Split (1)

train · ~1.24B rows (showing the first 1.67M)

text stringlengths 8 1.01M
Math 129-002 General Resources for Students Trigonometry The following are lessons and worksheets that constitute a quick course in trigonometry ideal for students reviewing before taking a calculus course. Read the lesson, try the worksheet, and check your solutions. These files could also be used by a student studying trigonometry for the first time. Geometry The files found by clicking the following link constitute a quick review of major geometry topics taught at the high school level. They are ideal for a student reviewing for a placement exam or a course that uses geometry.
A good working knowledge of elementary math must be acquired for success in all upper level math courses. The student in elementary math learns the basic math skills he/she will need in order to solve problems in algebra, geometry, trigonometry, and calculus. Here you learn the basic math that you will need for many of the courses you will take later.
Basic Maths Practice Problems For Dummies Paperback Click on the Google Preview image above to read some pages of this book! Ready to put pencil to paper and brush up on your maths skills? With practice problems and fully worked-out solutions, Basic Maths Practice Problems For Dummies, UK Edition, is the perfect revision tool. Whether you're returning to school, studying for an adult numeracy test, helping the kids with homework, or seeking the confidence that a firm maths foundation provides in everyday encounters, Basic Maths Practice Problems For Dummies, UK Edition, provides you with the practice you need to commit mathematics techniques to memory. Maths Practice Problems For Dummies can be used alone or in conjunction with Basic Maths For Dummies. The topics covered in Maths Practice Problems For Dummies and the order in which they're presented, support the U.K. Adult Numeracy Core Curriculum and can be used in preparation for the Entry Level 3, Level 1, and Level 2 Adult Numeracy Tests.
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education. Math 1300 Greatest Common Factor and Factoring by GroupingSection 4.1 Notes(Review) Factoring Definition: A factor is a number, variable, monomial, or polynomial which is multiplies by another number, variable, monomial, or polynomial to obtain a M 1314lesson 2 Math 1314 Lesson 2 One-Sided Limits and Continuity One-Sided Limits1Sometimes we are only interested in the behavior of a function when we look from one side and not from the other. Example 1: Consider the function f ( x) =x x . Math 1300Section 1.7 NotesSolving Linear Inequalities An inequality is similar to an equation except instead of an equal sign = you find one of the following signs: <, , >, or . Now > and < are strict inequalities, and and are inequalities that Math 1310 Absolute Value EquationsSection 2.8 NotesNearly everyone can say that the absolute value of 3 is _. But I want you to start thinking of absolute value as a distance from zero. If I tell you to read out loud and draw the equation \|x\| = 3 Math 1300Section 1.3 NotesGCD (Greatest Common Divisor) 1) Write each of the given numbers as a product of prime factors. 2) The GCD of two or more numbers is the product of all prime factors common to every number. Examples: 1. Find the GCD of 2 M 13103.5 Maximum and Minimum Values1A quadratic function is a function which can be written in the form f ( x) = ax 2 + bx + c ( a 0 ). Its graph is a parabola.Every quadratic function f ( x) = ax 2 + bx + c can be written in standard form: Test-Taking Information Math 1314 Spring 2009There will be four tests during the course of the semester and a mandatory, comprehensive final exam. Test 1 counts 8% of your semester grade and test s 2 4 each count 12% of your semester grade. The fi Math 1310 1. Homework is due before class begins. a. True b. FalsePopper #012. I must bubble in _ on homework and popper scantrons or I will get a zero for that grade. a. Section number b. Assignment number c. Grading ID d. All of the above 3. If Math 1313 Section 19280 1. Homework is due before class begins. a. True b. FalsePopper 01 Form A2. I must bubble in _ on popper scantrons or I will get a zero for that grade. a. Section number b. Assignment number c. Grading ID d. Form A e. All o Math 1313 Course Objectives Chapter.Section Objective and Examples Material Covered by End of Week # 11.2Given two points on a line, determine the slope and equation of the line in point-slope form and slopeintercept form. Example: Find the equat 1Math 1313Section 7.4 Section 7.4 Use of Counting Techniques in ProbabilitySome of the problems we will work will have very large sample spaces or involve multiple events. In these cases, we will need to use the counting techniques from the ch Lecture 1Section 2.1 The Ideal of LimitDenition of LimitSection 2.2Jiwen He11.1Section 2.1 The Ideal of LimitThe Ideal of LimitGraphical Introduction to Limitxclim f (x) = L In taking the limit of a function f as x approaches c, it Second ExamProbability MATH 3338-10853 (Fall 2006) September 25, 2006This exam has 3 questions, for a total of 100 points. Please answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue o First ExamProbability MATH 3338-10853 (Fall 2006) September 13, 2006This exam has 2 questions, for a total of 0 points. Please answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on t
Buy print & eBook together and save 40% Description Theory and application of a variety of mathematical techniques in economics are presented in this volume. Topics discussed include: martingale methods, stochastic processes, optimal stopping, the modeling of uncertainty using a Wiener process, Itô's Lemma as a tool of stochastic calculus, and basic facts about stochastic differential equations. The notion of stochastic ability and the methods of stochastic control are discussed, and their use in economic theory and finance is illustrated with numerous applications. Quotes and reviews @from:R. Kihlstrom @qu:This book will almost certainly become a basic reference for academic researchers in finance. It will also find wide use as a textbook for Ph.D. students in finance and economics. @source:Mathematical Reviews
Does anybody here know anything concerning prentice hall worksheets? I'm a little puzzled and I don't know how to finish my math homework regarding this topic. I tried reading all materials about it that could help me figure things out but I still don't get. I'm having a hard time answering it especially the topics algebra formulas, mixed numbers and interval notation. It will take me days to answer my algebra homework if I can't get any help. It would really help me if someone can recommend anything that can help me with my math homework. Well of course there is. If you are determined about learning prentice hall worksheets, then Algebra Buster can be of great help to you. It is designed in such a manner that almost anyone can use it. You don't need to be a computer professional in order to operate the program. Yeah! That's a great substitute to the costly private coaching and expensive online coaching. The single page formula list provided there has helped me in every Algebra 1 internal that I have had in the past. Even if you are an intermediate in Intermediate algebra, the Algebra Buster is very useful since it offers both simple and challenging exercises and drills for practice.
Introduction to Matlab 7 for Engineers 9780072548181 ISBN: 0072548185 Edition: 2 Pub Date: 2004 Publisher: McGraw-Hill Summary: This is a simple, concise book designed to be useful for beginners and to be kept as a reference. MATLAB is presently a globally available standard computational tool for engineers and scientists. The terminology, syntax, and the use of the programming language are well defined and the organization of the material makes it easy to locate information and navigate through the textbook. The text covers all the major cap...abilities of MATLAB that are useful for beginning students. An instructor's manual and other web resources are available
Course Detail Registration Curriculum & Instruction: Math as a Second Language EDCI 200 Z3 (CRN: 60994) 3 Credit Hours—Seats Available! Jump Navigation About EDCI 200 Z3 This course lays the groundwork for all the Vermont Mathematics Initiative courses that follow. A major theme is understanding algebra and arithmetic through language. The objective is to provide a solid conceptual understanding of the operations of arithmetic, as well as the interrelationships among arithmetic, algebra, and geometry. Topics include arithmetic vs. algebra; solving equations; place value and the history of counting; inverse processes; the geometry of multiplication; the many faces of division; rational vs. irrational numbers and the one-dimensional geometry of numbers. All of the topics in this course are taught in the context of the mathematics curriculum in grades K-6.
Select new releases include FREE streaming with the purchase of the DVD or audio CD. Enjoy instantly on your computer, laptop, tablet or smartphone. COURSE DESCRIPTION One of the greatest achievements of the human mind is calculus. It justly deserves a place in the pantheon of our accomplishments with Shakespeare's plays, Beethoven's symphonies, and Einstein's theory of relativity. In fact, most of the differences in the way we experience life now and the way we experienced it at the beginning of the 17th century emerged because of technical advances that rely on calculus. Calculus is a beautiful idea exposing the rational workings of the world; it is part of our intellectual heritage. The True Genius of Calculus Is Simple Calculus, separately invented by Newton and Leibniz, is one of the most fruitful strategies for analyzing our world ever devised. Calculus has made it possible to build bridges that span miles of river, travel to the moon, and predict patterns of population change. Yet for all its computational power, calculus is the exploration of just two ideas—the derivative and the integral—both of which arise from a commonsense analysis of motion. All a 1,300-page calculus textbook holds, Professor Michael Starbird asserts, are those two basic ideas and 1,298 pages of examples, variations, and applications. Many of us exclude ourselves from the profound insights of calculus because we didn't continue in mathematics. This great achievement remains a closed door. But Professor Starbird can open that door and make calculus accessible to all. Why You Didn't Get It the First Time Professor Starbird is committed to correcting the bewildering way that the beauty of calculus was hidden from many of us in school. He firmly believes that calculus does not require a complicated vocabulary or notation to understand it. Indeed, the purpose of these lectures is to explain clearly the concepts of calculus and to help you see that "calculus is a crowning intellectual achievement of humanity that all intelligent people can appreciate, enjoy, and understand." He adds: "The deep concepts of calculus can be understood without the technical background traditionally required in calculus courses. Indeed, frequently the technicalities in calculus courses completely submerge the striking, salient insights that compose the true significance of the subject. "In this course, the concepts and insights at the heart of calculus take center stage. The central ideas are absolutely meaningful and understandable to all intelligent people—regardless of the level or age of their previous mathematical experience. Historical events and everyday action form the foundation for this excursion through calculus." Two Simple Ideas After the introduction, the course begins with a discussion of a car driving down a road. As Professor Starbird discusses speed and position, the two foundational concepts of calculus arise naturally, and their relationship to each other becomes clear and convincing. Professor Starbird presents and explores the fundamental ideas, then shows how they can be understood and applied in many settings. Expanding the Insight Calculus originated in our desire to understand motion, which is change in position over time. Professor Starbird then explains how calculus has created powerful insight into everything that changes over time. Thus, the fundamental insight of calculus unites the way we see economics, astronomy, population growth, engineering, and even baseball. Calculus is the mathematical structure that lies at the core of a world of seemingly unrelated issues. As you follow the intellectual development of calculus, your appreciation of its inner workings will deepen, and your skill in seeing how calculus can solve problems will increase. You will examine the relationships between algebra, geometry, trigonometry, and calculus. You will graduate from considering the linear motion of a car on a straight road to motion on a two-dimensional plane or even the motion of a flying object in three-dimensional space. Designed for Nonmathematicians Every step is in English rather than "mathese." Formulas are important, certainly, but the course takes the approach that every equation is in fact also a sentence that can be understood, and solved, in English. This course is crafted to make the key concepts and triumphs of calculus accessible to nonmathematicians. It requires only a basic acquaintance with beginning high-school level algebra and geometry. This series is not designed as a college calculus course; rather, it will help you see calculus around you in the everyday world. LECTURES 24Lectures Calculus is a subject of enormous importance and historical impact. It provides a dynamic view of the world and is an invaluable tool for measuring change. Calculus is applicable in many situations, from the trajectory of a baseball to changes in the Dow Jones average or elephant populations. Yet, at its core, calculus is the study of two ideas about motion and change. The example of a car moving down a straight road is a simple and effective way to study motion. An everyday scenario that involves running a stop sign and the use of a camera illustrates the first fundamental idea of calculus: the derivative. You are kidnapped and driven away in a car. You can't see out the window, but you are able to shoot a videotape of the speedometer. The process by which you can use information about speed to compute the exact location of the car at the end of one hour is the second idea of calculus: the integral. The moving car scenario illustrates the Fundamental Theorem of Calculus. This states that the derivative and the integral are two sides of the same coin. The insight of calculus, the Fundamental Theorem creates a method for finding a value that would otherwise be hard or impossible to get, even with a computer. Change is so fundamental to our vision of the world that we view it as the driving force in our understanding of physics, biology, economics—virtually anything. Graphs are a way to visualize the derivative's ability to analyze and quantify change. The derivative lets us understand how a change in one variable affects a dependent quantity. We have studied this relationship with respect to time. But the derivative can be abstracted to many other dependencies, such as that of the area of a circle on the length of its radius, or supply or demand on price. One of the most useful ways to consider derivatives is to view them algebraically. We can find the derivative of a function expressed algebraically by using a mechanical process, bypassing the infinite process of taking derivatives at each point. The description of moving objects is one of the most direct applications of calculus. Analyzing the trajectories and speeds of projectiles has an illustrious history. This includes Galileo's famous experiments in Pisa and Newton's theories that allow us to compute the path and speed of projectiles, from baseballs to planets. Optimization problems—for example, maximizing the area that can be enclosed by a certain amount of fencing—often bring students to tears. But they illustrate questions of enormous importance in the real world. The strategy for solving these problems involves an intriguing application of derivatives. Archimedes devised an ingenious method that foreshadowed the idea of the integral in that it involved slicing a sphere into thin sections. Integrals provide effective techniques for computing volumes of solids and areas of surfaces. The image of an onion is useful in investigating how a solid ball can be viewed as layers of surfaces. The integral involves breaking intervals of change into small pieces and then adding them up. We use Leibniz's notation for the integral because the long S shape reminds us that the definition of the integral involves sums. Calculus is useful in many branches of mathematics. The 18th-century French scientist Georges Louis Leclerc Compte de Buffon used calculus and breadsticks to perform an experiment in probability. His experiment showed how random events can ultimately lead to an exact number. Zeno's Arrow Paradox concerns itself with the fact that an arrow traveling to a target must cover half the total distance, then half the remaining distance, etc. How does it ever get there? The concept of limit solves the problem. Zeno's Arrow Paradox shows us that an infinite addition problem (1/2 + 1/4 + 1/8 + . . .) can result in a single number: 1. Similarly, it is possible to approximate values such as π or the square root of 2 by adding up the first few hundred terms of infinite sum. Calculators use this method when we push the "sin" or square root keys. We have seen how to analyze change and dependency according to one varying quantity. But many processes and things in nature vary according to several features. The steepness of a mountain slope is one example. To describe these real-world situations, we must use planes instead of lines to capture the philosophy of the derivative. Calculus plays a central role in describing much of physics. It is integral to the description of planetary motion, mechanics, fluid dynamics, waves, thermodynamics, electricity, optics, and more. It can describe the physics of sound, but can't explain why we enjoy Bach. Many money matters are prime examples of rates of change. The difference between getting rich and going broke is often determined by our ability to predict future trends. The perspective and methods of calculus are helpful tools in attempts to decide such questions as what production levels of a good will maximize profit. Whether looking at people or pachyderms, the models for predicting future populations all involve the rates of population change. Calculus is well suited to this task. However, the discrete version of the Verhulst Model is an example of chaotic behavior—an application for which calculus may not be appropriate. There are limits to the realms of applicability of calculus, but it would be difficult to exaggerate its importance and influence in our lives. When considered in all of its aspects, calculus truly has been—and will continue to be—one of the most effective and influential strategies for analyzing our world that has ever been devised and objects for demonstrations, this course is available exclusively on DVD.
Mathematics Levels: Find qualifications and resources Mathematics Entry Pathways The Entry Pathways qualification in Mathematics has been re-written into units. Centres will be able to choose from this list to create a flexible course of their own. Each unit will have its own learning outcomes, assessment objectives, content guidance, resources, advice and assessment suggestions. The new suite of qualifications is centre assessed and externally moderated. There is a choice of an 8 credit Award or a 13 credit Certificate at each Entry 2 and Entry 3. Candidates can study Entry 1 units and achieve an Award and Certificate at Entry 1 in Personal Progress. Further details can be found on the Personal Progress web pages.
Applied Basic Math Worksheets - 2nd edition Summary: Worksheets for Classroom or Lab Practice offer extra practice exercises for every section of the text, with ample space for students to show their work. These lab- and classroom-friendly workbooks also list the learning objectives and key vocabulary terms for every text section, along with vocabulary practice problems. 032169774X No writing or highlighting. Fast Shipping!!! Ships NEXT business day. Expedited shipping available. *United States orders ONLY! No APO/FPO addresses* For used books, only the ordered b...show moreook is guaranteed. Supplemental materials that may be included if the book is purchased as new are not guaranteed to be included or usable due to the used nature of the ordered book. ...show less $16
Intended to bridge the gap between the standard calculus sequence and more abstract upper-division mathematics courses, this successful text provides a firm foundation in sets, logic, and mathematical proof methods. The Second Edition includes a smoother transition from the concepts of logic to actual use of these concepts in proving theorems; additional applications; several essays about prominent mathematicians and their work; and the addition of exercises for student writing.
Statistics for Non-Mathematicians The course will intoduce statistics to the beginner. Topics covering measures of central tendency, dispersion and probability theory will be discusssed. Nice and Noughtie Numbers This course shows how numbers are fundamental to many aspects of our civilization. It covers topics such as counting systems, prime numbers, the importance of zero, musical scales, bell ringing, the calendar and seasons, and encryption of messages. The Number Mysteries (Online) It is hard to imagine a world without numbers, but how natural is mathematics? We explore this very question through numerous online activities and "at home" experiments, which allow you to interact with mathematics as you will have never done before. Introduction to Topology We will study the basic theory and the topological properties of the Möbius bands, the torus and the Klein bottles to explain why a topologist cannot distinguish between a doughnut and a tea cup. You Can Count on It - Maths in Finance In this brief course we shall look at how mathematics contributes to finance and business. Our course is suitable for people with previous experience of mathematics at the sixth-form level and aims to provide an elementary introduction to the mathematics. Alternatively you can perform a keyword search on all our courses using the 'Find courses' box on this page.
A Collection of Ideas and Activities David A. Young These activities are a collection of ideas designed to either exploit the capabilities of the TI-82 Graphics Calculator, explore "change" in a mathematics class, do stuff, and/or all of the above. All these activities would be useful with students as they prepare for calculus and/or life, and, in some cases, useful once the student has made it into calculus. Some of the activities may be done on a TI-81 Graphics Calculator, or a spreadsheet. The instructions, when specific, will be for the TI-82. 1. Mapping The Doubling Function In an effort to visualize the effect of iterating the function f(x) = 2x and its orbits [ A First Course In Chaotic Dynamical Systems Theory and Experiment , by Robert L. Devaney, pp. 24-25, 1992, Addison-Wesley Publishing Company ] , you can use the sequence mode or, from the home screen, use the "ANS" key. If we are interested in the unit circle, centered on the origin, we can start with a "seed" of some angle (x), representing a point on the circle. If you choose 72 as the starting angle (seed) then we have f(x) = 2x which becomes f(72) = 272 = 144. This then becomes f(144) = 288, and so on as we iterate. When the value of the function exceeds 360, we will want to use modular division on the value { f(x) mod 360 } to get the adjusted angle. This will give you the whole number remainder from normal division. If we continue the iterations with the next value, 288, we get 576 which should be 216 since 576 mod 360 is 216, or 576-360 = 216, which is actually the method we will use on the TI-82. If you could use the mod function on the TI-82, you would continue with larger values of x, but only report values less than or equal to 360. This could lead to a rounding error, which we will also experience in a variation of this method. To do this from the sequence mode on the TI-82, place the calculator in the appropriate mode by pressing , and highlighting the "seq" option on the function line, then pressing also select the "Dot"mode. [The up/down/left/right keys are used to move the cursor around the screen.] Next you will need to place the appropriate function in the "Y=" menu and select an appropriate set of values in the "WINDOW" menu before you graph. Press and key in the function Un = 2Un-1 - (360(2(Un-1 )>360) ) and turn the Vn line off. To get the Un-1 symbol press . Now select a window to view the graph in. Use these values: Un Start = 72; nStart = 0; n Min = 0; n Max = 25; Xmin = 0; Xmax = 25; Xscl = 0; Ymin = 0; Ymax = 375; Yscl = 0. Make sure you're in the "Time" graph mode under "FORMAT" in the "WINDOW" menu. Now press and you will see the orbits. As you trace, you will see a pattern. This may also be seen in the "TABLE", and you may extend the number of iterations by increasing n Max and Xmax equally. You would now experiment with different seed values, which would be placed in Un Start. This same pattern can be seen from the home screen when using the "ANS" key. Clear the screen and key in 72 as your seed. Now create the following code: (2Ans)-(360(2Ans > 360)) and press enter. The value of 144 appears. If you repeat the iteration by continuing to press the enter key you will see the same pattern: 72, 144, 288, 216, 72, .... If you wish to start with another seed, simply key it in and press , then recall the code you used by pressing until it appears on the screen, then press and find the orbits of that value. You might want to try the following values as a seed: 8, 23, 30, 15, and 57. If you wish to look at the same problem when one rotation about the circle, 360°, is referred to as 1, then we would have 72° become 72/360 which is 1/5 or 0.2. To look at this problem we could enter our seed, now in terms of a fraction of a rotation, from the home screen and use the following code: fPart(2Ans)Frac. This will generate a series of fractions that will show a cycle of 4. Experimenting with other fractional rotations may show a cycle, with some seeds resulting in the aforementioned rounding error. Some values to experiment with: 1/4, 1/45, 1/7, 1/11. This idea can also be investigated in the sequence mode of the TI-82 by returning to "Y=" and changing the Un line to equal fPart (2Un-1 ). You will need to reset your window as follows: Un Start = 0.2; nStart = 0; n Min = 0; n Max = 25; Xmin = 0; Xmax = 25; Xscl = 0; Ymin = -0.5; Ymax = 1.5; Yscl = 0. When you graph and trace you will see the pattern. If you experiment with different seeds in Un Start you will get different orbits. The patterns, in some cases, will degenerate due to computer error; to see this you will need to extend n Max and Xmax equally. You may also participate in the TI-82's ability to perform more than one operation during one execution, using the ": " option. You can use the "Pt-On(" operation with "PRx(", and "PRy( " and the fact that R = 1, and = (2Ans)-(360(2Ans > 360)), if you are looking at angles in degrees. This will plot the points (x, y) as they would appear on the unit circle, assuming you have the appropriate range and have already entered the seed angle. You will need to press and to get each iteration and use "ClrDraw" when you change seed angles. Make sure you have all the "STAT PLOTs" off as well as all the functions in "Y=" from the function mode. Since we are using angles, the mode should be set to degrees, "Degree". 2. Regressive Gender Mathematics An article by Nicholas D. Kristof titled "Chinese Turn to Ultrasound, Scorning Baby Girls for Boys" from the New York Times, dated July 21, 1993 reports that pregnant women in China are bribing their doctors to find out, from an ultrasonic scan, if they are going to have a boy or a girl. The bribes range from $35.00 to $50.00, with an abortion thrown in for free if the baby will be a girl. One village reports that they have only had one girl born there in the last year. This trend is reflected in data from the Chinese census. Listed below are the data for the number of males born for each 100 females each year, for several years. Males per Year 100 Females 1953 103.8 1964 104.9 1982 113.8 1990 113.8 1992 118.5 If we look at these data, it seems natural to ask if there is a pattern so that we may predict the number of males to females in the future. When you plot these data on the TI-82, you will see with the scatter plot what looks like a quadratic, or an exponential. By using various regression techniques and looking at residuals, you will not see a good fit. This may be related to a change in the dynamic since 1953 and/or 1964. If you only look at the data after 1964, there really isn't enough data to examine. You could find additional, more current, data and continue the analysis. Questions to investigate: • What if the trend continues? What are the implications to society, lifestyle, and work? • What are the data for your city (state, country, other countries) of the number of males and females born each year? • Would a decreasing, or increasing, birth rate have any effect on the data, or your predictions? • How many doctors in your city use the ultrasonic scan and how do the future parents react? Any difference in reaction by the mother or father? • Why do people have the ultrasonic scan done? Would you have one for your pre-kid? Are you male or female? • Who gives more of the ultrasonic scans, male or female doctors? 3. Algebra On The TI-82 Just as the TI-81 opened up the minds of both students and teachers in Algebra I, as well as changed the curriculum, so will the TI-82. The following are some ideas to help start, and stoke, the fire. Order Of Operations A major problem with students' understanding of algebra is their lack of a feel for "Order of Operations". The TI-82 has a logic menu that contains, among other things, the operator "and". If you use this, from the home screen, you can create a series of statements that represent the steps of simplification of an expression. If one strings these statements together with the "and" statement, the calculator will report that the simplification was correct, or not. The "and" will report a value of "1" if the statements on either side of it are both true, "1". If either side is false, the "and" reports "0", which is false. Suppose that you have the expression 33 - 3(5+4) to simplify. The following code, on the TI-82, would be a representation of the steps in simplification. (33-3(5+4))=(33-3(9)) and (33-3(9))=(33-27) and (33-27)=(6) Once these symbols are keyed in and the user presses , the TI-82 will report the value of "1" for true. That is, the simplification was done correctly. This exercise can be expanded to more sophisticated expressions. Some additional benefits of this activity include: giving the student experience with working with parentheses, and having the student become familiar with the TI-82 keyboard. Another way to investigate this concept, as it occurs in simplifying expressions with variables, is to place, in a list, the values of two or more equivalent expressions (the original and the simplified forms). For a simple example, let us look at 4(X + 2). We would expect the student to write this as 4X + 8, probably because we want her to undo this when we teach factoring. To do this on the TI-82, use the "seq(" option under the "LIST" menu. This is obtained by pressing the keys, and selecting option 5. The code we will use to place some values of X in list L1 is: seq(X,X,1,25,1) -> L1. We then need to place a list of values into L2 and L3 for each of the expressions, 4(X+2) and 4X + 8. We could do this using the "seq(" command in the home screen, as before, but let us try a different method that is quicker. Go to the list menu and select "Edit". Move the cursor to the L2 column and up into the heading of the list. Now key in 4(L1+2) and press enter. This will fill the L2 column with values of the expression, using the listed values of L1 for X. Repeat this technique for the L3 list using 4(L1)+8. Now, if the student moves up and down the list, she will see the values in L2 and L3 are the same. This is only a sample of values, but it shows, for that domain, that the expressions are equivalent. This technique can be used for additional forms of an expression. There are 6 lists, 5 that the student could use. You could also create different X values, in L1. Value of a Function The TI-82 can be used in several ways to show the value of a function. This concept seems to elude many algebra students, resulting in problems in later courses. If we have the expression "3X2 - 5X" and we are interested in its value when X=4, such as in the situation where X is the score on the AP Calculus Examination when there are "3X2 - 5X" hours of study per week. On the TI-82 you can place the expression in the "Y=" menu and with a good window: Xmin = -8.8; Xmax = 10; Xscl = 1; Ymin = -10; Ymax = 25; Yscl = 1, you can trace to the point that X=4 and see that the value of the function is 28. Another method would be to get the table of values by pressing . Moving up or down the X column, you will see different values for X and the value of the function, assuming that you have placed the expression in the "Y=" menu, as before, and depending on your table set-up, "TblSet". Again the student will see a value of 28 when X is 4. The next method is performed in the home screen using the TI-82's function notation. One may create the expression f(x) on the calculator and collect values such as f(4). To do this, we will look at Y1(4), and press enter. Again we assume that the expression is in the "Y=" menu under Y1. The key-strokes, from the home screen, are as follows: . You will see the Y1 on the screen. Now key in the value desired, 4, in parenthesis so that you have Y1(4). If you then press you will get the value of the function, 28. This is different from the TI-81, which would, given the same key-strokes, multiply the value of the function, Y1 , for whatever value was stored in X times 4. That result would have been f(x)*4. The final method suggested is also created from the home screen. The student will key in the expression 3X2 - 5X, replacing each X with the number of interest, in this case 4. The screen should look like this, before enter is pressed: 3(4)2 - 5(4). This results in the same value, 28, as before. If a student is exposed to these four methods, and is allowed to explore, with calculator in hand, the idea of the "value of a function" will have been presented in several different styles to her. This might result in a greater, and longer, understanding of the concept. Undefined Values and Domain Restrictions The TI-82's "TABLE" can be used to help show a student the undefined values of a function. If the function is placed in "Y=" and the "TblSet" is on the correct step, "Tbl", the table will show "ERROR" at those difficult points. The "nice" range on the TI-82 graph is a multiple of 94 for X and a multiple 62 for Y. But this is not needed when using the table. In the case of f(x) = we will find that when x is 5, the table reports the error. The "TABLE" can also be used to search for needed values, as is a common need in the Computer Intensive Algebra program from Penn State. The student would place a function in the "Y=" list, preferably a function that has some meaning, and then use the table to search for a particular value, either in the X or Y column. If f(x) = 5x2 + 4, where x is the number of puppies sold at a market in a day, and f(x) is the length, in centimeters, of their left ears, when placed end-to-end, the question might be "How many puppies do you need to sell to get enough ears to reach the nearest dogwood tree, which is 251 centimeters away?". If you set your "TblMin", under the "TblSet" menu, to 0, and set the step, "Tbl" to 1, the table will reveal that the value is between 7 and 8 puppies. If you return to the "TblSet" menu and change "TblMin" to 7 and "Tbl" to 0.2, your table will zoom in on the value needed. Repeating this you should find a x value near 251 cm using 0.01 for "Tbl". The discussion might lead to the prudence of reporting your answer in parts of puppies, and if this is OK, were the parts sold with the ears or not! Solving Equations with Variables on Both Sides When students are learning to solve equations that have variables on both sides of the equal sign, the TI-82 lists can be of use. If your problem is to solve 2X - 10 = 11 - X, you can place these in the list and have them evaluated for a series of X values. From the home screen on the TI-82, use the following code: seq(X,X,1,25,1) -> L1: 2L1 - 10 -> L2 : 11 - L1-> L3 followed by enter. This will place a set of X values in list 1, and appropriate values for each of the expressions in list 2 and 3. By looking at the lists the student will see that the two expressions have the same value, 4, when X is 7, so the solution, and the value the student would get when she checks it, appear in one fell swoop. If you select a set of expressions in the original equation that don't have integer solutions between 0 and 26, you will need to repeat the above code, changing only the L1 list. You might want to look at the two expressions between 7 and 8. You might do this after seeing the list for values of X from 1 to 25, that is, seeing that the two list did not have an equal value, but noted a "change" between values of X at 7 and 8. From the home screen press , and this will bring back the code listed above. If you have done some other calculations on the home screen, you may need to call back "ENTRY" several times to get the right code. Once you have the code retrieved, edit it by moving the cursor to the segment "seq(X,X,1,25,1) -> L1" and strike over it, leaving that segment looking like: seq(X,X,7,8,0.1) -> L1 . The rest of the code should remain unmolested, and when you are ready, press . This will recalculate, as before, with a new domain Again, this visualization might open up the students to some insight to the world of algebra.
