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High School Mathematics Bridging innovation and tradition Bogged down by rote-memorization drills and predictable homework exercises, EDC's Al Cuoco was frustrated teaching math in the 1970's. "Like many math teachers, I was always dissatisfied with most of the commercially available curricula I had." Over the past five years, he has been working on behalf of today's teachers "to create the texts I always yearned for." As principal designer of a major mathematics textbook initiative, the CME Project, he says he is nearing his goal. "While these texts have been in development for over five years," states Cuoco, "in a real sense I've been working on the ideas in this program for close to four decades." Many high school mathematics teachers still face the dilemma that Cuoco did years ago. They must choose between traditional texts, on the one hand, that follow an accepted structure and progression—algebra, geometry, advanced algebra, and precalculus—but do not integrate lessons and themes across topics and chapters, and, on the other hand, more progressive texts that challenge students yet organize the material in a manner that is unfamiliar to teachers and parents. "In far too many classrooms, mathematics is taught as a disconnected set of facts and procedures, a body of knowledge to be learned in much the same way as one learns a list of terms for a vocabulary test," says Cuoco, who works in EDC's Center for Mathematics Education. The CME Project, funded by the National Science Foundation (NSF), features a series of textbooks focusing more on comprehension of core math concepts and less on rote memorization of facts and formulas. These new texts present mathematics in progressive and innovative ways, challenging students to develop robust mathematical proficiency. The new texts will be available in fall 2007. Rater than forcing students to churn through chapter after chapter of disjointed topics—from graphing equations to triangle trigonometry to complex numbers—without connecting themes and ideas, CME texts present ideas thoroughly for students to get a firm handle on the material. Topics are revisited in later chapters to deepen students' understanding of them and their connection with other ideas, while the clutter of extraneous topics is omitted. Drawing on lessons learned from high-performing countries in the Pacific Rim and Northern Europe, the program also employs the best American models that call for "experience before formality." This practice encourages students to grapple on their own with ideas and problems before the teacher presents the lesson in class. The texts go beyond "real life" examples to make math interesting. Many of the tasks posed by CME are purely mathematical, such as "find the sum of integers between one and 100" and "find a simple rule that would generate the following input/output table of numbers." "We were surprised to discover when asking our student advisory board that they found these purely mathematical problems to be very realistic," says Cuoco. "They didn't need a 'real-life' situation or context to grasp the meaning behind the problems and apply their problem-solving skills." The program has drawn on the expertise of teachers, mathematicians, researchers, and students and has been extensively field tested in sites across the country—urban, suburban, and rural. The geometry and precalculus courses were field tested for their initial release, and the newer course materials have been field tested nationally for the last 2-3 years. While CME sets high expectations for students, field tests have demonstrated that these expectations can be met by students of all abilities and backgrounds. The new texts will be published in two stages by Prentice Hall which is promoting them at the National Council of Teachers of Mathematics conference. The first collection of bound books will be released in November 2007 for adoption in 2008, starting with Algebra 1. The next two books will be published six months after that. 'Open and Closed' The new CME texts balance their conceptual emphasis with an ample supply of examples, formulas, and reference resources. "We wanted to develop a curriculum that is both open and closed," states Cuoco. "Previous texts developed by EDC were very open—activities and problems designed to help students discover results for themselves with few stated theorems, definitions, or worked-out sample problems. Teachers told us they loved the open-ended presentation of material, but they wanted more closure within the student text. These new texts provide this closure, serving as a reference for students with results and examples, for instance, if they were out sick one day or simply wanted to revisit content months later." With CME, students start each lesson with a problem set before instruction serving as a preview—a simple numerical and geometric context—for the ideas that will follow. They then are provided worked-out examples or dialogs to explain the methods, helping to bring closure and serve as a reference for later. Students can then practice their newly developed skills and methods with practice problems. Each chapter begins with activities accessible to all students and ends with problems that will challenge the most advanced. The CME Project builds upon an approach developed by EDC, Connected Geometry, funded by NSF in 1992. In 1999 NSF funded EDC to use similar methods and approaches to develop Mathematical Methods, a precalculus text, and in 2003 they funded the completion of the four-year program through the development of both Algebra 1 and 2 courses.
6 Total Time: 6h 52m Use: Watch Online Access Period: 90 Days Created At: 08/06/2009 Last Updated At: 11/29/2013 This Series of 6 Lessons will teach you about exponents and logarithms - solving exponential equations - graphing exponential & logarithmic functions - change from exponential form to logarithmic form - change from logarithmic form to exponential form - common & natural logs - laws for logaarithms, power, quotient & power - solving equatins using the laws for logarithms - change of base rule - solving equations using the change of base rule The first part of the lesson is dedicated to defining some basic terminology: properties of power or exponents, and what is and what isn't an exponential equation. Then the author solves problems. She solves 5 exponential equations with the same base, 20 exponential equations with different bases, 6 exponential equations with two solutions, 2 exponential equations using a linear system of equations, 2 exponential equations using factoring and finally, she reviews each section with 6 more example equations. A great lesson for anyone who needs to see examples of how to solve exponential equations vs. just reading them from a book. Below are the descriptions for each of the lessons included in the series: Exponents & Logs: Graphing Functions 405 This 64 minute exponents & logarithms lesson studies the graphs of the exponential function and the inverse of the exponential function, which is the logarithm: This lesson will show you how to: - graph exponential functions and summarize the characteristics of the graphs - find the inverse of the exponential function - graph logarithmic functions and summarize the characteristics of the graphs - understand the x and y intercepts, an asymptote, domain & range, growth and decay functions, and the reflection property Sample question: Given the exponential function y = 2^x, write its inverse in exponential form On the same grid, draw the graphs of y = 2^x and its inverse x = 2^y. Show the line of reflection y = x This lesson contains explanations of the concepts and 13 example questions with step by step solutions plus 3 interactive review questions with solutions. Lesson that will help you with the fundamentals of this lesson: - 400 Solving Exponential Equations ( Exponents & Logs: Working With Logarithms 410 This 67 minute exponents & logarithms lesson begins with the relationship between exponents and logarithms and focuses on solving for an unknown in a logarithmic equation and learning to evaluate logarithms with different bases: This lesson will show you how to: - change from exponential form to logarithmic form - change from logarithmic form to exponential form - identify and use a common log - identify and use a natural log (ln, base e) - solve for unknowns in a logarithmic equation - evaluate logarithms, for example log base 7(49 cube root 7) + log base 27(3^3 times 81 ^1/2) - find the number positi0n and the base position This lesson contains explanations of the concepts and 32 example questions with step by step solutions plus 5 interactive review questions with solutions. Exponents & Logs: Laws For Logarithms 415 This 59 minute exponents & logarithms lesson will show you how to use the three main laws for Logarithms: - the product law for logarithms - the quotient law for logarithms - the power law for logarithms This lesson will also show how the Laws for Logarithms correspond to the laws for exponents. This lesson contains explanations of the concepts and 21 example questions with step by step solutions plus 6 interactive review questions with solutions. Exponents & Logs: Using Logarithm Laws 420 This 84 minute exponents & logarithms lesson will show you how to solve many different types of logarithmic equations using the Laws for Logarithms (product, quotient & power) and a combination of the laws. For example, you'll learn how to solve for x and verify: log(3x + 2) + log(x – 1) = 2 This lesson contains explanations of the concepts and 17 example questions with step by step solutions plus 5 interactive review questions with solutions. Exponents & Logs: Change of Base Rule 425 This 61 minute exponents & logarithms lesson will show you how to: - use the change of base rule to evaluate logarithms with any base - solve exponential equations using the Change of Base Rule - solve logarithmic equations using the Change of Base Rule This lesson contains explanations of the concepts and 23 example questions with step by step solutions plus 5 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson: - 400 Solving Exponential Equations ( - 405 Graphing Exponential & Logarithmic Functions ( - 410 Working with Logarithms ( - 415 The Laws for Logarithms ( - 420 Solving Equations Using the Laws for Logarithms (
INSTRUCTOR INFORMATION: COURSE DESCRIPTION: Some of this course is a review of Elementary Algebra and includes: properties, linear equations and inequalities, exponents, polynomials, factoring, rational expressions, and radicals. There is a more advanced discussion of quadratic equations and systems of equations. The new material covers conic sections, functions, exponential and logarithmic functions. This course is not open to students with credit in a higher numbered math course except Math 130. This is a five unit course. For an official copy of the course objectives, contact the Math/Sci/Eng office, room 345. PREREQUISITE: MATH 45 or the equivalent skill level as determined by the Southwestern College Mathematics Assessment or equivalent RECOMMENDED PREPARATION: RDG 56 or the equivalent skill level as determined by the Southwestern College Reading Assessment or equivalent
Covers answers to all textual exercises and problem set. ✓ Comprehensive ... Std . IX - Geometry. 1. Lines and Angles. 01 ... There is exactly one plane passing through a line and a point, not on the line. The book contains non-standard geometric problems of a level higher than that of the problems ... and detailed structuring in accordance with the methods of solution is adopted. ...... Set S = SABC, S1 = SGDQ, S2 = SIEQ, S3 = SHFQ. Then. Problems and results for the ninth week. Mathematics ... (a) Choose one of them and let that person answer the question; or ... What amounts should they set up to make this game fair? 16. ... Compute the expectation and standard deviation of. under policies set by the State Board of Education. ... the content standard that each question is measuring, and the year each ... In selecting test questions for release, three criteria are used: (1) the ... 2 Jul 2013 ... Math homework = no explanations and eight problems a night. ... has become standard among most math teachers to give .... after you answer problems incorrectly. ... I entered my second math class of Fall Term as a ninth ... The answer is no in codimension one, as the set of the compact leaves is a compact set. ...... 1 which is the standard extension ...... the Seventh International Colloquium on Differential Geometry held in ... visit math.college.hmco.com/students and follow the. Statistics ... How do variance and standard deviation measure data spread? ... The mode of a data set is the value that occurs most frequently. ... Linking Concepts, Problem 1; and the trade. MATH 365, Section 1 ... One purpose of this set of problems is to get you to think some more about the geometry of ... 1.1 of our text) of the standard basis vectors e1 = [1,0] and e2 = [0,1], which lie in the ... Explain briefly why your answer is. courses has been an issue in every decade, and discussion of who ... standard in the first place? We see today ... noting, for example, that no one would want to ... sets). Grade 10: geometry (add solid geometry, coor- dinate geometry, sets). You have been recommended to take Plane and Solid Geometry next yearl ... The packet includes example boxes before each problem set to remind you ... Circle yo swears t err place the final answer - ... Fllw ail one t each set of problems. Standard 1 – Number and Numerical Operations. ... Standard 2 – Geometry and Measurement. .... Beginning in 1981–82, ninth-grade students were required to pass the ... approximately 10 minutes to answer each open-ended question. Solution of the quadratic equations ... Derivation of standard results of finding the nth term and sum of first n terms and ... events, not using set notation. UNIT VI : COORDINATE GEOMETRY. 1. LINES (In ... 28 Aug 2013 ... Students who entered the ninth (9 th. ) ... Applied Algebra I or Applied Algebra 1A and 1B (both for 1 unit) ... Geometry or Calculus or ..... See the answer to Question 14. ..... Is there a schedule set up for mailing award letters? A. problem‐solving and to foster the first standard of mathematical practice from the ... challenge most eighth and ninth grade students, and Level E should be challenging .... (Teacher solicits answers from students) ... Set your clock to 4 o' clock. Not one of these strategies, in and of itself, has shown to have significant ... standard deviation), which ... General Math is Not the Answer ... Algebra 1. 9th Grade. Algebra 1A. 10th Grade. Algebra 1B. 11th Grade ... Both are word problems, set. mathematics, geometry for elementary and middle school teachers ... answering any question may involve more than one ... operations on the standard number systems (e.g., closure ... Order any finite set of real numbers and recognize.
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More About This Textbook Overview The mathematics of tournament design are surprisingly subtle, and this book, an extensively revised version of Ellis Horwood's popular Combinatorial Designs: Construction Methods, provides a thorough introduction. It includes a new chapter on league schedules, which discusses round robin tournaments, venue sequences, and carry-over effects. It also discusses balanced tournament designs, double schedules, and bridge and whist tournament design. Readable and authoritative, the book emphasizes throughout the historical development of the material and includes numerous examples and exercises giving detailed
702509 / ISBN-13: 9780201702507 Elementary and Intermediate Algebra: Graphs and Models The Bittinger Graphs and Models Series helps readers learn algebra by making connections between mathematical concepts and their real-world ...Show synopsisThe Bittinger Graphs and Models Series helps readers learn algebra by making connections between mathematical concepts and their real-world applications. Abundant applications, many of which use real data, offer students a context for learning the math. The authors use a variety of tools and techniques--including graphing calculators, multiple approaches to problem solving, and interactive features--to engage and motivate all types of learners.Hide synopsis Description:Very Good. 0201702509 HB/no DJ. 2000, 1st print. Book only, no...Very Good. 0201702509 HB/no DJ. 2000, 1st print. Book only, no DVDs or CDs. Ships next day. Book is in very good shape, no scribbles, highlighting or underlining, has a sticker on the spine and back, has a couple of little nicks near the spine and the right top corner, has a line mark across the pages on the top and bottom edge pages
Synopses & Reviews Publisher Comments: Algebra is accessible and engaging with this popular text from Charles "Pat" McKeague! ELEMENTARY AND help you to move through each new concept with ease. Real-world applications in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book's multimedia learning resources, including CengageNOW for ELEMENTARY AND INTERMEDIATE ALGEBRA, a personalized online learning companion. Synopsis: About the Author Charles P. "Pat" McKeague earned his B.A. in Mathematics from California State University, Northridge, and his M.S. in Mathematics from Brigham Young University. A well-known author and respected educator, he is a full-time writer and a part-time instructor at Cuesta College. He has published twelve textbooks in mathematics covering a range of topics from basic mathematics to trigonometry. An active member of the mathematics community, Professor McKeague is a popular speaker at regional conferences, including the California Mathematics Council for Community Colleges, the American Mathematical Association of Two-Year Colleges, the National Council of Teachers of Mathematics, the Texas Mathematics Association of Two-Year Colleges, the New Mexico Mathematics Association of Two-Year Colleges, and the National Association for Developmental Education. He is a member of the American Mathematics Association for Two-Year Colleges, the Mathematics Association of America, the National Council of Teachers of Mathematics, and the California Mathematics Council for Community Colleges. "Synopsis" by Netread,
Advances in science and technology are driven by the development of rigorous mathematical foundations for the study of both theoretical and experimental models. With certain methodological variations, this type of study always comes down to the application of analytic or computational integration procedures, making such tools indispensible. With... more... Following the success of Higher Maths Through Practice & Example, Peter Westwood has produced a similarly useful textbook for Intermediate 2 level. Based on classroom experience of what works - and what doesn't, years of teaching and examining experience contribute to a collection of worked examples for all areas of the syllabus - and a wealth... more... This monograph provides a complete and self-contained account of the theory, methods, and applications of constant-sign solutions of integral equations. In particular, the focus is on different systems of Volterra and Fredholm equations. The presentation is systematic and the material is broken down into several concise chapters. An introductory chapter... more... Complete support for the bestselling textbook with hundreds of questions, enabling students to practise and consolidate what they have learnt throughout the course. This practice book:. - Develops students' skills and helps them prepare effectively for the exam with graduated questions, including harder exam-style questions- Helps students to recallThis book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations.... more...
Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who: Have no exposure to elementary algebra, Have had a previously unpleasant experience with elementary algebra, or Need to review algebraic concepts and techniques. Use of this book will help the student develop the insight and intuition necessary to master algebraic techniques and manipulative skills. The text is written to promote problem-solving ability so that the student has the maximum opportunity to see that the concepts and techniques are logically based and to be comfortable enough with these concepts to know when and how to use them in subsequent sections, courses, and non-classroom situations. Intuition and understanding are some of the keys to creativity; we believe that the material presented will help make these keys available to the student. This text can be used in standard lecture or self-paced classes. To help students meet these objectives and to make the study of algebra a pleasant and rewarding experience, Elementary Algebra is organized as follows. Pedagogical Features The work text format gives the student space to practice algebraic skills with ready reference to sample problems. The chapters are divided into sections, and each section is a complete treatment of a particular topic, which includes the following features: Objectives Each chapter begins with a set of objectives identifying the material to be covered. Each section begins with an overview that repeats the objectives for that particular section. Sections are divided into subsections that correspond to the section objectives, which makes for easier reading. Sample Sets Elementary Algebra contains examples that are set off in boxes for easy reference. The examples are referred to as Sample Sets for two reasons: They serve as a representation to be imitated, which we believe will foster understanding of algebra concepts and provide experience with algebraic techniques. Sample Sets also serve as a preliminary representation of problem-solving techniques that may be used to solve more general and more complicated problems. The examples have been carefully chosen to illustrate and develop concepts and techniques in the most instructive, easily remembered way. Concepts and techniques preceding the examples are introduced at a level below that normally used in similar texts and are thoroughly explained, assuming little previous knowledge. Practice Set A parallel Practice Set follows each Sample Set, which reinforces the concepts just learned. The answers to all Practice Sets are displayed with the question when viewing this content online, or at the end of the chapter in the print version. Section Exercises The exercises at the end of each section are graded in terms of difficulty, although they are not grouped into categories. There are an ample number of problems; after working through the exercises, the student will be capable of solving a variety of challenging problems. The problems are paired so that the odd-numbered problems are equivalent in kind and difficulty to the even-numbered problems. Answers to the odd-numbered problems are provided with the exercise when viewed online, or at the back of the chapter in the print version. Exercises for Review This section consists of problems that form a cumulative review of the material covered in the preceding sections of the text and is not limited to material in that chapter. The exercises are keyed by section for easy reference. Summary of Key Concepts A summary of the important ideas and formulas used throughout the chapter is included at the end of each chapter. More than just a list of terms, the summary is a valuable tool that reinforces concepts in preparation for the Proficiency Exam at the end of the chapter, as well as future exams. The summary keys each item to the section of the text where it is discussed. Exercise Supplement In addition to numerous section exercises, each chapter includes approximately 100 supplemental problems, which are referenced by section. Answers to the odd-numbered problems are included with the problems when viewed online and in the back of the chapter in the print version. Proficiency Exam Each chapter ends with a Proficiency Exam that can serve as a chapter review or a chapter evaluation. The proficiency Exam is keyed to sections, which enables the student to refer back to the text for assistance. Answers to all Proficiency Exam problems are included with the exercises when viewed online, or in the back of the chapter in the print version. Content The writing style is informal and friendly, offering a no-nonsense, straightforward approach to algebra. We have made a deliberate effort not to write another text that minimizes the use of words because we believe that students can be study algebraic concepts and understand algebraic techniques by using words and symbols rather than symbols alone. It has been our experience that students at the elementary level are not experienced enough with mathematics to understand symbolic explanations alone; they also need to read the explanation. We have taken great care to present concepts and techniques so they are understandable and easily remembered. After concepts have been developed, students are warned about common pitfalls. Arithmetic Review This chapter contains many examples of arithmetic techniques that are used directly or indirectly in algebra. Since the chapter is intended as a review, the problem-solving techniques are presented without being developed. Therefore, no work space is provided, nor does the chapter contain all of the pedagogical features of the text. As a review, this chapter can be assigned at the discretion of the instructor and can also be a valuable reference tool for the student. Basic Properties of Real Numbers The symbols, notations, and properties of numbers that form the basis of algebra, as well as exponents and the rules of exponents, are introduced in Basic Properties of Real Numbers. Each property of real numbers and the rules of exponents are expressed both symbolically and literally. Literal explanations are included because symbolic explanations alone may be difficult for a student to interpret. Basic Operations with Real Numbers The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of ∣x∣∣x∣ size 12{ lline x rline } {} Algebraic Expressions and Equations Operations with algebraic expressions and numerical evaluations are introduced in Algebraic Expressions and Equations. Coefficients are described rather than merely defined. Special binomial products have both literal symbolic explanation and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form. Solving Linear Equations and Inequalities In this chapter, the emphasis is on the mechanics of equation solving, which clearly explains how to isolate a variable. The goal is to help the student feel more comfortable with solving applied problems. Ample opportunity is provided for the student to practice translating words to symbols, which is an important part of the "Five-Step Method" of solving applied problems (discussed in (Reference) and (Reference)). Factoring Polynomials Factoring is an essential skill for success in algebra and higher level mathematics courses. Therefore, we have taken great care in developing the student's understanding of the factorization process. The technique is consistently illustrated by displaying an empty set of parentheses and describing the thought process used to discover the terms that are to be placed inside the parentheses. The factoring scheme for special products is presented with both verbal and symbolic descriptions, since not all students can interpret symbolic descriptions alone. Two techniques, the standard "trial and error" method, and the "collect and discard" method (a method similar to the "ac" method), are presented for factoring trinomials with leading coefficients different from 1. Graphing Linear Equations and Inequalities in One and Two Variables In this chapter the student is shown how graphs provide information that is not always evident from the equation alone. The chapter begins by establishing the relationship between the variables in an equation, the number of coordinate axes necessary to construct the graph, and the spatial dimension of both the coordinate system and the graph. Interpretation of graphs is also emphasized throughout the chapter, beginning with the plotting of points. The slope formula is fully developed, progressing from verbal phrases to mathematical expressions. The expressions are then formed into an equation by explicitly stating that a ratio is a comparison of two quantities of the same type (e.g., distance, weight, or money). This approach benefits students who take future courses that use graphs to display information. The student is shown how to graph lines using the intercept method, the table method, and the slope-intercept method, as well as how to distinguish, by inspection, oblique and horizontal/vertical lines. Rational approachRoots, Radicals, and Square Root Equations The distinction between the principal square root of the number xx, xx, and the secondary square root of the number xx, xx, is made by explanation and by example. The simplification of Quadratic Equations Methods of solving quadratic equations as well as the logic underlying each method are discussed. Factoring, extraction of roots, completing the square, and the quadratic formula are carefully developed. The zero-factor property of real numbers is reintroduced. The chapter also includes graphs of quadratic equations based on the standard parabola, y=x2y=x2, and applied problems from the areas of manufacturing, population, physics, geometry, mathematics (number and volumes), and astronomy, which are solved using the five-step method. Systems of Linear Equations Beginning with the graphical solution of systems, this chapter includes an interpretation of independent, inconsistent, and dependent systems and examples to illustrate the applications for these systems. The substitution method and the addition method of solving a system by elimination are explained, noting when to use each method. The five-step method is again used to illustrate the solutions of value and rate problems (coin and mixture problems), using drawings that correspond to the actual solution
This video evaluates expressions using a calculator only capable of arithmetic calculations. The purpose of the video is to have students review order of operations and understand the effect of... More... This video evaluates expressions using a calculator only capable of arithmetic calculations. The purpose of the video is to have students review order of operations and understand the effect of round off error
Hello gals and guys I require some guidance to work out this grade 7 cambridge mathematics test papers which I'm unable to do on my own. My homework assignment is due and I need assistance to work on gcf, linear algebra and interval notation . I'm also thinking of hiring a math tutor but they are expensive. So I would be really appreciative if you can extend some assistance in solving the problem. How about giving some more information of what precisely is your problem with grade 7 cambridge mathematics test papers? This would assist in finding out ways to search for an answer. Finding a tutor these days quickly enough and that too at a fee that you can meet can be a wearisome task. On the other hand, these days there are programs that are to be had to assist you with your math problems. All you require to do is to choose the most suited one. With just a click the right answer pops up. Not only this, it assists you to arriving at the answer. This way you also get to find out how to get at the correct answer. Even I've been through that phase when I was trying to figure out a solution to certain type of questions pertaining to mixed numbers and hyperbolas. But then I found this piece of software and I felt as if I found a magic wand. In a flash it would solve even the most difficult problems for you. And the fact that it gives a detailed step-by-step explanation makes it even more handy. It's a must buy for every math student. Algebrator is the program that I have used through several math classes - Intermediate algebra, Algebra 1 and College Algebra. It is a really a great piece of algebra software. I remember of going through problems with exponential equations, leading coefficient and factoring expressions. I would simply type in a problem from the workbook , click on Solve – and step by step solution to my math homework. I highly recommend the program.
The Program Learning Outcomes for the Mathematics Track of the Mathematics Major are given below. The Course-by-Outcomes Table then shows how the courses making up the Mathematics Track develop each of the Program Learning Outcomes. Finally, the main measures used to evaluate the success of the Program and locate any areas of concern can be found in the Program Assessment Measures. Knowledge: We aim to produce individuals who K1. Understand mathematical concepts and theory, are able to apply them in various fields, and relate them to principles of Maharishi Vedic Science. K2. Appreciate the full range of mathematics from its deepest foundational levels, to its expressions in algebra, analysis, and geometry, to its applications in all areas of human endeavor. K3. Have a working knowledge of the elements of single and multivariable calculus, discrete mathematics, linear algebra, probability, abstract algebra, and real analysis. Skills: We aim to produce individuals who are able to S1. Solve problems creatively in mathematics and its applications. S2. Use good number sense to decide whether answers are in the right ball park (orders of magnitude, rules of thumb), are meaningful (rounded appropriately, accuracy, extraneous roots, etc.), and are correct (checking answers when possible). S3. Construct rigorous proofs of mathematical theorems at the level of abstract algebra and elementary real analysis. Justify answers. S4. Critique and find errors in proofs, mathematical arguments, and solutions of problems of others. S5. Model natural phenomena and use mathematics effectively in the client disciplines such as engineering, physics, computer science, life sciences, management, and business. S6. Use appropriate software such as Graphing Calculator, Maple, Mathematica, Fathom, Geometer's Sketchpad, and Excel to investigate concepts, ideas, and data. S7. Effectively use software such as Power Point, MS Word, and TeX to make lively and powerful oral and written presentations. S8. Communicate mathematics clearly and logically to others, both orally and in writing. S9. Find and evaluate sources of mathematical information, and integrate new knowledge into their knowledge base. Values: We aim to produce individuals V1. Who are self-confident, both personally and mathematically V2. Who behave in a harmonious, helpful, and uplifting way with others, including when working on group projects and when explaining mathematics to others. V3. Who exhibit positive attitudes towards personal growth and the daily habits that cultivate personal growth and success in life. V4. Who are clear on their personal strengths and career goals. V5. Who see mathematics as a normal, natural part of their own intelligence, and as a natural foundation for understanding the orderliness at the core of any phenomenon in nature and society. V6. Appreciate the source of all knowledge in the Self.
Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Algebra, Arithmetic, and Trigonometry- the second published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,800 detailed definitions, written in a clear, readable style, complete with alternative meanings, and related references.From Abelian cohomology to zero ring and from the very basic to the highly advanced, this unique lexicon includes terms associated with arithmetic, algebra, and trigonometry, with natural overlap into geometry, topology, and other related areas.A ccessible yet rigorous, concise but comprehensive, the Dictionary of Algebra, Arithmetic, and Trigonometry is your key to accuracy in writing or understanding scientific, engineering, and mathematical literature. less
Circle Drawing Experiment - Thomas Denney Draw a figure on the grid by clicking and dragging. Upon release of the mouse button, this JavaScript calculates a "perfect circle" accuracy score by using the sketch's perimeter as the circumference of a perfect circle, and comparing its area to the ...more>> The Coffeecup Caustic - Roy Williams You are drinking from a cylindrical cup in the sunshine. Sometimes, when the sun shines into the cup, you can see a crescent of light as the sunshine reflects from the inside of the cup onto the surface of the drink. This Java applet illustrates the optics ...more>> Colégio de Gaia, Grupo de Matematica Math resources in Portuguese: Galeria de Sketches - a gallery of JavaSketchpad and Geometer's Sketchpad problems and sketches including the Pythagorean theorem (o Teorema de Pitágoras), Vector Addition (Adicao de Vectores), cutting a cube/parallelepiped ...more>> College Entrance Exam Math Prep - EduCAD A free, interactive library of the most complex math problem types found on the SAT® or ACT® college entrance exams. The "show next step" button provides a hint about the strategy to take; a correct answer submitted with the "check answer" button ...more>> Complex Numbers & Trig - Alan Selby Complex Numbers and the Distributive Law for Complex Numbers, offering a short way to reach and explain trigonometry, the Pythagorean theorem, trig formulas for dot- and cross-products, the cosine law, and a converse to the Pythagorean theorem. A geometric ...more>> Compvter Romanvs (Natural Math) - Edward R. Hobbs A Roman numeral calculator. "Caesar has proclaimed Compvter Romanvs to be the official calcvlator of the Roman Empire. Yov now have at yovr disposal the latest in high technology to assist in all manner of nvmerical problems. Yes, whether yov're bvilding ...more>> Connexions - Rice University Connexions is a non-profit start-up launched at Rice University in 1999 that aims to reinvent how we write, edit, publish, and use textbooks and other learning materials. It is a global repository of educational content that can be described in four words ...more>> Constructor - Soda Constructor animates and edits two-dimensional models made out of masses and springs. The springs can be controlled by a wave to make pulsing muscles, and you can construct models that bounce, roll, walk, etc. Try some of the ready-made models or build ...more>> Convex Hull Algorithms - Tim Lambert An applet that demonstrates some algorithms for computing the convex hull of points in three dimensions. See the points from different viewpoints; see how the Incremental algorithm constructs the hull, face by face; while it's playing, look at it from ...more>> Cool School Tools - Tim Fahlberg Shockwave whiteboard movies on algebra, geometry, probability, statistics, the mathematics of finance, and more. A whiteboard movie (WM) is a multimedia screen recording of writing on an electronic whiteboard (real or virtual) with or without voice and/or ...more>>
