boros Charm could be useful in Naya (all its modes are possibly relevant). What are your goals with the deck? Are you taking it to an FNM? Is it just a casual deck? That said, I'll respond based on my admittedly poor deck building knowledge. You don't have many good turn 1 plays in the deck. You seem to be building an aggro deck, but you can't put any creatures on the field until turn 2 or, more likely, turn 3. To remedy that, I'd add something like Shadow Alley Denizen or Stromkirk Noble (the former is more budget friendly). For other standard legal options, have a look here. Depending on your budget, dual lands might be an option to help mana fixing. Cavern of Souls, is another card that would work well with your Vampire theme, but is too pricey for a budget deck.

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