Summary: Intended for introductory courses in basic mathematics, this comprehensive text teaches the skills necessary for practical work involving architectural and mechanical drafting, electronics, welding, air conditioning, aviation, and automotive mechanics, and machining and construction. The authors have carefully organized the material to provide flexibility: the text can be used in a lecture class, in a laboratory setting, or for self-paced instruction. Each chapter is...show more divided into frames that present the individual concepts on which the major concepts are based. To ensure student comprehension, each concept is first explained and then illustrated with an example. Questions about the material test students' understanding of the concepts, and the answers are found on the right side of each page. Exercise sets throughout the chapters and self tests at the end of each chapter provide further opportunity for students to master the material. In all, the text presents more than 3,000 problems and exercises. ...show less Former Library book. Shows definite wear, and perhaps considerable marking on inside. 100% Money Back Guarantee. Shipped to over one million happy customers. Your purchase benefits world literacy! $18.78 +$3.99 s/h Acceptable BookSleuth Danville, CA Fast Shipping ! Used books may not include access codes, CDs or other supplements. $76.75 +$3.99 s/h Good LOOK AT A BOOK OH Miamisburg, OH 198505340514293.96 +$3.99 s/h New Bookeyez2 snellville, GA Brand New Title. We're a Power Distributor; Your satisfaction is our guarantee! $295.87 +$3.99 s/h New Extremely_Reliable Richmond, TX Buy with confidence. Excellent Customer Service & Return policy. $340.50 +$3.99 s/h Like
Elementary Computer Mathematics by Kenneth R. Koehler - University of Cincinnati Blue Ash College , 2002 This book is an introduction to the mathematics used in the design of computer and network hardware and software. We will survey topics in computer arithmetic and data representation, logic and set theory, graph theory and computer measurement. (985 views) Topics in Discrete Mathematics by A.F. Pixley - Harvey Mudd College , 2010 This text is an introduction to a selection of topics in discrete mathematics: Combinatorics; The Integers; The Discrete Calculus; Order and Algebra; Finite State Machines. The prerequisites include linear algebra and computer programming. (1485 views) Discrete Mathematics - Wikibooks , 2012 Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. This book will help you think well about discrete problems: problems where tools like calculus fail because there's no continuity. (1830 views) Temporal Networks by Petter Holme, Jari Saramäki - arXiv , 2011 In this review, the authors present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamic systems. (2169 views) Lecture Notes in Discrete Mathematics by Marcel B. Finan - Arkansas Tech University , 2001 This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. The text covers the mathematical concepts that students will encounter in computer science, engineering, Business, and the sciences. (5424 views) Introduction To Finite Mathematics by J. G. Kemeny, J. L. Snell, G. L. Thompson - Prentice-Hall , 1974 This book introduces college students to the elementary theory of logic, sets, probability theory, and linear algebra and treats a number of applications either from everyday situations or from applications to the biological and social sciences. (5917 views) Languages and Machines by C. D. H. Cooper - Macquarie University , 2008 This is a text on discrete mathematics. It includes chapters on logic, set theory and strings and languages. There are some chapters on finite-state machines, some chapters on Turing machines and computability, and a couple of chapters on codes. (7131 views) generatingfunctionology by Herbert S. Wilf - A K Peters, Ltd. , 2006 The book about main ideas on generating functions and some of their uses in discrete mathematics. Generating functions are a bridge between discrete mathematics and continuous analysis. The book is suitable for undergraduates. (8861 views)
Units Include:Activities can be used as stand-alone instruction for beginning learners or as supplemental activities to current textbook instruction.Pre-Algebra binder topics include: Number Theory, Integers and Decimals, Operations with Fractions and Mixed Numbers, Percents, Graphing and the Coordinate Plane, plus many more!Geometry binder topics include: Exploring Geometry, Polygons and an Introduction to Logic, Perimeter and Circles, Volume, plus many more!Algebra binder topics include: Number Sense, Lines and the Coordinate Plane, Operations with Polynomials, Systems, Quadratic Equations, Exponential Functions, plus many more!Real Numbers, Absolute Value Equations and Inequalities, and Matrices, Quadratics and Ellipses, Exponents and Logarithms, Rational Expressions, Rational Functions, Function Operations, plus many more!Corresponding SMART Notebook interactive lessons are available for each subject.Binders are appropriate for struggling learners in grades 6 to 12. Product Information Age(s) : 12-18 Grade Level(s) : 5-12 Language : English Usage Ideas : 100 Reproducible activities reinforce math skills in 3 key areas: pre-algebra, geometry, and algebra. Activities can be used as stand-alone instruction for beginning learners or as suplemental activities to current textbook instruction. Pre-Algebra binder
Core Mathematics for Cambridge IGCSE - Teacher's Resource Kit (with CD) This new Teacher's Resource Kit offers expert support for your Cambridge IGCSE teaching. The Teacher's Guide includes lesson plans and worksheets, while the Teacher's CD offers a host of customisable worksheets and ready-made editable PowerPoints. Fully endorsed by University of Cambridge International Examinations. Author: Bettison, I ISBN: 9780199138739 Published in 2011. Published by Oxford University Press, UK More information on Core Mathematics for Cambridge IGCSE - Teacher's Resource Kit (with CD) [New window] Core Mathematics for Cambridge IGCSE (with CD-ROM) Third Edition The third edition of Core Mathematics for Cambridge IGCSE has been written for students following the University of Cambridge International Examinations syllabus for IGCSE Core Mathematics. Written by a highly experienced author for the international classroom, this title covers all aspects of the syllabus content in an attractive and engaging format, and provides a wealth of support for students. Author: Rayner, D. ISBN: 9780199138722 Published in 2011. Edition: 3rd Published by Oxford University Press, UK More information on Core Mathematics for Cambridge IGCSE (with CD-ROM) Third Edition [New window] Essential Mathematics for Cambridge IGCSE Extended Specifically written for the Extended curriculum of the University of Cambridge International Examinations IGCSE Mathematics syllabus (0580). Written by a highly experienced author the book provides comprehensive coverage of the syllabus using carefully chosen examples and a large range of practice questions. A supporting CD-ROM provides a set of eighty-five presentations covering all the material in the book. Author: Pemberton, S. ISBN: 9780199128747 Published in 2012. Published by Oxford University Press, UK More information on Essential Mathematics for Cambridge IGCSE Extended [New window] Essential Mathematics for IGCSE Extended Teacher Resource Kit Supports the IGCSE Mathematics Extended syllabus. Written by a highly experienced author the book builds deeper understanding and retention, while encouraging enjoyment of mathematics and active learning. Recommended by CIE. Author: Barton, D ISBN: 9780199136209 Published in 2012. Published by Oxford University Press, UK More information on Essential Mathematics for IGCSE Extended Teacher Resource Kit [New window]
A course on outdated mathematics that is not necessary when a higher level of math has been reached. Its main purpose is to amplify the beauty of Calculus, where everything is so much easier thanks to the derivative. Pre-Calculus Student: Hey, can you help me with my pre-calculus homework? Me: No, I'm a mathematician.
Reston CalculusDuring this level course, students gain proficiency in solving linear equations, inequalities, and systems of linear equations. New concepts include solving quadratic equations and inequalities, exploring conics, investigating polynomials, and applying/using matrices to organize and interpret data. Students will also investigate exponential and logarithmic functions
Elementary Number Theory and Its Applications 9780321237071 ISBN: 0321237072 Edition: 5 Pub Date: 2004 Publisher: Addison-Wesley Summary: Elementary Number Theory and Its Applicationsis noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the m...athematical content and the exercises. The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years
About Pythagoras This page includes information on the focus and scope of Pythagoras as well as the policies and publication procedures. For details on how to prepare and submit a manuscript via the online manuscript submission system, please see the instructions for authors. Pythagoras is a scholarly research journal that provides a forum for the presentation and critical discussion of current research and developments in mathematics education at both national and international level. Pythagoras publishes articles that significantly contribute to our understanding of mathematics teaching, learning and curriculum studies, including reports of research (experiments, case studies, surveys, philosophical and historical studies, etc.), critical analyses of school mathematics curricular and teacher development initiatives, literature reviews, theoretical analyses, exposition of mathematical thinking (mathematical practices) and commentaries on issues relating to the teaching and learning of mathematics at all levels of education. Open Access refers to free and unrestricted access via the Internet to articles published in Pythagoras. This free access has usage limitations as stipulated in the Creative Commons Attribution (CC-BY) usage license. The license allows redistribution and reuse of all articles on the condition that Pythagoras is appropriately credited. Pythagoras has a double-blinded peer review process. Manuscripts are initially examined by editorial staff and are sent by the Editor-in-Chief to two expert independent reviewers, either directly or by a Section Editor. The editors do not inform the reviewers of the identity of the author(s). The reviewers' identities are not disclosed to the authors either. The reviewers' comments as well as recommendations regarding an article's form may be passed on to the corresponding author and may also include suggested revisions. Manuscripts that are not approved for publication will not be returned to the submitting author in any format. Please note that AOSIS OpenJournals do not retain copies of rejected articles. The peer review process aims to ensure that all published articles: present the results of primary scientific research report results that have not been published elsewhere are scientifically sound provide new scientific knowledge where experiments, statistics and other analyses are performed to a high technical standard and are described in sufficient detail so that another researcher will be able to reproduce the experiments described provide conclusions that are presented in an appropriate manner and are supported by the data are presented in an intelligible and logic manner and are written in clear and unambiguous English meet all applicable research standards with regard to the ethics of experimentation and research integrity adhere to appropriate reporting guidelines and community standards for data availability. The journal publisher, AOSIS OpenJournals, is a member of the CrossCheck plagiarism detection initiative. In the event of suspected plagiarism in submitted works CrossCheck is available to the editors of Pythagoras to detect instances of overlapping and similar text. AOSIS OpenJournals endorses and applies the standards of the Committee on Publication Ethics (COPE), which promotes integrity in peer-reviewed research publications. Pythagoras publishes one issue per year. Individual articles are published as soon as they are ready for publication by adding them to the table of contents of the 'current' volume and issue. In this way, Pythagoras aims to speed up the process of manuscript publication from submission to becoming available on the website. Since 2010, each second issue of Pythagoras is dedicated to the publication of articles themed and focused on practical theology. Special issues may be added on an ad hoc basis to the journal throughout a particular year and will form part of consecutive issues thereafter. Authors will be able to check the progress of their manuscript via the submission system at any time by logging into the journal website's personalised section. Monographs and special issues that formed part of Pythagoras through the years: Additionally, Pythagoras uses the LOCKSS (Lots of Copies Keep Stuff Safe) system to create a distributed archiving system amongst participating libraries and permits those libraries to create permanent archives of the journal for purposes of preservation and restoration. List of approved South African journals: Journals that do not appear in the abovementioned international indices but are published in South Africa and meet specific criteria may be included in this list. In conclusion: Pythagoras meets the criteria of the DoHET (see List of approved South African journals as maintained by the DoHET and Arts and Humanities Citation Index). It is therefore accredited and approved by the DoHET for its inclusion in the subsidy system for being a research publication for South Africa.
Pre-Algebra Tutorial Videos - This video set follows the Math 201 textbook Pre-Algebra by McKeague, 4th ed. They can be found on the computers in the math lab streamed from a central server. Beginning Algebra Tutorial Videos - This video set follows the Math 121 textbook Beginning Algebra by McKeague, 5th ed. They can also be found on the computers in the math lab streamed from a central server.
Not only helpful with math, but that's what I use it for. You can type in pretty much any kind of problem and it will solve it, or at least give you helpful information that will lead to the solution. I'm taking an online college algebra class at the moment and I could probably pass the class using nothing but this. EDIT: This is also really helpful, often even more helpful than WolframAlpha: Wolfram alpha is REALLY overkill for all high school math. It really should only be used for calculus, and even with calculus it has trouble with large integrations and derivatives. Personally I don't suggest you use Wolfram Alpha unless you already know how to do the math and just need it to reduce a ridiculously complex problem. Otherwise you're gimping yourself in the long run by relying on a piece of technology to do your work instead of knowing how to do it yourself. Besides, for simple algebra it only takes a few seconds to solve in your head. It takes 7 times as long to type that into wolfram alphaA generic graphing calculator can do everything you need to know in math class up until calculus. Until that point, using Wolfram Alpha is overkill. The only upside to it I can think of at this moment is the additional notation that you learn from using Wolfram Alpha. etc. Their full, pay-to-download program (Mathematica) is great as well, but the notation is a bitch to learn. The notation is just LaTeX. If you're going to do anything in the sciences or maths, you'll need to learn LaTeX anyway. Mathematica scripting is also pretty strait forward and very user friendlyEssentially, I'd liken Mathematica to photoshop - it's friendly enough for simple and familiar computations, but there's a certain amount of complexity inherent in its versatility. I probably know about 5% of the commands, as a generous estimateNot really sure if on topic or not, but: For anyone wanting to use those Wolfram addons, but with difficulties with the notation - you could always mess around with the online equation editor: It shows what the formula gives, and the source as well.
Background for Digital Filing CabinetsThe world is making progress toward achieving free, universal elementary school education. This, of course, is merely a step toward providing free PreK-12 or PreK-16 or lifelong education for all people of all ages throughout the world. Information and Communication Technology (ICT) is making a steadily growing contribution toward eventual achievement of these visionary goals. Open Source Textbooks. This Web Page explores the idea of providing free, open source textbooks and instructional materials to students took keep, edit, add marginal notes and comments, and so on. Introduction to Math Education DFC Each academic discipline has its own discipline-specific educational goals and ways of achieving these goals. In our current school curriculum, it is useful to think of how to improve education in specific disciplines. This Web Page focuses specifically on the idea of a Math Education Digital Filing Cabinet. It is important to remember, however, that most problems people encounter are interdisciplinary. Math is an important aid to representing and attempting to solve problems in every academic discipline. Thus, math needs to be taught in a manner that facilitates transfer of learning to other disciplines, and other disciplines need to be taught in a manner that helps students learn to make effective use of math in the disciplines. The Math Education Digital Filing Cabinet project is based on three assumptions: That all people of the world are entitled to a free, good quality education. Good quality is to be determined by contemporary standards; however, it should prepare students to become and remain responsible citizens and lifelong learners who can adjust to life in a changing world. This education should be designed to empower learners by helping them gain levels of expertise in diverse areas that meet their own specific needs and interests, the needs and interests of their community, and the needs and interests of the world. Knowledge and skills in math and in using math to help represent and solve problems are an important outcome of a good education. The Math Digital Filing Cabinet project is very large and is just in its infancy. This IAE-pedia page is being used to explore various aspects of the project. Eventually there will be separate Digital Filing Cabinet drawers for various groups of math teachers. For example, the needs of an elementary school teacher are quite different than the needs of a College of Education Math Methods teacher or a university Department of Mathematics faculty member who provides math content instruction to preservice elementary and secondary school teachers. Math Education for Teachers of Math Math is a broad, deep discipline with a long history. A person can spend a lifetime studying and doing research on math content and still know only a small fraction of the totality of collected math knowledge. Similar statements hold for a person exploring the history of math, the teaching of math, and the applications of math in various non-math disciplines. A person who is teaching math or teaching teachers to teach math needs to be knowledgeable in three overlapping areas of mathematics: Math content knowledge. Math pedagogical knowledge. Math pedagogical content knowledge (PCK). The diagram given below is applicable in every academic discipline. Math Content Knowledge There is a huge and steadily growing accumulation of math content knowledge. On a worldwide basis, many thousands of math researchers are contributing to this accumulation. The challenge of this huge and steadily growing accumulation of math content knowledge can be examined from how it affects elementary teachers, secondary school math teachers, and higher education math teachers. The situation is roughly as follows: A typical elementary school teacher has studied math up through the 11th or 12th grade, has taken a Math For Elementary Teachers course or sequence of courses in college,and has taken a Math Methods course. This persons "peak" math content is the material covered in Math for Elementary Teachers, which may have College Algebra as a prerequisite. A typical secondary school math teacher has a math content preparation that lies in the range of two years of college math to a bachelor's degree in math. In a number of states, there is a strong emphasis on high school math teachers having a bachelor's degree in math. A typical teacher of math in a higher education institution has math content preparation that lies someplace in the range of a bachelors degree in math to a Doctorate in math. For most teachers of math, there is a considerable difference between their highest level of math content course work and their current level of math content knowledge and skill. On the one hand, we know that people tend to forget the details of coursework that they are not using on a regular basis.Thus, for example, a typical fourth grade teacher will gradually forget most of the details of math content learned in high school and above. On the other hand, the research-oriented math faculty in a college of university university will be routinely actively engaged in maintaining and expanding their math content knowledge. Thus, especially in their areas of research, their content knowledge will be well above the level achieved while in school. Math Pedagogical Knowledge A relatively strong rule of thumb is that teachers teach the way they were taught. The pedagogical knowledge gained by years and years of observing teachers (being taught by teachers) create a powerful mind set on how teaching is done. Think about your experiences as a math student in elementary school, in secondary school, and in college. During these years of your schooling, you learned how elementary teachers typically teach math, how secondary school math teachers typically teach math, and how college math teachers typically teach math. In secondary school, for example, the math class might begin with students handing in an assignment that they started working on during the previous math class. This is followed by a discussion of assignment problems, presentation of some new material, a new assignment, and seat work for the remainder of the period. The class may well include students doing some work at the chalk board, and the teacher will likely use an overhead projector, computer projector, chalkboard, or white board in the presentation. The amount of interaction between the teacher and students may vary considerably depending on the students and the teacher. Some teachers may have students interact in small groups to explore a problem of mathematical task. In college math courses, demonstration and lecture tend to dominate. The teacher demonstrates and explains how to solve various problems that were in the homework assignment. The teacher lectures and demonstrates on the new material to be presented. Students take notes, and they ask questions about parts of the demonstration and lecture that they do not understand. From time to time the teacher asks a question and accepts ananswer from some volunteer in the class. A student in a preservice teacher eduction program has repeatedly seen examples of math teaching and has gained quite a bit of math pedagogical knowledge. Research indicates that teachers tend to teach the way they were taught. It is hard for a teacher at any level to break the math pedagogical knowledge patterns they grew up with. This creates an interesting and large challenge to the math education community as research suggests new and possible better ways to facilitate student learning. Here is an example. Consider the idea of student-centered teaching, small group discussions, and team projects in teaching and learning math. How does a preservice teacher who has seldom or never participated in such teaching/learning environments learn to make effective use of these teaching techniques? For another example, how does one make effective use of a computer hooked to a projection system and to the Internet while teaching a math unit of study? At the current time, relatively few students are seeing good examples of this in their elementary school secondary school, and college math courses. The idea of virtual manipulatives is related to this. Many elementary school math teachers are comfortable with students using physical manipulatives. What are advantages disadvantages of using computer-based manipulatives? Math Pedagogical Content Knowledge The idea of pedagogical content knowledge (PCK) has received a lot of attention and has been the focus of quite a bit of research and teacher education since it was first proposed by Lee Shulman in the mid 1980s. Quoting from the [ Technology Pedagogical Content Knowledge Website: This knowledge includes knowing what teaching approaches fit the content, and likewise, knowing how elements of the content can be arranged for better teaching. This knowledge is different from the knowledge of a disciplinary expert and also from the general pedagogical knowledge shared by teachers across disciplines. PCK is concerned with the representation and formulation of concepts, pedagogical techniques, knowledge of what makes concepts difficult or easy to learn, knowledge of students' prior knowledge and theories of epistemology. It also involves knowledge of teaching strategies that incorporate appropriate conceptual representations, to address learner difficulties and misconceptions and foster meaningful understanding. It also includes knowledge of what the students bring to the learning situation, knowledge that might be either facilitative or dysfunctional for the particular learning task at hand. This knowledge of students includes their strategies, prior conceptions (both "naïve" and instructionally produced); misconceptions students are likely to have about a particular domain and potential misapplications of prior knowledge. Liping Ma is well known for her 1999 book Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the U.S. Her book provides good examples of math PCK needed by elementary school teachers. She argues that even though elementary school math teachers in China have had quite a bit less formal math instruction than similar teachers in the United States, the Chine teachers have better PCK because their elementary and secondary school teachers had better PCK. Information and Communication Technology Information and Communication Technology (ICT) is affecting the content, pedagogy, and PCK of every academic discipline. Here is a very brief summary of the current and future situation: Computers can solve or significantly help to solve some of the problems in each academic discipline. The ICT content in any particular discipline varies with the discipline. However, ICT is now important enough in each discipline so that the content being taught to students needs to reflect capabilities and limitations of ICT in the discipline. ICT provides a variety of pedagogical aids. For example, computer-assisted learning and distance learning are of growing importance in each academic discipline. Teachers in each discipline are faced by the challenge of how to help students learn to use ICT as an aid to knowing and using the discipline being taught. ICE brings some general aids to teaching and learning, such as computer-assisted learning, distance learning, and use of multimedia in classroom instructional. Each specific discipline has its own ways of dong this and its own discipline-specific materials that are relevant to such tasks. Math games and puzzles, along with some information about suitable uses to improve the quality of math education that students using the games and puzzles are apt to gain. Archival copies of grade books from past years. A library of books, magazines, journals, and articles to support personal needs and needs of one's students. Overhead projector foils. There are lots of different possibilities. For example, many teachers find it useful to have various sizes of black line masters of graph paper. Of course, blank foils and appropriate marking pens are a needed part of this collection. Physical manipulatives. Examples include blocks, spinners, geoboards, dice, and so on. Teachers making use of class sets of such manipulatives need a lot of drawer and/or shelf space. Video tapes, audio tapes, CDs, and DVDs. In each case, a teacher may have both prerecorded and blank recordable media. Storage boxes and containers. Papers and tests received from and/or ready to be handed back to students. Etc. etc. etc. Some items might be stored in either a physical filing cabinet or a DFC, or both. Some possible examples include grade books, quizzes and tests, lesson plans, handouts for use by students. A physical filing cabinet might consist of some materials stored at home, some stored in one's classroom, and some stored elsewhere, such as a storage room in one's school. ideally, all of the contents would be easily accessible when you want to access them. This is an obvious problem with the storage and retrieval of physical materials. As an example, usually one wants to avoid the cost of having duplicate copies of reference books that one might want to refer to at home and at school. With physical materials, there is an ongoing problem of guarding against possible disasters. What happens if there is a fire or flood in the space where your materials are stored? What happens if materials are stolen or maliciously destroyed? If a teacher moves to a new teaching job, who gets to keep the physical materials? Here is an important question. As the collection grows, how does one organize it so that needed materials are quickly retrieved? Here are two interesting aspects of an answer. First, one only tends to collect and store materials that are specifically relevant to the job. One has a good working knowledge of how to use the materials on the job. Thus, one has a type of personal "ownership" of the materials. Second, the materials are often stored in a manner so that one's kinesthetic sense, visual memory, and a quick glance tend to help in quick retrieval. It is an interesting exercise to compare and contrast this with retrieval of information stored in a computer. Math DFC: Where to Put It? Anything that can be stored in a computer can be part of your DFC. A major question is, where do you want to store your Math DFC contents. Two general choices are: On your own personal computer or computers. On a server. This might be a local server, such as in your school building or district. It might be a server located thousands of miles away. (Indeed, you may have no idea where your materials are being stored.) Nowadays, you are apt to have part of your DFC on your own personal computer and part on servers. In either case, you need to be concerned with having the material regularly backed up in a "off site" location and having your materials protected from physical and electronic threats. You also need to decide what parts of your DFC you want to make available to other people. Suppose, for example, that all of the contents of your DFC are stored on a laptop computer that you regularly carry between home and school. You might have a home desktop microcomputer where you keep a backup copy of your DFC. If your storage and backup are just on these two computers, have the risk of both computers being damaged at the same time by fire, storm, or flood. Thus, you still need to have some form of off site backup storage. When you want to share a document with a particular person you can send it as an email attachment, copy it onto a CD or DVD and hand the person the physical medium, copy the material onto a thumb drive and watch as the person copies it into his or her computer, and so on. In all of these cases you have considerable control over who receives the material. Of course, you don't know who might get copies from this person. The Information Age Education (IAE) Websites provide an example of storage on a server. The company running the server provides automatic backup. In addition, Information Age Education staff periodically make an off site backup. The Web Page you are currently reading is stored on a server, along with the MediaWiki software that is used in creating, editing, storing, and retrieving the material. All of the content can be accessed from any place in the world by anyone who can access the Internet. Most of the pages in the Website are open to online editing by readers. That is, people from around the world can log onto the site, add and/or edit pages, add comments, and so on. The content stored on the Website (along with Joomla! software) is open to reading and download by people throughout the world. However, the content posted on this Website cannot be changed by the readers. A third alternative available when storing on a server is to have the contents password protected. Then, only people who know the password can log on and access the content. In summary, storage on a server run by a reputable and responsible organization provides for off site backup and for ease of access by people throughout the world. Access to the content may be restricted through use of some sort of password protection system. Math DFC: Making It Yours It does little good to collect lots of stuff into a DFC and have no idea what is there or how and why you might want to use it some day. You need to have personal ownership and understanding of the content of your DFC. Today's search engines make it relatively easy to retrieve thousands (indeed, millions) of articles on various topics that are relevant to teaching and learning math. Each time you find an article of personal use to you, think about adding it to your DFC. One way to do this is via an annotated bibliography. Put an entry into the "references" section of DFC that contains a proper citation to the article, including a link to its website if the article is on the web. Then write a brief paragraph (in essence, a note to yourself) explaining what this article means to you and why or how you might want to use it in the future. Teachers are used to the idea of developing lesson plans, using the lesson plans, and writing comments to themselves about what they will do the same and what they will do different the next time they use the lesson plans. This is an excellent example of steadily increasing the value of material in one's filing cabinets. At the end of a teaching day, spend just a few minutes writing notes in each of the lesson plans you have used that day. Think of these as notes to your future self—things that you want your future self to know about the next time the lesson plan is used. Another aspect of personalization is organizing the material in a form that helps you to quickly find and retrieve a particular item you are interested in. If your personal DFC is on your own computer, you may want to use a structure of file folders. An elementary school teacher, for example, might want to have a separate file folder for each of the subject areas she or he teaches. A DFC can be searched electronically, and it can have an indexing system that is specifically designed to fit the needs of its owner. This is a key idea. Think in terms of deciding upon a list of Categories (using the term the way a Wiki does), being able to easily add or delete categories, and being able to index the various entries in one's DFC. The combination of indexing using Categories and use of a search engine is a powerful aid to finding what is in your DFC. A Sample Collection of Relevant Materials Math is considered to be one of the basics of education. We want all students to gain contemporary levels of knowledge and skills in reading, writing, and math. One of the specific goals of the IAE-pedia is to aid in the creation, collection, and dissemination of a Math Education Digital Filing Cabinet of materials designed to serve the needs of teachers and their students. The underlying model for this Digital Filing Cabinet is a collection of free, open source materials that can made available to teachers and students throughout the world. The IAE-pedia contains a number of articles designed to help improve informal and formal math education. Some of these articles are listed below. The list given below also contains some links to articles located elsewhere. The notion of "concrete," from concrete manipulatives to pedagogical sequences such as "concrete to abstract," is embedded in educational theories, research, and practice, especially in mathematics education. In this article, I consider research on the use of manipulatives and offer a critique of common perspectives on the notions of concrete manipulatives and concrete ideas. I offer a reformulation of the definition of "concrete" as used in psychology and education and provide illustrations of how, accepting that reformulation, computer manipulatives may be pedagogically efficacious. Computational Thinking. Cuts across all disciplines. Includes an emphasis on math modeling that makes use of human brain and computers. David Moursund Editorials. A collection of all of the editorials that David Moursund wrote for the Oregon Computing Teacher, The Computing Teacher, and Learning and Leading with Technology. Empowering Learners and Teachers. This document includes a specific discussion of empowering students through teaching of reading and math. It includes the calculator and the digital watch in its examples. Folk Math. A seminal article by Eugene Maier that draws a parallel between Folk Music (music that the ordinary people learn and do or use), and Folk Math. Contrasts Folk Math with School Math. See also: Eugene Maier. Gene is a world class math educator. This collection of short articles is well suited for use in preservice and inservice math education, and by others interested in the quality of math education that children are currently receiving. Free Math Software. There is a huge and growing amount of free math software, math education software, math-oriented games, and so on. Johnson, Jerry (n.d.). Math NEXUS. Jerry Johnson's Math NEXUS Website is an excellent example of a math education digital filing cabinet. It is designed to meet the needs of students and faculty interested in math