This document gives a brief description of the various courses in calculus and some of the intermediate level courses in mathematics. It provides advice and pointers for planning your course selections. If you are a Mathematics Concentrator, or are considering entering the Mathematics Concentration, and if you are seeking some overview of the courses and how they fit together, then this document is for you. However, the guidelines presented below are exactly that: guidelines. Keep them in mind when you are deciding how to structure your program, but be sure to talk to your advisor in the Mathematics Department or to the Director of Undergraduate Studies before you turn in your study card each semester. Math 1a/b is the standard first-year calculus sequence. If you are thinking about majoring in math and have not taken calculus before, take Math 1 as soon as possible! If you have had a year of calculus in high school, and if you have passed the Advanced Placement examination in BC Calculus with a score of 4 or better, then you may be advised to begin with Math 21 a/b, the second-year calculus sequence. If you scored a 5 on the BC Calculus exam and if you are advised to take Math 21 a/b, then you may wish to consider taking Math 23 or Math 25 or 55 instead of Math 21. Be warned: Math 23, 25 and 55 are intense but very rewarding courses, and both 25 and 55 require extensive work outside the classroom. To succeed in the latter two, you must be very committed to mathematics from the start. Regardless of which calculus course you take, keep in mind that it is important to absorb ideas thoroughly. It's a bad idea to push yourself too far too fast. For more guidance on choosing your first math course at Harvard please read the pamphlet ``Beyond Math 1: Which math course is for you?'', which you can obtain from Cindy Jimenez, the Undergraduate Program Coordinator (room 334), or from the undergraduate section of the Department's web site. No single program is ideal for all math concentrators. You should design your curriculum based on your background, interests, and future plans. You are strongly urged to consult with your academic advisor or with the Director of Undergraduate Studies in deciding which courses are best suited for you. Do not plan to meet with your advisor on the day study cards are due, since advisors usually don't have more than a few minutes to spend with each student that day. Make an appointment with your advisor well before study cards are due. You should allot about half an hour, so you can discuss your plan of study in depth. Math 23, 25, 55, 101, 112, and 121 are six courses in which you learn to write proofs, meeting (often for the first time) a style of mathematics in which definitions and proofs become part of the language. Students are generally advised not to take any upper-level math courses before completing (or, at least, taking concurrently) one of these. Math 101 serves three main goals. It lets a student sample the three major areas of mathematics: analysis, algebra, and topology/geometry; it introduces the notions of rigor and proof; and it lets the student have some fun doing mathematics. If you are considering concentrating in Mathematics but are not sure that you are ready to take Math 23, 25 or 55, or if you simply want a glimpse of what ``higher'' math is all about, you are urged to include Math 101 early in your curriculum. Math 101 can be taken concurrently with either Math 21a or 21b. This course is only offered in the fall. If you have had some experience with rigorous proofs and want a different taste of ``higher'' math, you might consider Math 152 in the fall. Neither Math 101 nor Math 152 is appropriate for people from Math 25, Math 55 or (with rare exceptions) Math 23. Math 23, 25 and 55 are the three introductory courses for students with strong math interests. They are geared towards new students. Math 25 and 55 are much more intensive than Math 23, but require much more out of class time. Students who don't wish to make the time commitment will do well to choose Math 23. Meanwhile Math 55 should be taken only by students with extensive college level math backgrounds. Each year several first-year students ask to skip the Math 25/55 level and start with Math 122 or another 100-level course. The Department, based on many years of experience, strongly discourages this. Even if you have taken several years of math at another university, even if you have seen every topic to be covered in Math 25 or 55, you will not be bored in these accelerated courses. The topics covered in Math 25 and 55 are not as important as the level and the depth of mathematical maturity at which they are taught. Taking Math 25 or 55 is the most intense mathematical experience you are going to have in any Harvard course, shared with the most talented of your peers. You may learn more advanced material in other 100- and 200-level courses, but never with the same speed and depth as in Math 25 or 55. These courses are not taught in any other university because no other university has the same caliber of first-year mathematicians. And the courses are simply a lot of fun. Many students who have skipped 25 and 55 have been dissatisfied with their decision. In any event, you must speak with the Director of Undergraduate Studies if you plan to skip the Math 21-55 level. Math 112 and Math 121 are courses suitable for students from Math 21, and they provide an alternative entry-point for the department's more advanced courses in Analysis and Algebra respectively. They should not be normally be taken by students who have been through Math 23 or 25. If you are a sophomore and have taken Math 21 but are not yet comfortable with writing proofs, then consider including these courses in your plan of study. If you have taken Math 23, 25 or 55, or if you have taken Math 21 and gained some experience in writing proofs through courses such as Math 101, 112 and 121, then you are ready to take some of the courses at the 100-level that form the core of the Mathematics curriculum. Most of the courses at this level can be classified as belonging to one of the three main streams of mathematics: ``Analysis'', ``Algebra'' and ``Geometry and Topology''. Courses belonging to these areas are numbered in the ranges 110-119, 120-129 and 130-139 respectively. In each stream, there are two courses which are regarded as ``core'' courses, making a total of six central courses. These are: It is not necessary to include all six of these courses in your plan of study, but here are some points to bear in mind. Students from Math 55 will have covered in 55 the material of Math 122 and Math 113. If you have taken 55, you should look first at Math 114, Math 123 and the Math 131-132 sequence. With the exception just noted, you should consider including Math 122 early on in your curriculum. Algebra is a basic language of modern mathematics, and it is hard to comprehend advanced material without some familiarity with groups and related topics in algebra. The same remark applies to Math 123, to a lesser degree. By the same token, Math 113 should also be taken early on as Complex Analysis is used in many other fields of mathematics. You will also find the topology you learn in Math 131 useful in many other areas: amongst other things, it provides the mathematical language with which to discuss continuity and limits in wide generality. Math 123 cannot be taken before Math 122; but in the other two streams, the courses can be taken in either order. Thus, Math 114 can be taken before or after Math 113, and the same applies to Math 131 and 132. You should try to fulfill the distribution requirement (i.e., the requirement to take at least one course in analysis, algebra, and geometry) early in your academic career. By your junior or senior year, you should be exposed to the main branches of mathematics; then you can choose the department's advanced courses. In any case, most 200-level courses assume (at least informally) familiarity with the basic tools of analysis, algebra, and topology. At this level, there are many other courses to choose from: Number theory in Math 124 or Math 129, Differential Geometry in Math 136, Probability in Math 154, Logic and Set Theory in Math 141 and Math 143, amongst others. It is a good idea to take a tutorial (Math 99r) during the sophomore or junior year. Many students found the tutorial to be one of the best courses they took at Harvard. Tutorials generally satisfy the Math Expository requirement and often lead to senior thesis topics. More about tutorials appears below. Students wishing to take a rigorous course in mathematical logic in years when Math 141, 142, 143, or 144 are not offered at Harvard should consider taking logic courses at M.I.T. In any event, the Harvard courses offer a good introduction to model theory, set theory and recursion theory -- the three main branches of Mathematical Logic. Students interested in the more philosophical aspects of logic and/or in proof or set theory may want to take Philosophy 143, and those interested in mathematics of computation should look into Computer Science 121 and some of the other theoretical CS courses. Students interested in Combinatorics should look at Math 155, and may also want to look up M.I.T.'s listings in that area. If you want M.I.T. courses to count for the concentration credit, you must get permission in advance from the Director of Undergraduate Studies, Prof. Peter Kronheimer (kronheim@math). Students are encouraged to take courses from a variety of professors in the department and not just to ``follow'' one teacher. It is advisable to be exposed to different views and styles of doing mathematics. The difference between 100-level and 200-level courses is fairly easy to summarize: 100-level courses are designed for undergraduates, whereas the 200-level courses are generally designed for graduate students. As far as course material goes, the 100-level courses are designed to offer a comprehensive view of all the major fields in pure mathematics. They emphasize the classical examples and problems that started each field going and they all lead to one of the fundamental results that motivates the further development of the field. In contrast, a 200-level course will assume you understand the basic ideas of a field. A 200-level course will set out the systematic, abstract foundations for a field and develop tools needed to get to the present frontiers. The 100-level courses give you a good overview of mathematics, they foster intellectual growth, and they prepare you for your chosen career. This is not true of 200-level courses. These courses assume that you are interested in the subject, and that you are already fairly certain of becoming an academic mathematician. The amount you learn in such a course is often also entirely up to you. Your prerequisites, though correct according to the course catalog, may be entirely inadequate. Many courses are paired into 100-level and 200-level sequences:
Algebra A will offer students an opportunity to identify and analyze patterns, strengthen their computation of numbers and algebraic expressions, solve multi-step equations and investigate real-life problems in an algebraic manner. Algebra 2 Course Description Algebra 2 will offer students an opportunity to build on concepts taught in Algebra 1, Geometry and previous Algebra 2 classes (if B, C, D) while adding new concepts to the students' repertoire of mathematics.Over four trimesters, students will develop an understanding that algebraic thinking is an accessible and powerful tool that can be used to model and solve real-world problems (Michigan Merit Curriculum Course/Credit Requirements). Physics A and B Course Description Physics is the study of the principles and processes that are the foundation of all sciences. Topic covered are: mechanics (how and why things move), wave energy (including light and sound), electricity and magnetism, and modern physics (including relativity). This course will be covering Physics in a "conceptual" nature. This course provides knowledge into all of the essential Physics standards as outlined by the State of Michigan.
Beginning and Intermediate Algebra - 3rd edition ISBN13:978-0077350086 ISBN10: 0077350081 This edition has also been released as: ISBN13: 978-0073384214 ISBN10: 0073384216 Summary: Miller/O'Neill/Hyde continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Beginning and Intermediate 2e. The practice of many instructors in the classroom is to present examples and have their students solve similar problems. This is realized through the Skill Practice Exercises that directly follow the examples in the textbook. Throughout the text, the authors have integrated many Study Tips and Avoiding Mistakes hints, which are reflecti...show moreve of the comments and instruction presented to students in the classroom. In this way, the text communicates to students, the very points their instructors are likely to make during lecture, helping to reinforce the concepts and provide instruction that leads students to mastery and success. The authors included in this edition, Problem-Recognition Exercises, that many instructors will likely identify to be similar to worksheets they have personally developed for distribution to students. The intent of the Problem-Recognition exercises, is to help students overcome what is sometimes a natural inclination toward applying problem-sovling algorithms that may not always be appropriate. In addition, the exercise sets have been revised to include even more core exercises than were present in the first edition. This permits instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills and develop the knowledge they need to make a successful transition into College Algebra. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class, as they do inside class with their instructor. For even more support, students have access to a wealth of supplements, including McGraw-Hill's online homework management system, MathZoneNice condition with minor indications of previous handling. Book selection as BIG as Texas. $30.51 +$3.99 s/h Good SellBackYourBook Aurora, IL 0077350081 Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!! $30.51 +$3.99 s/h Acceptable SellBackYourBook Aurora, IL 007735008136.75 +$3.99 s/h Good CR Booksellers Punta Gorda, FL 0077350081 Used, in good condition. Book only. May have interior marginalia or previous owner's name63.65 +$3.99 s/h Good PaperbackshopUS Secaucus, NJ Used - Very Good Book. Shipped from US within 4 to 14 business days. Established seller since 2000 $121.66 +$3.99 s/h New Stork Group Phoenix, MD Brand new and unread! Join our growing list of satisfied customers! $165
More About This Textbook Overview The representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from and readers can download source code and solutions to selected exercises from the book's web
This course emphasizes elements of Liberal Arts mathematics and Finite Mathematics. Itfocuses on problem solving in such areas as algebra, geometry, probability, statistics and logic.Students will be exposed also to some general ideas about the application of above concepts toreal situations. Case studies and word problems will be a very important component of thiscourse. 1. Being able to recognize algebraic expressions and operate with them. Apply algebraicmanipulations to solve geometric problems involving areas, surfaces, volumes andconversion units.2. Being able to recognize concepts from probability and counting techniques, and solverelated problems.3. Being able to apply concepts from descriptive statistics.4. Being able to operate with problems from logic.5. Being able to apply concepts from mathematics to solve applied problems in areas ofbusiness, sociology, science and technology. approach. In a blended course, students complete 50% of the learning activities online (i.e.Blackboard), and the other learning activities (50%) takes place in the face-to-face classroom.Here is what students should expect in this course:  Face-to-Face Meetings : Class will meet 2 times a week in the classroom, wherestudents ask questions to clarify what they did not understand from the course readingsand e-Lectures. Students will also demonstrate and discuss how to work problems fromthe course textbook that will count toward their participation grade. Finally, students takethe scheduled tests during the class meetings.  Online Learning Resources : Supplementary resources such as videos, animations,Power Point presentations, handouts, and math links will be available in Blackboard(Bb).  Available Assistance : Students have many alternatives to seek assistance to succeedin this course: (a) Visit the math center to get individual assistance from the instructor(see office hours info); (b) Visit the math center during business hours to sign up for atutoring session; (c) Ask questions using the Question thread in the discussion board of Blackboard (questions will be answered within 24 hours); and (d) Class discussions area great opportunity to learn collaboratively the course content.  Reflection Journals : Students will post a reflection in the Bb discussion board on whatthey have learned in the course. These reflections are based on instructor's guidedquestions.  Bb Quizzes : Students will watch e-lectures in Bb and take an online quiz based on thecontent.
Mtc ssample05Document Transcript Test Code: CS (Short answer type) 2005 M.Tech. in Computer ScienceThe candidates for M.Tech. in Computer Science will have to take twotests – Test MIII (objective type) in the forenoon session and Test CS(short answer type) in the afternoon session. The CS test booklet will havetwo groups as follows. GROUP AA test for all candidates in analytical ability and mathematics at the B.Sc.(pass) level, carrying 30 marks. GROUP BA test, divided into several sections, carrying equal marks of 70 inmathematics, statistics, and physics at the B. Sc. (Hons.) level and incomputer science, and engineering and technology at the B.Tech. level. Acandidate has to answer questions from only one of these sectionsaccording to his/her choice.The syllabus and sample questions of the CS test are given below.Note: All questions in the sample set are not of equal difficulty. Theymay not carry equal marks in the test. Syllabus GROUP ALogical Reasoning.Elements of set theory. Permutations and combinations. Functions andrelations. Theory of equations. Inequalities.Limit, continuity, sequences and series, differentiation and integrationwith applications, maxima-minima, elements of ordinary differentialequations, complex numbers and De Moivre's theorem.Elementary Euclidean geometry and Trigonometry.Elementary number theory, divisibility, congruences, primality.Determinants, matrices, solutions of linear equations, vector spaces, linearindependence, dimension, rank and inverse. 