education, and it serves as an outlet for his own personal creativity. Lockhart, Paul (2002). A Mathematician's Lament. Retrieved 4/24/08: Argues that math should be considered an art, compares with music and painting, and "blasts" our current math education system. Math Education. Discusses different answers to the questions, "What is mathematics." Emphasizes the need for students to gain increasing insight into possible answers as they progress in their math studies. The Math Forum Is...the leading online resource for improving math learning, teaching, and communication since 1992. We are teachers, mathematicians, researchers, students, and parents using the power of the Web to learn math and improve math education. We offer a wealth of problems and puzzles; online mentoring; research; team problem solving; collaborations; and professional development. Students have fun and learn a lot. Educators share ideas and acquire new skills. Math Maturity. An introduction to a general measure of student progress toward learning mathematics for long term use and understanding. Introduction to Using Games in Education: A Guide for Teachers and Parents. The Mind and the Computer: Problem Solving in the Information Age. College Student's Guide to Computers in Education. Moursund Editorial: High Tech—High Touch. Explores the need for education to provide an appropriate balance between high technology and strongly people-oriented low or no technology. From the November 1985 issue of The Computing Teacher. International and domestic comparisons show that American students have not been succeeding in the mathematical part of their education at anything like a level expected of an international leader. Particularly disturbing is the consistency of findings that American students achieve in mathematics at a mediocre level by comparison to peers worldwide. On our own "National Report Card"—the National Assessment of Educational Progress (NAEP)—there are positive trends of scores at Grades 4 and 8, which have just reached historic highs. This is a sign of significant progress. Yet other results from NAEP are less positive: 32% of our students are at or above the "proficient" level in Grade 8, but only 23% are proficient at Grade 12. Consistent with these findings is the vast and growing demand for remedial mathematics education among arriving students in four-year colleges and community colleges across the nation. Moreover, there are large, persistent disparities in mathematics achievement related to race and income—disparities that are not only devastating for individuals and families but also project poorly for the nation's future, given the youthfulness and high growth rates of the largest minority populations. Oregon_Mathematics-OCTM. Email messages facilitating an increased level of communication and discussion among members of the Oregon Council of Teachers of Mathematics. Problem Solving. Problem solving lies at the core of each academic discipline. Many of the general ideas and strategies used in problem solving in one discipline can transfer to other disciplines. This is especially true of math problem solving, since math is an important component of many other disciplines. Science & Technology Museum Math Exhibit. Explores possible answers to the question, "What is math?" Analyzed some components of a science and technology exhibit on math. Explores the idea of making an elementary school classroom and overall curriculum more mathematical. Two Brains Are Better Than One. Explores educational implications of human brain and computer brain working together to solve problems in math and other areas. What is Computer Science? Computer science is a discipline closely related to mathematics. In many cases, today's Computer and Information Science Departments were "spun off" from Math departments. In many other cases, Computer Science and Math are still together in one college or university department. MathWorld is the web's most extensive mathematical resource, provided as a free service to the world's mathematics and internet communities as part of a commitment to education and educational outreach by Wolfram Research, makers of Mathematica. MathWorld has been assembled over more than a decade by Eric W. Weisstein with assistance from thousands of contributors. Since its contents first appeared online in 1995, MathWorld has emerged as a nexus of mathematical information in both the mathematics and educational communities. It not only reaches millions of readers from all continents of the globe, but also serves as a clearinghouse for new mathematical discoveries that are routinely contributed by researchers. Its entries are extensively referenced in journals and books spanning all educational levels, including those read by researchers, elementary school students and teachers, engineers, and hobbyists. Women and ICT. ICT and mathematics overlap. Many of the women who were pioneers in the computer field were mathematicians. The Math Forum is a leading center for mathematics and mathematics education on the Internet. Operating under Drexel's School of Education, our mission is to provide resources, materials, activities, person-to-person interactions, and educational products and services that enrich and support teaching and learning in an increasingly technological world. Our online community includes teachers, students, researchers, parents, educators, and citizens at all levels who have an interest in math and math education. Making math-related web resources more accessible Want to use or develop educational technology? Visit Math Tools, the Forum's community digital library supporting the use and development of software for mathematics education. When a generic Web directory falls short of your mathematics needs, visit the Forum Internet Mathematics Library, which covers math and math education Web sites in depth. In our collaboration with the Mathematical Association of America, Mathematical Sciences Digital Library (MathDL), we collect mathematics instructional material with authors' statements and reader reviews; and catalogs mathematics commercial products, complete with editorial reviews, reader ratings and discussion groups. The Problems Library offers a convenient interface for searching and browsing the collective archives of the six Problem of the Week services. Providing high-quality math and math education content There's a lot of material on the Web, but how good is it, and how does it take advantage of new technologies or implement new pedagogy? We have worked with teachers, students, and researchers to put the best of their materials on the Web. This collaborative work is available via the Forum's Teacher Exchange: Forum Web Units. Teachers are invited to use the Web interface to contribute their own lessons. This is an excellent and growing set of math materials for preservice and inservice math teachers at all grade levels. Some examples of the categories of material being made available include: Problem of the Week. Quote of the Week. Statistic of the Week Humor of the Week Website of the Week Resource of the Week Also from the Math Forum, see their Library. This is a very large collection of materials and links to materials. Math Resources from the Southern Oregon Education Service District. Retrieved 2/5/08: A nice collection of computer-based resources of use to teachers and to teachers of teachers. Permission is granted to copy, distribute and/or modify these documentsTechnological Pedagogical Content Knowledge (TPCK) attempts to capture some of the essential qualities of knowledge required by teachers for technology integration in their teaching, while addressing the complex, multifaceted and situated nature of teacher knowledge. At the heart of the TPCK framework, is the complex interplay of three primary forms of knowledge: Content (CK), Pedagogy (PK), and Technology (TK). … the TPCK framework builds on Shulman's idea of Pedagogical Content Knowledge. Research in the area of educational technology has often been critiqued for a lack of theoretical grounding. In this article we propose a conceptual framework for educational technology by building on Shulman's formulation of ''pedagogical content knowledge'' and extend it to the phenomenon of teachers integrating technology into their pedagogy. This framework is the result of 5 years of work on a program of research focused on teacher professional development and faculty development in higher education. It attempts to capture some of the essential qualities of teacher knowledge required for technology integration in teaching, while addressing the complex, multifaceted, and situated nature of this knowledge. We argue, briefly, that thoughtful pedagogical uses of technology require the development of a complex, situated form of knowledge that we call Technological Pedagogical Content Knowledge (TPCK). In doing so, we posit the complex roles of, and interplay among, three main components of learning environments: content, pedagogy, and technology. We argue that this model has much to offer to discussions of technology integration at multiple levels: theoretical, pedagogical, and methodological. In this article, we describe the theory behind our framework, provide examples of our teaching approach based upon the framework, and illustrate the methodological contributions that have resulted from this work. The National Library of Virtual Manipulatives (NLVM) is an NSF supported project that began in 1999 to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-12 emphasis). The project includes dissemination and extensive internal and external evaluation. Learning and understanding mathematics, at every level, requires student engagement. Mathematics is not, as has been said, a spectator sport. Too much of current instruction fails to actively involve students. One way to address the problem is through the use of manipulatives, physical objects that help students visualize relationships and applications. We can now use computers to create virtual learning environments to address the same goals. There is a need for good computer-based mathematical manipulatives and interactive learning tools at elementary and middle school levels. Our Utah State University team is building Java-based mathematical tools and editors that allow us to create exciting new approaches to interactive mathematical instruction. The use of Java as a programming language provides platform independence and web-based accessibility. The NLVM is a resource from which teachers may freely draw to enrich their mathematics classrooms. The materials are also of importance for the mathematical training of both in-service and pre-service teachers. Lessons: " Site Reviews: -- Tired of looking through page after page of search-engine hits trying to find a site that might have something useful? These categorized Internet links have all been reviewed by Purplemath. Free Online Tutoring and Lessons Quizzes and Worksheets Other Useful Sites and Services Only those sites with something immediately useful (and free) for algebra students are listed. You won't find math jokes, biographies, or recreational math sites here. Instead, check these review for sites containing lessons, tutoring forums, worksheets, articles on "how math is used in real life", and more. Homework Guidelines: "How to suck up to your teacher." -- English teachers tell students explicitly how to format their papers. Math teachers, on the other hand, frequently just complain about how messy their students' work is. Neat homework can aid your comprehension and maybe make your teacher like you better. These Homework Guidelines for Mathematics will give you a leg up, explaining in clear terms what your math teacher is looking for. Study Skills Self-Survey: "Do I have what it takes?" -- Much of your success or failure in algebra can be laid at the feet of your study habits. Do you have good math study habits? Take this survey and find out. This five page research article includes a discussion of math learning. It begins by noting that most of what one learns in a course is not retained very long. It argues that a change in study habits can make a very large difference in long term retention. Roughly speaking, the authors argue that the design of the seat work and homework in the typical math book is poor if one's goal is long term retention. In the two paragraphs that follow, Spacers divide their study time into two sessions with a space in between. Massers mass their study time into one concentrated session. Quoting from the article: Because the experiments described thus far required subjects to learn concrete facts, it is natural to wonder whether the results of these studies will generalize to tasks requiring more abstract kinds of learning. To begin to explore this question, we have been assessing the effects of overlearning and spacing in mathematics learning. For example, in one experiment (Rohrer & Taylor, 2006), students were taught a permutation task and then assigned either three or nine practice problems. The additional six problems, which ensured heavy overlearning, had no detectable effect on test scores after one or four weeks. In another experiment with the same task (Rohrer & Taylor, in press), a group of Spacers divided four practice problems across two sessions separated by one week, whereas a group of Massers worked the same four problems in one session. When tested one week later, the Spacers outscored the Massers (74% vs. 49%). Furthermore, the Massers did not reliably outscore a group of so-called Light Massers who worked only half as many problems as the Massers (49% vs. 46%). This apparent ineffectiveness of overlearning and massing is troubling because these two strategies are fostered by most mathematics textbooks. In these texts, each set of practice problems consists almost entirely of problems relating solely to the immediately preceding material. The concentration of all similar problems into the same practice set constitutes massing, and the sheer number of similar problems within each practice set guarantees overlearning. Alternatively, mathematics textbooks could easily adopt a format that engenders spacing. With this shuffled format, practice problems relating to a given lesson would be distributed throughout the remainder of the textbook. For example, a lesson on parabolas would be followed by a practice set with the usual number of problems, but only a few of these problems would relate to parabolas. Other parabola problems would be distributed throughout the remaining practice sets. SAGE is a free open source alternative to Magma, Maple, Mathematica, and Mathlab. It is available for Windows, Mac OSX, and Linux. Quoting from the Website: Use SAGE for studying a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra. SAGE makes it easy for you to use most mathematics software together. SAGE includes interfaces to Magma, Maple, Mathematica, MATLAB, and MuPAD, and the free programs Axiom, GAP, GP/PARI, Macaulay2, Maxima, Octave, and Singular. The Shodor Foundation is a non-profit research and education organization dedicated to the advancement of science and math education, specifically through the use of modeling and simulation technologies. Welcome to the Shodor's Curriculum Materials portal. There are several ways for you to browse our resources: Search by grade level Find the materials that are specifically geared towards a particular educational level. Search by subject matter Locate all of the available Shodor resources for a subject or field of study. Browse all projects View a list of all of Shodor's Curriculum Materials projects. Use this tool to find a specific project that you have used before. Interactive Teaching Environments The Shodor Foundation staff and associates are developing interactive tools and simulations that enable and encourage exploration and discovery through observation, conjecture, and modeling activities. These Modeling and Simulation Technology for Education Reform (MASTER) tools are part of on-going collaborations with the National Center for Supercomputing Applications (NCSA) and other education organizations. Simulations and supporting materials developed by Foundation staff form the basis of international science collaborations presently demonstrating network technologies involving middle and high schools of the Department of Defense Education Activity (DoDEA). A growing portfolio of MASTER tools are being fully integrated with new collaboration tools and on-line research facilities to create authentic scientific experiences. All tools, simulations, and supporting curriculum materials are designed in accordance with the National Science Education Standards and the National Math Education Standards. Links to Other IAE Resources This is a collection of IAE publications related to the IAE document you are currently reading. It is not updated very often, so important recent IAE documents may be missing from the list. This component of the IAE-pedia documents is a work in progress. If there are few entries in the next four subsections, that is because the links have not yet been added.
Video Summary: This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations
Search form Main menu You are here Modules 2013–14 MTH4110 Mathematical Structures Description This module is intended to introduce students to the concerns of mathematics, namely clear and accurate exposition and convincing proofs. It will attempt to instil the habit of being "precise but not pedantic". The module covers an informal account of sets, functions and relations, and a sketch of the number systems (natural numbers, integers, rational, real and complex numbers), outlining their construction and main properties. Natural numbers and induction. Integers and rational numbers with a sketch of the construction. Real numbers (treated as infinite decimal and binary expansions) including some completeness properties. Countability of the rationals and uncountability of the reals. Complex numbers. The complex plane with cartesian and polar coordinates; addition and multiplication. Statement of the Fundamental Theorem of Algebra.
Group theory is one of the most fundamental branches of mathematics. This volume of the Encyclopaedia is devoted to two important subjects within group theory. The first part of the book is concerned with infinite groups. The authors deal with combinatorial group theory, free constructions through group actions on trees, algorithmic problems, periodic groups and the Burnside problem, and the structure theory for Abelian, soluble and nilpotent groups. They have included the very latest developments; however, the material is accessible to readers familiar with the basic concepts of algebra. The second part treats the theory of linear groups. It is a genuinely encyclopaedic survey written for non-specialists. The topics covered include the classical groups, algebraic groups, topological methods, conjugacy theorems, and finite linear groups. This book will be very useful to all mathematicians, physicists and other scientists including graduate students who use group theory in their work. [via] "... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum [via] Modern number theory, according to Hecke, dates from Gauss's quadratic reciprocity law. The various extensions of this law and the generalizations of the domains of study for number theory have led to a rich network of ideas, which has had effects throughout mathematics, in particular in algebra. This volume of the Encyclopaedia presents the main structures and results of algebraic number theory with emphasis on algebraic number fields and class field theory. Koch has written for the non-specialist. He assumes that the reader has a general understanding of modern algebra and elementary number theory. Mostly only the general properties of algebraic number fields and related structures are included. Special results appear only as examples which illustrate general features of the theory. A part of algebraic number theory serves as a basic science for other parts of mathematics, such as arithmetic algebraic geometry and the theory of modular forms. For this reason, the chapters on basic number theory, class field theory and Galois cohomology contain more detail than the others. This book is suitable for graduate students and research mathematicians who wish to become acquainted with the main ideas and methods of algebraic number theory. [via]
9780618135realgebra Prealgebra, 5/e, is a consumable worktext that helps students make the transition from the concrete world of arithmetic to the symbolic world of algebra. The Aufmann team achieves this by introducing variables in Chapter 1 and integrating them throughout the text. This text's strength lies in the Aufmann Interactive Method, which enables students to work with math concepts as they're being introduced. Each set of matched-pair examples is organized around an objective and includes a worked example and a You Try It example for students. In addition, the program emphasizes AMATYC standards, with a special focus on real-sourced data. The Fifth Edition incorporates the hallmarks that make Aufmann developmental texts ideal for students and instructors: an interactive approach in an objective-based framework; a clear writing style; and an emphasis on problem solving strategies, offering guided learning for both lecture-based and self-paced courses. The authors introduce two new exercises designed to foster conceptual understanding: Interactive Exercises and Think About It
For 1st year algebra, we will work with trinomials without a coefficient of the squared term. Factoring Trinomials (A1.2.E; A1.5.C; A1.1.D) ... BigIdea: Interpret and graph situations modeled by exponential functions. Enrichment Practice Reteaching Problem Solving or Enrichment Developing Big Ideas in Algebra thru Technology and Hands on Activities ... This idea was also a Classroom Grant Award winner from last year. ... We have examples for use in Algebra 1 & 2, geometry, and Calculus that we have copied for you and with a little preparation, ... BigIdea: The place values to the right of the decimal point in the base-ten system names numbers less than one. EQ: ... MG 2.1* MG 2.2* Algebra and Functions ⅔** AF 2.1* prescription for determining a second number when a first number is given. Open the door to future mathematical learning for ALL students by making a unifying idea of mathematics a ... Hear about the big ideas behind this book. Do ... (Sketchpad) that remove the abstraction from algebra and give it meaning. Topics will be from algebra 1& 2, trigonometry, & pre ... Count forward beginning from a given number within the known sequence (instead of having to begin at 1). CC.K.CC.2 ... GLE captures the bigidea (conceptual understanding) of magnitude of numbers. CCSS ... a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a ... Created by GMAT Club and big thanks to hgp2k for making this spreadsheet shine Analysis ... Main Idea Ecoefficiency Social Science Supporting Ideas ... 2* Algebra First-degree equations Properties of numbers Geometry Area 5* ... take the DSAT Exam and look over the CST "Released Questions" prior to planning your lessons so that you have a good idea of the level of teaching that needs to be ... How Big is 1 Million? 8A 12A 16A Expanded Notation 18A ... ALGEBRA & FUNCTIONS AF1.2...Expressions with Parenthesis ... Use the idea that builders and mechanics always quote ... Teachers should ensure that students are not put off by the word 'Algebra'. This will be a big misconception to battle but it is vital that this first indroduction is a success as it ... Algebra2 FDPRP I know not to round during ... ... using inspection, long division, or a computer algebra system for more complex examples. Rubric (A ... Big Ideas - Themes Common Core Standard Skills ... for GOAL SETTING purposes and represent a suggestion of how long it should take students to acquire a specific content idea or skill. ... How Big is 1,000? Problem Solving: Number ... take the DSAT Exam and look over the CST "Released Questions" prior to planning your lessons so that you have a good idea of the level of teaching that needs ... ALGEBRA & FUNCTIONS...CLUSTER 3 NUMBER SENSE... CLUSTER 2 NUMBER SENSE ... What's the BigIdea, Ben Franklin? What's Under My Bed? Where Do You Think You're Going, Christopher Columbus? Where the Wild Things Are ... Adventurous World of Algebra, The, Program 2: Functions Adventurous World of Algebra, The, Program 3: Linear Equations Back to School Idea Book Trend Enterprise Inc. General Hoerr, Thomas ... Big Ben is Dead Paperback Book Building Wings: How I Made It Through School ... Pre-Algebra Copy 2 Pre-Algebra Copy 3 Pre-Algebra: DVD & Copy 4
Our users: If you are having problems with algebra and you cant find a simple way to learn, you must try Algebrator, you will never believe what its capable of doing. Diane Flemming, NV This algebra tutor will never turn you down. Always ready for any equation you enter, to help you wherever you get stuck; it makes an ideal tutor. I am really glad with my decision to buy the software. Charlotte Beecham, IN I found the Algebrator helpful. I still have a lot to learn about using it. I do believe it was worth the money I paid for it. I have one more math class to take and I am sure I will put the Algebrator to good use then! Trevor Smith, OK12-18: quadratic equation by square root property , (h+k) aptitude questions with solutions +Free Algebra Problem Solver Online properties of addition printables worksheets third grade permutations and combinations examples how to enter cube root on ti 83 matlab quadratic graph prentice hall algebra 2 answer key how to solve equations with fractions simplifying expressions online why is hard for student to learn how to solving addition and subtraction equations
Created by educators, for educators, Algebra'scool is a dynamic teaching system covering a full year of Algebra I instruction. Algebr'scool is a great resource that can be used to support STEM curricula. This exciting and revolutionary series presents comprehensive mathematics curricula through effective and entertaining animations, lively graphics, concrete examples and real-world explanations - making it easy for students to grasp and understand the content. Developed by BestQuest Teaching Systems, the Algebra'scool Teaching System Content Package provides comprehensive instructional material covering a complete Algebra I curriculum, including operations and expressions; linear equations; inequalities; functions; polynomials; quadratic equations; rational and radical equations; probability and statistics. It supports standards from both the National Council of Teachers of Mathematics (NCTM) and Common Core and State Standards for mathematics. This package consists of 37 hours of content reflected in 99 algebra lessons and includes 25 short videos profiling professionals who use algebra in their careers. Algebra'scool provides all of the effective tools a teacher needs to support student learning. Each video lesson comes with supplemental print materials that cover the curriculum and extend the video instruction. Package now includes 943 PDF documents consisting of teacher's guides and student worksheets filled with lesson notes, guided practice, independent and additional practice and manipulative exercises. Teacher's guides provide a complete manual accompanying the lessons, complete with teaching tips, answers to the student problems, glossaries of key terms and module tests. $500/yr/school Annual license subscription per school/library An additional hard drive may need to be purchased to host additional content packages
Categories Mathematics: Most read books Wouldn't it be great if there were a statistics book that made histograms, probability distributions, and chi square analysis more enjoyable than going to the dentist? _Head First Statistics_ brings this typically dry subject to life, teaching you everything you want and need ... Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: _Head First Algebra_ is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything f... Need to learn statistics as part of your job, or want some help passing a statistics course? _Statistics in a Nutshell_ is a clear and concise introduction and reference that's perfect for anyone with no previous background in the subject. This book gives you a solid understan... Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'l... Need to learn statistics for your job? Want help passing a statistics course? _Statistics in a Nutshell_ is a clear and concise introduction and reference for anyone new to the subject. Thoroughly revised and expanded, this edition helps you gain a solid understanding of stati... Some years ago, a survey of 'A'-level maths students indicated that 90% taking the exam had not covered the whole syllabus. This information came as no surprise to those who, like Keith Gregson, were meeting these students as undergraduates in the biological sciences or in eng... This book is an extemsion of the lecture notes for a course in algebra and geometry for first-year undergraduates of mathematics and physical sciences. Except for some rudimentary knowledge in the language of set theory the prerequisites for using the mai Fundamental Concepts of Mathematics serves primarily as a textbook for the A-level examination. It also coverrs important topics that are often omitted due to the lack of time in the undergraduate courses, and thus is a supplementary reference for univers This book aims to illustrate with practical examples the applications of linear optimization techniques. It is written in simple and easy to understand language and has put together a useful and comprehensive set of worked examples based on real life problems. The topics inclu... These proceedings contain most of the contributions to the Göttingen-Jerusalem Conference 2008 on "Symmetries in Algebra and Number Theory" including three addresses given at the conference opening, and two contributions to the Satellite Conference "On the Legacy of Hermann We... Portfolio optimization is a widely studied problem in finance dating back to the work of Merton from the 1960s. While many approaches rely on dynamic programming, some recent contributions use martingale techniques to determine the optimal portfolio allocation. Using the latte... This is the first volume of a three volume collection of Andrey Nikolaevich Tyurin's Selected Works. It includes his most interesting articles in the field of classical algebraic geometry, written during his whole career from the 1960s. Most of these papers treat different pro...
0495108952 9780495108955 easy with tools found throughout the text such as objectives, vocabulary definitions, calculator examples, good advice for studying, concept reviews, and chapter tests. Through caution remarks that alert you to common pitfalls and how and why segments that explain and demonstrate concepts and skills in a step-by-step format, you will easily build confidence in your own skills. «Show less... Show more» Rent Fundamentals of Mathematics 9th Edition today, or search our site for other Van Dyke
Whether teaching calculus at the introductory or AP level, at a high school or college, there is no better way to explore this rich study of movement and change than through dynamic animation. Calculus In Motion™ animations are packaged on a CD and perform equally well on either the Windows or Macintosh platform. An instruction booklet is included. The animations described below must be opened by The Geometer's Sketchpad v4 or v5 (no prior versions), owned and sold by Key Curriculum Press ( on either Windows or Macintosh platforms. Although a detailed instruction manual is included on the CD-ROM (PDF format), most of the animations can be run successfully using only the on-screen information. ARC LENGTH Develop the idea of arc length using any f(x), parametric, or polar curve & any number of partitions. AREA BETWEEN 2 CURVES Sweeping horizontally or vertically, the first animation explains the main idea, then 8 specific examples follow with changeable intervals, and finally, 2 animations (one for vertical sweeps and one for horizontal) you can enter any desired curves as well as the boundaries of integration. DEF. OF A DERIVATIVE DEF. OF INTEGRATION INVERSE FUNCTIONS Drag h to 0 to see PQ become the tangent line. See the limit process in action. Also, create the numerical derivative. Sweep left or right to accumulate the integral using standard changeable geometric shapes. Also vary the start and stop points. Using animated tangent lines, compare the derivatives of inverse functions. "Morph" the curves using sliders. (also for precalculus) GRAPHERS Explore slope using animated tangent lines. See any desired combination of f ', f '', area, and F. "Morph" each graph using sliders. A 7th animation (not shown below) allows the user to enter any desired function and applies all of the same animated features to it. (also for precalculus) RELATED RATES A click of a button advances time to commence the action to these classic problems. Other buttons reveal the values and graphs of the rates. RIEMANN SUMS Choose rectangles using left endpoints, right endpoints, or midpoints; or trapezoids to approximate an integral for any number partitions from 1 to 80! Functions can be morphed by dragging sliders, or use the first page to type in any desired function for f(x). VOLUMES ON A BASE Visualize these shapes one step at a time. Start by rotating the xy-plane to horizontal. View a few stationary slices, then a sweeping slice, and finally, an accumulating slice. Rotate the solid any time for other viewing angles. Choose from an assortment of bases and cross-sections. VOLUMES BY REVOLUTION These animations cover both the disk/washer technique and the cylindrical shell technique. Develop the process by first revolving one lone rectangle. Next, revolve several rectangles in a region and stack or nest the results. Finally, revolve any desired region (bounded by 1 or 2 functions of choice) on an interval of choice, about any horizontal or vertical axis. SLOPE FIELDS + EULER'S METHOD To introduce what a slope field is, use the graph of f ' to see its values controlling a gliding dynamic "slope column". Snapshots of this column are the slope field. A tangent segment "pilots" the field to draw f. Once understood, a different animation allows any differential equation to be entered and generates the slope field. Manually follow the field to draw f or use Euler's Method (includes explanation of E.M. and numerical table of data). Easily adjustable. LIMITS Explore the ε, ∂ definition of limits. Evaluate the limits (full, left-hand or right-hand) of any function (including piece-wise defined) as x →a or as x→±∞ MACLAURIN & TAYLOR SERIES Enter any f(x). Overlay a Maclaurin or Taylor Series polynomial of degree n & use it to approximate the value of f(x) at any point t. Vertical gray bands show where the power series is within a chosen tolerance to f(x). As n increases, the band widens.
Short description This dictionary includes explanations of over 200 mathematical words and phrases. Other features include: multiplication tables; table of squares and cubes; frequently-used fractions, decimals and percentages; metric and imperial units; simple coordinate graphs; angle and circle rules.
Introduction to Probability and focuses on the utility of probability in solving real-world problems for students in a one-semester calculus-based probability course. Theory is developed to a practical degree and grounded in discussion of its practical uses in solving real-world problems. Numerous applications using up-to-date real data in engineering and the life, social, and physical sciences illustrate and motivate the many ways probability affects our lives. The text's accessible presentation carefully progresses from routine to more difficult problems to suit students of different backgrounds, and carefully explains how and where to apply methods. Students going on to more advanced courses in probability and statistics will gain a solid background in fundamental concepts and theory, while students who must apply probability to their courses engineering and the sciences will develop a working knowledge of the subject and appreciation of its practical power.
For algebra-based introductory physics courses taken primarily by pre-med, agricultural, technology, and architectural students. This best-selling algebra-based physics text is known for its elegant ...
New MAA Book: Visual Group Theory Nathan Carter's colorful text, Visual Group Theory, approaches the learning of group theory visually. Its topics and theorems are accompanied by visual demonstrations of the meaning and importance of groups, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. It allows students to see groups, to experiment with groups—and to understand the significance of groups, subgroups, homomorphisms, products, and quotients. Defining groups as collections of actions, the opening chapters anchor readers' intuitions with puzzles and symmetrical objects. This approach leads to Cayley diagrams, which embody the visualization technique central to the book because of their unique ability to make group structure visually apparent. Highlights: Includes more than 300 full-color illustrations Moves from the basics of group theory to Sylow theory and Galois theory An applications chapter shows how group theory describes the symmetry of crystals, dancing, art, architecture, and much more About the Author: Now at Bentley University, Nathan Carter earned a Ph.D. in mathematics from Indiana University, Bloomington. He received the University of Scranton Excellence in Mathematics award in 1999, an Indiana University Rothrock Teaching award in 2003, and a Bentley University Innovation in Teaching award in 2007. This is his first book, based on lessons learned while writing the software Group Explorer.
algebra GeoGebra, a GPL-licensed teaching and learning tool that integrates geometry, algebra, and calculus, benefits both teachers and students alike. Developed by Markus Hohenwarter at Florida Atlantic University, GeoGebra constructs geometrical figures and demonstrates the relationship between geometry and algebra. GeoGebra can help you create interactive demonstrations and precise images of geometric figures for inclusion in teaching and testing materials.
Introduction To Algorithms 2nd Edition Solutions In its new edition, Introduction to Algorithms continues to provide a comprehensive introduction to the modern study of algorithms. The revision has been updated to reflect changes in the years since the book's original publication. New chapters on the role of algorithms in computing and on probabilistic analysis and randomized algorithms have been included. Sections throughout the book have been rewritten for increased clarity, and material has been added wherever a fuller explanation has seemed useful or new information warrants expanded coverage
Mathematics is the language and tool of the sciences, a cultural phenomenon with a rich historical traditions, and a model of abstract reasoning. Historically, mathematical methods and thinking have proved extraordinarily successful in physics, and engineering. Nowadays, it is used successfully in many new areas, from computer science to biology and finance. A Mathematics concentration provides a broad education in various areas of mathematics in a program flexible enough to accommodate many ranges of interest. The study of mathematics is an excellent preparation for many careers; the patterns of careful logical reasoning and analytical problem solving essential to mathematics are also applicable in contexts where quantity and measurement play only minor roles. Thus students of mathematics may go on to excel in medicine, law, politics, or business as well as any of a vast range of scientific careers. Special programs are offered for those interested in teaching mathematics at the elementary or high school level or in actuarial mathematics, the mathematics of insurance. The other programs split between those which emphasize mathematics as an independent discipline and those which favor the application of mathematical tools to problems in other fields. There is considerable overlap here, and any of these programs may serve as preparation for either further study in a variety of academic disciplines, including mathematics itself, or intellectually challenging careers in a wide variety of corporate and governmental settings. Elementary Mathematics Courses. In order to accommodate diverse backgrounds and interests, several course options are available to beginning mathematics students. All courses require three years of high school mathematics; four years are strongly recommended and more information is given for some individual courses below. Students with College Board Advanced Placement credit and anyone planning to enroll in an upper-level class should consider one of the Honors sequences and discuss the options with a mathematics advisor. Students who need additional preparation for calculus are tentatively identified by a combination of the math placement test (given during orientation), college admission test scores (SAT or ACT), and high school grade point average. Academic advisors will discuss this placement information with each student and refer students to a special mathematics advisor when necessary. Two courses preparatory to the calculus, MATH 105 and 110, are offered. MATH 105 is a course on data analysis, functions and graphs with an emphasis on problem solving. MATH 110 is a condensed half-term version of the same material offered as a self-study course taught through the Math Lab and is only open to students in MATH 115 who find that they need additional preparation to successfully complete the course. A maximum total of 4 credits may be earned in courses numbered 103, 105, and 110. MATH 103 is offered exclusively in the Summer half-term for students in the Summer Bridge Program. MATH 127 and 128 are courses containing selected topics from geometry and number theory, respectively. They are intended for students who want exposure to mathematical culture and thinking through a single course. They are neither prerequisite nor preparation for any further course. No credit will be received for the election of MATH 127 or 128 if a student already has credit for a 200-(or higher) level mathematics course. Each of MATH 115, 185, and 295 is a first course in calculus and generally credit can be received for only one course from this list. The Sequence 115-116-215 is appropriate for most students who want a complete introduction to calculus. One of MATH 215, 285, or 395 is prerequisite to most more advanced courses in Mathematics. The sequences 156-255-256, 175-176-285-286, 185-186-285-286, and 295-296-395-396 are Honors sequences. Students need not be enrolled in the LS&A Honors Program to enroll in any of these courses but must have the permission of an Honors advisor. Students with strong preparation and interest in mathematics are encouraged to consider these courses. MATH 185-285 covers much of the material of MATH 115-215 with more attention to the theory in addition to applications. Most students who take MATH 185 have taken a high school calculus course, but it is not required. MATH 175-176 assumes a knowledge of calculus roughly equivalent to MATH 115 and covers a substantial amount of so-called combinatorial mathematics as well as calculus-related topics not usually part of the calculus sequence. MATH 175 and 176 are taught by the discovery method: students are presented with a great variety of problem and encouraged to experiment in groups using computers. The sequence MATH 295-396 provides a rigorous introduction to theoretical mathematics. Proofs are stressed over applications and these courses require a high level of interest and commitment. Most students electing MATH 295 have completed a thorough high school calculus. MATH 295-396 is excellent preparation for mathematics at the advanced undergraduate and graduate level. Students with strong scores on either the AB or BC version of the College Board Advanced Placement exam may be granted credit and advanced placement in one of the sequences described above; a table explaining the possibilities is available from advisors and the Department. In addition, there is one course expressly designed and recommended for students with one or two semesters of AP credit, MATH 156. Math 156 is an Honors course intended primarily for science and engineering concentrators and will emphasize both applications and theory. Interested students should consult a mathematics advisor for more details. In rare circumstances and with permission of a Mathematics advisor, reduced credit may be granted for MATH 185 or 295 after MATH 115. A list of these and other cases of reduced credit for courses with overlapping material is available from the Department. To avoid unexpected reduction in credit, student should always consult an advisor before switching from one sequence to another. In all cases a maximum total of 16 credits may be earned for calculus courses MATH 115 through 396, and no credit can be earned for a prerequisite to a course taken after the course itself. Students completing MATH 116 who are principally interested in the application of mathematics to other fields may continue either to MATH 215 (Analytic Geometry and Calculus III) or to MATH 216 (Introduction to Differential Equation -- these two courses may be taken in either order. Students who have greater interest in theory or who intend to take more advanced courses in mathematics should continue with MATH 215 followed by the sequence MATH 217-316 (Linear Algebra-Differential Equations). MATH 217 (or the Honors version, MATH 513) is required for a concentration in Mathematics; it both serves as a transition to the more theoretical material of advanced courses and provides the background required to optimal treatment of differential equations in MATH 316. MATH 216 is not intended for mathematics concentrators. Special Departmental Policies. All prerequisite courses must be satisfied with a grade of C- or above. Students with lower grades in prerequisite courses must receive special permission of the instructor to enroll in subsequent courses. MATH 105. Data, Functions, and Graphs. Instructor(s): Prerequisites & Distribution: (4). (MSA). (QR/1). May not be repeated for credit. Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110. MATH 105 serves both as a preparatory course to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who complete MATH 105 are fully prepared for MATH 115. ThisMATH 107. Mathematics for the Information Age. Section 001. Instructor(s): Karen Rhea Prerequisites & Distribution: Three to four years high school mathematics. (3). (MSA). (QR/1). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. From computers and the Internet to playing a CD or running an election, great progress in modern technology and science has come from understanding how information is exchanged, processed and perceived. MATH 110. Pre-Calculus (Self-Study). Instructor(s): Prerequisites & Distribution: See Elementary Courses above. Enrollment in MATH 110 is by recommendation of MATH 115 instructor and override only. (2). (Excl). May not be repeated for credit. No credit granted to those who already have 4 credits for pre-calculus mathematics courses. A maximum of four credits may be earned in MATH 101, 103, 105, and 110. The course covers data analysis by means of functions and graphs. MATH 110 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. The course is a condensed, half-term version of MATH 105 (MATH 105 covers the same material in a traditional classroom setting) designed for students who appear to be prepared to handle calculus but are not able to successfully complete MATH 115. Students who complete MATH 110 are fully prepared for MATH 115. Students may enroll in MATH 110 only on the recommendation of a mathematics instructor after the third week of classes. ENROLLMENT IN MATH 110 IS BY PERMISSION OF MATH 115 INSTRUCTOR ONLY. COURSE MEETS SECOND HALF OF THE TERM. STUDENTS WORK INDEPENDENTLY WITH GUIDANCE FROM MATH LAB STAFF. MATH 115. Calculus I. Instructor(s): Prerequisites & Distribution: Four years of high school mathematics. See Elementary Courses above. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit usually is granted for only one course from among 115, 185, and 295. No credit granted to those who have completed MATH 175. The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to concentrate in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam. The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing, and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. MATH 185 is a somewhat more theoretical course which covers some of the same material. MATH 175 includes some of the material of MATH 115 together with some combinatorial mathematics. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions, and Graphs). MATH 116 is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186. The cost for this course is over $100 since the student will need a text (to be used for MATH 115 and 116) and a graphing calculator (the Texas Instruments TI-83 is recommended). See MATH 115 for a general description of the sequence MATH 115-116-215. Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285. MATH 127. Geometry and the Imagination. Section 001. Instructor(s): Emina Alibegovic Prerequisites & Distribution: Three years of high school mathematics including a geometry course. Only first-year students, including those with sophomore standing, may pre-register for First-Year Seminars. All others need permission of instructor. (4). (MSA). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed a 200- (or higher) level mathematics course (except for MATH 385 and 485). First-Year Seminar Credits: (4). Course Homepage: No homepage submitted. This course introduces students to the ideas and some of the basic results in Euclidean and non-Euclidean geometry. Beginning with geometry in ancient Greece, the course includes the construction of new geometric objects from old ones by projecting and by taking slices. The next topic is non-Euclidean geometry. This section begins with the independence of Euclid's Fifth Postulate and with the construction of spherical and hyperbolic geometries in which the Fifth Postulate fails; how spherical and hyperbolic geometry differs from Euclidean geometry. The last topic is geometry of higher dimensions: coordinatization — the mathematician's tool for studying higher dimensions; construction of higher-dimensional analogues of some familiar objects like spheres and cubes; discussion of the proper higher-dimensional analogues of some geometric notions (length, angle, orthogonality, etc. ) This course is intended for students who want an introduction to mathematical ideas and culture. Emphasis on conceptual thinking — students will do hands-on experimentation with geometric shapes, patterns, and ideas. This course is designed for students who seek an introduction to the mathematical concepts and techniques employed by financial institutions such as banks, insurance companies, and pension funds. Actuarial students, and other mathematics concentrators should elect MATH 424, which covers the same topics but on a more rigorous basis requiring considerable use of calculus. Topics covered include: various rates of simple and compound interest, present and accumulated values based on these; annuity functions and their application to amortization, sinking funds, and bond values; depreciation methods; introduction to life tables, life annuity, and life insurance values. This course is not part of a sequence. Students should possess financial calculators. MATH 186. Honors Calculus II. Instructor(s): Prerequisites & Distribution: Permission of the Honors advisor. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit is granted for only one course from among MATH 116, 156, 176, 186, and 296. Waitlist Code: 5: Students in LSA College Honors may request overrides from the Honors Office; other students may request them from the Math Dept Office, 2084 East Hall. MATH 214. Linear Algebra and Differential Equations. Instructor(s): Prerequisites & Distribution: MATH 115 and 116This course is intended for second-year students who might otherwise take MATH 216 (Introduction to Differential Equations) but who have a greater need or desire to study Linear Algebra. This may include some Engineering students, particularly from Industrial and Operations engineering (IOE), as well as students of Economics and other quantitative social sciences. Students intending to concentrate in Mathematics must continue to elect MATH 217. While MATH 216 includes 3-4 weeks of Linear Algebra as a tool in the study of Differential Equations, MATH 214 will include roughly 3 weeks of Differential Equations as an application of Linear Algebra. The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to concentrate in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a midterm and final exam. Topics Maple software. MATH 285 is a somewhat more theoretical course which covers the same material. For students intending to concentrate in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is MATH 217. Students who intend to take only one further mathematics course and need differential equations should take MATH 216. MATH 216. Introduction to Differential Equations. Instructor(s): Prerequisites & Distribution: MATH 116, 119, 156, 176, 186, or 296. Not intended for Mathematics concentrators. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit can be earned for only one of MATH 216, 256, 286, or 316 engineering and the sciences. Math concentrators and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316. After There is a weekly computer lab using MATLAB software. This course is not intended for mathematics concentrators, who should elect the sequence MATH 217-316. MATH 286 covers much of the same material in the honors sequence. The sequence MATH 217-316 covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 404 covers further material on differential equations. MATH 217 and 417 cover further material on linear algebra. MATH 371 and 471 cover additional material on numerical methods. MATH 217. Linear Algebra. Instructor(s): Prerequisites & Distribution: MATH 215, 255, or 285 Engineering and the sciences. Math concentrators and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316. These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved. Therefore the student entering MATH 217 should come with a sincere interest in learning about proofs. The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of Rn; linear dependence, bases, and dimension; linear transformations; eigenvalues and eigenvectors; diagonalization; and inner products. Throughout there will be emphasis on the concepts, logic, and methods of theoretical mathematics. MATH 417 and 419 cover similar material with more emphasis on computation and applications and less emphasis on proofs. MATH 513 covers more in a much more sophisticated way. The intended course to follow MATH 217 is 316. MATH 217 is also prerequisite for MATH 412 and all more advanced courses in mathematics. Instructor(s): Hendrikus Gerardus Derksen One of the best ways to develop mathematical abilities is by solving problems using a variety of methods. Familiarity with numerous methods is a great asset to the developing student of mathematics. Methods learned in attacking a specific problem frequently find application in many other areas of mathematics. In many instances an interest in and appreciation of mathematics is better developed by solving problems than by hearing formal lectures on specific topics. The student has an opportunity to participate more actively in his/her education and development. This course is intended for superior students who have exhibited both ability and interest in doing mathematics, but it is not restricted to honors students. This course is excellent preparation for the Putnam exam. Students and one or more faculty and graduate student assistants will meet in small groups to explore problems in many different areas of mathematics. Problems will be selected according to the interests and background of the students. MATH 296. Honors Mathematics II. Section 001. Instructor(s): Brian D Conrad Prerequisites & Distribution: Prior knowledge of first year calculus and permission of the Honors advisor. (4). (Excl). (BS). (QR/1). May not be repeated for credit. Credit is granted for only one course from among MATH 156, 176, 186, and 296. Credits: (4). Course Homepage: No homepage submitted. The sequence MATH 295-296-395-396 is a more intensive honors sequence than MATH 185-186-285-286. The material includes all of that of the lower sequence and substantially more. The approach is theoretical, abstract, and rigorous. Students are expected to learn to understand and construct proofs as well as do calculations and solve problems. The expected background is a thorough understanding of high school algebra and trigonometry. No previous calculus is required, although many students in this course have had some calculus. Students completing this sequence will be ready to take advanced undergraduate and beginning graduate courses. This sequence is not restricted to students enrolled in the LS&A Honors Program. The precise content depends on material covered in MATH 295 but will generally include topics such as infinite series, power series, Taylor expansion, metric spaces. Other topics may include applications of analysis, Weierstrass Approximation theorem, elements of topology, introduction to linear algebra, complex numbers. Waitlist Code: 5: Students in LSA College Honors may request overrides from the Honors Office; other students may request them from the Math Dept Office, 2084 East Hall. MATH 310. Elementary Topics in Mathematics. Section 001 — Math Games & Theory of Games. Instructor(s): Morton Brown Prerequisites & Distribution: Two years of high school mathematics. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. The current offering of the course focuses on game theory. Students study the strategy of several games where mathematical ideas and concepts can play a role. Most of the course will be occupied with the strructure of a variety of two person games of strategy: tic-tac-toe, tic-tac-toe misere, the French military game, hex, nim, the penny dime game, and many others. If there is sufficient interest students can study: dots and boxes, go moku, and some aspects of checkers and chess. There will also be a brief introduction to the classical Von Neuman/Morgenstern theory of mixed strategy games. One of the main goals of the course (along with every course in the algebra sequence) is to expose students to rigorous, proof-oriented mathematics. Students are required to have taken MATH 217, which should provide a first exposure to this style of mathematics. A distinguishing feature of this course is that the abstract concepts are not studied in isolation. Instead, each topic is studied with the ultimate goal being a real-world application. As currently organized, the course is broken into four parts: the integers "mod n" and linear algebra over the integers mod p, with applications to error correcting codes; some number theory, with applications to public-key cryptography; polynomial algebra, with an emphasis on factoring algorithms over various fields, and permutation groups, with applications to enumeration of discrete structures "up to automorphisms" (a.k.a. Pólya Theory). MATH 412 is a more abstract and proof-oriented course with less emphasis on applications. EECS 303 (Algebraic Foundations of Computer Engineering) covers many of the same topics with a more applied approach. Another good follow-up course is MATH 475 (Number Theory). MATH 312 is one of the alternative prerequisites for MATH 416, and several advanced EECS courses make substantial use of the material of MATH 312. MATH 412 is better preparation for most subsequent mathematics courses. MATH 316. Differential Equations. Section 001. Instructor(s): Arthur G Wasserman Prerequisites & Distribution: MATH 215 and 217. (3). (Excl). (BS). May not be repeated for credit. Credit can be earned for only one of MATH 216, 256, 286, or 316. Credits: (3). Course Homepage: No homepage submitted. This is an introduction to differential equations for students who have studied linear algebra (MATH 217). It treats techniques of solution (exact and approximate), existence and uniqueness theorems, some qualitative theory, and many applications. Proofs are given in class; homework problems include both computational and more conceptually oriented problems. First-order equations: solutions, existence and uniqueness, and numerical techniques; linear systems: eigenvector-eigenvalue solutions of constant coefficient systems, fundamental matrix solutions, nonhomogeneous systems; higher-order equations, reduction of order, variation of parameters, series solutions; qualitative behavior of systems, equilibrium points, stability. Applications to physical problems are considered throughout. MATH 216 covers somewhat less material without the use of linear algebra and with less emphasis on theory. MATH 286 is the Honors version of MATH 316. MATH 471 and/or MATH 572 are natural sequels in the area of differential equations, but MATH 316 is also preparation for more theoretical courses such as MATH 451. MATH 333. Directed Tutoring. Instructor(s): Prerequisites & Distribution: Enrollment in the secondary teaching certificate program with concentration in mathematics. Permission of instructor required. (1-3). (Excl). (EXPERIENTIAL). May be repeated for credit for a maximum of 3 credits. Offered mandatory credit/no credit. Credits: (1-3). Course Homepage: No homepage submitted. An experiential mathematics course for exceptional upper-level students in the elementary teacher certification program. Students tutor needy beginners enrolled in the introductory courses (MATH 385 and MATH 489) required of all elementary teachers. MATH 351. Principles of Analysis. Section 001. Instructor(s): Morton Brown Prerequisites & Distribution: MATH 215 and 217. (3). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 451. Credits: (3). Course Homepage: No homepage submitted. The content of this course is similar to that of MATH 451 but MATH 351 assumes less background. This course covers topics that might be of greater use to students considering a Mathematical Sciences concentration or a minor in Math. Course content includes: analysis of the real line, rational and irrational numbers, infinity — large and small, limits, convergence, infinite sequences and series, continuous functions, power series and differentiation. MATH 354. Fourier Analysis and its Applications. Section 001. Instructor(s): Mahdi Asgari Prerequisites & Distribution: MATH 216, 256, 286, or 316. (3). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 450 or 454. Credits: (3). Course Homepage: No homepage submitted. This course is an introduction to Fourier analysis at an elementary level, emphasizing applications. The main topics are Fourier series, discrete Fourier transforms, and continuous Fourier transforms. A substantial portion of the time is spent on both scientific/technological applications (e.g., signal processing, Fourier optics), and applications in other branches of mathematics (e.g., partial differential equations, probability theory, number theory). Students will do some computer work, using MATLAB, an interactive programming tool that is easy to use, but no previous experience with computers is necessary. MATH 371 / ENGR 371. Numerical Methods for Engineers and Scientists. Section 001. Instructor(s): David Gammack Prerequisites & Distribution: ENGR 101; one of MATH 216, 256, 286, or 316. (3). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in Math 471. CAEN lab access fee required for non-Engineering students. Credits: (3). Lab Fee: CAEN lab access fee required for non-Engineering students. Course Homepage: No homepage submitted. This is a survey course of the basic numerical methods which are used to solve practical scientific problems. Important concepts such as accuracy, stability, and efficiency are discussed. The course provides an introduction to MATLAB, an interactive program for numerical linear algebra. Convergence theorems are discussed and applied, but the proofs are not emphasized. Objectives of the course Develop numerical methods for approximately solving problems from continuous mathematics on the computer Implement these methods in a computer language (MATLAB) Apply these methods to application problems Computer language: In this course, we will make extensive use of Matlab, a technical computing environment for numerical computation and visualization produced by The MathWorks, Inc. A Matlab manual is available in the MSCC Lab. Also available is a MATLAB tutorial written by Peter Blossey. MATH 396. Honors Analysis II. Section 001. Instructor(s): Mario Bonk This course is a continuation of MATH 395 and has the same theoretical emphasis. Students are expected to understand and construct proofs. Differential and integral calculus of functions on Euclidean spaces. Students who have successfully completed the sequence MATH 295-396 are generally prepared to take a range of advanced undergraduate and graduate courses such as MATH 512, 513, 525, 590, and many others. MATH 412. Introduction to Modern Algebra. Instructor(s): Prerequisites & Distribution: MATH 215, 255, or 285; and 217. (3). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 512. Students with credit for MATH 312 should take MATH 512 rather than 412. One credit granted to those who have completed MATH 312. Credits: (3). Course Homepage: No homepage submitted. This course is designed to serve as an introduction to the methods and concepts of abstract mathematics. A typical student entering this course has substantial experience in using complex mathematical (calculus) calculations to solve physical or geometrical problems, but is unused to analyzing carefully the content of definitions or the logical flow of ideas which underlie and justify these calculations. Although the topics discussed here are quite distinct from those of calculus, an important goal of the course is to introduce the student to this type of analysis. Much of the reading, homework exercises, and exams consists of theorems (propositions, lemmas, etc.) and their proofs. MATH 217 or equivalent required as background. The initial topics include ones common to every branch of mathematics: sets, functions (mappings), relations, and the common number systems (integers, rational numbers, real numbers, and complex numbers). These are then applied to the study of particular types of mathematical structures such as groups, rings, and fields. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials. Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied. MATH 312 is a somewhat less abstract course which substitutes material on finite automata and other topics for some of the material on rings and fields of MATH 412. MATH 512 is an Honors version of MATH 412 which treats more material in a deeper way. A student who successfully completes this course will be prepared to take a number of other courses in abstract mathematics: MATH 416, 451, 475, 575, 481, 513, and 582. All of these courses will extend and deepen the student's grasp of modern abstract mathematics. MATH 417. Matrix Algebra I. Instructor(s): Prerequisites & Distribution: Three courses MATH 513. Credits: (3). Course Homepage: No homepage submitted. Many problems in science, engineering, and mathematics are best formulated in terms of matrices — rectangular arrays of numbers. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. Diversity rather than depth of applications is stressed. This course is not intended for mathematics concentrators, who should elect MATH 217 or 513 (Honors). Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations. MATH 419 is an enriched version of MATH 417 with a somewhat more theoretical emphasis. MATH 217 (despite its lower number) is also a more theoretical course which covers much of the material of MATH 417 at a deeper level. MATH 513 is an Honors version of this course, which is also taken by some mathematics graduate students. MATH 420 is the natural sequel, but this course serves as prerequisite to several courses: MATH 452, 462, 561, and 571. MATH 419. Linear Spaces and Matrix Theory. Instructor(s): Prerequisites & Distribution: Four terms of college mathematics in MATH 513. Credits: (3). Course Homepage: No homepage submitted. MATH 419 covers much of the same ground as MATH 417 but presents the material in a somewhat more abstract way in terms of vector spaces and linear transformations instead of matrices. There is a mix of proofs, calculations, and applications with the emphasis depending somewhat on the instructor. A previous proof-oriented course is helpful but by no means necessary. Basic notions of vector spaces and linear transformations: spanning, linear independence, bases, dimension, matrix representation of linear transformations; determinants; eigenvalues, eigenvectors, Jordan canonical form, inner-product spaces; unitary, self-adjoint, and orthogonal operators and matrices, and applications to differential and difference equations. MATH 417 is less rigorous and theoretical and more oriented to applications. MATH 217 is similar to MATH 419 but slightly more proof-oriented. MATH 513 is much more abstract and sophisticated. MATH 420 is the natural sequel, but this course serves as prerequisite to several courses: MATH 452, 462, 561, and 571. MATH 425 / STATS 425. Introduction to Probability. Instructor(s): Mathematics faculty This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215. Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis. STATS 426 is a natural sequel for students interested in statistics. MATH 523 includes many applications of probability theory. This course introduces students to the theory of probability and to a number of applications. Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. There will be approximately 10 problem sets. Grade will be based on two 1-hour midterm exams, 20% each; 20% homework; 40% final exam. pText (required): Sheldon Ross, A First Course in Probability, 6th edition, Prentice-Hall, 2002. MATH 450. Advanced Mathematics for Engineers I. Instructor(s): Prerequisites & Distribution: MATH 215, 255, or 285. (4). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 354 or 454. Credits: (4). Course Homepage: No homepage submitted. Although this course is designed principally to develop mathematics for application to problems of science and engineering, it also serves as an important bridge for students between the calculus courses and the more demanding advanced courses. Students are expected to learn to read and write mathematics at a more sophisticated level and to combine several techniques to solve problems. Some proofs are given, and students are responsible for a thorough understanding of definitions and theorems. Students should have a good command of the material from MATH 215, and 216 or 316, which is used throughout the course. A background in linear algebra, e.g. MATH 217, is highly desirable, as is familiarity with Maple software. Topics include a review of curves and surfaces in implicit, parametric, and explicit forms; differentiability and affine approximations; implicit and inverse function theorems; chain rule for 3-space; multiple integrals; scalar and vector fields; line and surface integrals; computations of planetary motion, work, circulation, and flux over surfaces; Gauss' and Stokes' Theorems; and derivation of continuity and heat equation. Some instructors include more material on higher dimensional spaces and an introduction to Fourier series. MATH 450 is an alternative to MATH 451 as a prerequisite for several more advanced courses. MATH 454 and 555 are the natural sequels for students with primary interest in engineering applications. MATH 451. Advanced Calculus I. Instructor(s): Prerequisites & Distribution: MATH 215 and one course beyond MATH 215; or MATH 255 or 285. Intended for concentrators; other students should elect MATH 450. (3). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 351. Credits: (3). Course Homepage: No homepage submitted. This course has two complementary goals: (1) a rigorous development of the fundamental ideas of calculus, and (2) a further development of the student's ability to deal with abstract mathematics and mathematical proofs. The key words here are "rigor" and "proof"; almost all of the material of the course consists in understanding and constructing definitions, theorems (propositions, lemmas, etc.) and proofs. This is considered one of the more difficult among the undergraduate mathematics courses, and students should be prepared to make a strong commitment to the course. In particular, it is strongly recommended that some course which requires proofs (such as MATH 412) be taken before MATH 451. Topics include: logic and techniques of proof; sets, functions, and relations; cardinality; the real number system and its topology; infinite sequences, limits, and continuity; differentiation; integration, and the Fundamental Theorem of Calculus; infinite series; and sequences and series of functions. There is really no other course which covers the material of MATH 451. Although MATH 450 is an alternative prerequisite for some later courses, the emphasis of the two courses is quite distinct. The natural sequel to MATH 451 is 452, which extends the ideas considered here to functions of several variables. In a sense, MATH 451 treats the theory behind MATH 115-116, while MATH 452 does the same for MATH 215 and a part of MATH 216. MATH 551 is a more advanced version of Math 452. MATH 451 is also a prerequisite for several other courses: MATH 575, 590, 596, and 597. MATH 452. Advanced Calculus II. Section 001 — Multivariable Calculus and Elementary Function Theory. Instructor(s): Lukas I Geyer Prerequisites & Distribution: MATH 217, 417, or 419; and MATH 451. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. This course does a rigorous development of multivariable calculus and elementary function theory with some view towards generalizations. Concepts and proofs are stressed. This is a relatively difficult course, but the stated prerequisites provide adequate preparation. Topics include: MATH 551 is a higher-level course covering much of the same material with greater emphasis on differential geometry. Math 450 covers the same material and a bit more with more emphasis on applications, and no emphasis on proofs. MATH 452 is prerequisite to MATH 572 and is good general background for any of the more advanced courses in analysis (MATH 596, 597) or differential geometry or topology (MATH 537, 635). MATH 454. Boundary Value Problems for Partial Differential Equations. Instructor(s): Prerequisites & Distribution: MATH 216, 256, 286, or 316. (3). (Excl). (BS). May not be repeated for credit. Students with credit for MATH 354 can elect MATH 454 for one credit. No credit granted to those who have completed or are enrolled in MATH 450. Credits: (3). Course Homepage: No homepage submitted. This course is devoted to the use of Fourier series and other orthogonal expansions in the solution of boundary-value problems for second-order linear partial differential equations. Emphasis is on concepts and calculation. The official prerequisite is ample preparation. Classical representation and convergence theorems for Fourier series; method of separation of variables for the solution of the one-dimensional heat and wave equation; the heat and wave equations in higher dimensions; spherical and cylindrical Bessel functions; Legendre polynomials; methods for evaluating asymptotic integrals (Laplace's method, steepest descent); Fourier and Laplace transforms; and applications to linear input-output systems, analysis of data smoothing and filtering, signal processing, time-series analysis, and spectral analysis. Both MATH 455 and 554 cover many of the same topics but are very seldom offered. MATH 454 is prerequisite to MATH 571 and 572, although it is not a formal prerequisite, it is good background for MATH 556. MATH 462. Mathematical Models. Section 001. Instructor(s): David Bortz Prerequisites & Distribution: MATH 216, 256, 286, or 316; and MATH 217, 417, or 419. (3). (Excl). (BS). May not be repeated for credit. Students with credit for MATH 362 must have department permission to elect MATH 462. Credits: (3). Course Homepage: No homepage submitted. This course will cover biological models constructed from difference equations and ordinary differential equations. Applications will be drawn from population biology, population genetics, the theory of epidemics, biochemical kinetics, and physiology. Both exact solutions and simple qualitative methods for understanding dynamical systems will be stressed. MATH 471. Introduction to Numerical Methods. Instructor(s): Prerequisites & Distribution: MATH 216, 256, 286, or 316; and 217, 417, or 419; and a working knowledge of one high-level computer language. (3). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in MATH 371 or 472. Credits: (3). Course Homepage: No homepage submitted. This is a survey of the basic numerical methods which are used to solve scientific problems. The emphasis is evenly divided between the analysis of the methods and their practical applications. Some convergence theorems and error bounds are proven. The course also provides an introduction to MATLAB, an interactive program for numerical linear algebra, as well as practice in computer programming. One goal of the course is to show how calculus and linear algebra are used in numerical analysis. Topics may include computer arithmetic, Newton's method for non-linear equations, polynomial interpolation, numerical integration, systems of linear equations, initial value problems for ordinary differential equations, quadrature, partial pivoting, spline approximations, partial differential equations, Monte Carlo methods, 2-point boundary value problems, and the Dirichlet problem for the Laplace equation. MATH 371 is a less sophisticated version intended principally for sophomore and junior engineering students; the sequence MATH 571-572 is mainly taken by graduate students, but should be considered by strong undergraduates. MATH 471 is good preparation for MATH 571 and 572, although it is not prerequisite to these courses. MATH 475. Elementary Number Theory. Section 001. Instructor(s): Muthukrishnan Krishnamurthy Prerequisites & Distribution: At least three terms of college mathematics are recommended. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. This is an elementary introduction to number theory, especially congruence arithmetic. Number theory is one of the few areas of mathematics in which problems easily describable to a layman (is every even number the sum of two primes?) have remained unsolved for centuries. Recently some of these fascinating but seemingly useless questions have come to be of central importance in the design of codes and cyphers. The methods of number theory are often elementary in requiring little formal background. In addition to strictly number-theoretic questions, concrete examples of structures such as rings and fields from abstract algebra are discussed. Concepts and proofs are emphasized, but there is some discussion of algorithms which permit efficient calculation. Students are expected to do simple proofs and may be asked to perform computer experiments. Although there are no special prerequisites and the course is essentially self-contained, most students have some experience in abstract mathematics and problem solving and are interested in learning proofs. A Computational Laboratory (Math 476, 1 credit) will usually be offered as an optional supplement to this course. Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity, and quadratic fields. MATH 575 moves much faster, covers more material, and requires more difficult exercises. There is some overlap with MATH 412 which stresses the algebraic content. MATH 475 may be followed by Math 575 and is good preparation for MATH 412. All of the advanced number theory courses, MATH 675, 676, 677, 678, and 679, presuppose the material of MATH 575, although a good student may get by with MATH 475. Each of these is devoted to a special subarea of number theory. MATH 476. Computational Laboratory in Number Theory. Section 001. Instructor(s): Muthukrishnan Krishnamurthy Prerequisites & Distribution: Prior or concurrent enrollment in MATH 475 or 575. (1). (Excl). (BS). May not be repeated for credit. Credits: (1). Course Homepage: No homepage submitted. Students will be provided software with which to conduct numerical explorations. Students will submit reports of their findings weekly. No programming necessary, but students interested in programming will have the opportunity to embark on their own projects. Participation in the laboratory should boost the student's performance in MATH 475 or MATH 575. Students in the lab will see mathematics as an exploratory science (as mathematicians do). Students will gain a knowledge of algorithms which have been developed (some quite recently) for number-theoretic purposes, e.g., for factoring. No exams. Instructor(s): This course is designed for students who intend to teach junior high or high school mathematics. It is advised that the course be taken relatively early in the program to help the student decide whether or not this is an appropriate goal. Concepts and proofs are emphasized over calculation. The course is conducted in a discussion format. Class participation is expected and constitutes a significant part of the course grade. Topics covered have included problem solving; sets, relations and functions; the real number system and its subsystems; number theory; probability and statistics; difference sequences and equations; interest and annuities; algebra; and logic. This material is covered in the course pack and scattered points in the text book. There is no real alternative, but the requirement of MATH 486 may be waived for strong students who intend to do graduate work in mathematics. Prior completion of MATH 486 may be of use for some students planning to take MATH 312, 412, or 425. MATH 489. Mathematics for Elementary and Middle School Teachers. Instructor(s): Prerequisites & Distribution: MATH 385 or 485. (3). (Excl). May not be repeated for credit. May not be used in any graduate program in mathematics. Credits: (3). Course Homepage: No homepage submitted. This course, together with its predecessor MATH 385, provides a coherent overview of the mathematics underlying the elementary and middle school curriculum. It is required of all students intending to earn an elementary teaching certificate and is taken almost exclusively by such students. Concepts are heavily emphasized with some attention given to calculation and proof. The course is conducted using a discussion format. Class participation is expected and constitutes a significant part of the course grade. Enrollment is limited to 30 students per section. Although only two years of high school mathematics are required, a more complete background including pre-calculus or calculus is desirable. Topics covered include fractions and rational numbers, decimals and real numbers, probability and statistics, geometric figures, and measurement. Algebraic techniques and problem-solving strategies are used throughout the course. MATH 490. Introduction to Topology. Section 001 — An Introduction to Point-Set and Algebraic Topology. Instructor(s): Elizabeth A Burslem Prerequisites & Distribution: MATH 412 or 451 or equivalent experience with abstract mathematics. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. This course in an introduction to both point-set and algebraic topology. Although much of the presentation is theoretical and proof-oriented, the material is well-suited for developing intuition and giving convincing proofs which are pictorial or geometric rather than completely rigorous. There are many interesting examples of topologies and manifolds, some from common experience (combing a hairy ball, the utilities problem). In addition to the stated prerequisites, courses containing some group theory (MATH 412 or 512) and advanced calculus (MATH 451) are desirable although not absolutely necessary. The topics covered are fairly constant but the presentation and emphasis will vary significantly with the instructor. These include point-set topology, examples of topological spaces, orientable and non-orientable surfaces, fundamental groups, homotopy, and covering spaces. Metric and Euclidean spaces are emphasized. Math 590 is a deeper and more difficult presentation of much of the same material which is taken mainly by mathematics graduate students. MATH 433 is a related course at about the same level. MATH 490 is not prerequisite for any later course but provides good background for MATH 590 or any of the other courses in geometry or topology. MATH 501. Applied & Interdisciplinary Mathematics Student Seminar. Section 001. Prerequisites & Distribution: At least two 300 or above level math courses, and graduate standing; Qualified undergraduates with permission of instructor only. (1). (Excl). May be repeated for credit for a maximum of 6 credits. Offered mandatory credit/no credit. Credits: (1). Course Homepage: No homepage submitted. The Applied and Interdisciplinary Mathematics (AIM) student seminar is an introductory and survey course in the methods and applications of modern mathematics in the natural, social, and engineering sciences. Students will attend the weekly AIM Research Seminar where topics of current interest are presented by active researchers (both from U-M and from elsewhere). The other central aspect of the course will be a seminar to prepare students with appropriate introductory background material. The seminar will also focus on effective communication methods for interdisciplinary research. MATH 501 is primarily intended for graduate students in the Applied & Interdisciplinary Mathematics M.S. and Ph.D. programs. It is also intended for mathematically curious graduate students from other areas. Qualified undergraduates are welcome to elect the course with the instructor's permission. Student attendance and participation at all seminar sessions is required. Students will develop and make a short presentation on some aspect of applied and interdisciplinary mathematics. MATH 512. Algebraic Structures. Section 001 — Basic Structures of Modern Abstract Algebra. Instructor(s): Robert L Griess Jr Prerequisites & Distribution: MATH 451 or 513. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. Student Body: mainly undergrad math concentrators with a few grad students from other fields Background and Goals: This is one of the more abstract and difficult courses in the undergraduate program. It is frequently elected by students who have completed the 295--396 sequence. Its goal is to introduce students to the basic structures of modern abstract algebra (groups, rings, and fields) in a rigorous way. Emphasis is on concepts and proofs; calculations are used to illustrate the general theory. Exercises tend to be quite challenging. Students should have some previous exposure to rigorous proof-oriented mathematics and be prepared to work hard. Students from Math 285 are strongly advised to take some 400-500 level course first, for example, Math 513. Some background in linear algebra is strongly recommended Content: The course covers basic definitions and properties of groups, rings, and fields, including homomorphisms, isomorphisms, and simplicity. Further topics are selected from (1) Group Theory: Sylow theorems, Structure Theorem for finitely-generated Abelian groups, permutation representations, the symmetric and alternating groups (2) Ring Theory: Euclidean, principal ideal, and unique factorization domains, polynomial rings in one and several variables, algebraic varieties, ideals, and (3) Field Theory: statement of the Fundamental Theorem of Galois Theory, Nullstellensatz, subfields of the complex numbers and the integers mod p. Alternatives: Math 412 (Introduction to Modern Algebra) is a substantially lower level course covering about half of the material of Math 512. The sequence Math 593--594 covers about twice as much Group and Field Theory as well as several other topics and presupposes that students have had a previous introduction to these concepts at least at the level of Math 412. Subsequent Courses: Together with Math 513, this course is excellent preparation for the sequence Math 593 — 594. Text Book: Abstract Algebra, Second Edition by David Dummit and Richard Foote. MATH 513. Introduction to Linear Algebra. Instructor(s): William E Fulton Prerequisites & Distribution: MATH 412. (3). (Excl). (BS). May not be repeated for credit. Two credits granted to those who have completed MATH 214, 217, 417, or 419. Credits: (3). Course Homepage: No homepage submitted. Prerequisites: Math 412 or Math 451 or permission of the instructor Background and Goals: This is an introduction to the theory of abstract vector spaces and linear transformations. The emphasis is on concepts and proofs with some calculations to illustrate the theory. Content: Topics are selected from: vector spaces over arbitrary fields (including finite fields); linear transformations, bases, and matrices; eigenvalues and eigenvectors; applications to linear and linear differential equations; bilinear and quadratic forms; spectral theorem; Jordan Canonical Form. This corresponds to most of the first text with the omission of some starred sections and all but Chapters 8 and 10 of the second text. Alternatives: Math 419 (Lin. Spaces and Matrix Thy) covers much of the same material using the same text, but there is more stress on computation and applications. Math 217 (Linear Algebra) is similarly proof-oriented but significantly less demanding than Math 513. Math 417 (Matrix Algebra I) is much less abstract and more concerned with applications. Subsequent Courses: The natural sequel to Math 513 is Math 593 (Algebra I). Math 513 is also prerequisite to several other courses: Math 537, 551, 571, and 575, and may always be substituted for Math 417 or 419. Section 001. This course is a continuation of MATH520 (a year-long sequence). It covers the topics of reserving models for life insurance; multiple-life models including joint life and last survivor contingent insurances; multiple-decrement models including disability, retirement and withdrawal; insurance models including expenses; and business and regulatory considerations. MATH 523. Risk Theory. Section 001 — Risk Management. Instructor(s): Conlon Required Text: "Loss Models-from Data to Decisions", by Klugman, Panjer and Willmot, Wiley 1998. Background and Goals: Risk management is of major concern to all financial institutions and is an active area of modern finance. This course is relevant for students with interests in finance, risk management, or insurance. It provides background for the professional exams in Risk Theory offered by the Society of Actuaries and the Casualty Actuary Society. Contents: Standard distributions used for claim frequency models and for loss variables, theory of aggregate claims, compound Poisson claims model, discrete time and continuous time models for the aggregate claims variable, the Chapman-Kolmogorov equation for expectations of aggregate claims variables, the Poisson process, estimating the probability of ruin, reinsurance schemes and their implications for profit and risk. Credibility theory, classical theory for independent events, least squares theory for correlated events, examples of random variables where the least squares theory is exact. Grading: The grade for the course will be determined from performances on homeworks, a midterm and a final exam. MATH 525 / STATS 525. Probability Theory. Section 001. Instructor(s): Gautam Bharali Prerequisites & Distribution: MATH 451 (strongly recommended) or 450. MATH 425 would be helpful. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. Background: This course is a fairly rigorous study of the mathematical basis of probability theory. There is some overlap of topics with Math 425, but in Math 525, there is a greater emphasis on the proofs of major results in probability theory. This course and its sequel - Math 526 - are core courses for the Applied and Interdisciplinary Mathematics (AIM) program. Content: The notion of a probability space and a random variable, discrete and continuous random variables, independence and expectation, conditional probability and conditional expectations, generating functions and moment generating functions, the Law of Large Numbers, and the Central Limit Theorem comprise the essential core of this course. Further topics, to be decided later (and, if feasible, selected according to audience interest), will be covered in the last month of the semester. Alternatives: EECS 501 covers some of the above material at a lower level of mathematical rigor. Math 425 (Introduction to Probability) is recommended for students with substantially less mathematical preparation. Instructor(s): Virginia R Young Risk management is of major concern to all financial institutions and is an active area of modern finance. This course is relevant for students with interests in insurance, risk management, or finance. We will cover the following topics: advanced topics in credibility theory, risk measures and premium principles, optimal (re)insurance, reinsurance products, and reinsurance pricing. I assume that you have taken MATH 523, Risk Theory. In fact, one can think of this course as a continuation of MATH 523 with emphasis on applying the material learned in Risk Theory to more practical settings. The official text for the course is a set of notes available at UM.CourseTools. In addition, an excellent book concerning modern reinsurance products is Integrating Corporate Risk Management by Prakash Shimpi, published by Texere. I suggest that you buy this book, but I do not require that you do so. MATH 531. Transformation Groups in Geometry. Section 001. Instructor(s): Emina Alibegovic Prerequisites: MATH 412 or 512 would be helpful, but neither is necessary. Text required: None. Text recommended: Armstrong, Groups and Symmetry; Lyndon: Groups and Geometry. textbook comment: Your class notes and my handouts will be sufficient. The books I listed contain some of the material we will cover, but not all of it. Course description: The purpose of this course is to explore the close ties between geometry and algebra. We will study Euclidean and hyperbolic spaces and groups of their isometries. Our discussions will include, but will not be limited to, free groups, triangle groups, and Coxeter groups. We will talk about group actions on spaces, and in particular group actions on trees. MATH 555. Introduction to Functions of a Complex Variable with Applications. Section 001. Instructor(s): Divakar Viswanath Prerequisites & Distribution: MATH 450 or 451. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. Recent Texts: Complex Variables and Applications, 6th ed. (Churchill and Brown); Student Body: largely engineering and physics graduate students with some math and engineering undergrads, and graduate students in the Applied and Interdisciplinary Mathematics (AIM) program Background and Goals: This course is an introduction to the theory of complex valued functions of a complex variable with substantial attention to applications in science and engineering. Concepts, calculations, and the ability to apply principles to physical problems are emphasized over proofs, but arguments are rigorous. The prerequisite of a course in advanced calculus is essential. This course is a core course for the Applied and Interdisciplinary Mathematics (AIM) graduate program. Content: Differentiation and integration of complex valued functions of a complex variable, series, mappings, residues, applications. Evaluation of improper real integrals, fluid dynamics. This corresponds to Chapters 1--9 of Churchill. Alternatives: Math 596 (Analysis I (Complex)) covers all of the theoretical material of Math 555 and usually more at a higher level and with emphasis on proofs rather than applications. Subsequent Courses: Math 555 is prerequisite to many advanced courses in science and engineering fields. MATH 557. Methods of Applied Mathematics II. Section 001. Prerequisites & Distribution: MATH 217, 419, or 513; 451 and 555. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. Prerequisites: (1) one of the following: Math 217, 419, or 513 (i.e. a course in linear algebra); (2) one of the following: Math 216, 256, 286, 316, or 404 (i.e. a course in differential equations); (3) Math 451 (or an equivalent course in advanced calculus); (4) Math 555 (or an equivalent course in complex variables). Text: There is no required text. Lecture notes will be made available to students from the instructor's website. Recommended texts will be announced in class. Audience: Graduate students and advanced undergraduates in applied mathematics, engineering, or the natural sciences. Background and Goals: In applied mathematics, we often try to understand a physical process by formulating and analyzing mathematical models which in many cases consist of differential equations with initial and/or boundary conditions. Most of the time, especially if the equation is nonlinear, an explicit formula for the solution is not available. Even if we are clever or lucky enough to find an explicit formula, it may be difficult to extract useful information from it and in practice, we must settle for a sufficiently accurate approximate solution obtained by numerical or asymptotic analysis (or a combination of the two). This course is an introduction to the latter of these two approximation methods. The material covered in the textbook includes the nature of asymptotic approximations, asymptotic expansions of integrals and applications to transform theory (Fourier and Laplace), regular and singular perturbation theory for differential equations including transition point analysis, the use of matched expansions, and multiple scale methods. The time remaining after studying these topics will be devoted to the derivation of several famous canonical model equations of applied mathematics (e.g. the Korteweg-de Vries equation and the nonlinear Schroedinger equation) using multiscale asymptotics. Students will come to understand how these equations arise again and again from fields of study as diverse as water wave theory, molecular dynamics, and nonlinear optics. Grading: Students will be evaluated on the basis of homework assignments and also participation and lecture attendance. MATH 558. Ordinary Differential Equations. Section 001. Instructor(s): Andrew J Christlieb Prerequisites & Distribution: MATH 450 or 451. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. Prerequisites: Basic Linear Algebra, Ordinary Differential Equations (math 216), Multivariable Calculus (215) and Either Advanced Calculus (math 451) or an advanced mathematical methods course (e.g. Math 454); preferably both. Course Objective: This course is an introduction to the modern qualitative theory of ordinary differential equations with emphasis on geometric techniques and visualization. Much of the motivation for this approach comes from applications. Examples of applications of differential equations to science and engineering are a significant part of the course. There are relatively few proofs. Course Description: Nonlinear differential equations and iterative maps arise in the mathematical description of numerous systems throughout science and engineering. Such systems may display complicated and rich dynamical behavior. In this course we will focus on the theory of dynamical systems and how it is used in the study of complex systems. The goal of this course is to provide a broad overview of the subject as well as an in-depth analysis of specific examples. The course is intended for students in mathematics, engineering, and the natural sciences. Topics covered will include aspects of autonomous and driven two variable systems including the geometry of phase plane trajectories, periodic solutions, forced oscillations, stability, bifurcations and chaos. Applications to problems from physics, engineering and the natural sciences will arise in the course by way of examples in lecture ad through the homework problems. We will cover material from Chapters 1-5 and 8-13 of the text. Textbook Nonlinear Ordinary Differetial Equations, Oxford Press. by: D.W. Jordan and P. Smith References Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer. John Guckenheimer and Philip Holmes Nonlinear Differential Equations and Dynamical Systems, Springer. Ferdinand Verhulst Applications of Centre Manifold Theory, Springer. J. Carr Nonlinear Systems, Chambridge. P.G. Drazin Course Objectives: To provide first-year graduate students with basic understanding of linear programming, its importance, and applications. To discuss algorithms for linear programming, available software and how to use it intelligently. Section 001. Instructor(s): John R Stembridge Prerequisite: MATH 512 or an equivalent level of mathematical maturity. This course will be an introduction to algebraic combinatorics. Previous exposure to combinatorics will not be necessary, but experience with proof-oriented mathematics at the introductory graduate or advanced undergraduate level, and linear algebra, will be needed. Most of the topics we cover will be centered around enumeration and generating functions. But this is not to say that the course is only about enumeration — questions about counting are a good starting point for gaining a deeper understanding of combinatorial structure. Some of the topics to be covered include sieve methods, the matrix-tree theorem, Lagrange inversion, the permanent-determinant method, the transfer matrix method, and ordinary and exponential generating functions. Recommended text: R. Stanley, Enumerative Combinatorics, Vol. I Cambridge Univ. Press, 1997. MATH 567. Introduction to Coding Theory. Section 001. Instructor(s): Hendrikus Gerardus Derksen Prerequisites & Distribution: One of MATH 217, 419, 513. (3). (Excl). (BS). May not be repeated for credit. Credits: (3). Course Homepage: No homepage submitted. Student Body: Undergraduate math majors and EECS graduate students Background and Goals: This course is designed to introduce math majors to an important area of applications in the communications industry. From a background in linear algebra it will cover the foundations of the theory of error-correcting codes and prepare a student to take further EECS courses or gain employment in this area. For EECS students it will provide a mathematical setting for their study of communications technology. Content: Introduction to coding theory focusing on the mathematical background for error-correcting codes. Shannon's Theorem and channel capacity. Review of tools from linear algebra and an introduction to abstract algebra and finite fields. Basic examples of codes such and Hamming, BCH, cyclic, Melas, Reed-Muller, and Reed-Solomon. Introduction to decoding starting with syndrome decoding and covering weight enumerator polynomials and the Mac-Williams Sloane identity. Further topics range from asymptotic parameters and bounds to a discussion of algebraic geometric codes in their simplest form. MATH 571. Numerical Methods for Scientific Computing I. Section 001. Instructor(s): James F EppersonThis course is an introduction to numerical linear algebra, a core subject in scientific computing. Three general problems are considered: (1) solving a system of linear equations, (2) computing the eigenvalues and eigenvectors of a matrix, and (3) least squares problems. These problems often arise in applications in science and engineering, and many algorithms have been developed for their solution. However, standard approaches may fail if the size of the problem becomes large or if the problem is ill-conditioned, e.g. the operation count may be prohibitive or computer roundoff error may ruin the answer. We'll investigate these issues and study some of the accurate, efficient, and stable algorithms that have been devised to overcome these difficulties. The course grade will be based on homework assignments, a midterm exam, and a final exam. Some homework exercises will require computing, for which Matlab is recommended. MATH 572. Numerical Methods for Scientific Computing II. Section 001. Instructor(s): Divakar ViswanathMath 572 is an introduction to numerical methods for solving differential equations. These methods are widely used in science and engineering. The four main segments of the course will cover the following topics: MATH 592. Introduction to Algebraic Topology. Section 001. Instructor(s): Igor Kriz The purpose of this course is to introduce basic concepts of algebraic topology, in particular fundamental group, covering spaces and homology. These methods provide the first tools for proving that two topological spaces are not topologically equivalent (example: the bowling ball is topologically different from the teacup). Other simple applications of the methods will also be given, for example fixed point theorems for continuous maps. Prerequisites: basic knowledge of point set topology, such as from 590 or 591. Books: There is no ideal text covering all this material on exactly the level needed (basic but rigorous). Recommended texts include Munkres: Elements of Algebraic topology (for homology) and J.P.May: A concise course in algebraic topology (for fundamental group and covering spaces). Both texts include topics which will not be covered in 592, and are also suitable textbooks for the next course in algebraic topology, 695.
Math Department Introduction The Mathematics Department of Loyola Academy offers courses in Algebra, Geometry, Pre-Calculus, Calculus and Statistics at all levels from introductory to Honors and Advanced Placement. While only three years of math are required for graduation, the majority of our students take courses for four years. The Mathematics Department provides a challenging, thought-provoking curriculum that is intellectually stimulating and college preparatory in nature, regardless of track level. In addition to traditional course work, students can apply to participate in the Clavius Scholars program. The Mathematics Department furthers its commitment to high quality education through the selection of first-rate textbooks and integration of technology. Students are required to purchase a TI-83 or TI-84 graphing calculator, which is incorporated into instruction. Teachers utilize computer labs and classroom computers for exploration and demonstration, further integrating technology into instruction. Course Tracking Loyola Academy requires that students complete a minimum of three credits of mathematics for graduation, while four years of study is strongly recommended. Incoming freshmen are placed in a track using a combination of the results of the STS test and grade school records. Focused attention is given to mathematics and quantitative sub-scores, while also considering the verbal and composite score. Incoming freshmen who have taken Algebra 1 or beyond during middle school will be placed in a course commensurate with their ability. The goal of the Mathematics Department is to find the best possible placement for each of our students. Multiple tracks exist in order to best meet varying student needs. While the majority of students stay in their assigned track for the duration of their Loyola Academy career, track placement is reevaluated on an annual basis. Minimum grade requirements must be met in order to maintain current track placement. Student performance and teacher recommendation can result in a change in a student's track placement for subsequent academic years. Math Lab The Mathematics Department recognizes that students sometimes need additional assistance in order to be successful. The Math Lab, located on the first floor of the library, is open daily and is staffed by two part-time math teachers in addition to members of the Mathematics Department. The Math Lab serves a variety of functions by offering homework help, assisting students who have been absent and providing help to students preparing for quizzes and tests. Loyola Academy's Program for 7th or 8th grade Talented Math Students (LAPTMS) Loyola Academy is offering a program for talented junior high math students. The Loyola Academy Program for Talented Math Students (LAPTMS) will seek to develop the talents of the area's brightest math students by offering an accelerated math curriculum in which participants will have the opportunity to complete Advanced Placement Calculus and post-Calculus courses by the end of high school. The Loyola Program for Talented Math Students is based on a similar program that has been offered by Johns Hopkins University since 1979, and is currently offered by several other leading universities across the country (i.e.; Northwestern University and Duke University). Loyola Academy's Program for Talented Math Students is open to students entering at the Algebra 1 or Geometry level of math. Students may begin the program in 7th or 8th grade. LAPTMS 7th or 8th Grade Registration Form.
Flexible Organization: Organization of chapters, sections, and projects allows for a variety of course configurations depending on desired course goals, topics, and depth of coverage. Numerous and Varied Problems: Throughout the text, section exercises of varying levels of difficulty give students hands-on experience in modeling, analysis, and computer experimentation. Emphasis on Systems: Systems of first order equations, a central and unifying theme of the text, are introduced early, in Chapter 3, and are used frequently thereafter. Linear Algebra and Matrix Methods: Two-dimensional linear algebra sufficient for the study of two first order equations, taken up in Chapter 3, is presented in Section 3.1. Linear algebra and matrix methods required for the study of linear systems of dimension n (Chapter 6) are treated in Appendix A. Contemporary Project Applications: Optional projects at the end of Chapters 2 through 10 integrate subject matter in the context of exciting, contemporary applications in science and engineering, such as controlling the attitude of a satellite, ray theory of wave propagation, uniformly distributing points on a sphere, and vibration analysis of tall buildings. Computing Exercises: In most cases, problems requiring computer generated solutions and graphics are indicated by an icon. Visual Elements: In addition to a large number of illustrations and graphs within the text, physical representations of dynamical systems and interactive animations available in WileyPLUS provide students with a strong visual component to the subject. Control Theory: Ideas and methods from the important application area of control theory are introduced in some examples and projects, and in the last section on Laplace Transforms, all of which are optional. Recurring Themes and Applications: Important themes and applications, such as dynamical system formulation, phase portraits, linearization, stability of equilibrium solutions, vibrating systems, and frequency response are revisited and reexamined in different applications and mathematical settings. Chapter Summaries: A summary at the end of each chapter provides students and instructors with a birds-eye view of the most important ideas in the chapter.