1 where [a] denotes the largest integer less than or equal to a.A5. Let bqbq-1…b1b0 be the binary representation of an integer b, i.e., q b = ∑ 2 j b j , bj = 0 or 1, for j = 0, 1, …, q. j =0 Show that b is divisible by 3 if b0 − b1 + b2 − K +(−1) q bq = 0 .A6. A sequence {xn} is defined by x1 = 2, xn+1 = 2 + x n , n =1,2, … Show that the sequence converges and find its limit.A7. Is sin ( x \| x \| ) differentiable for all real x? Justify your answer.A8. Find the total number of English words (all of which may not have proper English meaning) of length 10, where all ten letters in a word are not distinct. a1 a 2 aA9. Let a0 + + + ..... + n = 0 , where ai's are some real 2 3 n+1 2 n constants. Prove that the equation a 0 + a 1 x + a 2 x + ... + a n x = 0 has at least one solution in the interval (0, 1).A10. Let φ (n) be the number of positive integers less than n and having no common factor with n. For example, for n = 8, the numbers 1, 3, 5, 7 have no common factors with 8, and hence φ(8) = 4. Show that (i) φ ( p) = p − 1 , (ii) φ ( pq) = φ ( p)φ (q) , where p and q are prime numbers.A11. A set S contains integers 1 and 2. S also contains all integers of the form 3x+ y where x and y are distinct elements of S, and every element of S other than 1 and 2 can be obtained as above. What is S? Justify your answer.A12. Let f be a real-valued function such that f(x+y) = f(x) + f(y) ∀x, y ∈ R. Define a function φ by φ(x) = c + f(x), x ∈ R, where c is a real constant. Show that for every positive integer n, φ n ( x) = (c + f (c ) + f 2 (c) + ..... + f n −1 (c)) + f n ( x); where, for a real-valued function g, g n (x ) is defined by 6 g 0 ( x ) = 0, g 1 ( x) = g ( x), g k +1 ( x) = g ( g k ( x)).A13. Consider a square grazing field with each side of length 8 metres. There is a pillar at the centre of the field (i.e. at the intersection of the two diagonals). A cow is tied with the pillar using a rope of length 83 metres. Find the area of the part of the field that the cow is allowed to graze.A14. There are four geometrical objects in the form of square, rhombus, circle and triangle. Each one is made from one of the 4 different materials gold, copper, silver, and bronze and coloured differently using blue, red, green and yellow paints. The square is of green colour. The blue object is made of bronze. The circle is not red. The triangle is not made of gold. The square is not made of copper. The rhombus is not blue and is not made of silver. The circle is not made of bronze. The triangle is not yellow. The red object is not made of copper. Deduce logically the colour and material of the circle.A15. A milkmaid has a 4-litre can full of milk and two other empty cans of 2.5 litre and 1.5 litre sizes respectively. She is to divide the milk equally in two cans. Find out the procedure to do this in a minimum number of operations. GROUP B Mathematics x n +3M1. Let 0 < x1 < 1. If xn+1 = 3x + 1 , n = 1,2,3, … n 5x n +3 (i) Show that xn+2 = 3x +5 , n = 1,2,3, … n (ii) Hence or otherwise, show that lim xn exists. n →∞ (iii) Find lim xn . n →∞M2. (a) A function f is defined over the real line as follows: 7 ⎧ x sin π , x > 0 f ( x) = ⎨ x ⎩0, x = 0. Show that f ′(x) vanishes at infinitely many points in (0,1). (b) Let f : [0,1] → ℜ be a continuous function with f(0) = 0. Assume that f ′ is finite and increasing on (0,1). f ( x) Let g ( x) = x x ∈ (0,1) . Show that g is increasing.M3. (a) Prove the inequality ex > 1+(1+x) log(1+x), for x > 0. x (b) Show that the series ∑ n(1 + nx) 2 is uniformly convergent on [0,1].M4. Consider the function of two variables F(x,y) = 21x - 12x2 - 2y2 + x3 + xy2. (a) Find the points of local minima of F. (b) Show that F does not have a global minimum.M5. Find the volume of the solid given by 0 ≤ y ≤ 2 x , x 2 + y 2 ≤ 4 and 0≤ z≤ x.M6. (a) Let A, B and C be 1×n, n×n and n×1 matrices respectively. Prove or disprove: Rank(ABC) ≤ Rank(AC). (b) Let S be the subspace of R4 defined by S = {(a1, a2, a3, a4) : 5a1 - 2a3 -3a4 = 0}. Find a basis for S.M7. Let A be a 3×3 matrix with characteristic equation λ − 5λ = 0. 3 2 (i) Show that the rank of A is either 1 or 2. (ii) Provide examples of two matrices A1 and A2 such that the rank of A1 is 1, rank of A2 is 2 and Ai has characteristic equation λ3 - 5λ2 = 0 for i = 1, 2.M8. Define B to be a multi-subset of a set A if every element of B is an element of A and elements of B need not be distinct. The ordering of elements in B is not important. 8 For example, if A = {1,2,3,4,5} and B = {1,1,3}, B is a 3-element multi-subset of A. Also, multi-subset {1,1,3} is the same as the multi-subset {1,3,1}. (a) How many 5-element multi-subsets of a 10-element set are possible? (b) Generalize your result to m-element multi-subsets of an n-element set (m < n).M9. Let G be the group of all 2×2 non-singular matrices with matrix multiplication as the binary operation. Provide an example of a normal subgroup H of G such that H ≠ G and H is not a singleton.M10. Let R be the field of reals. Let R[x] be the ring of polynomials over R, with the usual operations. (a) Let I ⊆ R[x] be the set of polynomials of the form a0 +a1x +....+ anxn with a0 = a1 = 0. Show that I is an ideal. (b) Let P be the set of polynomials over R of degree ≤ 1. Define ⊕ and Θ on P by (a0 +a1x) ⊕ (b0 +b1 x) = (a0 + b0)+(a1 +b1)x and (a0 +a1x) Θ (b0 + b1x) = a0b0 + (a1b0 +a0b1)x. Show that (P, ⊕, Θ ) is a commutative ring. Is it an integral domain? Justify your answer.M11. (a) If G is a group of order 24 and H is a subgroup of G of order 12, prove that H is a normal subgroup of G. (b) Show that a field of order 81 cannot have a subfield of order 27.M12. (a) Consider the differential equation: d2y dy 2 cos x + sin x − 2 y cos 3 x = 2 cos5 x. dx dx By a suitable transformation, reduce this equation to a second order linear differential equation with constant coefficients. Hence or otherwise solve the equation. (b) Find the surfaces whose tangent planes all pass through the origin. 9 M13. (a) Consider the following two linear programming problems: P1: Minimize x1 subject to x1 + x2 ≥ 1 − x1 − x2 ≥ 1 where both x1 and x2 are unrestricted. P2: Minimize x1 subject to x1 + x2 ≥ 1 − x1 − x2 ≥ 1 x1 ≥ 0, x2 ≥ 0. Solve both the LPs. Write the duals of both the LPs and solve the duals. (b) If an LP is infeasible, what can you say about the solution of its dual?M14. Solve the following linear programming problem without using Simplex method: minimize 6 w1 + 8 w2 + 7 w3 + 15 w4 + w5 subject to w1 + w3 + 3 w4 ≥ 4, w2 + w3 + w4 – w5 ≥ 3, w1, w2, w3, w4, w5 ≥ 0.M15. (a) Show that a tree on n vertices has at most n−2 vertices with degree > 1. (b) Show that in an Eulerian graph on 6 vertices, a subset of 5 vertices cannot form a complete subgraph.M16. (a) Show that the edges of K4 can be partitioned into 2 edge-disjoint spanning trees. (b) Use (a) to show that the edges of K6 can be partitioned into 3 edge-disjoint spanning trees. (c) Let Kn denote the complete undirected graph with n vertices and let n be an even number. Prove that the edges of Kn can be partitioned into exactly n/2 edge-disjoint spanning trees. 10 StatisticsS1. (a) X and Y are two independent and identically distributed random variables with Prob[X = i] = pi, for i = 0, 1, 2, ….. Find Prob[X < Y] in terms of the pi values. (b) Based on one random observation X from N(0, σ2), show that √π/2 \|X\| is an unbiased estimate of σ.S2. (a) Let X0, X1, X2, … be independent and identically distributed random variables with common probability density function f. A random variable N is defined as N = n if X1 ≤ X 0 , X 2 ≤ X 0 , , X n−1 ≤ X 0 , X n > X 0 , n = 1, 2, 3, Find the probability of N = n . (b) Let X and Y be independent random variables distributed uniformly over the interval [0,1]. What is the probability that the integer closest to Y is 2? XS3. If a die is rolled m times and you had to bet on a particular number of sixes occurring, which number would you choose? Is there always one best bet, or could there be more than one?S4. Let X 1 , X 2 and X3 be independent random variables with Xi following a uniform distribution over (0, iθ), for i = 1 , 2, 3 . Find the maximum likelihood estimate of θ based on observations x1 , x 2 , x3 on X 1 , X 2 , X 3 respectively. Is it unbiased? Find the variance of the estimate.S5. New laser altimeters can measure elevation to within a few inches, without bias. As a part of an experiment, 25 readings were made on the elevation of a mountain peak. These averaged out to be 73,631 inches with a standard deviation (SD) of 10 inches. Examine each of the following statements and ascertain whether the statement is true or false, giving reasons for your answer. (a) 73631 ± 4 inches is a 95% confidence interval for the elevation of the mountain peak. (b) About 95% of the readings are in the range 73631 ± 4 inches. 11 (c) There is about 95% chance that the next reading will be in the range of 73631 ± 4 inches.S6. Consider a randomized block design with two blocks and two treatments A and B. The following table gives the yields: Treatment A Treatment B Block 1 a b Block 2 c d (a) How many orthogonal contrasts are possible with a, b, c and d? Write down all of them. (b) Identify the contrasts representing block effects, treatment effects and error. (c) Show that their sum of squares equals the total sum of squares.S7. Let X be a discrete random variable having the probability mass function p (x) = Λx(1- Λ)1-x, x = 0, 1, where Λ takes values ≥ 0.5 only. Find the most powerful test, based 1 2 on 2 observations, for testing H0 : Λ = against H1 : Λ = , with 2 3 level of significance 0.05.S8. Let X1, X2, …, Xn be n independent N(θ,1) random variables where −1 ≤ θ ≤ 1. Find the maximum likelihood estimate of θ and show that it has smaller mean square error than the sample mean X .S9. Let t1, t2, …tk be k independent and unbiased estimators of the same k t parameter θ with variances σ 12 ,σ 2 ,Kσ k2 . Define t as ∑ i . Find 2 i =1 k k E( t ) and the variance of t . Show that ∑ (t i =1 i − t ) 2 /{k (k − 1)} is an unbiased estimator of var( t ).S10. Consider a simple random sample of n units, drawn without replacement from a population of N units. Suppose the value of Y1 is unusually low whereas that of Yn is very high. Consider the following estimator of Y , the population mean. 12 S13. In a factory, the distribution of workers according to age-group and sex is given below. Sex Age-group Row ↓ 20-40 yrs. 40-60 yrs. total Male 60 40 100 Female 40 10 50 Column Total 100 50 150 Give a scheme of drawing a random sample of size 5 so that both the sexes and both the age-groups are represented. Compute the first-order inclusion probabilities for your scheme. PhysicsP1. A beam of X-rays of frequency v falls upon a metal and gives rise to photoelectrons. These electrons in a magnetic field of intensity H describe a circle of radius γ. Show that ⎡ 1 ⎤ 2 ⎢ ⎛1 + e2 2 H 2 ⎞ 2 ⎥ h(v − v 0 ) = m 0 c ⎜ ⎟ −1 ⎢⎜ m 2 c 4 ⎟ ⎥ ⎢⎝ 0 ⎠ ⎥ ⎣ ⎦ where v0 is the frequency at the absorption limit and m0 is the rest mass of the electron, e being expressed in e.s.u.P2. An ideal gas goes through a cycle consisting of alternate isothermal and adiabatic curves as shown in the figure. AB, CD, and EF are isothermal curves at temperatures T1 , T2 and T3 respectively, while BC, DE, and FA are adiabatic curves. Find the efficiency of such a cycle, if in each isothermal expansion the gas volume increases by the same factor. 14 P3. Two long coaxial cylindrical metal tubes of length L (the inner one of radius a, the outer one of radius b) stand vertically in a tank of dielectric oil having susceptibility χe and mass density ρ. The inner tube is maintained at potential V and the outer cylinder is grounded. To what height h above the oil level outside the two cylinders will the oil rise in the space between the tubes?P4. (a) Compute the rate at which our Sun is losing its mass, given that the mean radius R of Earths orbit is 1.5 × 108 Km and the intensity of solar radiation at the Earth is 4/π ×103 Watt/m2. If the present mass of our Sun is 2 × 1030 Kg, how long is it expected to last? (b) Find the proper length of a rod in the laboratory frame of reference if its velocity is v = c/2, its length is l = 1 metre, and the angle between the rod and its direction of motion is 45 deg.P5. (a) Three rigid spheres A, B, and C of masses 10, 5, and 1 unit respectively are arranged in a row as shown in the figure (the centers of the spheres are collinear). Initially, all spheres are at rest. Next, A moves towards B with some velocity to collide with B. As a result, B moves towards C and collides with C. 15 (i) If all the collisions are direct (head-on) and perfectly elastic, what is the ratio of the final velocities of A, B, and C? (ii) If the collisions are assumed to be perfectly inelastic, what is the percentage of energy absorbed in the whole inelastic process? (b) A test tube of mass 4 gm and diameter 1.5 cm floats vertically in a large tub of water. It is further depressed vertically by 2 cm from its equilibrium position and suddenly released, whereby the tube is seen to execute a damped, oscillatory motion in the vertical direction. If the resistive force due to viscous damping offered by water to the tube in motion is √π Dv, where v is the instantaneous velocity of the tube in water, and D is the diameter of the tube in cm, then find the time period of oscillation of the tube. (Assume that there is no ripple generated in the water of the tub.)P6. An electron is confined to move within a linear interval of length L. Assuming the potential to be zero throughout the interval except for the two end points, where the potential is infinite, find the following: (a) probability of finding the electron in the region 0 < x < L/4, when it is in the lowest (ground) state of energy; (b) taking the mass of the electron me to be 9 × 10-31 Kg, Plancks constant h to be 6.6 × 10-34 Joule-sec and L = 1.1 cm, determine the electrons quantum number when it is in the state having an energy equal to 5 × 10-32 Joule. 16 P7. Consider the following circuit in which an a.c. source of V volts at a frequency of 106/π cycles/sec is applied across the combination of resistances and inductances. The total rms current flowing through the circuit as measured by an a.c. ammeter is 10 amp. Find the rms current I1 flowing through the upper branch of impedances. The self inductance of the two coils are as shown in the figure. The mutual inductance between the coils is 2 mH and is such that the magnetization of the two coils are in opposition.P8. (a) Consider the circuit shown below. (i) Will there be any current flowing through the arm BC when the switch S is closed? (ii) Calculate the steady state voltage across each of the two capacitors in the figure. 17 (b) A coil of resistance 30Ω and inductance 20 mH is connected in parallel with a variable capacitor across an a.c. supply of 25V amplitude, and frequency 1000/π Hz. The capacitance of the capacitor is varied until the current taken from the supply is a minimum. For this condition, find (i) the value of the capacitance; (ii) the amplitude of the current.P9. (a) Calculate the donor concentration of an n-type Germanium specimen having a specific resistivity of 0.1 ohm-metre at 300K, if the electron mobility µe = 0.25 metre2/Volt-sec at 300K, and the magnitude of the electronic charge is 1.6 × 10-19 Coulomb. (b) An n-type Germanium specimen has a donor density of 1.5 ×1015 cm-3. It is arranged in a Hall effect experiment where the magnitude of the magnetic induction field B is 0.5 Weber/metre2 and current density J = 480 amp/metre2. What is the Hall voltage if the specimen is 3 mm thick? 18 P10. A conducting rod AB makes contact with metal rails AD and BC r which are 50cm apart in a uniform magnetic field B = 1.0 wb/m2 perpendicular to the place ABCD. The total resistance (assumed constant) of the circuit ADCB is 0.4Ω. (b) What is the direction and magnitude of e.m.f. induced in the rod when it is moved to the left with a velocity of 8m/s? (c) What force is required to keep the rod in motion? (d) Compare the rate at which mechanical work is done by the force r F with the rate of development of electric power in the circuit.P11. An elementary particle called ∑-, at rest in laboratory frame, decays spontaneously into two other particles according to Σ − → π − + n . The masses of ∑-, π- and n are M1, m1, and m2 respectively. (a) How much kinetic energy is generated in the decay process? (b) What are the ratios of kinetic energies and momenta of π and − n?P12. (a) A set of binary operations is said to be functionally complete if and only if every switching function can be expressed entirely by means of operations from this set. Prove that the nor operation is functionally complete. (b) Given a switching function: f(x,y,z) = xyz + xyz + xyz + xyz + xyz + xyz, find the canonical product-of-sums form for f.P13. (a) Find the relationship between L, C and R in the circuit shown in the figure such that the impedance of the circuit is independent of frequency. Find out the impedance. 19 (b) Find the value of R and the current flowing through R shown in the figure when the current is zero through R′. Computer ScienceC1. (a) A grammar is said to be left recursive if it has a non-terminal A such that there is a derivation A ⇒ + Aα for some sequence of symbols α. Is the following grammar left-recursive? If so, write an equivalent grammar that is not left-recursive. A → Bb A→a B →Cc B→b C → Aa C→c 20 (b) An example of a function definition in C language is given below: char fun (int a, float b, int c) { /* body / … } Assuming that the only types allowed are char, int, float (no arrays, no pointers, etc.), write a grammar for function headers, i.e., the portion char fun(int a, …) in the above example.C2. a) Construct a binary tree whose pre-order and in-order traversals are CBAFDEHGJI and ABCDEFGHIJ respectively. b) Convert it into an AVL tree with minimum number of rotations. c) Draw the resultant AVL tree upon deletion of node F.C3. a) A relation R(A, B, C, D) has to be accessed under the query σB=10(R). Out of the following possible file structures, which one should be chosen and why? i) R is a heap file. ii) R has a clustered hash index on B. iii) R has an unclustered B+ tree index on (A, B). b) If the query is modified as πA,B(σB=10(R)), which one of the three possible file structures given above should be chosen in this case and why? c) Let the relation have 5000 tuples with 10 tuples/page. In case of a hashed file, each bucket needs 10 pages. In case of B+ tree, the index structure itself needs 2 pages. If the disk needs 25 msecs. to read or write a disk page, what would be the disk access time for answering the above queries?C4. Let A and B be two arrays, each of size n. A and B contain numbers in sorted order. Give an O(log n) algorithm to find the median of the combined set of 2n numbers.C5. a) Consider a pipelined processor with m stages. The processing time at every stage is the same. What is the speed-up achieved by the pipelining? b) In a certain computer system with cache memory, 750 ns (nanosec) is the access time for main memory for a cache miss and 50 ns is the access time for a cache hit. Find the percentage 21 decrease in the effective access time if the hit ratio is increased from 80% to 90%.C6. (a) A disk has 500 bytes/sector, 100 sectors/track, 20 heads and 1000 cylinders. The speed of rotation of the disk is 6000 rpm. The average seek time is 10 millisecs. A file of size 50 MB is written from the beginning of a cylinder and a new cylinder will be allocated only after the first cylinder is totally occupied. i) Find the maximum transfer rate. ii) How much time will be required to transfer the file of 50 MB written on the disk? Ignore the rotational delay but not the seek time. (b) Following are the solutions for the two process (pi and pj) critical section problem. Find the errors (if any) in these solutions and rectify them. The notations have usual meanings and i = 0, 1; j = 1-i. Solution 1 Pi: repeat while flag [j] do skip; flag [i] = true; critical section; flag [i] = false; exit section; until false; Solution 2 Pi: repeat flag[i] = true; while flag [j] do skip ; critical section: flag [i] = false ; exit section; until false;C7. (a) A computer on a 6 Mbps network is regulated by a token bucket. The bucket is filled at a rate of 2 Mbps. It is initially filled to capacity with 8 Megabits. How long can the computer transmit at the full 6 Mbps? (b) Sketch the Manchester encoding for the bit stream 0001110101. 22 (c) If delays are recorded in 8-bit numbers in a 50-router network, and delay vectors are exchanged twice a second, how much bandwidth per (full-duplex) line is consumed by the distributed routing algorithm? Assume that each router has 3 lines to other routers.C8. Consider a binary operation shuffle on two strings, that is just like shuffling a deck of cards. For example, the operation shuffle on strings ab and cd, denoted by ab \|\| cd, gives the set of strings {abcd, acbd, acdb, cabd, cadb, cdab}. (a) Define formally by induction the shuffle operation on any two strings x, y ∈ Σ. (b) Let the shuffle of two languages A and B, denoted by A \|\| B be the set of all strings obtained by shuffling a string x ∈ A with a string y ∈ B. Show that if A and B are regular, then so is A \|\| B.C9. (a) Minimize the switching function w′xy′z + wx′y′z + w′xyz′ + wx′yz′. (b) A certain four-input gate G realizes the switching function G(a, b, c, d) = abc + bcd. Assuming that the input variables are available in both complemented and uncomplemented forms: (i) Show a realization of the function f(u, v, w, x) = Σ (0, 1, 6, 9, 10, 11, 14, 15) with only three G gates and one OR gate. (ii) Can all switching functions be realized with {G, OR} logic set ?C10. Consider a set of n temperature readings stored in an array T. Assume that a temperature is represented by an integer. Design an O(n + k log n) algorithm for finding the k coldest temperatures.C11. Assume the following characteristics of instruction execution in a given computer: • ALU/register transfer operations need 1 clock cycle each, • each of the load/store instructions needs 3 clock cycles, and • branch instructions need 2 clock cycles each. (a) Consider a program which consists of 40% ALU/register transfer instructions, 30% load/store instructions, and 30% branch instructions. If the total number of instructions in this program is 10 billion and the clock frequency is 1GHz, then 23 compute the average cycles per instruction (CPI), total execution time for this program, and the corresponding MIPS rate. (b) If we now use an optimizing compiler which reduces the total number of ALU/register transfer instructions by a factor of 2, keeping the number of other instruction types unchanged, then compute the average CPI, total time of execution and the corresponding MIPS rate for this modified program.C12. A tape S contains n records, each representing a vote in an election. Each candidate for the election has a unique id. A vote for a candidate is recorded as his/her id. (i) Write an O(n) time algorithm to find the candidate who wins the election. Comment on the main memory space required by your algorithm. (iii) If the number of candidates k is known a priori, can you improve your algorithm to reduce the time and/or space complexity? (iv) If the number of candidates k is unknown, modify your algorithm so that it uses only O(k) space. What is the time complexity of your modified algorithm?C13. (a) The order of a regular language L is the smallest integer k for which Lk = Lk+1, if there exists such a k, and ∞ otherwise. (i) What is the order of the regular language a + (aa)(aaa)? (ii) Show that the order of L is finite if and only if there is an integer k such that Lk = L, and that in this case the order of L is the smallest k such that Lk = L*. (b) Solve for T(n) given by the following recurrence relations: T(1) = 1; T(n) = 2T(n/2) + n log n, where n is a power of 2.C14. Let L1 and L2 be two arrays each with n = 2k elements sorted separately in ascending order. If the two arrays are placed side by side as a single array of 2n elements, it may not be found sorted. All the 2n elements are distinct. Considering the elements of both the arrays, write an algorithm with k + 1 comparisons to find the n-th smallest element among the entire set of 2n elements. 24 Engineering and TechnologyE1. A rocket weighing 50,000 kg has been designed so as to eject gas at a constant velocity of 250 meters/sec. Find the minimum rate at which the rocket should lose its mass (through ejection of gas) so that the rocket can just take off.E2. A particle of mass m is attached to a fixed point by means of a string of length l and hangs freely. Show that if it is pushed horizontally with a velocity greater than 5 gl , it will completely describe a vertical circle.E3. A chain of total length L = 4 metre rests on a table top, with a part of the chain hanging over the edge, as shown in the figure below. Let α be the ratio of the length of the overhanging part of the chain to L. If the coefficient of friction between the chain and the table top is 0.5, find the values of α for which the chain remains stationary. If α = 0.5, what is the velocity of the chain when the last link leaves the table?E4. A flywheel of mass 100 kg and radius of gyration 20 cm is mounted on a light horizontal axle of radius 2 cm, and is free to rotate on bearings whose friction may be neglected. A light string wound on the axle carries at its free end a mass of 5 kg. The system is released from rest with the 5 kg mass hanging freely. If the string slips off the axle after the weight has descended 2 m, prove that a couple of moment 10/π2 kg.wt.cm. must be applied in order to bring the flywheel to rest in 5 revolutions.E5. The truss shown in the figure rotates around the pivot O in a vertical plane at a constant angular speed ω. Four equal masses (m) hang from the points B, C, D and E. The members of the truss are rigid, 25 weightless and of equal length. Find a condition on the angular speed ω so that there is compression in the member OE.E6. In the circuit shown below, the Op-Amp is an ideal one. (a) Show that the conditions for free oscillation can be met in the circuit. (b) Find the ideal value of R to meet the conditions for oscillation. (c) Find the frequency of oscillation. (Assume π = 3.14).E7. Two bulbs of 500cc capacity are connected by a tube of length 20 cm and internal radius 0.15 cm. The whole system is filled with oxygen, the initial pressures in the bulbs before connection being 10 cm and 15 cm of Hg, respectively. Calculate the time taken for the pressures to become 12 cm and 13 cm of Hg, respectively. Assume that the coefficient of viscosity η of oxygen is 0.000199 cgs unit. 26 E8. Two identical watch glasses with negligible thickness are glued together. The rear one is silvered [see Figure(a)]. Sharp focus is obtained when both object and image distance are equal to 20 cm. Suppose the space between the glasses is filled with water (refractive index = 4/3) [see Figure (b)]. Calculate d [Figure (b)] for which a sharp real image is formed.E9. (a) Two systems of equal mass m1 and m2 and heat capacity C are at temperatures T1 and T2 respectively (T1 > T2). If the first is used as source and the second as sink, find the maximum work obtainable from such an arrangement. (b) A Carnot engine A operates between temperatures T1 and T2 whose dissipated heat at T2 is utilised by another Carnot engine B operating between T2 and T3. What is the efficiency of a third engine that operates between T1 and T3 in terms of the efficiencies hA and hB of engines A and B respectively?E10. (a) A system receives 10 Kcal of heat from a reservoir to do 15 Kcal of work. How much work must the system do to reach the initial state by an adiabatic process? (b) A certain volume of Helium at 15˚C is suddenly expanded to 8 times its volume. Calculate the change in temperature (assume that the ratio of specific heats is 5/3).E11. A spherical charge distribution has a volume density ρ, which is a function of r, the radial distance from the center of the sphere, as given below. ⎧ A / r , A is constant for 0 ≤ r ≤ R ρ= ⎨ ⎩ 0 , for r > R Determine the electric field as a function of r, for r ≥ R. Also deduce the expression for the electrostatic potential energy U(r), given that U(∞) = 0 in the region r ≥ R. 27 E12. Consider the distribution of charges as shown in the figure below. Determine the potential and field at the point p.E13. A proton of velocity 107 m/s is projected at right angles to a uniform magnetic induction field of 0.1 w/m2. How much is the path of the particle deflected from a straight line after it has traversed a distance of 1 cm? How long does it take for the proton to traverse a 900 arc? E14. (a) State the two necessary conditions under which a feedback amplifier circuit becomes an oscillator. (b) A two-stage FET phase shift oscillator is shown in the diagram below. (i) Derive an expression for the feedback factor β. (ii) Find the frequency of oscillation. (iii) Establish that the gain A must exceed 3.E15. A circular disc of radius 10cm is rotated about its own axis in a uniform magnetic field of 100 weber/m2, the magnetic field being perpendicular to the plane of the disc. Will there be any voltage developed across the disc? If so, then find the magnitude of this voltage when the speed of rotation of the disc is 1200 rpm. 28 E16. A 3-phase, 50-Hz, 500-volt, 6-pole induction motor gives an output of 50 HP at 900 rpm. The frictional and windage losses total 4 HP and the stator losses amount to 5 HP. Determine the slip, rotor copper loss, and efficiency for this load.E17. A 20 KVA, 2000/200 V two-winding transformer is to be used as an auto-transformer with a constant source voltage of 2000 V. At full load with unity power factor, calculate the power output, power transformed and power conducted. If the efficiency of the two- winding transformer at 0.7 power factor is 90%, find the efficiency of the auto-transformer.E18. An alternator on open-circuit generates 360 V at 60 Hz when the field current is 3.6 A. Neglecting saturation, determine the open- circuit e.m.f. when the frequency is 40 Hz and the field-current is 24 A.E19. A 150 KVA, 4400/440 volt single phase transformer has primary and secondary resistance and leakage reactance values as follows: Rp = 2.4 Ω, Rs = 0.026 Ω, Xp =5.8 Ω, and Xs = 0.062 Ω. This transformer is connected with a 290 KVA transformer in parallel to deliver a total load of 330 KVA at a lagging power factor of 0.8. If the first transformer alone delivers 132 KVA, calculate the equivalent resistance, leakage reactance and percentage regulation of the second transformer at this load. Assume that both the transformers have the same ratio of the respective equivalent resistance to equivalent reactance.E20. The hybrid parameters of a p-n-p junction transistor used as an amplifier in the common-emitter configuration are: hie = 800Ω, hfe = 46, hoe = 8 x 10-5 mho, hre = 55.4 x 10-4. If the load resistance is 5 kΩ and the effective source resistance is 500 Ω, calculate the voltage and current gains and the output resistance.E21. Find the equivalent resistance between the points A and D of the circuit shown in the diagram. 29 E22. (a) Design a special purpose counter to count from 6 to 15 using a decade counter. Inverter gates may be used if required. (b) For a 5 variable Boolean function the following minterms are true: (0, 2, 3, 8, 10, 11, 16, 17, 18, 24, 25 and 26). Find a minimized Boolean expression using Karnaugh map.E23. In the figure, consider that FF1 and FF2 cannot be set to a desired value by reset/preset line. The initial states of the flip-flops are unknown. Determine a sequence of inputs (x1, x2) such that the output is zero at the end of the sequence. Output 30
Course Info Intended Audience This class is designed to refresh prerequisite mathematical knowledge (analysis, linear algebra, discrete math, and probability/statistics) for graduate studies in engineering and the applied sciences. The content of this course is relevant to people in the following fields:
Prentice Hall Middle School Math 6th Grade Course 1 1 (Grade 6) covers a combination of rational numbers, patterns, geometry, and integers in preparation for one-step and two-step equations and inequalities 6 kit includes: Parent Guide Pamphlet for Homeschoolers Course 1 Textbook Course 1 6 (Course 1) Student Workbook Retail Price: $9.97 CBD Price: $8.99 ( Available to ship on or about 01/15/14. ) This Prentice Hall Student Workbook accompanies the textbook in the sold-separately Prentice Hall Mathematics Course 1 This Algebra Readiness transition course covers algebraic expressions and integers, solving one-step equations and inequalities, area and volume, and linear functions Middle-school kit includes: Parent Guide Pamphlet for Homeschoolers Algebra Readiness Textbook Algebra Readiness Algebra Readiness Student Workbook Retail Price: $9.97 CBD Price: $8.99 ( Available to ship on or about 01/07/14. ) This Prentice Hall Student Workbook accompanies the textbook in the sold-separately Prentice Hall Mathematics Algebra Readiness Course 2 TextbookPrentice Hall Middle School Math 7th Grade Course 2 2 (Grade 7) presents a structured approach to a variety of topics such as ratios, percents, equations, inequalities, geometry, graphing, and probability 7 kit includes: Parent Guide Pamphlet for Homeschoolers Course 2 Textbook Course 2 Course 2 All-in-One Student Workbook Version A Retail Price: $9.97 CBD Price: $8.99 ( In Stock ) This Prentice Hall All-in-One Student Workbook accompanies the sold-separately Prentice Hall Mathematics Course 2 Textbook. "Daily notetaking pages" provide the lesson objective, "key concepts," additional fill-in-the-blank "example" problems, and quick check problems. The practice problem pages follow the same lesson instructions as the textbook, but provide different problems for each chapter. The Guided Problem Solving pages lead students through a step-by-step solution to an application problem. Vocabulary pages contain a variety of activities to increase reading and math understanding, including graphic organizers and review puzzles. The Daily Notebooking Pages are all first (in order of lesson) and are then followed by a section with the Practice, Guiding Problem, and Vocabulary worksheets. The Practice & Guided Problem worksheets alternate in lesson order, with the vocabulary worksheets all at the end of that chapter's section. Course 2. Grade 7. Version A. 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Prentice Hall Mathematics: Algebra 1 Student Workbook Retail Price: $10.47 CBD Price: $9.49 ( In Stock ) This Prentice Hall Student Workbook accompanies the textbook in the sold-separately Prentice Hall Mathematics Algebra 1 section corresponds to a section in the text, with objectives clearly laid out. 567 perforated newsprint-like pages, softcover. Prentice Hall High School Math Geometry 10. Geometry anything 896 pages, hardcover. The workbook provides complete daily support for the lesson, 95 perforated, three-hole-punched pages, softcover. This kit includes: Parent Guide Pamphlet for Homeschoolers Geometry Textbook, 896 pages, hardcover Geometry Teacher's Edition, 860 pages, hardcover Workbook Teacher's Guide, 95 pages, softcover Student Workbook, 503 pages, softcover Prentice Hall Mathematics Geometry Student Workbook Retail Price: $10.47 CBD Price: $9.49 ( In Stock ) This Prentice Hall Student Workbook accompanies the textbook in the sold-separately Prentice Hall Mathematics Geometry TextbookPrentice Hall High School Math Algebra 2 Algebra 2 reviews key Algebra 1 concepts before moving on to traditional advanced Algebra topics; the comprehensive table of contents also allows one to easily include trigonometry, statistics, or precalculus readiness. Grade 11 Perforated, three-hole-punched pages, softcover. This workbook provides complete daily support for the lesson in the textbook (in the above-linked kit), and includes a daily note-taking 603 perforated, newsprint-like pages, softcover.
Search community continue The purpose of this unit of three lessons is to develop pattern-based thinking through the exploration of a pattern that has more than one attribute and more than one unit of repeat. This is the second of three algebra units* written specifically to support the Patterns and Relationships student e-ako pathway. The table below locates this unit relative to other relevant algebra units of work, and to the student e-ako pathway. The focus of this unit is on developing pattern-based thinking through the exploration of more complex combinations of repeating patterns. This unit of work supports the development of the content ideas in student e-ako 8 in particular.
Math Course Takes 'Real Life' Approach to Algebra Educational courseware publisher American Education Corp. is taking a new approach to answering the age-old question, "What does algebra have to do with real life?" The company has announced the release of a new course for its A+nyWhere Learning System program. Algebra I: A Function Approach Part 1 is the first semester segment of a full-year algebra course geared to grades 9 and 10, and, in addition to the fundamental concepts and tools of algebra, the course aims to relate the material to "real life." Taking the fundamentals and applying them to real-world situations using exercises in relevant scenarios allows students to realize the practical uses of linear and quadratic equations, graphs and coordinates, functions, and other algebraic concepts. The A+nyWhere program is computer based, so students taking courses like Algebra I can use a number of tools incorporated into the software to aid in their assignments and overall comprehension of the material. These tools include onscreen standard and scientific calculators, pictures and diagrams, video tutorials, exercises, practice exams, and, for upper-level courses, interactive feedback
Part of the Integrated Mathematics Scheme, this book is aimed at lower ability Year Ten students. It has four strands to the work. These are: • Food and clothes • Entertainment • The future • Science and computers The mathematics covered includes place value, plane shapes, substitution into formulae,… From the Integrated Mathematics Scheme, this book is designed for students who were likely to be taking examinations equivalent to the foundation level GCSE. The book contains 30 units, split into three sections each containing ten units. Units 1 to 10 cover: Four rules applied to fractions, applications of fractions, standard… Part of the Integrated Mathematics Scheme, this book is aimed at lower ability Year Eleven students. It has four strands to the work. These are: • The home • People and children • The community and its money • Life at work Each area of mathematics is set in a real life context. The mathematics covered… This Year Eight textbook from the Integrated Mathematics Scheme contains 30 units split into three sections each containing ten units. There are basic exercises (M units) followed by more challenging exercises (E units) covering the same topics in each file. Units 1 to 10 cover: • Use of negative numbers in coordinates,… From the Integrated Mathematics Scheme, this book is designed for students who were likely to be taking examinations equivalent to higher level GCSE. The book contains 30 units, split into three sections each containing ten units. Units 1 to 10 cover: Calculating long multiplication and long division without the use of a calculator,Finding Out About Food is an introductory textbook for food technology lessons and was written for students aged nine to fourteen. Each chapter contains a number of self-contained units and comprises experiments and practical activities, and ends with sets of questions and quizzes to reinforce understanding. Ideas are also given… These study notes were produced by the BP Educational Service in 1981. They provide information on how oil is transported from the oil fields to the refinery for processing. The resource describes pipelines, loading and unloading oil at marine terminals and the development of tankers and supertankers. The booklet also discussesThese study notes were produced by the BP Educational Service in 1981 to provide students with information on the oil industry. After a brief history of oil drilling from the eighteenth century, there is a detailed description of the development of rotary drilling from 1900 onwards with some discussion of safety precautions. The… This handbook was developed in collaboration with the BP Educational Service and the Association for Science Education. First published in 1980, the units in the book were based on work originally undertaken by physics teachers at various BP centres and demonstrate the applications of physics in industry. Each unit describes anScience to Sixteen, first published in 1980, was written as a reference book for students aged 14-16. It provides information, illustrated by full colour photographs and drawings, on a range of physics, chemistry and biology topics. At the end of each chapter there are examination level questions for students to test their understanding.