This book introduces the reader to the basic math used for neural network calculation. This book assumes the reader has only knowledge of college algebra and computer programming. This book begins by showing how to calculate output of a neural network and moves on to more advanced training methods such as backpropagation, resilient propagation and Levenberg Marquardt optimization. The mathematics needed by these techniques is also introduced. Mathematical topics covered by this book include first, second, Hessian matrices, gradient descent and partial derivatives. All mathematical notation introduced is explained. Neural networks covered include the feedforward neural network and the self organizing map. This book provides an ideal supplement to our other neural books. This book is ideal for the reader, without a formal mathematical background, that seeks a more mathematical description of neural networks. Neural Networks and Learning Machines, Third Edition is renowned for its thoroughness and readability. This well-organized and completely up-to-date text remains the most comprehensive treatment of neural networks from an engineering perspective. This is ideal for professional engineers and research scientists. Matlab codes used for the computer experiments in the text are available for download at: Refocused, revised and renamed to reflect the duality of neural networks and learning machines, this edition recognizes that the subject matter is richer when these topics are studied together. Ideas drawn from neural networks and machine learning are hybridized to perform improved learning tasks beyond the capability of either independently. Provides a comprehensive foundation of neural networks, recognizing the multidisciplinary nature of the subject, supported with examples, computer-oriented experiments, end of chapter problems, and a bibliography. DLC: Neural networks (Computer science). In response to the exponentially increasing need to analyze vast amounts of data, Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition provides scientists with a simple but systematic introduction to neural networks. Beginning with an introductory discussion on the role of neural networks in scientific data analysis, this book provides a solid foundation of basic neural network concepts. It contains an overview of neural network architectures for practical data analysis followed by extensive step-by-step coverage on linear networks, as well as, multi-layer perceptron for nonlinear prediction and classification explaining all stages of processing and model development illustrated through practical examples and case studies. Later chapters present an extensive coverage on Self Organizing Maps for nonlinear data clustering, recurrent networks for linear nonlinear time series forecasting, and other network types suitable for scientific data analysis. With an easy to understand format using extensive graphical illustrations and multidisciplinary scientific context, this book fills the gap in the market for neural networks for multi-dimensional scientific data, and relates neural networks to statistics. Sandhya Samarasinghe obtained her MSc in Mechanical Engineering from Lumumba University in Russia and an MS and PhD in Engineering from Virginia Tech, USA. Her neural networks research focuses on theoretical understanding and advancements as well as practical implementations. Over the last decade, the study of complex networks has expanded across diverse scientific fields. Increasingly, science is concerned with the structure, behavior, and evolution of complex systems ranging from cells to ecosystems. Modern network approaches are beginning to reveal fundamental principles of brain architecture and function, and in Networks of the Brain, Olaf Sporns describes how the integrative nature of brain function can be illuminated from a complex network perspective. Highlighting the many emerging points of contact between neuroscience and network science, the book serves to introduce network theory to neuroscientists and neuroscience to those working on theoretical network models. Brain networks span the microscale of individual cells and synapses and the macroscale of cognitive systems and embodied cognition. Sporns emphasizes how networks connect levels of organization in the brain and how they link structure to function. In order to keep the book accessible and focused on the relevance to neuroscience of network approaches, he offers an informal and nonmathematical treatment of the subject. After describing the basic concepts of network theory and the fundamentals of brain connectivity, Sporns discusses how network approaches can reveal principles of brain architecture. He describes new links between network anatomy and function and investigates how networks shape complex brain dynamics and enable adaptive neural computation. The book documents the rapid pace of discovery and innovation while tracing the historical roots of the field. The study of brain connectivity has already opened new avenues of study in neuroscience. Networks of the Brain offers a synthesis of the sciences of complex networks and the brain that will be an essential foundation for future research. This important work describes recent theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Chapters survey research on pattern classification with binary-output networks, including a discussion of the relevance of the Vapnik Chervonenkis dimension, and of estimates of the dimension for several neural network models. In addition, Anthony and Bartlett develop a model of classification by real-output networks, and demonstrate the usefulness of classification with a "large margin." The authors explain the role of scale-sensitive versions of the Vapnik Chervonenkis dimension in large margin classification, and in real prediction. Key chapters also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient, constructive learning algorithms. The book is self-contained and accessible to researchers and graduate students in computer science, engineering, and mathematics. Introduction to Neural Networks with C#, Second Edition, introduces the C# programmer to the world of Neural Networks and Artificial Intelligence. Neural network architectures, such as the feedforward, Hopfield, and self-organizing map architectures are discussed. Training techniques, such as backpropagation, genetic algorithms and simulated annealing are also introduced. Practical examples are given for each neural network. Examples include the traveling salesman problem, handwriting recognition, financial prediction, game strategy, mathematical functions, and Internet bots. All C# source code is available online for easy downloading. Understanding Neural Networks is an introductory text to artificial neural networks. The book begins with examining biological neurons in the human brain and defining their real world mathematical and electronic equivalent. Building upon this foundation the book contains hardware and software projects that illustrate neural networks. Hardware projects include a op-amp neuron that tracks a light source, speech recognition system, and machine vision system. Software projects include a Preceptron program and Back-Propagation networks. Are you webmaster? Go to webmaster forum to get as much as website building knowledge and free tools.
Algebra 1 Algebra 1 introduces students to the idea of generalizing statements through the use of variables. As one student astutely pointed out, "it's just like what we did in arithmetic but with letters". Students work with real numbers and variables along with algebraic properties to solve equations and inequalities in one or two variables. Solutions are introduced numerically and graphically. Teaching emphasizes concepts that allow students to approach problems in a variety of ways.
GraspMath Learning Systems TI-83 Video Tutor Please Note: Pricing and availability are subject to change without notice. This video is approximately two hours in length and is designed to gradually take students through the features of the TI-83 graphing calculator. The video is designed for high school students, college students and professionals needing assistance in learning the features of the TI-83. This comprehensive instructional video demonstrates the following features of the TI-83:
These are the advanced problems (along with advanced probability, trig, etc.). I wouldn't worry too much about those assuming you have sufficient algebra and geometry skills (you can often break down the more advanced problems into more manageable problems assuming you have sufficient problem solving skills). _________________
Thoroughly classroom-tested over the past two years, this book integrates problem solving, theory, and algorithms with insights into professional practice using commercial software. This easy-to-read book narrows the gap between academia and industry in an effort to better prepare students and professionals for integer programming as it is used in the current working environment. The book makes liberal use of examples and flowcharts. Each new concept or algorithm is illustrated by a numerical example, and each chapter contains 3-5 figures, such as flowcharts or simple geometric drawings, to illustrate the concepts in the text. Modeling is emphasized because the insertion of integer variables in a linear program enables much more rich and realistic representations of decision situations.
...ractice Problems Involving Computation 1 Assume you have a black hole of initial mass M0 and some specified initial spin and that it accretes matter at the innermost stable circular orbit Write a computer program to calculate the dimensionless spin parameter j a M J M 2 of the hole as a function... ...omputability and Modeling Computation What are some really impressive things that computers can do Land the space shuttle and other aircraft from the ground Automatically track the location of a space or land vehicle Beat a grandmaster at chess Are there any things that computers can t do Yes... ...omputation Calculators and Common Sense A Position of the National Council of Teachers of Mathematics Question Is there a place for both computation and calculators in the math classroom NCTM Position School mathematics programs should provide students with a range of knowledge skills and tools... 1 0 1 Sample Computational Problems Factoring a polynomial To factor a polynomial place the insertion point inside or to the right of the polynomial select Factor from the Compute menu Example 1 5x5 5x4 1 0 2 10x3 10x2 5x 5 5 x 2 3 1 x 1 Finding the roots of a polynomial To nd the roots of a polynomial place the insertion point inside or to the rig... ...age 1 of 4 Models of computation indicates problems that have been selected for discussion in section time permitting Problem 1 In lecture we saw an enumeration of FSMs having the property that every FSM that can be built is equivalent to some FSM in that enumeration A We didn t deal with FSMs...
Excursions in Classical Analysis Hongwei Chen Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof. The author presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that might at first glance, not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis. The carefully selected assortment of problems presented at the end of the chapters includes 22 Putnam problems, 50 MAA Monthly problems, and 14 open problems. These problems are not related to the chapter topics, but connect naturally to other problems and even serve as introductions to other areas of mathematics. The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order.
A General Overview of Maple Maple is a general purpose computer algebra system, designed to solve mathematical problems and produce high-quality technical graphics. It is easy to learn, but powerful enough to calculate difficult integrals in seconds. Maple incorporates a high-level programming language which allows the user to define his own procedures; it also has packages of specialized functions which may be loaded to do work in group theory, linear algebra, and statistics, as well as in other fields. It can be used interactively or in batch mode, for teaching or research. Maple is classified by UITS as a General Purpose Software. Documentation is available in all Student Technology Centers and the Center for Statistical and Mathematical Computing. UITS Public Facilities consultants can provide assistance in accessing the program. The Center for Statistical and Mathematical Computing (812/855-4724 or email to statmath@iu.edu) can answer basic to advanced questions. NOTE: If you are a student using Maple for a class exercise, questions about your class work should be directed first to your instructors. Program Functionality: Excellent Breadth of Functionality: Excellent Maple has over 2500 functions available. A basic core collection is loaded at startup, and specialized packages are available, for topics from statistics to geometry. Reliability and Robustness: Good Maple is very robust, and reliable. However, no computer program can replace understanding! People do mathematics, computers don't. State of the Art: Excellent Maple is one of the leading mathematics programs, noted for its algebraic and analytic prowess. Export to LaTeX or HTML are provided. Maple is relatively good about not returning "wrong" answers. Inverse functions remain the big problem for computer algebra systems. They appear in places where they might not be expected (definite integrals, for example), so any result from a CAS should be checked. Maple handles inverse functions fairly well, although the resulting fastidiousness can be surprising. Maple can [to some extent] handle assumption, such as "n is an integer" or "theta lies between 0 and Pi/2", which increases its power and precision, and makes it possible to deal with convergence conditions and inverse functions relatively well. User Friendliness: Fair Maple is the most user-friendly of the mathematical software available at IUB, but Maple's command-line language requires some investment in training before the program can be easily used. Maple's language is easily understood by those trained with any procedural language (such as Basic or C); its command names and syntax are mostly straightforward and easily understood. Electronic Help Resources: Excellent Network-based help: Excellent The Knowledge Base has answers to several frequently asked Maple questions. Program Help System: Excellent The Help System is excellent; it includes examples and discussion as well as syntax. A "New Users' Tour" makes it easy to get started, with hyperlinks to additional topics. To get help on a known command, use the ? command -- for example, ?plot . "?" by itself gets help on the help system. When the command is unknown, you can search for a topic, or do a full-text search of the help system. At the top of a help window is a "Help Browser" which lists topics by category, with up to five levels of increasing detail. Local Availability: Excellent Indiana University at Bloomington has a site license for Maple; IUPUI also owns such a license. Consequently, the latest version of Maple [as of a month before the current semester started] will be installed in all UITS public computing facilities, and many of the UITS timesharing systems.For details, see the Math Software Availability page. Further, Maple may be obtained at greatly reduced prices for departmental and personal workstations at these locations: see the Sales page for more information. Local Support & Training: Excellent Document Availability: Excellent Locally produced documents are also available free of charge from UITS Stat/Math Center. UITS makes basic manuals available in document racks in the Student Technology Centers. Full documentation is available for reference and short term loan from various Software Manual Locations. Documents are also available for reference at the UITS Stat/Math Center. Training Availability: Excellent UITS offers Steps classes for Getting Started With Maple free of charge to students. Instructors may request a specially arranged class for introducing their students to Maple by contacting UITS IT Training Group (855-3499). User Group: Good To join the international Maple Users' Group [mailing list], send e-mail to majordomo@daisy.uwaterloo.ca containing the line subscribe maple-list. UITS Consulting Support: Full Support Consulting support is available from Stat/Math Consulting from 9 am to 5 pm (M-F) via email, phone, and for walkins (an appointment is recommended for walkin consulting). Other Consulting Support: Good Registered Maple license owners can contact the vendor directly with the number provided with the license agreement: phone 800-267-6563. Students with the student edition should contact Brooks-Cole at 800-214-2661, or send e-mail to support@brookscole.com
Specification Aims The aims of this course are to develop an understanding of convergence in its simplest setting. To explain the difference between a sequence and a series in the mathematical context. To lay foundations for further investigation of infinite processes, in particular differential and integral calculus. Brief Description of the unit The notion of limit underlies the differential and integral calculus, a central topic in Mathematics. A good understanding of this concept was developed in the early nineteenth century, many years after the calculus was first used, and this is essential for more advanced calculus. The main purpose of this course is to provide a formal introduction to the concept of limit in its simplest setting: sequences and series. Learning Outcomes On successful completion of this module students will be able to know the definition of the limit of a sequence. be able to find the limit of a wide class of sequences. be able to decide on convergence or divergence of a wide class of series. know that a power series has a radius of convergence, and know how to find it. Future topics requiring this course unit Syllabus Null sequences, properties of the class of null sequences, the standard list of null sequences. Convergent sequences, properties of the class of convergent sequences, including Algebra of Limits. Sequences diverging to infinity, the Reciprocal Rule, subsequences and the subsequence strategy. Ratio Test, L'Hôpital's Rule and the Integral Approximation Rule for sequences. The Monotone Convergence Theorem and the sequence (1+1/n)². Convergent series, the geometric series and the harmonic series. Series with non-negative terms, the Comparison Test, the Limit Comparison Test, the Ratio Test and the Integral Test. The Alternating Series Test, absolute and conditional convergence of series, power series and radius of convergence.
Unit 4 Introduction In our last unit we move up from two to three dimensions. Now we will have three main objects of study: Triple integrals over solid regions of space. Surface integrals over a 2D surface in space. Line integrals over a curve in space. As before, the integrals can be thought of as sums and we will use this idea in applications and proofs. We'll see that there are analogs for both forms of Green's theorem. The work form will become Stokes' theorem and the flux form will become the divergence theorem (also known as Gauss' theorem). To state these theorems we will need to learn the 3D versions of div and curl
Courses COURSES FOR CREDIT ALGEBRA I Grades 9–12 July 8–August 9, 2013 9:30 a.m.–1:30 p.m. $1,250 Algebra I is an introductory course that places an emphasis on the systematic development of the language through which most of mathematics is communicated. It provides the foundations for a systematic way to represent mathematical relationships and analyze change, as well as the mathematical understanding to operate with concepts at an abstract level, and then apply those concepts in a process that fosters generalizations and insights beyond the original content. Topics covered are: properties of the number system, linear functions, inequalities, operations on real numbers and polynomials, exponents, radicals, and quadratics. Successful completion of this course prepares students for Geometry and Algebra II. ALGEBRA II The study of functions and an extension of the concepts of Algebra I and many of the concepts of geometry are covered. Topics covered are: linear and quadratic equations and functions; systems of equations and inequalities; polynomials and rational polynomial expressions; polynomial functions; conic sections; exponential and logarithmic functions; probability and statistics. Prerequisite: Algebra I with a grade of C or better, or teacher recommendation. SUMMER PACKETS MATH PACKET Grades 6–12 (C/A Students only) August 12–16, 2013 9:30 a.m.–12:00 p.m. $300 Open to Commonwealth Academy students only, this course is designed to help students complete their summer math packets. READING PACKET Grades 6–12 (C/A Students only) August 12–16, 2013 12:30 p.m.–3:00 p.m. $300 Open to Commonwealth Academy students only, this course is for those students in need of assistance with their summer reading work (projects, reading logs). Both books must be read prior to attending for the student to receive the full benefit of the course. EXTENDED CARE BEFORE AND AFTER CARE Students enrolled in Algebra I July 8–August 9, 2013 (Mon.–Thurs. only) 8:30 a.m.–9:30 a.m. 1:30 p.m.–3:00 p.m. $10/hour or $20/day We will hold before and after care services throughout the week to allow parents to drop their students off early or pick them up later in the day. The service is provided beginning at 8:30 a.m. and ends at 3:00 p.m. Payment for these services must be made in advance.
Computational Mathematics Colleges A program that focuses on the application of mathematics to the theory, architecture, and design of computers, computational techniques, and algorithms. Includes instruction in computer theory,cybernetics, numerical analysis, algorithm development, binary structures, combinatorics, advanced statistics, and
Algebra Homework Help Ordinary algebra is a topic almost everyone studies to some extent in high school. Even so, it's easy to forget basic skills, and many people find themselves having difficulty in math classes later in life because of those forgotten skills. We offer Algebra homework help to get you caught up and ready to take this subject by storm. Typical topics in a basic, college-level class in ordinary algebra will include: Graphs, Functions, and Models Functions, Equations, and Inequalities Polynomial and Rational Functions Exponential and Logarithmic Functions Systems of Equations and Matrices Conic Sections Sequences, Series, and Probability A truly great website for getting help and extra practice in ordinary algebra at all levels is the Virtual Math Lab of West Texas A&M University.
The Department Algebra and Geometry Section The Algebra and Geometry Section includes the following fields of Mathematics: Abstract Algebra, Differential Geometry, Number Theory, Mathematical Logic, Differential and Algebraic Topology, Algebraic Geometry, etc. Algebra developed mainly in the 19th and 20th centuries and its aim was the solution of specific problems in Geometry, Number Theory and the Theory of Algebraic Equations. It also contributed to a better understanding of the existing solutions to such problems. Today, Algebra's contribution to other sciences, such as that of Computer Science, is invaluable. Differential Geometry constitutes one of the main branches of mathematics and deals with the study of metric concepts on manifolds, such as metrics and curvature. The classic period of Differential Geometry was the 19th century, during which the local theory of curves and surfaces - now known as elementary Differential Geometry - developed as an application of Infinitesimal Calculus. In the 20th century the field developed rapidly, based on the recent achievements of the theory of Partial Differential Equations, Algebraic Topology and Algebraic Geometry. The dynamics and fruitfulness of Differential Geometry is also a result of its interaction with other sciences, such as Physics (Theory of Relativity), etc.
Toolbar Search Google Appliance Mathematics, BS What Is the Study of Mathematics? Mathematics reveals hidden patterns that help us understand the world around us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems. As. -From Everybody Counts: A Report to the Nation on the Future of Mathematics Education (c) 1989 National Academy of Sciences Why Should I Consider this Major? The special role of Mathematics in education is a consequence of its universal applicability. The results of Mathematics-theorems and theories-are both significant and useful; the best results are also elegant and deep. Through its theorems, Mathematics offers science both a foundation of truth and a standard of certainty. In addition to theorems and theories, Mathematics offers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols. Experience with mathematical modes of thought builds mathematical power-a capacity of mind of increasing value in this technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to suggest alternatives. Mathematics empowers us to understand better the information-laden world in which we live. -From Everybody Counts: A Report to the Nation on the Future of Mathematics Education (c) 1989 National Academy of Sciences Empowered with the critical thinking skills that Mathematics develops, recent Mathematics graduates from Western have obtained positions in a variety of fields including actuarial science, cancer research, computer software development, business management and the movie industry, among many others. The skills acquired in our program have prepared graduates for further academic studies in Mathematics, Computer Science, Physics, Biology, Chemistry, Oceanography and Education.Coursework Requirements MATH 204 Elementary Linear Algebra MATH 224 Multivariable Calculus and Geometry I MATH 225 Multivariable Calculus and Geometry II MATH 226 Limits and Infinite Series MATH 304 Linear Algebra MATH 312 Proofs in Elementary Analysis Note: The pair MATH 203 and 303 may be substituted for MATH 204 and 331. Choose either: MATH 124 Calculus and Analytic Geometry I MATH 125 Calculus and Analytic Geometry II or MATH 134 Calculus I Honors MATH 135 Calculus II Honors or MATH 138 Accelerated Calculus One course from: MATH 302 Introduction to Proofs Via Number Theory MATH 309 Introduction to Proofs in Discrete Mathematics No fewer than 31 approved credits in mathematics or math-computer science, including at least two of the following pairs: One course from: MATH 303 - Linear Algebra and Differential Equations II MATH 331 - Ordinary Differential Equations Together with one of: MATH 415 - Mathematical Biology MATH 430 - Fourier Series and Applications to Partial Differential Equations MATH 431 - Analysis of Partial Differential Equations MATH 432 - Systems of Differential Equations Only one of the pairs from the above group can be used The following pair: MATH 341 - Probability and Statistical Inference MATH 342 - Statistical Methods The following pair: MATH 401 - Introduction to Abstract Algebra MATH 402 - Introduction to Abstract Algebra The following pair: MATH 421 - Methods of Mathematical Analysis I MATH 422 - Methods of Mathematical Analysis II The following pair: MATH 441 - Probability MATH 442 - Mathematical Statistics The following pair: M/CS 335 - Linear Optimization M/CS 435 - Nonlinear Optimization The following pair: M/CS 375 - Numerical Computation M/CS 475 - Numerical Analysis Supporting Courses At least 19 credits from 400-level courses in mathematics or math-computer science except MATH 483, and including at most one of MATH 419 or MATH 420. One of: CSCI 139 Programming Fundamentals in Python CSCI 140 Programming Fundamentals in C++ CSCI 141 Computer Programming I MATH 207 Mathematical Computing Note: If the supporting sequence from CSCI below is chosen, this requirement is fulfilled. One of the following sequences: PHYS 161 - Physics with Calculus I PHYS 162 - Physics with Calculus II PHYS 163 - Physics with Calculus III OROR CSCI 141 - Computer Programming I CSCI 145 - Computer Programming & Linear Data Structures CSCI 241 - Data Structures CSCI 301 - Formal Languages and Functional Programming And one of: CSCI 305 - Analysis of Algorithms and Data Structures I CSCI 330 - Database Systems CSCI 345 - Object Oriented Design CSCI 401 - Automata and Formal Language Theory OR ECON 206 - Introduction to Microeconomics ECON 207 - Introduction to Macroeconomics ECON 306 - Intermediate Microeconomics And one of ECON 375 - Introduction to Econometrics ECON 470 - Economic Fluctuations and Forecasting ECON 475 - Econometrics Language competency in French, German or Russian is strongly recommended for those students who may go to graduate school. Students who are interested in the actuarial sciences should complete: MATH 441 and 442, M/CS 335 and 435, M/CS 375 and 475 as part of their major programs. GURs: The courses below satisfy GUR requirements and may also be used to fulfill major requirements. QSR: CSCI 139, 140, 141, 145; MATH 124, 125, 134, 135, 138 SSC: ECON 206, 207 LSCI: CHEM 121, 122, 123, 125, 126, 225; PHYS 161, 162, 163 "The Department of Mathematics has very highly qualified faculty who excel as both teachers and scholars. We have expertise in both pure and applied mathematics as well as statistics and math education. Our instructional focus is to establish a sound understanding of the fundamental concepts as well as mastery of the related analytical and computational skills. We have small classes and strive for active involvement of students in their learning. Our graduates are extremely well prepared for the workplace and for more advanced studies in math and related fields." - Tjalling Ypma, Faculty "The focus of the math department is to give students a strong background in problem solving and applying those skills. There is a wide range of mathematicians at Western, making it easy to find professors who share your interests and help you maximize your potential. They take teaching and advising very seriously; my advisor was always available for help with my resume' and planning my courses and my future. I am confident that Western has prepared me for success in graduate school and beyond. Whether your goals are professional or academic, being a Math major at Western will help you to succeed." - Malcolm Rupert, Student Notable Alumni Jeanie Light Software engineer, Google Software engineer, Google Charles Clark Co-Director, Joint Quantum Institute, National Institute of Standards and Technology
In Precalculus students use the following as tools to express generalizations and to analyze and understand a variety of mathematical relationships and real-world phenomena: Functions Equations Sequences Series Vectors Limits Precalculus topic instructional simulation Modeling is an overarching theme of this Precalculus course support service. Students build on and expand their experiences with functions from Algebra I, Geometry and Algebra II as they continue to explore the characteristics and behavior of functions (including rate of change and limits), and the most important families of functions that model real world phenomena (especially transcendental functions). Teachers can guide their students through deeper study of functions, equations, sequences, series, vectors, and limits to enable them to successfully express generalizations and to analyze and understand a variety of mathematical relationships and real-world phenomena. Though I am an experienced teacher, every section or topic in Precalculus provides me with a new way to introduce and teach the course. I find creative problems, demonstrations, and interactive animations to engage each student. Agile Mind gives me access to resources that make me a better teacher. As a result I have better students. - Marty Romero, Math Chair, Wallis Annenberg HS, Los Angeles, CA Sign up for a tour to experience how Agile Mind services can work for you and your students. You will be contacted by one of our representatives.
... More About This Book Math cards review pre-algebra, elementary and intermediate algebra, coordinate and plane geometry, and trigonometry. The Reading cards present strategies to maximize time and determine correct answers. The Science cards cover data representation, research summaries, and conflicting viewpoints. The Writing cards offer tips for creating a strong essay. All cards have corner punch holes that accommodate an enclosed metal key-ring-style card holder. Students can use the ring to arrange flash cards in sequences that best fit their study
Textbooks—published by Key Curriculum Press Each student will receive a hardback text book for use at home and in school. The textbooks have many features to support student learning including: Detailed examples Glossary and index Selected hints and answers Additionally, students receive a code from their teacher to access their textbook online. The online book has interactive features which enable students to link from pages in the book to additional practice problems, dynamic explorations, and calculator notes. Online Resources Electronic resources are available for Algebra, Geometry, Algebra 2, Pre-Calculus and Calculus. You can explore the resources for each book by going to the Kendall Hunt math website. These resources include: A Guide for Parents(in English and Spanish)—A brief summary of each chapter, includes tips for working with students, chapter summary exercises and review exercises with complete solutions. Condensed Lessons(in English and Spanish)—A detailed explanation of each lesson. These can provide extra help for students who have fallen behind or missed class, as well as support for adults who want to understand the details of the mathematics. More Practice Your Skills—a set of additional exercises for each lesson in the book for students who want extra practice. Calculator Notes, Programs and Data—helpful information, programs and tips for using calculators for specific activities. Dynamic Explorations—Structured investigations available online so students and their families can explore mathematics concepts at home.
Product Details Published: 2003 Isbn: 1-885581-45-9 Pages: 193 Math is an important part of everyday life and an integral part of the skills necessary to become certified in the safety profession. Many who pursue certification have long since completed their college math courses and have not actively pursued the math skills they once had. Background Math provides the basics necessary to successfully negotiate the math included on the certification exams, as well as a handy primer for those who already have their credentials. Topics include: Calculator selection and use, including BCSP rules for calculators, strategies for examinations and hierarchy for operations Fractions, reciprocals, proportions, rounding and absolute value Exponents, roots and logarithms and antilogs Systems of measurement, including English, metric, conversions and dimensional analysis Notation, both scientific and engineering Algebraic properties and simple equations, including variables, commutation, associative and distributive properties, order of operations, rules of equations, multiplying polynomials, and solving equations
a short, focused introduction to MATLAB. and should be useful to both beginning and experienced users. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB's programming features, graphical capabilities, and desktop interface. An especially attractive feature are the many worked-out applications to mathematics, economics, science, and engineering.
MATHEMATICS COURSES - MATH MATH 1020. Fundamentals of Geometry (3) Su, F, S An introduction to the definitions, methods, and logic of geometry. Prerequisite: MATH ND0960 or placement test. MATH QL1030. Contemporary Mathematics (3) Su, F, S Topics from mathematics which convey to the student the beauty and utility of mathematics, and which illustrate its application to modern society. Topics include geometry, statistics, probability, and growth and form. Prerequisite: MATH 1010 or ACT Math score 23 or higher or placement test. MATH QL1040. Introduction to Statistics (3) Su, F, S Basic concepts of probability and statistics with an emphasis on applications. Prerequisite: MATH 1010 or Math ACT score 23 or higher or placement test. MATH SI1220. Calculus II (4) Su, F, S MATH 1630. Discrete Mathematics Applied to Computing (4) An overview of the fundamentals of algorithmic, discrete mathematics applied to computation using a contemporary programming language. Topics include logic, proofs, sets, functions, counting, relations, graphs, trees, Boolean algebra, and models of computation. This course includes programming. Prerequisites: MATH QL1050 or MATH QL1080, and CS SI1400 or ability to program in a contemporary computer language and the consent of the instructor. MATH 2010. Mathematics for Elementary Teachers I (3) Su, F, S Prospective elementary school teachers revisit mathematics topics from the elementary school curriculum and examine them from an advanced perspective including arithmetic, number theory, set theory and problem solving. Prerequisite: MATH QL1050. MATH 2020. Mathematics for Elementary Teachers II (3) Su, F, S Prospective elementary school teachers revisit mathematics topics from the elementary school curriculum and examine them from an advanced perspective including probability, statistics, geometry and measurement. Prerequisite: MATH QL1050 and MATH 2010. MATH 2110. Foundations of Algebra (3) An introduction to Abstract Algebra, Number Theory and Logic with an emphasis on problem solving and proof writing. Prerequisite: MATH SI1210. MATH 3410, 3420. Probability and Statistics (3-3) F, S MATH 3550. Introduction to Mathematical Modeling (3) F or S Formulation, solution and interpretation of mathematical models for problems occurring in areas of physical, biological and social science. Prerequisite: MATH 2210, MATH 2270 or 2280, or consent from instructor. MATH 3610. Graph Theory (3) F Principles of Graph Theory including methods and models, special types of graphs, paths and circuits, coloring, networks, and other applications. Prerequisite: MATH SI1210. MATH 3750. Dynamical Systems (3) S (alternate years) MATH 3810. Complex Variables (3) F or S or Su Analysis and applications of a function of a single complex variable. Analytic function theory, path integration, Taylor and Laurent series and elementary conformal mapping are studied. Prerequisite: MATH 2210. MATH 4110. Modern Algebra I (3) F Logic, sets, and the study of algebraic systems including groups, rings, and fields. Prerequisite: MATH 2270. Basic topics in secondary mathematics are taught to prospective teachers using a variety of methods of presentation and up-to-date technology, including the use of graphing calculators and computers. Prerequisite: MATH SI1220. Aspects of teaching advanced mathematics in a high school setting, including methods of presentation, exploration, assessment and classroom management. An emphasis is placed on the use of computers, graphing calculators, and other technology. Prerequisite: MTHE 3010. MTHE SI3060. Probability and Statistics for Elementary Teachers (3) F Basic Probability and statistics with an emphasis on topics and methods pertinent to prospective elementary school teachers. Prerequisite: MATH 2010 and MATH 2020. MTHE SI3070. Geometry for Elementary Teachers (3) F Basic Geometry with an emphasis on the topics and methods pertinent to prospective elementary school teachers. Prerequisite: MATH 2010 and MATH 2020. MTHE SI3080. Number Theory for Elementary Teachers (3) S MTHE 4010. Capstone Mathematics for High School Teachers I (3) S Prospective high school teachers revisit mathematics topics from the secondary school curriculum and examine them from an advanced perspective. The major emphasis is on topics from algebra. Prerequisites: MATH 2110 and MATH 3120. MTHE 4020. Capstone Mathematics for High School Teachers II (3) S Prospective high school teachers revisit mathematics topics from the secondary school curriculum and examine them from an advanced perspective. The major emphasis is on topics from geometry. Prerequisite: MTHE 4010. Topics in secondary mathematics are taught to in-service teachers using a variety of methods and technology to make them better prepared for teaching secondary mathematics. Expository presentations about a current mathematics education research area are expected. MTHE 6350. Linear Algebra (3) MTHE 6410, 6420. Probability and Statistics (3-3) The mathematical content of probability and statistics at the undergraduate post calculus level. An understanding of the application of probability and statistics is also stressed. Co-requisite: MTHE 5310 or prerequisite of MTHE 5220 and consent of instructor. Further prerequisites: MTHE 6410 for 6420. MTHE 6550. Introduction to Mathematical Modeling (3) Formulation, solution and interpretation of mathematical models for problems occurring in areas of physical, biological and social science. Prerequisite: MTHE 5310 and 5350. MTHE 6610. Graph Theory (3) Principles of Graph Theory including methods and models, special types of graphs, paths and circuits, coloring, networks, and other applications. Prerequisite: MTHE 5210. MTHE 6640. Differential Equations II (3) MTHE 6650. Complex Variables (3) Analysis and applications of a function of a single complex variable. Analytic function theory, path integration, Taylor and Laurent series and elementary conformal mapping are studied. Prerequisite: MTHE 5310 and 5350. MTHE 6660. Modern Algebra I (3) Logic, sets, and the study of algebraic systems including groups, rings, and fields. Prerequisite: MTHE 5350.