Problem Solving Approach to Mathematics for Elementary School Teachers More than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teachers since ...Show synopsisMore than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teachers since its first edition, and it remains the gold standard today. This text not only helps students learn the material by promoting active learning and developing skills and concepts--it also provides an invaluable reference to future teachers by including professional development features and discussions of today's standards. The Eleventh Edition is streamlined to keep students focused on what is most important. The Common Core State Standards (CCSS) have been integrated into the book to keep current with educational developments. The Annotated Instructor's Edition offers new Integrating Mathematics and Pedagogy (IMAP) video annotations, in addition to activity manual and e-manipulative CD annotations, to make it easier to incorporate active learning into your course. MyMathLab(R) is available to offer auto-graded exercises, course management, and classroom resources for future teachers. To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit ... com/teachingmathHide synopsisDescription:Very Good. This is a loose-leaf edition text book (same content...Very Good. This is a loose-leaf edition text book (same content, just cheaper! ! ). May not contain access card/supplementary materials. Second day shipping available, ships same or next day. GET BOMBED! ! This is the U.S. student edition as pictured
Mathematics "Today's world is more mathematical than yesterday's, and tomorrow's world will be more mathematical than today's. As computers increase in power, some parts of mathematics become less important while other parts become more important. While arithmetic proficiency may have been 'good enough' for many in the middle of the century, anyone whose mathematical skills are limited to computation has little to offer today's society that is not done better by an expensive machine." Mathematics Placement Incoming freshmen at Clarion Campus are placed into their first college mathematics course based on the high school mathematics courses and grades in addition to the SAT and ACT mathematics score. This placement is determined during the Orientation process. Incoming freshman at Venango College are given a mathematics placement exam to determine the appropriate mathematics course.
Sol Garfunkel revolutionized colleges' and universities' approaches to teaching mathematics to students with non-scientific majors with the creation of the television series "For All Practical Purposes." The textbook with the same name was the first widely accepted text in the now burgeoning field of Mathematics for the Liberal Arts. For almost three decades, Dr. Garfunkel has served as Executive Director of COMAP, a non-profit organization whose mission is to improve mathematics education for students of all ages. One of the major driving forces behind mathematics curriculum design, he has guided COMAP to develop extensive high-quality "instructional resources for innovative educators." COMAP resources include CD-ROMs, periodicals, textbooks, videos, DVDs, MCM/ICM and HiMCM Contests and numerous projects for elementary schools, high schools and undergraduate institutions. COMAP's television series "Against All Odds" has helped open up the study of statistics for the general student. In the television series "Algebra: In Simplest Terms", host Sol Garfunkel explains how algebra is used for solving real-world problems and clearly explains concepts that may baffle many students. Dr. Garfunkel will talk about "Math is Everywhere, Math is More, and the Fafuffnik-Chaim Yankel Effect."
Photocopy Master book. Students are required to utilise a range of problem solving strategies in their approach to reaching solutions for these interesting problems. Cool cartoon characters add a highly motivating element to the process of working through the problems. more... New look versions of Pythagoras, Galileo and Archimedes are some of the characters presented in cartoon form in this photocopy master book, lending a stimulating element to problem solving. A variety of brain teasers is also included for copying onto cards to make class sets. more... Sequential blackline master activities in the area of geometry and spatial mathematics. Covers the major learning areas such as identifying different types of angles, using a protractor to measure angles, using known rules to calculate the size of angles and construction of angles using either a compass or a protractor. more... Bob Miller's fail-safe methodology helps students grasp basic math and pre-algebra. All of the courses in the junior high, high school, and college mathematics curriculum require a thorough grounding in the fundamentals, principles, and techniques of basic math and pre-algebra, yet many students have difficulty grasping the necessary concepts. Utilizing... more... Everything you need to know to ace the math sections of the NEW SAT!. He's back! And this time Bob Miller is helping you tackle the math sections of the new and scarier SAT! Backed by his bestselling ''Clueless'' approach and appeal, Bob Miller's second edition of SAT Math for the Clueless once again features his renowned tips, techniques, and insider... more... Learn how to easily do quick mental math calculations Speed Math for Kids is your guide to becoming a math genius--even if you have struggled with math in the past. Believe it or not, you have the ability to perform lightning quick calculations that will astonish your friends, family, and teachers. You'll be able to master your multiplication tablesFlummoxed by formulas? Queasy about equations? Perturbed by pi? Now you can stop cursing over calculus and start cackling over Math, the newest volume in Bill Robertson's accurate but amusing Stop Faking It! best sellers. As Robertson sees it, too many people view mathematics as a set of rules to be followed, procedures to memorize, and theorems... more... Blending theoretical constructs and practical considerations, the book presents papers from the latest conference of the ICTMA, beginning with the basics (Why are models necessary? Where can we find them?) and moving through intricate concepts of how students perceive math, how instructors teach-and how both can become better learners. Dispatches as... more...
With over 300 illustrations, 300 miniprograms, and many examples, this textbook explains the classical theory of curves and surfaces, how to define and compute standard geometric functions, and how to apply techniques from analysis. It highlights important theorems and alleviates the drudgery of computations such as the curvature and torsion of a curve in space.
+ By Loughborough University "Want to pass that math exam?" Study with the help of this app and start understanding everything about maths Mathscard a-level is an Android application created by Loughborough University that includes many examples of math formulas and graphs that will help students study and review for their exams. This is appropriate for AS and A2 math level and for using it you just need to tap on the subject you want to read about and navigate through the content (Vectors, Numerical methods, Circle & Coordinate geometry and some more). In addition, there's also an index with all the contents included in the app in case you want to look through it and decide depending on your mood. This tool is very useful for students and people who enjoy maths and want to review their knowledge. The design is great, the interface is clean and easy to use and there are no bugs, apparently. If you were looking for a tool that helped you study maths, this will be the perfect choice. Developed by Loughborough University, the mathscard app contains hundreds of examples of pure maths formulae and graphs/diagrams. Designed specifically for AS and A2 Level maths, the mathscard app is based on the hugely successful award-winning mathscard fold-out formulae sheet and is designed to help students with their exam revision when at home or on the move. Vectors, numerical methods, circle and coordinate geometry, sequences and series, algebra and graphs, trigonometry and calculus are all covered in this handy resource. Useful content. However, titles on start screen fail to display properly. This is a key part of the app and needs fixing right away! (72) by A Google User on 25/11/2012 Has many integration formulas, tips, and tricks. Some of which you may not know. I'm a diff eq student and even I learned some new things! Only issue is that the chapter and names of sections don't display text, at the start screen, so I have to guess wha (72) by thaslima on 25/10/2011 It covers everything, but I think 5MB too much. (72) by LuAnn on 06/07/2011 Great review. You have to have a good grasp of the functions in order to understand it tho. (72) by Etienne on 06/04/2011 For no reason at all, there are TWO home buttons on the 'more' menu. But clean, easy and professional to the standard of excellence. HTC Wildfire
Tagged QuestionsI am 21 and have got into computer programming. Doing very well in my degree. Would love to get into computer science but feel I am being held back by my basic knowledge of maths. I got an A at GCSE,I am a self learner. The problem I have is that I usually have a problem finding good sources to learn mathematics. Wikipedia is sort of good, but it usually just defines specific terms from a field tried Google but there isn't much information on this and I would really like some insights into actuarial studies, the mathematics involved and how it compars to the mathematics in a bachelor of ... I took a rather disappointing multivariable calculus course this semester -- the (visiting) professor was not demanding at all. We didn't get to what is in most standard calculus III curriculum. WhatI am trying to find only journals or trustworthy magazines which can help math students to study math more efficiently and productively. I am not asking about books in this thread. In particular, I am ... I just jumped into a project related to an estimation algorithm. It needs to build measures between two distributions. I found a lot of papers in this field required a general idea from differential'm looking for a somewhat sequential list of books to learn math beyond calculus at home. I've taken calc 3 and am going further but I'm having a lot of trouble nailing down a real order of things ...
More About This Book Be rational - follow easy-to-grasp instructions for working with rational and radical equations, from dealing with negative exponents to fiddling with fractional exponents Know your functions - discover how to use exponential and logarithmic functions to solve algebraic
Notebook. Undergraduate mathematics notes. Including "On the symmetrical form of the equation of the parabola" "On some expressions for the area of a triangle" etc. Creator: John Couch Adams, 1819-1892. 68 leaves; paper.
David Cohen's PRECALCULUS, WITH UNIT-CIRCLE TRIGONOMETRY, Fourth Edition, focuses on teaching mathematics, using a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. The author is known for his clear writing style and the numerous quality exercises and applications he includes in his respected texts. In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greater emphasis. Many sections now contain more examples and exercises involving app... MORElications and real-life data. While this edition takes the existence of the graphing calculator for granted, the material is arranged so that one can teach the course with as much or as little graphing utility work as he/she wishes.
books.google.com - After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime.... Relativity
Mathematics Of Voting And Elections A Hands-on Approach 9780821837986 ISBN: 0821837982 Pub Date: 2005 Publisher: American Mathematical Society Summary: The results of an election depend not just upon the wishes of the electorate, but also upon the mathematics used to calculate the result. Using numerous case studies & featuring discussions of actual elections from the perspectives of both politics & popular culture, this text explores vote counting systems. Hodge, Jonathan K. is the author of Mathematics Of Voting And Elections A Hands-on Approach, publishe...d 2005 under ISBN 9780821837986 and 0821837982. One hundred six Mathematics Of Voting And Elections A Hands-on Approach textbooks are available for sale on ValoreBooks.com, five used from the cheapest price of $21.83, or buy new starting at $48.08
This Student Solution Manual provides complete solutions to all the odd-numbered problems in Foundation Mathematics for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to arrive at the correct answer and improve their problem-solving skills.This Student Solution Manual provides complete solutions to all the odd-numbered problems in Essential Mathematical Methods for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to select an appropriate method, improving their problem-solving skills. Student SolutionManual for Essential Mathematical Methods for the Physical SciencesEnglish \| ... : 0521141028 \| 251 pages \| PDF \| 1.8 mbThis Student SolutionManual provides complete solutions to all the odd-numbered ... -step, so they can clearly see how the solution is reached, and understand any mistakes in their ... Solution Manual of Principles of Geotechnical Engineering by BM DasSolution Manual of Principles of Geotechnical Engineering by BM Das \| Size : 7.85 MB Description this is the Solution Manual of Principles of Geotechnical Engineering by BM Das More books and lectures coming soon SolutionManual of Principles of Geotechnical Engineering by BM Das SolutionManual of Principles of Geotechnical Engineering by BM Das \| Size : 7.85 MBDescriptionthis is the SolutionManual of ... do seed the torrents so that it is shared with everyone else... more books and lectures will be uploaded soon... SolutionManual Of Advanced Engineering Mathematics By Erwin Kreyszig SolutionManual Of Advanced Engineering Mathematics By Erwin Kreyszig \| Size : 15.24 MB DescriptionThis is the solutionmanual to ... Now readers can get all the accuracy and authority of the best-selling intermediate accounting book in the new second edition of this brief, streamlined version! Fundamentals of Intermediate Accounting presents a balanced discussion of concepts and applications, explaining the rationale behind business transactions before addressing the accounting and reporting for those activities. Readers will gain a solid foundation in such areas as the standard-setting process, the three major financial statements, revenue recognition, income taxes, reporting disclosure issues, and much more. IntermediateAccounting - Principles and Analysis, 2nd EditionPublisher: W.l.y \| ... best-selling intermediateaccounting book in the new second edition of this brief, streamlined version! Fundamentals of IntermediateAccounting presents ... the rationale behind business transactions before addressing the accounting and reporting for those activities. Readers will gain ... From one of the premier authors in higher education comes a new linear algebra textbook that fosters mathematical thinking, problem-solving abilities, and exposure to real-world applications. Without From Contents: Vectors Systems of Linear Equations * Matrices and Matrix Algebra * Determinants * Matrix Models * Linear Transformations * Dimension and Structure * Diagonalizations * General Vector Spaces Appendix A: How to Read Theorems Appendix B: Complex Numbers
Basic College Mathematics - 4th edition Summary: Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Basic College Mathematics, Fourth Edition was written to help readers effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success50.4593799597 +$3.99 s/h New Balkanika Online WA Woodinville, WA PAPERBACK New 0321649400
Dijkstra's algorithm finds the shortest path for a given problem. Dijkstra's algorithm can be used to find the shortest route between two cities. This algorithm is so powerful that it not only finds the shortest path from a chosen source to a given destination, it also finds all of the shortest paths from the source to… Critical path analysis is a project management technique and is used to lay out all of the activities which are needed to complete a task. Starting some activities will depend on completing others first, while independent activities can be started any time. Critical path analysis helps to predict the project completion time. The… The purpose of bin packing is to pack a collection of objects into containers called bins. The bins are all the same size and the objects to be packed are different sizes. The aim is to pack the objects into the bins using the fewest possible bins. In this example students are asked to save computer files onto a CD. Bin packing:These resources commisioned by the Qualifications and Curriculum Agency (QCDA) are to support the linked pair of mathematics GCSEs piloted from September 2010, which were developed in response to Professor Adrian Smith's inquiry into post-14 mathematics education in 2004. Together they assess the National Curriculum mathematics…
Beginning Algebra - With CD - 5th edition Summary: KEY MESSAGE:Elayn Martin-Gay'sdevelopmental math textbooks and video resources are motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes greatly to the popularity and effectiveness of her video resources. This revision of Martin-Gay's algebra series continues this focus on students and what they need to be successful. Martin-Gay also strives t...show moreo provide the highest level of instructor and adjunct support. Review of Real Numbers; Equations, Inequalities, and Problem Solving; Graphing; Solving Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Roots and Radicals; Quadratic Equations For all readers interested in algebra, and for all readers interested in learning or revisiting essential skills in beginning algebra through the use of lively and up-to-date applications. ...show less, A FADED STAIN ON MOST OF THE PAGES AND A LITTLE WRINKLEDellBackYourBook Aurora, IL 0136007023
ASSE09-12.02 021, 2, 3 Domain: Arithmetic with Polynomials and Rational Expressions (AAPR) Learning Standards: Perform arithmetic operations on polynomials. Test Questions AAPR09-12.01 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication: add, subtract, and multiply polynomials. 45, 46, 47, 48 Learning Standards: Understand the relationship between zeros and factors of polynomials. Test Questions AAPR09-12.02 53, 55 AAPR09-12.03 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. 8, 9, 10, 18, 19, 54, 56, 57, 58 Learning Standards: Rewrite rational expressions. Test Questions AAPR09-12.06 ACED09-12.01 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 21, 36, 37, 44 ACED09-12.02 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 15, 39 ACED09-12.03 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 38, 40, 41, 42, 43 Domain: Interpeting Functions (FIF) Learning Standards: Interpret functions that arise in applications in terms of the context. Test Questions FIF09-12.0413, 17 FIF09-12.05 11, 12, 20, 27 Learning Standard: Analyze functions using different representations. Test Questions FIF09-12.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 22, 28, 29 FIF09-12.0914, 16 Domain: Building Functions (FBF) Learning Standards: Build a function that models a relationship between two quantities. Test Questions FBF09-12.01 Write a function that describes a relationship between two quantities.★ Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 33, 34, 35 Learning Standards: Build new functions from existing functions. Test Questions FBF09-12.03 Identify the effect on the graph of replacing f(x) by f(x) + k, kf
Prealgebra and Introductory Algebra (Paper) - 3rd edition Summary: Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Prealgebra& Introductory Algebra, Third Edition was written to help students effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for successBuy with Confidence. Excellent Customer Support. We ship from multiple US locations. No CD, DVD or Access Code Included. $89.97 +$3.99 s/h LikeNew Nivea Books Lynnwood, WA PAPERBACK Fine 0321644905
ADVANCED PLACEMENT STATISTICS Course Design Statistics is unlike any math course students have taken in their high school careers. Coming up with a numerical solution ... Statistic Syllabus.pdf AP Statistics Course Design Our AP Statistics course is designed as an activity-based mathematics course. Our school offers open enrollment into AP courses and the ... Psychology 240: Statistics in Psychology Summer session 2009: University of Massachusetts, Amherst Overview: This course is designed to provide you with a conceptual ... AP STATISTICS SYLLABUS Course Design The purpose of this AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing ... STATISTICS syllabus.pdf 326 Chapter Number and Title A.N. KOLMOGOROV General Laws of Probability There are national styles in science as well as in cuisine. Statistics, the science of data ... 1. In a strong man contest, the contestants must pull a car up an incline 13 feet long. Joe is the first contestant. With every tug, Joe pulls the car up the incline 3 ... 2 Learning Outcomes After you have successfully worked your way through the recommended study materials, you should be able to: explore ... Preface PASSING THE MINNESOTA BASIC SKILLS TEST IN MATHEMATICS will help students preparing for this mathematics test. This book will also assist students who have ...
Find a Sugar Hill, GA Algebra 1This algebra deals mostly with linear functions. Algebra 2 is a more advanced, more complex version of algebra 1. Here we get more involved with non-linear functions as well as imaginary and complex numbers.However since not everyone is starting from the same knowledge point they may need help developing the necessary basics. We will review the teachers methods to better understand them. If those are not clear, we will explore other methods so it makes sense to you.
Riemann Sum Approximations. Volumes by the Method of Cross Sections. Volumes by the Method of Cylindrical Shells. Arc Length and Surface Area of Revolution. Force and Work. Centroids of Plane Regions and Curves. The Natural Logarithm as an Integral. Inverse Trigonometric Functions. Hyperbolic Functions. Introduction. Infinite Sequences. Infinite Series and Convergence. Taylor Series and Taylor Polynomials. The Integral Test. Comparison Tests for Positive-Term Series. Alternating Series and Absolute Convergence. Power Series. Power Series Computations. Series Solutions of Differential Equations. 11. Vectors, Curves, and Surfaces in Space. Vectors in the Plane. Three-Dimensional Vectors. The Cross Product of Vectors. Lines and Planes in Space. Curves and Motion in Space. Curvature and Acceleration. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates
Visual Mathematics Series: Intermediate Geometry Problems The problems in this book are suggested for evaluating the concepts taught in the intermediate geometry class. The problems are of a highly visual ...Show synopsisThe problems in this book are suggested for evaluating the concepts taught in the intermediate geometry class. The problems are of a highly visual nature and meant to be challenging. The problems are designed to lead to a merging of geometry and art at the middle school level. The problems presented in this book include: Visual problems to determine area of various iterative polygon based shapes Visual representation of solid objects to determine their volume Visual medley of circles, squares, and triangles to determine their relationships Determining properties of angles, triangles, square, and rhombus Visual problems for determining equivalence of geometric properties of polygonal shapes Determination of area of objects using reference objects as basic elements Visual representations of lines and triangles to solve problems based on equations Identifying intersection points for an underlying visual diagram Application of Pythagorean Theorem to problems represented visually Applications of factorization and LCM to problems on area and volume Changes to area of triangles based on various construction techniques Inferences for area or angle measures of unknown elements in constructed diagrams
Summary: Also available as a two-volume set, this text is intended to give students depth and perspective in their knowledge of the mathematics taught in elementary school. The author believes that some key elements in achieving this depth and perspective are for students to write clear, logical explanations, for students to enhance their intuition by working with examples and by looking for patterns and connections, and for students to use mathematics in a variety of applica...show moretions. The book is centered around "class activities," which are designed for students to work on in class in small groups. The class activities foster engagement, exploration and discussion of the material, rather than passive absorption. Many exercises and problems are included at the end of each chapter. Working on these exercises and problems and justifying their solutions carefully and clearly is crucial to achieving depth of understanding of the material. Both students and instructors should find this material fun, interesting, and rewarding. ...show less The Concept of Measurement. Measurable Attributes. Converting From One Unit of Measurement to Another. The Moving and Combining Principles About Area. The Pythagorean Theorem. More Ways to Determine Areas. Areas of Triangles. Areas of Parallelograms. Areas of Circles and the Number Pi. How are Perimeter and Area Related? Principles for Determining Volumes. Volumes of Prisms, Cylinders, Pyramids, and Cones. Areas, Volumes, and Scaling. 4. Functions and Algebra. Patterns, Sequences, Formulas, and Equations. Functions. 5. Statistics. Designing Investigations and Gathering Data. Displaying Data. The Center of Data: Average and Median. The Spread of Data: Percentiles, Range. 6. Probability. Some Basic Principles of Probability. Fraction Multiplication and Probability. Appendix A: Cutouts for Exercises and Problems. List Price: $76.00 Used Currently Sold Out New $6.99 Save $69.01 (91%) FREE shipping over $25 In stock 30-day returns Condition: Brand New Order this book in the next 2 days, 14 hours and 49
Learning to use set notation in algebra means mastering the few symbols and understanding what each represents. Even without realizing it, you already think of things in sets. A baseball team is a set of players in which each player is an element or... More »
Ideas from Classroom Teachers for Functions See Navigating Through Algebra: Grades 9-12 (NCTM) for real-world types of activities for this topic. Students need practice determining domain and range of step functions by looking at their graphs. Finding the domain of a composite function can be difficult. The domain cannot always be determined by the simplified equation of the composite function. Students should consider various representations of functions: algebraic (as equations), graphical, numerical (e.g., in tabular form), and verbal. Relations that are not functions should also be considered. Students should graph functions, explore and discuss the behavior they see, and come to conclusions. There are many such activities in Algebra in a Technological World (NCTM, 1995). Students should investigate graphs of functions and their inverses to discover properties. Function composition can be difficult for students. On the one hand, they may see the results better by using more complicated functions, but on the other, they seem to be less intimidated if we start with composing simpler ones (like a linear function with a constant function). Inverses will be important as students learn how to solve different types of equations. I am assuming that at this point in the course students are familiar with the different types of functions. Depending on mathematics background, students at this level should be able to recognize graphs of standard functions: identity, squaring, cubing, reciprocal, square root, exponential, logarithmic, sine, cosine, absolute value, and greatest integer functions. A common theme throughout this year is how the study of algebraic functions is necessary to provide models for real-world situations. Investigations often begin with a set of data. If those data can be fit into an algebraic model, useful predictions can be made. I take 3-4 days to introduce the basic function families. Students should be able to match a function with its graph and vice versa. We then define intercepts, maxima, and minima. (You may distinguish between absolute extrema and local extrema of a function, as well as extrema on a closed interval.) Domain and range are included in the discussions of the parent function and in the identification of extrema. I spend another 3-5 days on composition of functions; this leads into discussion of inverse function from a chart, from a graph, or from a formula. Ask students to determine from the original function whether its inverse will also be a function. On inverse functions: Emphasis should be placed on illustrating inverses in numerical form (switch x and y in ordered pairs), algebraic form (switch x and y in the equation), and graphical form (reflection over y = x line). Also the definition of inverses relative to composition should be emphasized to illustrate why some functions are inverses (y = x^3 and y = x^(1/3)) and why some are not (y = x^2 and y = x^(1/2)), even though powers and roots are treated as inverse operations when solving equations.
I don't think you will find that a big problem. None of the main ideas of the book require any mathematical knowledge. Some of the examples are mathematical in nature. For instance, there is about twelve pages in chapter 6 that concerns using an infinite list object to represent a sequence of increasingly accurate approximations to the solution of a certain financial problem. People who have studied calculus will immediately understand the ideas here; people who haven't might understand them anyway, and even if you don't you can always skip those examples; most of them have nothing in particular to do with math. My own tendency is to write a lot of math stuff, because I find it very interesting, but while I was writing HOP I tried really hard to get rid of the mathematics, because I knew that a lot of people don't like
Discrete Mathematics 9780131593183 ISBN: 0131593188 Edition: 7 Pub Date: 2008 Publisher: Prentice Hall Summary: This textbook provides an accessible introduction to discrete mathematics, using an algorithmic approach that focuses on problem-solving techniques. Each chapter has a special section dedicated to showing students how to attack and solve problems. Johnsonbaugh, Richard is the author of Discrete Mathematics, published 2008 under ISBN 9780131593183 and 0131593188. Five hundred fifty seven Discrete Mathematics ...textbooks are available for sale on ValoreBooks.com, one hundred thirteen used from the cheapest price of $76.30, or buy new starting at $90 This is a Brand New Softcover International 7th edition textbook (Textbook only), which... [more] 7th edition textbook (Textbook only), which has virtually the same English content as the corresponding US edition. The m [more]
Description: Make math matter to students in all grades using Math Tutor: Algebra Skills! This 80-page book provides step-by-step instructions of the most common math concepts and includes practice exercises, reviews, and vocabulary definitions. The book covers factoring, exponents, variables, linear equations, and polynomials. It aligns with state, national, and Canadian provincial
CCSS Integrated Pathway: Mathematics I The CCSS Integrated Pathway: Mathematics I program is a complete set of materials built from the ground up to align 100% to the CCSS Integrated Pathway curriculum map and utilizes the 8 CCSS mathematical practices. This course is designed to empower teachers by equipping them with high quality, flexible materials for successfully teaching Integrated Pathway Math to all types of learners.
Elementary Algebra for CollegeToday's students are visual learners, and Angel/Runde offers a visual presentation to help them succeed in math. Visual examples and diagrams are used to explain concepts and procedures. New Understanding Algebra boxes and an innovative color coding system for variables and notation keep students focused. Short, clear sentences reinforce the presentation of each topic and help students overcome language barriers to learn math. TheAngel Developmental Algebra Seriesaddresses the needs of today's visual learners. In t... MOREhis new edition, students are introduced to key concepts by charts, diagrams, and the use of color in variables and notations to clearly illustrate the solution process. To further enhance this visual approach, the new Understanding Algebra feature has been added to make important points more identifiable and accessible. Real Numbers; Solving Linear Equations and Inequalities; Applications of Algebra; Exponents and Polynomials; Factoring; Rational Expressions and Equations; Graphing Linear Equations; Systems of Linear Equations; Roots and Radicals; Quadratic Equations For all readers interested in algebra. The Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight the variables and important notation to clearly illustrate the solution process. 2.4 Solving Linear Equations with a Variable on Only One Side of the Equation 2.5 Solving Linear Equations with the Variable on Both Sides of the Equation 2.6 Formulas 2.7 Ratios and Proportions 2.8 Inequalities in One Variable 3. Applications of Algebra 3.1 Changing Application Problems into Equations 3.2 Solving Application Problems 3.3 Geometric Problems 3.4 Motion, Money, and Mixture Problems 4. Exponents and Polynomials 4.1 Exponents 4.2 Negative Exponents 4.3 Scientific Notation 4.4 Addition and Subtraction of Polynomials 4.5 Multiplication of Polynomials 4.6 Division of Polynomials 5. Factoring 5.1 Factoring a Monomial from a Polynomial 5.2 Factoring by Grouping 5.3 Factoring Trinomials of the Form ax² + bx + c, a =1 5.4 Factoring Trinomials of the Form ax² + bx + c, a ≠1 5.5 Special Factoring Formulas and a General Review of Factoring 5.6 Solving Quadratic Equations Using Factoring 5.7 Applications of Quadratic Equations 6. Rational Expressions and Equations 6.1 Simplifying Rational Expressions 6.2 Multiplication and Division of Rational Expressions 6.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator 6.4 Addition and Subtraction of Rational Expressions 6.5 Complex Fractions 6.6 Solving Rational Equations 6.7 Rational Equations: Applications and Problem Solving 6.8 Variation 7. Graphing Linear Equations 7.1 The Cartesian Coordinate System and Linear Equations in Two Variables 7.2 Graphing Linear Equations 7.3 Slope of a Line 7.4 Slope-Intercept and Point-Slope Forms of a Linear Equation 7.5 Graphing Linear Inequalities 7.6 Functions 8. Systems of Linear Equations 8.1 Solving Systems of Equations Graphically 8.2 Solving Systems of Equations by Substitution 8.3 Solving Systems of Equations by the Addition Method 8.4 Systems of Equations: Applications and Problem Solving 8.5 Solving Systems of Linear Inequalities 9. Roots and Radicals 9.1 Evaluating Square Roots 9.2 Simplifying Square Roots 9.3 Adding, Subtracting, and Multiplying Square Roots 9.4 Dividing Square Roots 9.5 Solving Radical Equations 9.6 Radicals: Applications and Problem Solving 9.7 Higher Roots and Rational Exponents 10. Quadratic Equations 10.1 The Square Root Property 10.2 Solving Quadratic Equations by Completing the Square 10.3 Solving Quadratic Equations by the Quadratic Formula 10.4 Graphing Quadratic Equations 10.5 Complex Numbers Allen R. Angel received his AAS in Electrical Technology from New York City Community College. He then received his BS in Physics and his MS in Mathematics from SUNY at New Paltz, and he took additional graduate work at Rutgers University. He is Professor Emeritus at Monroe Community College in Rochester, New York where he served for many years as the chair of the Mathematics Department. He also served as the Assistant Director of the National Science Foundation Summer Institutes at Rutgers University from 1967–73. He served as the President of the New York State Mathematics Association of Two Year Colleges (NYSMATYC) and the Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). He is the recipient of many awards including a number of NISOD Excellence in Teaching Awards, NYSMATYC's Outstanding Contributions to Mathematics Education Award, and AMATYC's President Award. Allen enjoy tennis, worldwide travel, and visiting with his children and granddaughter. Dennis Runde received his BS and MS in mathematics from the University of Wisconsin—Platteville and Milwaukee, respectively. He has a PhD in Mathematics Education from the University of South Florida. He has been teaching for twenty years at State College of Florida, Manatee, and Sarasota Counties and for ten years at Saint Stephen's Episcopal School. Besides coaching little league baseball, his other interests include history, politics, fishing, canoeing, and cooking. He and his wife Kristin stay busy keeping up with their three sons–Alex, Nick, and Max.
Figures: Listening to Learners of Mathematics at Secondary School and Above This book is firmly based on listening to people in secondary schools and beyond as they go about discovering, learning and doing mathematics. ...Show synopsisThis book is firmly based on listening to people in secondary schools and beyond as they go about discovering, learning and doing mathematics. Chapters report on what is gained by listening to school students, undergraduates and adult learners. Sometimes the listening is informal; sometimes it is based on mathematics lessons or interviews. The accounts are used as models on which to base discussion of issues about mathematical understanding and about the views held about mathematics and approaches to
Rick Durrett's Home Page - Rick Durrett Research in the general area of probability theory, and more specifically in stochastic spatial models and their applications to ecology and genetics. Publications organized into books and papers, as well as s3 (stochastic spatial simulator) and stochastic ...more>> ROSSMANCHANCE.COM - Allan J. Rossman & Beth L. Chance Workshops and presentations, publications, and current projects by the authors of the Workshop Mathematics Project textbooks. See tables of contents, instructor guides, sample syllabi and exams, and answers to activities from books in the Workshop Statistics ...more>> Sara Billey Sara Billey researches combinatorics, algebra, Lie theory, algebraic geometry and probability. Her papers on these topics may be downloaded in PostScript or gzipped PostScript format. The syllabi and problem sets for her undergraduate courses, i.e. ...more>> Scheduling Random Walks - Ivars Peterson (MathTrek) Among networked computers, some sort of software scheduler must regulate data flow, but proving that a given scheduler not only prevents conflicts but also performs its duties efficiently can be surprisingly difficult. Computer scientists have found that The SELECT Math Project - Boston Public Schools The SELECT (Supporting Engaged Learning by Enhancing Curriculum with Technology) Math Project is a Boston Public Schools resource that features over 200 links to web-based virtual manipulatives and resources that directly support the mathematics curriculum ...more>> Shack's Math Problems - Michael Shackleford Pages of math problems ranging from basic math to differential equations. Each problem comes with a difficulty rating from one to four stars, roughly a measure of how much time it took Shackleford to do the problem. Includes answers and, usually, solutions. ...more>> Shai Simonson Shai Simonson is an associate professor of computer science and mathematics at Stonehill College. The site contains the article "How to Read Mathematics," which uses the probability of two people having the same birthday as an example. The site also ...more>> SIMMS IM LEVEL I - Research Project Help - T. DeBuff High School freshman-level integrated mathematics research projects, to be used with the Systemic Initiative for Montana Mathematics and Science Integrated Math (SIMMS IM), curriculum Level I. View project descriptions and find links to sites that will ...more>> Simple Math Problems - Ki Woo Song Selected math problems from a variety of sources. Solutions may either be requested via e-mail or looked up from the source (references to articles are provided.) Topics include algebraic expressions; probability; physics, geometry, proofs, and brain ... ...more>> Snow Day Calculator - David Sukhin Enter a ZIP code and number of school days already canceled there due to inclement weather, and the Snow Day Calculator predicts the probability of an early dismissal or no school the following day. Sukhin originally developed his predictive calculator ...more>> Software for mathematics education - Piet van Blokland Software for mathematical education that draws on David Tall's philosophy of teaching: use Graphic Calculus to visualize, explore, and conceptualize the graph of a linear function; analyze the data and simulations included with VUStat to learn statistics ...more>> Solid Gold Gnarly Math A Windows-compatible CD-ROM for kids, homeschoolers, parents, and teachers, designed to teach algebra, geometry, numbers, trigonometry, topology, and probability. It contains games, magic tricks, and other fun things, along with a Math Lab where kids ...more>> Stephen P. Booth A researcher working in physics and parallel computing. Articles and source -- code for random number generation (parallel generation and a generic Fortran-90 interface), and the xmountains program, which uses fractals to generate computer images of landscape. ...more>>
Math The Mathematics curriculum is presented in a combination of "block" classes and "track" classes. Block classes take place daily for a 3 to 4 week period. Block classes are required, offered by grade, and are geared toward the particular developmental stage of the students. Track classes are year-long classes which meet between two and five days each week. Students choose from the track class offerings to complete their graduation requirements and create an individualized path of study. High Mowing also offers Individualized math tutoring for those with different learning styles or particular challenges
Math All Math courses are offered at the basic, intermediate, and honors levels. Math Algebra I Geometry Algebra II Algebra II with Trigonometry Pre-Calculus Introduction to Calculus Course Descriptions Algebra I This full-year Algebra I course is in accordance with the Massachusetts Frameworks. The course focuses on the standard topics of algebra: signed numbers, exponents and roots, linear equations/inequalities, polynomials and scientific notation. It also develops strategies for problem-solving and checking answers. Practice with multiple choice, short-answer, and open-response questions reinforce and maintain standardized test-talking skills. Basic statistics and probability will be introduced. Algebra II This full-year Algebra II course is in accordance with the Massachusetts Frameworks and is a continuation of the algebraic concepts covered in Algebra I. The course focuses on the standard topics of algebra II: linear equations and functions, systems of linear equations, inequalities and absolute value, quadratic functions and factoring, imaginary numbers, polynomials expressions, and rational expressions. It also develops strategies for problem-solving, and checking answers. Practice with multiple choice, short-answer, and open-response questions reinforce and maintain standardized test-talking skills. Algebra II with Trigonometry This full-year course is a continuation of the algebraic concepts from Algebra I and Algebra II. It will emphasize the connection between algebra and geometry and introduce trigonometry. The focus of this course is polynomials, exponential/logarithmic functions, trigonometric functions and trigonometric identities. Geometry This full year geometry course is in accordance with the Massachusetts Frameworks. It includes topics such as formal proofs, measurements of angles, congruence of triangles, and parallelism. Other topics covered are polygons, ratio and proportion, and area. Students will learn to recognize when to apply theorems and postulates while problem solving. Pre-Calculus This full-year Pre-Calculus course is in accordance with the Massachusetts Frameworks. The course focuses on the standard topics of pre-calculus: basics of functions, polynomial and rational functions, exponential and logarithmic functions, trigonometry, and sequences and series. It also develops strategies for problem-solving and checking answers. Practice with multiple choice, short-answer, and open-response questions reinforce and maintain standardized test-talking skills. Introduction to Calculus This full year Introductory Calculus course is in accordance with the Massachusetts Frameworks. The course focuses on the standard topics of the preliminary topics of calculus: "basics of trigonometry", "functions, limits, and the derivative", "differentiation", "logarithmic functions", and "integration". It also develops strategies for problem solving and checking answers. Practice with multiple choice, short answer, and open response questions reinforce and maintain standardized test talking skills. Essex Agricultural and Technical High School admits students and makes available to them its advantages, privileges and courses of study without regard to race, color, sex, gender identity, religion, national origin, sexual orientation, disability, or home status.