MERLOT Search - materialType=Tutorial&category=2513&createdSince=2012-04-16&sort.property=dateCreated A search of MERLOT materialsCopyright 1997-2013 MERLOT. All rights reserved.Wed, 19 Jun 2013 18:26:08 PDTWed, 19 Jun 2013 18:26:08 PDTMERLOT Search - materialType=Tutorial&category=2513&createdSince=2012-04-16&sort.property=dateCreated 4434ClassifyingCompound Events:Tree Diagrams The objective is to teach the Common Core Standard MCC7.SP.8 in which students must Investigate chance processes and develop, use, and evaluate probability models. Students must understand that samples spaces can be represented using organized lists, tables, and tree diagrams, use tree diagrams, list and tables to find probability of compound events and understand that all the possible outcomes of a compound event can derive from tree diagrams, lists and tables.Statistika Moodle-a Ovde je vođena Moodle statistika u celom svetu. Gde se Moodle najviše koristi, koje verzije su najpopularnije, koji plugin-ovi se najčešće koriste.cuerpos geometricos cuerpos geometricosAlgebra Helper 1 App for iOS 'Learn solving two equations system by example, by plugging the equation Coefficients. You will be able to build your examples, which is the best way to learn Algebra. This application provide step by step solution to the two equation system in additions to providing the value of x and y. Enter the equation Coefficients and see the full solution which can be sent as an email message.״Solve and email solutions with steps of the two equations two variables system.״Do you want to solve the "two equations, two variables" instantly?Ax + By = C [1]Dx + Ey = F [2]All you need to do is enter the values for A, B, C, D, E, and F and select Solve to get the values of X and Y. For Example, one can enter the following values3x + -2y = -4-3 + 5y = 8 Why go through the hassle of performing complex steps of solving the equations, when this program will not only solve your equations reliably, but also will always get you the correct results guaranteed. This program will help you focus on solving the bigger problems in physics, calculus, complex financial and Engineering problems. Why spend money and time programming your programmable calculator when you can use this program already on your iPhone or iPod Touch.Current features -(1) Show step by step solution(2) Able to email the equation, with the detailed solutionAlgebra Helper will help you in your Math problems, and this is the first application focusing on Linear Algebra, two equations, two variables problem.'This app costs $1.99Solving Equations by Combining Like Terms This is a powerpoint slideshow designed to remediate the process of solving multi-step equations involving combining like terms.Algebra Study Guide An algebra study guide and problem solver to accompany the open online Elementary Algebra textbook published by Flat World Knowledge. This ebook is available for free on the Google Play store.
Math Courses • The first type involves operations with integers and rational numbers, and includes computation with integers and negative rationals, the use of absolute values , and ordering. • A second type involves operations with algebraic expressions using evaluation of simple formulas and expressions, and adding and subtracting monomials and polynomials. Questions involve multiplying and dividing monomials and polynomials, the evaluation of positive rational roots and exponents, simplifying algebraic fractions , and factoring. • The third type of question involves the solution of equations , inequalities, word problems. solving linear equations and inequalities, the solution of quadratic equations by factoring, solving verbal problems presented in an algebraic context, including geometric reasoning and graphing, and the translation of written phrases into algebraic expressions. The Algebraic Operations content area includes simplification of rational algebraic expressions, factoring and expanding polynomials, and manipulating roots and exponents. The Solutions of Equations and Inequalities content area includes the solution of linear and quadratic equations and inequalities, systems of equations, and other algebraic equations. The Coordinate Geometry area presents questions involving plane geometry, the coordinate plane, straight lines, conics, sets of points in the plane, and graphs of algebraic functions. The Functions content area includes questions involving polynomial, algebraic, exponential, and logarithmic functions. The Trigonometry area includes trigonometric functions. The Applications and other Algebra Topics area contains complex numbers, series and sequences, determinants, permutations and combinations, factorials, and word problems. A total of 20 questions are administered on this test. Sample question: If the 1st and 3rd terms of a geometric sequence are 3 and 27, respectively, then the 2nd term could be a) 6 b) 9 c) 12 d) 15 e) 18 (the correct answer is b) Here are some of the knowledge and skills associated with the College-Level Math test. •identify common factors •factor binomials and trinomials •manipulate factors to simplify complex fractions. •work with algebraic expressions involving real number exponents •factor polynomial expressions •simplify and perform arithmetic operations with rational expressions, including complex fractions •solve and graph linear equations and inequalities •solve absolute value equations •solve quadratic equations by factoring •graph simple parabolas •understand function notation, such as determining the value of a function for a specific number in the domain •a limited understanding of the concept of function on a more sophisticated level, such as determining the value of the composition of two functions •a rudimentary understanding of coordinate geometry and trigonometry •understand polynomial functions •evaluate and simplify expressions involving functional notation, including composition of functions •solve simple equations involving trigonometric functions, logarithmic functions, and exponential functions •perform algebraic operations and solve equations with complex numbers •understand the relationship between exponents and logarithms and the rules that govern the manipulation of logarithms and exponents •understand trigonometric functions and their inverses •solve trigonometric equations •manipulate trigonometric identities •solve right-triangle problems •recognize graphic properties of functions such as absolute value, quadratic, and logarithmic Note: Here are the USU course descriptions. If you don't recognize part of the description, plug it into the suggested above web sites or your internet search box. There is an abundance of information for you to review. MATH 1030 QL Quantitative Reasoning 3 Exploration of contemporary mathematical thinking, motivated by its application to problems in modern society. Emphasizes development of skill in analytical reasoning. Prerequisite: C- or better in MATH 1010 or Math ACT score of at least 23 (Math SAT score of at least 540) within the Math prerequisite acceptability time limit; or satisfactory score on Math Placement Test. MATH 1050 and 1060, or Math ACT score of at least 27 (Math SAT score of at least 620), or AP calculus score of at least 3 on the AB exam within the Math prerequisite acceptability time limit; or satisfactory score on Math Placement Test. Supplemental Resources (not required): CourseCompass with MyMathLab is an online course that can be used to access online activities and resources, such as video lectures, practice problems, and sample tests. You need a MyMathLab Student Access Code to access the course. Course Objectives: As the result of instructional activities, students will be able to: 1. Determine the x- and y- intercepts of a graph algebraically and graphically 2. Calculate the slope of a line 3. Write an equation of a line given the y-intercept and the slope 4. Write an equation of a line given one point and the slope 5. Write an equation of a line given two points 6. Write an equation of a vertical line 7. Write an equation of a horizontal line 8. Use a graphing calculator to draw a scatterplot 9. Use a graphing calculator to find a linear regression model, where appropriate 10. Use a linear regression equation to make predictions 11. Solve a linear inequality 12. Determine if a given relation is a function 13. Identify the family to which a function belongs 14. Identify the domain and range of a function 15. Evaluate a function 16. Graph a function 17. Apply transformations to basic functions 18. Create cost, revenue and profit functions 19. Find a break-even point 20. Find the equilibrium quantity and price given supply and demand functions 21. Determine whether a parabola opens upward or downward 22. Determine the vertex of a parabola graphically and algebraically using –b/2a 23. Determine the axis of symmetry of a parabola 24. Determine the maximum or minimum value of a quadratic function 25. Use a graphing calculator to find a quadratic regression model, where appropriate 26. Use a quadratic regression equation to make predictions 27. Use the simple interest formula 28. Use the compound interest formula 29. Determine whether a system of equations is consistent and independent, dependent, or inconsistent 30. Solve a system of linear equations graphically 31. Solve a system of linear equations algebraically using substitution 32. Solve a system of linear equations algebraically using elimination 33. Solve a system of linear equations using a matrix 34. Graph a linear inequality in two variables 35. Graph a system of linear inequalities and identify the feasible region 36. Formulate a linear programming model 37. Solve a linear programming model graphically 38. Define set, subset, empty set, universal set 39. List the elements of a set 40. Identify the number of elements in a set 41. Use the set operations of union, intersection, and complementation 42. Draw Venn Diagrams to illustrate relationships between sets 43. Determine the sample space of an experiment 44. Determine if two events are disjoint (mutually exclusive) 45. Calculate a factorial 46. Distinguish between a permutation and a combination 47. Calculate a permutation 48. Calculate a combination 49. Calculate basic probabilities 50. Use the addition rule for probability 51. Use the complement rule for probability 52. Calculate a conditional probability 53. Determine if two events are independent 54. Use the product rule for probability Do some lessons as a class instead of in pairs; enlarge a ruler and make a transparency - color code 1/4, 1/8, 1/16; calculators for some fraction work; clock model; probability meter; data ahead of time; use Post It notes to remind self of things needed in next lesson; 6.4 - collect data in P.E. class; collect data from weather map, sports page. etc. transparencies for direct teaching; partners for shared thinking (divide and conquer!); display rules for order of operations ; incorporate more whole group activities instead of partners; have students write PEMDAS (Please Excuse My Dear Aunt Sally) next to each Order of Operations problem. Cross off letters as you work through the problem ; give kids # cards & scramble - they have to get in correct order SKILLS STUDENTS WILL LIKELY DO WELL ON: exponential notation; using a calculator for exponents; many of the mental math and math box activities POTENTIAL 2-DAY LESSONS: possibly 7.4, 7.5 OTHER CONSIDERATIONS: cut +/- counters; learn games (7.1, 7.4, 7.6); can't do study link 7.1 without 10-digit calculator; post definitions; post number line (7.6); locate book , The King's Chessboard; MMR for 7.4 on sentence strips; overhead of slide rule; make +/- # cards; practice vocabulary (especially prefixes); NOTE: order of operations is listed as developing, but it is on ISTEP test
Algebra I October 5, 2012 The Algebra I students have been working on solving equations for particular variables. This math skill is one of the most important skills in mathematics. The students are working on understanding what solutions are and how to find them. The steps for solving these equations are a balancing act. They have to keep both sides of the equal sign balanced, like weights on a scale. Another aspect of solving equations is that students have the ability to check their solutions that they get. This ability to check their solutions increases the learning and depth of knowledge of the content
Cauchy's Cours d'analyse: An Annotated Translation (Sources and Studies in the History of Mathematics and Physical Sciences) In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d'analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the Cours d'analyse. For this translation, the authors have also added commentary, notes, references, and an index. The 18th century was a wealth of knowledge, exploration and rapidly growing technology and expanding record-keeping made possible by advances in the printing press. In its determination to preserve ...
Its a rather complex application that's aimed strictly at those comfortable with complex maths but the advantage GeoGebra offers over similar apps is that it provides multiple representations of objects that are all dynamically linked. The idea behind GeoGebra is to connect geometric, algebraic, and numeric representations in an interactive way. This can be done with points, vectors, lines, conic sections. GeoGebra allows you to directly enter and manipulate equations and coordinates enabling you to plot functions, work with sliders to investigate parameters, find symbolic derivatives, and use powerful commands like Root or Sequence. However, the complexity of the program is mind boggling for those new to such mathematical applications. It's very difficult to work out how to use from scratch although there are several very detailed tutorials to help you on your way. GeoGebra isn't a mathematical program for the faint hearted but if you have to deal with arithmetic, geometry, algebra and calculus on a regular basis, its very flexible. ]]>Download MathType 6.7 in Softonic]]>If you're scientific or mathematical work involves highly complex linear and non linear problem solving, then you may find that Octave provides the power you've been looking for. Octave is a high-level language developed by the open source community which functions simply by providing a command line interface for solving linear and nonlinear numeric problems. For those that are familiar with Matlab, they will have few problems picking up Octave because it works in conjunction with the former language. The program basically features several very powerful tools for solving the kind of linear algebra equations that would send shivers down the spine of even the most experienced mathematician. According to the developers, it also includes functions for manipulating polynomials and integrating differential and differential-algebraic equations if you know what those are in the first place! The one bonus for those familiar with other languages is that Octave can also be extended or used in conjunction with modules written in C++, C, Fortran and others. This is an extremely complex language that only those familiar with Matlab or Fortran will pick up quickly. Anyone else should be prepared to put a lot of hours in although the problem solving skills it will provide you with seem virtually limitless. ]]>Although kids love to play games, sometimes your PC can also be your best friend in educating them. Kid's Abacus 2. 0 is a free mathematical application designed to allow younger users to count from 1 to 100. The developers claims that the Maths Worksheets have been designed for ease of use, fast setup and interactivity. There are plenty of audio-visual and multimedia features built-in to help users learn the basics of counting. This is very much aimed at young learners though. There's nothing beyond counting possible here and it's a shame the developers didn't add a few more simple mathematical challenges to stretch young users. ]]>MathGame, unsurprisingly, is a mathematics game for junior schoolchildren and above. It features different game modes and difficulty settings, to suit the child. The game in MathGame is essentially a timer, which challenges you to speed up your calculations. The game mechanic is simple - solve addition, subtraction, division or multiplication problems. There are no fancy graphics, or anything particularly innovative about it. It's good for parents who want their kids to practice mathematics, and maybe the high score table and against the clock gameplay are enough to entice them to play. If your child hates maths, MathGame is not going to change their minds, as it doesn't do anything to make it fun! For adults, while it may be interesting to see how much of your times table you've forgotten, MathGame is so much less sophisticated that Nintendo's Brain Training games it looks pretty dull. Unless you donate to the developers, upon closing the game, you have to wait for a "nag window" to close, which is quite irritating. Unless you or your children enjoy doing simple calculations, you're unlikely to find much to enjoy with MathGame. ]]>Download Excel Regression Analysis 2.2 in Softonic]]>Download Math Games Level 1 1.0 in Softonic]]>Download Geometry Calculator 1.2 in Softonic]]>If you're a serious mathematician or studying advanced mathematics or physics, then Math Mechanixs will be of much interest to you. It is not a training aid or a spreadsheet program - rather it works using a Math Editor (as opposed to a Text Editor) allowing you to type the mathematical expressions similar to the way you would write them on a piece of paper. The software uses a multiple document interface so that you can work on multiple solutions simultaneously. There is a fully featured scientific calculator which includes a very useful integrated variables and functions list window so that you can easily track defined variables and functions. Particularly for those that have to produce mathematical presentations, Math Mechanics enables you to produce some very impressive 2D and 3D diagrams. The graphing utility allows you to label data points, as well as zoom, rotate and translate the graph. This can seem daunting at first but fortunately there are several tutorials available that will guide you through it. This a powerful and versatile mathematical software that anyone working on mathematical projects will find useful. Nowadays OpenStat has been expanded to handle all kinds of data, although the developer itself admits that it's not the "finished product" yet. This means that any results you gain from it, can't be guaranteed and should be double checked either by hand or using other software. OpenStat, rather than just present data in graph form, attempts to test and display data in one go, meaning it cuts out the need for a separate research package. It looks remarkably simple and generally, it is easy to use but it's actually quite a complex package, able to handle all kinds of algorithms and parameters that you define. However, the developer could have put more effort into making both the interface and graphs look better. In addition, according to the forum it does have problems handling certain formulas but this is probably because it's not the finished article yet. OpenStat is a simple to use but powerful statistical analysis and graphical display package that can handle most of what you throw at it. ]]>Download Math Calculator 2.1.10 in Softonic]]>This application is no longer available or supported. Those of us who feel more attracted by books may have enough with the Windows Calculator, but mathematics people definitely need something more. Here's where Derive 6 comes in handy by presenting you with a wide variety of mathematical tools ready to perform almost any kind of maths operation. The program displays a blank interface where you insert numbers, expressions, symbols and everything you need to create your calculations. The data is entered through a command line and added in consecutive lines on the program's interface. Besides using your keyboard, you can also use the program's buttons to enter certain symbols which may be harder to find on your keyboard configuration. You can then let Derive solve the problem and also get it printed on paper for further study. All the operators and commands are conveniently categorized into a menu which, together with a comprehensive help system, make the program very complete and easy to use – that is, if you have some basic maths knowledge. Otherwise, you may as well stick to the Windows Calculator! ]]>TexMakerX is an application that integrates many tools needed to develop documents with LaTeX. Amongst its many features are a unicode editor to write your LaTeX source files (including syntax highlighting, undo-redo, search-replace etc), 370 mathematical symbols and wizards to generate code. It also enables you to view documents by structure for easier navigation of a document. In other words, TexMakerX adds hundreds of symbols and characters to your computer that wouldn't normally be available. Although most general users may not find a use for LaTeX, it is particularly popular with mathematicians as it allows them to perform complex formulas which they can edit far more easily. TexMakerX allows you to work with multiple documents in separate tabs with numbered lines to make distinguishing projects and documents easier. Finally, TexMakerX also features an error console on as well as a spelling tool to keep mistakes to a minimum. TexMakerX will only mainly appeal to those with special typographical needs such as mathematicians but for anyone involved in LaTeX its a powerful tool.
Applied College Algebra: A Graphing Approach: Solutions Manual Book Description: Williams offers a refreshing and innovative approach to college algebra, motivating the topics with a variety of applications and thoroughly integrating the graphing calculator. Written in a clear and friendly voice that speaks to students with weak algebra skills, this text teaches students to look at math from both algebraic and geometric viewpoints. Williams focuses on the underlying concepts, introducing and using the graphing calculator as an integral means, not an end. New applications examples and exercises from a variety of fields motivate the key ideas and show students why math is useful and powerful. Packaged free with every new copy of the text, an ELECTRONIC COMPANION TO COLLEGE ALGEBRA CD-ROM is a dynamic and interactive college algebra tutorial. It covers key concepts through multiple representations: graphic, numerical, algebraic, and verbal. "Review Topics" boxes present the main ideas of the course and "Test Yourself" problems test student understanding. A workbook of additional examples and exercises is built into the CD-ROM.
Autograph is the only software to let you visualise maths in 2D and 3D with ease. There are no arcane commands to learn - just point and click. Left click to select an object and right click for a context sensitive menu of mathematical actions. With Autograph, it's just you and the maths - free to go wherever enquiry takes you! Optionally control Autograph from an iPad or Tablet PC wirelessly as you roam the classroom. See a video of The Perse School, Cambridge, using Autograph this way. Secret Weapons ... Autograph has three secret weapons to give you complete control. Slow Plot: the essential tool for "what happens next?" Dynamic Constant Controller: see changes on the fly, with steps Dynamic Animation Controller: brings maths to life Easily import data, represent it in Autograph, then export to Word or Web There's lots of educationally useful UK and world data on the Autograph website, but you can import data from anywhere on the web, or from Excel for instance, directly into Autograph by simple copy and paste. Represent, manipulate and analyse your data dynamically in Autograph with mathematical rigour and precision - proper histograms are offered for example, with variable class interval widths - then copy and paste into Word documents to print and share, or save it as a web page. Getting Going with Autograph To get started with Autograph, you might like to take a look at some short videos in the Videos and Resources sections which will show you Autograph in action. If you'd prefer to concentrate on learning your way around Autograph's interface, then here's a good video about the Standard Level of operation for starters, and some excellent Getting Going videos at the start of the Autograph Video Tutorial series here. Use Photos or Images as backgrounds to bring STEM topics to life Now you can bring maths to life with photos and images as your background. Import any graphic image, adjust the opacity so you can see your graphed model clearly, and fit functions to natural phenomena - whether it be fitting a quartic through five points to find the equation of an arch, or the trajectory of a projectile, or geometric features of architecture. A great way to relate maths to real world phenomena and engage attention. In Autograph 3.3, image handling has been improved: you can paste or drag image files into Autograph, and you can drag images straight off Firefox pages. Geometry has been expanded, with new angle measurement tools and marking. Text annotation is now dynamic too. There's a dockable results box, tabbed workspaces and a redesigned and expanded Help and Training system and more! In Autograph 3.3, many of the routines have been fine-tuned and operation is smoother. There is a superb new "Save to Web" facility. Autograph activites can be quickly created and saved to HTML (eg for use in a VLE or Wiki). Anyone opening such an activity for the first time in Internet Explorer, Firefox or Safari will automatuically download the Autograph Player (which is installed anyway for all Autograph users). All six 'Extras' have been completely re-written in stunning "Flash". The multi-lingual interface has been extended to 18 languages, including the world's first true right-to-left Arabic notation. The use of Autograph on Thin Client systems has been enabled. Autograph is now activated online, enabling the smooth continuation of use for trial users, and greatly simplifying the process of delivering the software to students on the popular Extended Licence. It is understood that many will want to take the opportunity to upgrade their licence to the popular Extended Licence to take advantage of the online activation. Autograph 3.3 on the Mac Download the Mac free trial. Autograph 3.3 now runs seamlessly on all Intel-based Apple Mac computers, including Mountain Lion. All the features of the PC version have been implemented () and AGG files will be fully interchangeable between the two systems. Where possible the Mac interface has been adopted, so Ctrl-Click gives a Right-Click. The CTRL key is otherwise affected by the APPLE (command) key/ () The Save to Web feature has only been partially implemented for MAC browsers; however this feature will be fully available in a future release of the MAC version.
Math 5 - Trigonometry Syllabus – Section 3386 - Fall '12 CATALOG COURSE DESCRIPTION: This course is the first of a two semester sequence preparing students for Calculus. In this course you will study functions with an emphasis on the trigonometric functions along with topics in analytic geometry. Topics will include a review of plane and coordinate geometry, functions, including function notation, transformations and inverses, definitions and graphs of the trigonometric functions, modeling periodic behavior, solving triangle problems with the Laws of Sines and Cosines, the conic sections, including an introduction to parametric and polar equations. CALCULATORS: You may be restricted to a scientific calculator or no calculator on some tests. EXAMS: There will be at least five chapter tests and a cumulative final exam. There may also be several projects, as circumstance demands. The point of these is to provide an opportunity to demonstrate your understanding of the concepts covered. As such, exam problems won't consist entirely of very familiar homework problems. Teaching and Learning: According to George Polya, we can articulate three major principles of learning (which governs teaching): 1. Active Learning. It has been said by many people in many ways that learning should be active, not merely passive or receptive; merely by reading books or listening to lectures or looking at moving pictures without adding some action of your own mind you can hardly learn anything and certainly you cannot learn much. There is another often expressed (and closely related) opinion: The best way to learn anyting is to discover it by yourself. Lichtenberg (an eighteenth century German physicist, better known a s a writer of aphorisms) adds an interesting point: "What you have been obliged to discover by yourself leaves a path in your mind which you can use again whn the need arises." Less colorful but perhaps more widely applicable, is the following statement: "For efficient learning, the learner should discover by himself as large a fraction of the material to be learned as feasible under the given circumstances." This is the principle of active learning (Arbeitsprinzip, in German) It is a very old principle: it underlies the idea of "Socratic Method." 2. Best Motivation. Learning should be active, we have said. Yet the learner will not act if he has no motive to act. He must be induced to act by some stimulus, by the hope of some reward, for instance. The interest of the material to be learned should be the best stimulus to learning and the pleasure of intensive mental activity should be the best reward for such activity. Yet, where we cannot obtain the best we should try to get the second best, or the third best, and less intrinsic motives of learning should not be forgotten. For efficient learning, the learner should be interested in the material to be learned and find pleasure in the activity of learning. Yet, beside these best motives for learning, there are other motives too, some of them desirable. (Punishment for not learning may be the least desirable motive.) Let us call this statement the principle of best motivation. 3. Consecutive phases. Let us start from an often quoted sentence of Kant: "Thus all human cognition begins with intuitions, proceeds from thence to conceptions, and ends with ideas." The English translation uses the terms "cognition, intuition, idea." I am not able (who is able?) to tell in what exact sense Kant intended to use these terms. Yet I beg your permission to present of Kant's dictum: Learning begins with action and perception, proceeds from thence to words and concepts, and should end in desirable mental habits. To begin with, please, take the terms of this sentence in some sense that you can illustrate concretely on the basis of your own experience. (to induce you to think about your personal experience is one of the desired effects.) "Learning" should remind you of a classroom with yourself in it as student or teacher. "Action and perception" should suggest manipulating and seeing concrete things such as pebbles, or apples, or Cuisenaire rods; or ruler and compasses; orinsturments in a laboratory; and so on. These principles proceed from a certain general outlook, from a certain philosophy, and you may have a different philosophy. Now, in teaching as in several other things, it does not matter much what your philosophy is or is not. It matters more whetner you have a philosophy or not. And it matters very much whether you try to live up t your philosophy or not . The only priniciples of teaching which I thoroughly dislike are those to which people pay only lip service. Problem Solving: Much of the course is centered around applying these definitions and theorem by solving problems. The basic outline for general problem solving devised by Polya is a four step program: 1. Understand the problem 2. Devise a plan for solving the problem 3. Carry out the plan 4. Look back HOMEWORK: Read the text, keep up with the assigned problems (as a minimum) and prepare questions about what you're learning for participation in class. You can expect to learn far more trigonometry individually or in small groups doing homework than you do in class. If you complete (and thoroughly understand) the homework assignment for each section, you will be well prepared to solve questions on tests and quizzes. At the beginning of each class, I will answer as many questions over the previous night's homework as time allows. Generally, you can expect to study at least 2 hours outside of class for every hour of class time. To get credit for homework you'll need to use an on-line homework site. We'll start with ILRN and then, after the first chapter on geometry, consider moving on to the WebAssign. For ILRN, your account has already been created. Sign on as a returning user and then use your mycod email address as your username and your 7-digit student number as your password. QUIZZES: There will be regular quizzes throughout the semester. These measure your attendance and give you feedback on current topics of study. GRADE: Your grade is a weighted average of homework, quiz, chapter test, & final exam scores: a. Interpret slope as a constant rate of change. b. Recognize and create linearity in tables, graphs, and/or equations. c. Solve systems of equations by using methods of elimination, substitution and graphing. d. Graph and/or find the equation of a circle given sufficient information. e. Solve quadratic equations by factoring, completing the square, and the quadratic formula. f. Recognize and create quadratic models for relations involving tables, graphs, and equations. g. Graph a parabola by finding the vertex, intercepts, and other symmetric points. h. Demonstrate understanding of definitions for function and its related terms: domain and range. i. Use appropriate notation for function equations and for describing domain and range. j. Demonstrate understanding of the exponential function, its scaling and growth factors. k. Understand how to solve similar triangle problems. l. Demonstrate understanding of triangle congruency theorems involving SSS, SAS, AAS. m. Basic knowledge about congruence relations such as the congruence of vertical angles n. Familiarity with Pythagorean theorem. o. Demonstrate understanding of deductive reasoning in the construction of a proof. Vectors including analytic and geometric representations and applications. Course Objectives: Upon completion of this course, students will be able to: Apply facts about angles, parallel lines and triangles to deduce further results about a geometric figure. Prove when two triangles are congruent or similar. Justify the lengths of sides in an isosceles right triangle and in a 30-60-90 triangle. Deduce the lengths of sides in quadrilaterals such as trapezoids and rectangles using basic definitions, Pythagorean Theorem, perimeter and/or area. Calculate the measure of a central angle in a circle using the measure of the intercepted arc and calculate the areas of geometric figures involving circles. Apply facts about plane geometric figures to deduce the surface area and volume of three dimensional geometric figures. Demonstrate an understanding of the concept of a function by identifying and describing a function graphically, numerically and algebraically. Calculate the domain and range for a function expressed as a graph or an equation. From a graph, estimate the intervals where a function is increasing, decreasing and/or has a maximum or minimum value. Use and interpret function notation to find "inputs" and "outputs" from the graph, table and/or an equation describing a function. From an equation, graph or table, calculate average rates of change by using a difference quotient or by using slopes of secant lines. Analyze average rates of change to determine the concavity of a graph. Demonstrate an understanding of the six basic transformations of functions by graphing translated functions including the quadratic functions. Represent a word problem (especially a geometric problem) with a function. Determine when a function has an inverse (one to one functions) and find the inverse function graphically or algebraically. Form new functions through addition, subtraction, multiplication, division and composition. Recognize classical and analytic definitions of the trigonometric functions. Solve triangles using right triangle trigonometry, the law of sines and the law of cosines.
Trigonometry - 10th edition Summary 10th Edition. Used - Acceptable. Text is generally clean; has used stickers on cover. Does not include online code or other supplements unless noted. Choose EXPEDITED shipping for faster delivery! $114.42
Gamma Mathematics Workbook has been completely updated to reflect the current requirements of Mathematics and Statistics in the New Zealand Curriculum. Award Winner - 2011 CLL Educational Publishing Awards Educational Publishing Awards - Best Book or Series in Secondary Publishing! It contains a ... Geography 2.4 3rd edition covers all the skills (thinking, practical and valuing) and key geographic concepts needed to help Year 12 students prepare for Geography Achievement Standard 2.4 (Apply concepts and geographic skills to demonstrate understanding of a given environment), as well as 2.5 (Con...
UltimaCalc is a scientific and mathematical calculator designed to occupy minimum screen area, making it immediately available for use. UltimaCalc can stay on top of other windows. Type a calculation as plain text, evaluate it, maybe edit it and re-calculate. Has a comprehensive context-sensitive help system. Calculates to 38 digit precision. The display can be limited to just 8, 12 or 16 digits, and digits grouped for readability. Two 'scientific' view modes show numbers always in exponent format. The 'engineering' mode uses suffixes such as k (kilo) and M (mega). View results in hexadecimal and as ratios. Functions available include logarithms to base 2, exp, two-argument inverse tangent; cube root (even of negative numbers); factorials, combinations, permutations, powers, modulus, GCD. Also floor and ceiling functions, absolute value, min, max, extract the fractional part of a number. Calculate the slope of a line given its end points. Even calculate definite integrals. Define your own functions and constants, saved as a plain text file. Find the date of Easter. Calculate future or past dates. Julian day numbers. Calculate the mean, median and standard deviation of a sample and its population. Create bar, line, pie charts. Add title, subtitle, labels. Adjust the layout, choose colours and hatching, save as an image. Regression: Plot a scatter chart and regression line. Fit a polynomial to data. Analyse the effects of multiple variables on data. Absolute deviation fit minimises the effects of outlying values. Plot functions: Specify starting and ending conditions and how variables change. Choose axis locations. Combine multiple plots. Save as an image. Solve triangles: Given one side and two other facts, calculate the unknowns. View the result graphically. Solve Simultaneous Linear Equations, and do Navigational calculations. Log calculations to a text file, or copy and paste into other programs. Save specialised calculations with notes in data files.
Essential Math With Application - 8th edition Summary: The latest book from Cengage Learning on Essential Mathematics As in previous editions, the focus in ESSENTIAL MATHEMATICS with APPLICATIONS remains on the Aufmann Interactive Method (AIM). Users are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of ''active participant'' is crucial to success. Presenting students with worked examples, and then providing ...show morethem with the opportunity to immediately work similar problems, helps them build their confidence and eventually master the concepts53.71 +$3.99 s/h Good BookSleuth Danville, CA Fast Shipping ! Used books may not include access codes, CDs or other supplements. $75.88 +$3.99 s/h Good text book recycle ny malone, NY 2010-01-01 Paperback Good We ship everyday and offer PRIORITY SHIPPING. $75.88 +$3.99 s/h Good text book recycle ny malone, NY 2010-01-01 Good We ship everyday and offer PRIORITY SHIPPING. $80.94
Matrix Multiplication In Matrix Multiplication, Professor Eaton begins with the dimension requirement as well as the resulting product matrix when two matrices are multiplied. After a robust example you will see the properties of matrix multiplication such as the associative property and distributive property. Make sure you understand everything with our four complete video examples at the end of the lesson. This content requires Javascript to be available and enabled in your browser. Matrix Multiplication Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
Red prices are already discounted. If you are due a discount ACE will bill you at the red price, or your discount off the original price, whichever is lowest. Saxon Math Grade 5/4 Complete Home School Kit [SX9781591413479] $89.50$82.34 Saxon Math Grade 5/4 Complete Home School Kit The Saxon Math Middle Grades textbooks move students from primary grades to algebra. Each course contains a series of daily lessons covering all areas of general math. Each lesson presents a small portion of math content (called an increment) that builds on prior knowledge and understanding. After an increment is introduced, it becomes a part of the student's daily work for the rest of the year. This cumulative, continual practice ensures that students will retain what they have learned. The home school kit for Math 5/4, Math 6/5, Math 7/6, and Math 8/7 consist of a student textbook with 120 lessons and 12 investigations, a Tests and Worksheets Booklet (which includes tests and fact practice worksheets), and a Solutions Manual (which offers step-by-step solutions to all lessons, investigations, and test questions). Algebra 1 2 includes a textbook, Home School Packet (31 test forms in addition to answers for all textbook problems and test questions), and a Solutions Manual.
*—"Core" math modules (PRE, ALG, GEO, TRI) are sold in packages. Buy any three for $395, or all four for $495. Geometry (GEO) EducAide's Geometry Database has been several years in the making—and well worth the wait! This collection of more than 5000 problems is simply unmatched in its breadth and depth of coverage, and the huge number of diagrams (more than 800) makes the database even more attractive. As a core module, the Geometry database is intended for regular classroom instruction. The wide range of topics and question-types makes it suitable for use with any textbook or course of study, including newer, integrated math courses. Although curriculums vary widely in scope and sequence, the database's topical organization makes it possible to locate just the right questions for tests, review worksheets, and daily lessons. In the database, you will find extensive coverage of both synthetic geometry (proofs and logic) and analytic geometry (measurement, coordinate systems, and connections to algebra). The question types include: short-answer, definitions, fill-in-the-blank, true-false, sometimes-always-never, logic exercises, and traditional two-column and paragraph proofs. In addition, algebra skills are integrated into perhaps 20% of the problems, so that students are continually working with variables and solving linear and quadratic equations and systems.
Preface -- Vector analysis, which had its beginnings in the middle of the 19th century, has in recent years, become an essential part of the mathematical background required of engineers, physicists, mathematicians and other scientists. This requirement is far from accidental, for not only does vector analysis provide a concise notation for presenting equations arising from mathematical formulations of physical and geometrical problems, but it is also a natural aid in forming mental pictures of physical and geometrical ideas. In short, it might very well be considered a most rewarding language and mode of thought for the physical sciences. . This Schaum's Outline gives you . . Practice problems with full explanations that reinforce knowledge. Coverage of the most up-to-date developments in your course field. In-depth review of practices and applications. . Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!
This article illustrates a practical way to connect and coordinate the teaching and learning of physics and mathematics. The starting point is the electrostatic potential, which is obtained in any introductory course of electromagnetism from the Coulomb potential and the superposition principle for any charge distribution. The necessity to develop solutions to the Laplace and Poisson differential equations is also recognized, identifying the Coulomb potential as the generating function of harmonic functions. Correspondingly, the convenience of expressing the electrostatic potential in terms of its multipole expansion in spherical coordinates, or as integral transforms based on harmonic functions in different coordinate systems, is also established. These connections provide a motivation for teachers and students to acquire the necessary mathematics as a basic tool in the study of electromagnetic theory, optics and quantum mechanics
Exams and Grading: There will be three exams given in the evening, from 6-7:30. See Exam Information for more detail. Your course grade will be based on a 600 point system as follows: Three evening exams 300 points Final exam 200 points Instructor's assignments 100 points Students with disability (documented through Disability Services for Students, 330 Memorial Union) should see their instructor as soon as possible to work out reasonable accommodations. General Information GOALS OF THIS COURSE: The primary goal of MTH 111 is to prepare you for further courses in mathematics, especially calculus.The calculus sequence is often an essential step toward degree and career objectives, so MTH 111 is also such a step. Thus MTH 111 is aimed at the student for whom it will be the first of an important series of courses rather than a last math course. This course is NOT a good choice simply to fulfill a general education requirement. It demands a very substantial amount of hard work for 3 credits. EXPECTATIONS: We expect that you will give this course 6-7 hours a week of your undivided attention, in addition to class time. This is an approximate figure of course, but don't assume that you can spend less time than this and still get a grade you'll like. We also expect that you will ATTEND YOUR CLASS. ADVICE: The key to success in this course is the problem material. It is very important that you try all the assigned problems listed on the syllabus. The problems chosen for each textbook section indicate what we feel is important in that section and which ideas and skills you should focus on. THE EXAMS WILL REFLECT THIS PROBLEM SELECTION! Also, an important part of this course is strengthening your algebra skills and using them in new ways. Much of your success in precalculus depends on your grasp of basic algebra -- be prepared to review basic algebra and seek help as needed. Practice Problems for Exams: Before each of the hour exams we will post, on this website, a set of practice problems for review. These problems will provide a good idea of the kinds of problems that will appear on the actual exam. Although answers will be posted shortly before the exam it is essential that you work the practice problems by yourself, before looking at the answers. Your instructor may require that you hand in your solutions. Precalculus also has a body of mathematical facts that you will have to learn. Be prepared to memorize some formulas and theorems as you learn about their meaning and uses.
Intermediate Algebra, An Individualized Approach Online Intermediate Algebra Overview This course assumes a degree of proficiency with Beginning and Elementary Algebra. Each new topic is introduced with a brief review of the needed knowledge from earlier courses, but the review is intended only as a refresher. The remainder of the course extends the topics of Elementary Algebra and begins a solid development of relations, functions, and their graphing. Every objective is thoroughly explained and developed. Numerous examples illustrate concepts and procedures. Students are encouraged to work through partial examples. Each unit ends with an exercise specifically designed to evaluate the extent to which the objectives have been learned. The student is always informed of any skills that were not mastered. Topics include: simplifying radical expressions and fractions rational number exponents polynomials equation solving inequalities and absolute values linear functions quadratic functions and relations (the conics) systems of equations The instruction depends only upon reasonable reading skills and conscientious study habits. With those skills and attitudes, the student is assured a successful math learning experience.
Find an Alpha, NJ Calculus combat this by helping my students see what the algebraic notation is describing (on a graph for example) so that it makes sense to them. In this way, graphing an inequality makes sense. Algebra 2 students are tasked with putting their previous knowledge to the test's available, they can experiment with math and science concepts and get instant feedback.
This pre-algebra math tutorial from NutshellMath offers introductory homework help in using variables and expressions. The teacher introduces the concept of algebraic variables as letters representing numbers and how they are used in algebraic expressions. Examples presented demonstrate writing algebraic expressions from textual descriptions and evaluating algebraic expressions for given values of variables. In writing expressions, the tutorial shows how to translate terms such as sum and quotient into addition or division in an algebraic expression. In evaluating these algebraic expressions, the given values for the variables can be substituted in for the letters representing those variables and the expression can be evaluated. As a precursor to studying equations, this introduction to variables and expressions is a first-step in understanding the language of algebra.
… Wearing Gauss's Jersey focuses on "Gauss problems," problems that can be very tedious and time consuming when tackled in a traditional, straightforward way but if approached in a more insightful fashion, can yield the solution much more easily and elegantly. The book shows how mathematical problem …The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explains how the study of the mathematical properties of musical rhythm generates common mathematical … Project Origami: Activities for Exploring Mathematics, Second Edition presents a flexible, discovery-based approach to learning origami-math topics. It helps readers see how origami intersects a variety of mathematical topics, from the more obvious realm of geometry to the fields of algebra, number … Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors' successful work with … R is the amazing, free, open-access software package for scientific graphs and calculations used by scientists worldwide. The R Student Companion is a student-oriented manual describing how to use R in high school and college science and mathematics courses. Written for beginners in scientific … Containing 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
Debra Carnes What will I learn in Pre-Algebra 1B? • fraction, decimal, and percent operations (+, -, x, ÷) • exponents and their rules • linear functions and graphs • Pythagorean theorem and describing congruent shapes • data displays Students will become experts in all operations using real numbers. This includes adding, subtracting, multiplying, and dividing fractions, decimals, and percents as we see these numbers every day in real life (cooking, driving, money, and more). These important skills are the foundation of mathematics for the rest of your life whether it is in high school, college, or just to balance your checkbook. Students will also begin to solve equations and graph functions--a very important skill to be successful in General Algebra in the 8th grade.
Curriculum Design: Pre-requisites/Co-requisites/Exclusions This course introduces the student to an area of Mathematics in which the concepts of linear algebra, analysis and geometry are harnessed together. It is shown how this leads to powerful and elegant generalizations of earlier results, many of which are fundamental to modern applications of analysis.
BOOK DETAILS Format: Paperback Pub. Date: Aug.24.2011 ISBN: 9781432766436 Publisher(s): Kenneth gives an overview of the book:,... Read full overview », instructors and general contractors. The first section of Applying Mathematics to Construction shows how to make calculations without the use of external tools and contains such innovative tricks as his conversion of a large number of feet to inches in seconds, mentally. Section two covers how materials are measured and sold and, like the first section, offers one simple formula after another to make on the spot calculations simply and immediately. Read an excerpt » Converting feet to inches without the use of a calculator ---- Take any number in feet like 34' Double the number 4 to the right 4 + 4 = 8 Put the number 8 to the side for now Always use the number 5 as the factor If the number is 4 or less use zero (0) If the number is 5 or greater use five (5) Example: 34 is less than 35 so use zero or (30) 5 times what number equals 30 5 x 6 = 30 Now add 30 plus 6 and you'll get 40 Combine the 40 and the 8 and you'll get 408" Note: never carry a number over I teach carpentry and telecommunications at Delgado Community College. I'm also a musician who likes playing the keyboards/piano in and around the great city of New Orleans on weekends. About Kenneth Hi my name is Kenneth Williams sr. I am a native New Orleanian who grew up in the Fisher Housing projects. I am the author of Applying Mathematics to Construction. I am a master instructor at Delgado Community College where I teach carpenrty and broadband ... Published Reviews He explains calculations effectively and includes detailed glossaries throughout the book. It is a practical manual for carpenters and other trade professionals to have on their book shelves. It is a...
AcademicsLinear Algebra Course Outline: Linear Algebra is important for its remarkable demonstration of abstraction and idealization on the one hand, and for its applications to many branches of math and science on the other. We will focus our study on n-dimensional real space, considering notions such as systems of linear equations, spanning sets, linear independence and the matrix representations of linear transformations. The course will follow the first seven chapters of Elementary Linear Algebra (5th ed.) by Larson, Edwards and Falvo (the 4th edition by Larson and Edwards is essentially the same, but if you use this edition you will have check the numbering of the homework assignments). The final two weeks will be given over to students to pursue a topic of interest further. Possibilities for this part of the course include connections to the Differential Equations course, the matrix representations of symmetries, consideration of complex or finite spaces, and others. Prerequisite: EMLS or equivalent Grades: Your grade will be calculated as follows: Final exam 40%, and 20% each for in-class quizzes, weekly homeworks and project work. 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: Bold numbered problems in the Assignment Responsibility section below are to be handed in for grading. Plaintext numbered problems are more drill and practice material that should be worked through to keep up with course material. By 4pm each Friday you are expected to hand in your solutions to the appropriate bold numbered questions (exactly which questions these are will be announced during the previous week). You may wish to discuss any assignments that you find difficult with me or the math tutor. Office hours: TBA Tutoring: Julie Shumway (jshumway@marlboro.edu) Assignment Responsibility. The following question numbers are from the 5th edition of Elementary Linear Algebra. If you have the 4th edition then you should check the copy on the reserve shelf in the library to make sure that you are attempting the right questions. The chapter material is the same, except that Section 3.5 in the 5th edition is Section 3.4 in the 4th.
Overview Calculus III is not really a continuation of Calculus I and II. It takes both of them to a whole new dimension - the third dimension. We will learn calculus that can be applied to the three dimensional world in which we live (but which we frequently ignore because it cannot be completely reproduced on paper or on screens). Reading I have intentionally chosen a very readable text. In addition to planning time to do homework, please take time to carefully read the sections in the book. Notice use of the words "time" and "carefully". Read the sections slowly and actively. If you do not understand some statement reread it, think of some potential meanings and see if they are consistent, and if all else fails, ask me. If you do not believe a statement, check it with your own examples. Finally, if you understand and believe the statements, consider how you would convince someone else that they are true, in other words, how would you prove them? Because the text is exceptionally accessible, we will structure classtime more as an interactive discussion of the reading than lecture. For each class day there is an assigned reading. Read the section before coming to class. If there are no questions from the reading we will discuss problems not a part of the problem sets during the class discussion. Grading Your grade in this course will be based upon your performance on various aspects. The weight assigned to each is designated below: Exams: Assignments: (5% each, complete 10) Exam 1 13% Problem Sets (5) 25% Exam 2 13% More (2) 10% Final Exam 25% Lab Writeups (3) 15% More may include extra problem sets, papers, or lab writeups. Problem set 3 is rather long and therefore worth 7%. Problem set 5 is rather short and therefore worth 3%. Problem Sets There will be five pairs of problem sets distributed throughout the semester. You must complete one of each pair. Problem sets are due on the scheduled dates. You are encouraged to consult with me outside of class on any questions toward completing the homework. You are also encouraged to work together on homework assignments, but each must write up their own well-written solutions. A good rule for this is it is encouraged to speak to each other about the problem, but you should not read each other's solutions. A violation of this policy will result in a zero for the entire assignment and reporting to the Dean of Students for a violation of academic integrity. I strongly recommend reading the suggestions on working such problems before beginning the first set. Each question will be counted in the following manner: 0 – missing question or plagiarised work 1 – question copied 2 – partial question 3 – completed question (with some solution) 4 – completed question correctly and well-written Each entire problem set will then be graded on a 90-80-70-60% (decile) scale. Late items will not be accepted. Problem sets will be returned on the following class day along with solutions to the problems. Because solutions will be provided, comments will be somewhat limited on individual papers. Please feel free to discuss any homework with me outside of class or during review. Laboratory Activities and Writeups We will regularly be spending parts of classes on maple activities. Activity files are in my outbox in a folder called "MultiMaple". You may access them via a browser here (after logging in with your Geneseo account). Please come to class prepared for the activity (i.e. with a maple-installed computer and the file loaded), but without having completed it before. We will not use class time to prepare. I strongly recommend reading the suggestions on writing lab writeups before submitting one. Follow-up questions are posted here and will be updated so as to include questions for each lab. Lab writeups may be turned in no more than three class days after the lab activity. Reports After attending a mathematics department colloquium (or other approved mathematics presentation) you may write a report. In your report, please explain the main point of the presentation and include a discussion of how this presentation affected your views on mathematics. A – Well written, answers the questions, and is interesting and insightful B – Well written and answers the questions C – Well written or answers the questions (convinces the reader that you were there) D – attempted Papers are due within a classweek of the colloquium presentation. I will gladly look at papers before they are due to provide comments. Exams There will be two exams during the semester and a final exam during finals week. If you must miss an exam, it is necessary that you contact me before the exam begins. Exams require that you show ability to solve unfamiliar problems and to understand and explain mathematical concepts clearly. The bulk of the exam questions will involve problem solving and written explanations of mathematical ideas. The first two exams will be an hour worth of material that I will two evening hours to complete. The final exam will be half an exam focused on the final third of the course, and half a cumulative exam. Exams will be graded on a scale approximately (to be precisely determined by the content of each individual exam) given by 100 – 80% A 79 – 60% B 59 – 40% C 39 – 20% D below 20% E For your interpretive convenience, I will also give you an exam grade converted into the decile scale. The exams will be challenging and will require thought and creativity (like the problems). They will not include filler questions (like the exercises) hence the full usage of the grading scale. Feedback Occasionally you will be given anonymous feedback forms. Please use them to share any thoughts or concerns for how the course is running. Remember, the sooner you tell me your concerns, the more I can do about them. I have also created a web-site which accepts anonymous comments. If we have not yet discussed this in class, please encourage me to create a class code. This site may also be accessed via our course page on a link entitled anonymous feedback. Of course, you are always welcome to approach me outside of class to discuss these issues as well. Social Psychology Wrong answers are important. We as individuals learn from mistakes, and as a class we learn from mistakes. You may not enjoy being wrong, but it is valuable to the class as a whole - and to you personally. We frequently will build correct answers through a sequence of mistakes. I am more impressed with wrong answers in class than with correct answers on paper. I may not say this often, but it is essential and true. Think at all times - do things for reasons. Your reasons are usually more interesting than your choices. Be prepared to share your thoughts and ideas. Perhaps most importantly "No, that's wrong." does not mean that your comment is not valuable or that you need to censor yourself. Learn from the experience, and always try again. Don't give up. Math Learning Center This center is located in South Hall 332 and is open during the day and some evenings. Hours for the center will be announced in class. The Math Learning Center provides free tutoring on a walk-in basis. Academic Dishonesty While working on assignments with one another is encouraged, all write-ups of solutions must be your own. You are expected to be able to explain any solution you give me if asked. Exams will be done individually unless otherwise directed students who miss class because of observance of religious holidays the opportunity to make up missed work. You are responsible for notifying me by September 10 of plans to observe a holiday.
In the Mathematics Area of Foundation Programme (FP) at Sultan Qaboos University (SQU), courses are offered at two levels: basic and advanced. Basic Mathematics is offered to those students who do not pass the Placement Test, while Advanced Mathematics is offered to those who do not pass the Exit Test. Furthermore, Advanced Mathematics has two separate streams: (i) Mathematics for Social Sciences and (ii) Mathematics for Sciences. Of these, "Mathematics for Social Sciences" is offered to the students admitted to the colleges of Arts & Social Sciences, Commerce & Economics, Education, and Law. The course, "Mathematics for Sciences" is offered to the colleges of Agriculture & Marine Sciences, Engineering, Medical & Health Sciences, Nursing, and Science. The medium of instruction of the courses is: Arabic for Arabic medium programmes, and English for English medium and bilingual programmes. The objectives of the Mathematics courses are to ensure that the students are equipped with the mathematical understanding and skills necessary to meet the cognitive and practical requirements of degree programmes in a variety of disciplines. The course learning outcomes are designed and categorized into the following three courses (the course ending with an odd integer indicates that the course is offered in English language, while the one ending with an even integer indicates that it is offered in Arabic language) : E-Learning with Moodle: The site has the online course materials for the FP Mathematics courses. Students are advised to visit the site frequently as all course announcements will be done through Moodle. In addition to important announcements, the site has several useful materials such as practice questions, review material, summaries and plotting utilities. Getting Help: Students are encouraged to visit the instructors and tutors who teach the course during their office hours. If the office hours are not suitable, they can be seen by appointment. The schedule of the course team office hours will be posted in Moodle. Important Remarks:  Students are not allowed to use cellular phones in the classroom. They should turn off their phones before entering the class. Also, cellular phones are not allowed to be used as calculators or for any other purpose.  Course material is cumulative and the student may be tested on any material previously covered in the course in any quiz or test.  The final exam is comprehensive and will include all material covered in the course.  The student should write his/her name, ID number and Section number on the front page of the answer paper.  Students should read carefully the instructions given in the question paper.  No books, lecture notes, dictionaries, electronic translators, graphing and programming calculators or mobile phones will be permitted in the exam room.  Sharing of calculators, erasers, pens, pencils, etc. will not be allowed. Academic Dishonesty All forms of academic dishonesty is prohibited and penalties are decided based on the University rules regulations. Academic dishonesty included (but not limited to) cheating, plagiarism, copying, collusion, falsification, signing for another person, etc. For more details please see Pages 36 and 37 of SQU Undergraduate Academic Regulations, 2005. Punctuality Students are required to attend their classes on time. Late attendance is not acceptable. The instructor has the right to refuse admission to latecomers. General Study Skills General Study Skills (GSS) is an area of FP with specific learning outcomes. The relevant learning outcomes of GSS are to be embedded into each of the three FP areas. With regard to the Mathematics courses, the students should be able to satisfy the following GSS learning outcomes (OAC, 2007): 1. Work in pairs or groups and participate accordingly i.e. take turns, initiate a discussion, interrupt 10. Use a contents page and an index to locate information in a book. 11. Extract relevant information from a book or article using a battery of reading strategies (e.g. skimming, scanning, etc.). 12. Locate a book/journal in the library using the catalogue. 13. Find topic¬-related information in a book/journal in the library using the catalogue.
College Geometry: Using the Geometer's Sketchpad, 1st Edition From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using The Geometer's Sketchpad, a book that is ideal for geometry courses for both mathematics and math education majors. The book's truly discovery-based approach guides students to learn geometry through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries. In the process, students hone their understanding of geometry and their ability to write rigorous mathematical proofs. Former Chapter 1 has been re-written as two chapters: Chapter 1: Using the Geometer's Sketchpad and Chapter 2: Constructing à Proving. The authors split these chapters into two in order to provide better explanation and deeper coverage of each topic. The introduction and development of proof skills in Chapters 3 and 4 has been revised in order to make the concept of proof more accessible to students. New Chapter 7: Finite Geometries has been added based on feedback from instructors who cover this topic in their geometry courses. Chapter 11: Hyperbolic Geometry has been expanded with additional problems and more in-depth coverage by the authors. Coverage of the Real Projective Plane in chapter 11 has been re-written to be more clear to students.
Schaum's Outline of Mathematical Methods for Business and Economics reviews the mathematical tools, topics, and techniques essential for success in business and economics today. The theory and solved problem format of each chapter provides concise explanations illustrated by examples, plus numerous problems with fully worked-out solutions. And you don't have to know advanced math beyond what you learned high school. The pedagogy enables you to progress at your own pace and adapt the book to your own needs. Description: This book covers all the theory and practical advice that actuaries need in order to determine the claims reserves for non life insurance. The book describes all the mathematical methods used to estimate loss reserves and shares the authors'
Sulphur Bluff AlDecimal and fraction arithmetic is a skill lost in modern technology needed for algebra. Solving application problems is not just math. Included concepts come from English, science, history, and others
Math For Elementary Teachers II – mth157 (3 credits) This course is the second in a two-part series designed for K–8 preservice teachers to address the conceptual framework for mathematics taught in elementary school. The focus of Part Two will be on measurement, geometry, probability, and data analysis. The relationship of the course concepts to the National Council of Teachers of Mathematics Standards for K–8 instruction is also addressed. Applications of Geometry Introduction to Geometry, ContinuedIntroduction to GeometryProbability Apply basic concepts of probability. Data Analysis Develop predictions based on data. Use appropriate statistical methods to analyze data
Comment After spending a good 10-20 minutes looking over the material, I realize this would be quite useful for students to understand a real-life application for math and making use of the equations for it. I looked through it briefly and followed the directions that is describing how to write the equation for that particular situation when comparing different plans. It's very well organized, much like a college syllabus, so it is easy to follow and navigate. The material accurately present concepts of graphing and how to apply a simple equation using the two factors to a graph, which can help us incorporate our understanding of it to harder and much more complicated problems. Although it is very short and intended more for the teacher as a teaching tool, it is still very easy to follow as it is broken down into clear sections, step by step, showing the methods and ways to approach the math.
Math There are two courses in the Mathematics Area of Developmental Studies, MAT0018 and MAT0028. The MAT0018 reviews whole numbers and covers integers, fractions and mixed numbers with signed numbers, decimals with signed numbers, order of operations, algebraic expressions, solving linear equations, ratios and proportions, percents, exponents, units of measures, and applications of the above topics. The MAT0028 covers algebraic expressions, algebraic equations and inequalities, exponents and polynomials, scientific notation, factoring polynomials, graphing linear equations and inequalities, rational expressions, radicals, linear and quadratic applications, and units of measurement. The book for both courses is a custom version of Bittinger, Ellenbogen, Beecher and Johnson, Prealgebra and Introductory Algebra, 3rd ed. Pearson, 2012, which is packaged with an access code to EdisonMyLabsPlus. This is the access to the homework which is done online at For MAT0018 and MAT0028, 40% of the final grade is from the tests, 40% of the final grade is from the exam, and the other 20% of the final grade will be decided by the instructor. The exam for MAT0018 has 50 multiple choice problems and counts 40% of the final grade. The exam for MAT0028 has 50 multiple choice problems. If a student scores 50% or higher on the MAT0028 exam, it will then count as 40% of the overall course grade. If the student does not score 50%, the course must be repeated. The instructors have created exam reviews, which will be available for students. The passing grades for MAT0018 and MAT0028 are A, B, or C. The course must be repeated if the student earns a D or F.
Powers and Roots of Complex Numbers and de Moivre's Formula In this lesson our instructor talks about powers and roots of complex numbers. He talks about de Moivre's formula and theorem. He does 2 examples of de Moivre's formula. He talks about roots of complex numbers and the origin of the fundamental theorem of algebra. He discusses the n-th root and does an example. Four extra example videos round up this lesson. This content requires Javascript to be available and enabled in your browser. Powers and Roots of Complex Numbers and de Moivre's Formula Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.