Miami Dade College MAC 1147 Pre Calculus Algebra & Trigonometry Course Description This course is primarily designed for students who expect to take one or more courses in the calculus sequence. The student will analyze and graph algebraic, exponential, logarithmic, piecewise-defined functions and conic sections. The student will solve polynomial, exponential and logarithmic equations, as well as systems of linear and nonlinear equations. The student will identify arithmetic and geometric sequences and series and solve related problems. The student will use the Binomial Theorem to expand polynomials and solve related problems. The student will use mathematical induction to prove statements regarding the properties of natural numbers. The student will analyze and graph trigonometric functions and inverse trigonometric functions. The student will learn and use the fundamental trigonometric identities and solve conditional trigonometric equations. The student will solve both right and oblique triangles. The student will perform operations on complex numbers in trigonometric form, work with vectors, and graph both polar and parametric equations. The student will solve applications and modeling problems related to the above topics. (5 hrs. lecture) Pre-requisite: MAC 1105 with a grade of C or better or equivalent Course Competencies: Competency 1: The student will demonstrate an understanding of polynomial functions by a. analyzing the graph of a polynomial function, its behavior near its zeros and its end behavior. b. using the appropriate theorems of polynomials to factor a polynomial function and find all its zeros. c. stating the Fundamental Theorem of Algebra. d. using appropriate rules or theorems to determine the existence, location and classification of the zeros of a polynomial function. e. using the appropriate theorems of polynomials to build a polynomial function given its zeros or its graph. f. graphing polynomial functions. Competency 2: The student will explore other algebraic functions by a. graphing transformations of a function given its graph or its equation. b. graphing piecewise functions that include nonlinear pieces. c. constructing and graphing functions that model real life applications and solving related problems. Competency 3: The student will demonstrate an understanding of the conic sections by a. identifying them as the result of intersecting a plane with a cone. b. writing an equation for a parabola, ellipse or hyperbola in standard form given sufficient information about the conic. c. graphing a parabola, ellipse or hyperbola in standard form given sufficient information about the conic or given its equation. d. solving application problems involving parabolas, ellipses, and hyperbolas. Competency 4: The student will demonstrate an understanding of sequences and series by a. defining sequences by using the general term or a recursive formula. b. classifying sequences as arithmetic, geometric or neither. c. adding the first n terms of a geometric or arithmetic sequence. d. using the summation notation properties to express and evaluate sums. e. finding the sum of a geometric series if it exists. f. proving a given statement is true using the principle of mathematical induction. g. solving application problems involving sequences. Competency 5: The student will apply the Binomial Theorem a. to expand powers of a binomial. b. to find a particular coefficient or term. Competency 6: The student will demonstrate an understanding of systems of equations by a. solving systems of three or more linear equations using matrices. b. solving systems of two nonlinear equations with two variables graphically and/or algebraically. Competency 7: The student will demonstrate an understanding of exponential and logarithmic functions by a. identifying the domain of logarithmic and exponential functions. b. graphing logarithmic and exponential functions using transformations. c. solving equations involving logarithmic and exponential functions. d. using mathematical modeling to solve applications of logarithmic and exponential functions. Competency 8: The student will demonstrate an understanding of rational functions by a. graphing rational functions which have asymptotes including vertical, horizontal and oblique. b. analyzing the behavior of the graph of a rational function about a point of discontinuity. c. analyzing the end behavior of the graph of a rational function in which the degree of the numerator is greater than the degree of the denominator plus one. Competency 9: The student will demonstrate an understanding of the trigonometric functions by a. defining the functions in three different ways: as ratios of sides of a right triangle, as functions of an angle in standard position in a Cartesian plane, and as functions of a real number, as represented by an arc length along the unit circle. b. graphing the trigonometric functions, and their transformations. c. finding approximate values of the trigonometric functions using a calculator. d. finding exact values of trigonometric functions of multiples of 30º or 45º and their radian equivalents. Competency 10: The student will demonstrate an understanding of inverse trigonometric functions by a. defining the inverse trigonometric functions and stating their domains and ranges. b. evaluating inverse trigonometric functions both with and without a calculator. Competency 11: The student will demonstrate an understanding of trigonometric identities by a. simplifying trigonometric expressions. b. finding exact values of trigonometric functions of sums and differences of angles and half-angles. c. proving trigonometric identities. Competency 12: The student will demonstrate an ability to solve conditional trigonometric equations by a. finding all solutions on a specified interval. b. finding all real number solutions. c. using identities to solve equations. Competency 13: The student will demonstrate an ability to solve triangles by a. solving right triangles. b. solving oblique triangles using the Law of Sines or the Law of Cosines. Competency 14: The student will demonstrate an understanding of complex numbers in trigonometric form by a. converting a complex number from standard (a + bi) form to trigonometric form, and vice versa. b. multiplying and dividing complex numbers in trigonometric form c. raising complex numbers to positive integer powers using DeMoivre's Theorem d. finding the n complex nth roots of a complex number Competency 15: The student will demonstrate an understanding of vectors by a. adding vectors geometrically. b. resolving vectors into components. c. adding vectors algebraically, both in component form and when expressed as linear combinations of the standard basis. Competency 16: The student will demonstrate an understanding of parametric equations by a. sketching the graphs of curves defined parametrically. b. eliminating the parameter to find a corresponding rectangular equation. Competency 17: The student will demonstrate an understanding of polar coordinates by a. converting from rectangular coordinates to polar coordinates and vice versa. b. transforming rectangular equations into polar equations and vice versa c. graphing polar equations. Competency 18: The student will demonstrate an understanding of applications of trigonometry by solving problems including, but not limited to a. arc lengths and areas of circular sectors. b. right triangles. c. oblique triangles. d. vectors
Download "Elementary Algebra Exercise Book I" by Wenlong Wang, Hao Wang for FREE. Read/write reviews, email this book to a friend and more... Elementary Algebra Exercise Book IComments for "Elementary Algebra Exercise Book I" Mr. Wenlong Wang Mr. Wenlong Wang is a retired mathematics educator in China. He has been working on algebra and geometry problems for many years, and has taught many students in the past few years. He is an expert and a senior researcher in mathematics education. Professor Hao Wang Dr. Wang has strong interests in interdisciplinary research of mathematical biology. His research group is working on areas as diverse as modeling stoichiometry-based ecological interactions, microbiology, infectious diseases, predator-prey interactions, habitat destruction and biodiversity, risk assessment of oil sands pollution. Mathematical models include ordinary differential equations, delay differential equations, partial differential equations, stochastic differential equations, integral differential/difference equations consists of the elementary aspects of linear algebra which depend mainly on row operations involving elementary manipulations of matrices. The field of scalars is typically the field of complex numbers.
Students use graphs, tables, number lines, verbal descriptions, and symbolic representations to analyze the domains of various functions. An activity sheet, discussion questions, lesson extensions, and suggestions for assessment are included. (author/sw)
mattst88's math stuff My Physics Equations are online. They provide a pretty good reference for basic mechanics, sounds, thermodynamics, light, electricity, and circuts. I'm continuing to add to this section of my site. We're currently studying magnetism in class now so expect it to be the next addition. If you notice any sorts of errors, be it with the actual equations, the HTML, or otherwise, please contact me.
MathematicsFormulaChart 8th Grade (PDF Documents) provides by doc.biasbias.com. And hosted at /doc11/Mathematics_Formula_Chart_8th_Grade.pdf. Full version of this PDF contains 10 attachment URLs, you also can download documents related will seek in vain for a formula they feel strongly should be included. Please send suggestions for amendments to the Secretary of the Teaching Committee, and they will be considered for incorporation in the next edition. The Utilize the conversions and formulas on the MathematicsChart to solve problems. Recognize abbreviations of measurement units. 5.10B Connect models for perimeter, ... top portion with formula as written on the Chart. 1 wk 7 d the bottom section. 1 wk 7 d Formula Reference Sheet Formulas for Area (A) and Circumference (C) Triangle A 1 2 bh 1 ... Explanation refers to the student using the language of mathematics to communicate how the student arrived at the solution. ... chart, or table. Include titles, ... Will the Grade 7 MathematicsFormulaChart be helpful on this problem? Why or why not? 3. How can I determine which variable I want get by itself? 4. What problem-solving strategy or strategies will I use to help solve this problem? 5. The Mathematics Formulary is made with teTEX and LATEX version 2.09. If you prefer the notation in which vectors are typefaced in boldface, uncomment the redefinition of the \vec ... If these limits both don't exist one can find Rwith the formula of Cauchy-Hadamard: 1 R Mathematics \| Standards for Mathematical Practice ... might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, ... Standards for Mathematical Practice Chart.pdf A Resource for Free-standing Mathematics Units Graphs of Functions in Excel ... • If it is not there, left click on View then Toolbars, then Chart to make it appear. • If it is not there, left click on View then ... Fill down copies the formula from A3 into the other cells, in each case ... Mathematics Test. Although you do not need to memorize these formulas, it is a good idea to be familiar with the contents of this page so that you will know when to use it. 1 2 1 2 1 3 1 3 y 2 y 1 x 2 x 1 x 1 x ... Formula Sheet. Title: GED Formula Sheet Author: Carin Lovell A Resource for Free-standing Mathematics Units Graphs of Functions in Excel ... Left click on cell A3 and enter the Excel formula =A2+1 ... In cell C2 type the formula =2*A2+3 and then copy the formula down to C12. Now select Chart tools, Design, Select Data and then click on ADD. The exact same formulachart is also found in the test booklet at the beginning of the mathematics test. The formula charts have changed over the years. The separate chart now has a metric ruler on one side and a customary ruler on the other side for students to use if
Worksheets for Classroom or Lab Practice for Integrated Arithmetic and Basic Algebra Summary KEY MESSAGE:Integrated Arithmetic and Basic Algebra, Fourth Edition, integrates arithmetic and algebra to allow students to see the big picture of math. Rather than separating these two subjects, this text helps students recognize algebra as a natural extension of arithmetic. As a result, students see how concepts are interrelated and are better prepared for future courses. KEY TOPICS: Adding and Subtracting Integers and Polynomials; Laws of Exponents, Products and Quotients of Integers and Polynomials; Linear Equations and Inequalities; Graphing Linear Equations and Inequalities; Factors, Divisors, and Factoring; Multiplication and Division of Rational Numbers and Expressions; Addition and Subtraction of Rational Numbers and Expressions; Ratios, Percents, and Applications; Systems of Linear Equations; Roots and Radicals; Solving Quadratic Equations MARKET: For all readers interested in algebra and basic algebra. Table of Contents R. Basic Ideas Reading and Writing Numerals Addition and Subtraction of Whole Numbers Multiplication of Whole Numbers Division of Whole Numbers A Brief Introduction to Fractions Addition and Subtraction of Decimal Numerals Multiplication and Division of Decimal Numerals Linear Measurement in the American and Metric Systems [new section] Adding and Subtracting Integers and Polynomials Variables, Exponents, and Order of Operations Perimeters of Geometric Figures Areas of Geometric Figures Volumes and Surface Areas of Geometric Figures Introduction to Integers Addition of Integers Subtraction of Integers and Combining Like Terms Polynomial Definitions of Combining Polynomials Laws of Exponents, Products and Quotients of Integers and Polynomials Multiplication of Integers Multiplication Laws of Exponents Products of Polynomials Special Products Division of Integers and Order of Operations with Integers Quotient Rule and Integer Exponents Power Rule for Quotients and Using Combined Laws of Exponents Division of Polynomials by Monomials An Application of Exponents: Scientific Notation Linear Equations and Inequalities Addition Property of Equality Multiplication Property of Equality Combining Properties in Solving Linear Equations Using and Solving Formulas Solving Linear Inequalities General, Consecutive Integer, and Distance Application Problems Money, Investment, and Mixture Application Problems Geometric Application Problems Graphing Linear Equations and Inequalities Reading Graphs and the Cartesian Coordinate System Graphing Linear Equations with Two Variables Graphing Linear Equations by Using Intercepts Slope of a Line Slope-Intercept Form of a Line Point-Slope Form of a Line Graphing Linear Inequalities with Two Variables Relations and Functions Factors, Divisors, and Factoring Prime Factorization and Greatest Common Factor Factoring Polynomials with Common Factors and by Grouping Factoring General Trinomials with Leading Coefficients of One Factoring General Trinomials with Leading Coefficient Other Than One Factoring Binomials Factoring Perfect Square Trinomials Mixed Factoring Solving Quadratic Equations by Factoring Multiplication and Division of Rational Numbers and Expressions Fractions and Rational Numbers Reducing Rational Numbers and Rational Expressions Further Reduction of Rational Expressions Multiplication of Rational Numbers and Expressions Further Multiplication of Rational Expressions Division of Rational Numbers and Expressions Division of Polynomials (Long Division) Addition and Subtraction of Rational Numbers and Expressions Addition and Subtraction of Rational Numbers and Expression with Like Denominators Least Common Multiple and Equivalent Rational Expressions The Least Common Denominator of Fractions and Rational Expressions Addition and Subtraction of Rational Numbers and Expressions with Unlike Denominators
A first course in mathematical analysis. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces. ... More > Originally developed to teach Math 444 at University of Illinois at Urbana-Champaign and later enhanced for Math 521 at University of Wisconsin-Madison. See Less Effects included: (1) You have the ability to look at a person's signature and be able to tell which doodle was drawn by them out of a choice of five. (2) Using graphology you can know enough about... More > a person's personality to make an accurate guess of which words or symbols they'd be drawn to. (3) Your spectators are each given business cards and asked to write down either their actual job or a job that they do not have on the backs of the cards. They then turn over the cards and sign them. Without having seen who wrote what on the cards – you can not only return each card to their rightful owner but you can also say who was telling the truth and who lied. more details at Mental-Magic.com< Less This book has been written due to the findings in my first book The Bermuda Unsolved. I spent two years in Bermuda researching the subject of lost planes and ships. I came to the conclusion that the... More > losses were real and due to an alien presence that was here to collect power from the deep oceaan trenches. I then having written the book The Bermuda Unsolved wrote this one The Bermuda Analysis that explains the activities of the aliens and their world wide presence including the Dragons Triangle off Japan. I then explored all the related subjects and the writers and found an exceptional amount of for want of a better word national involment. The last great tradgedy was flight 447 out of Brazil the only country in the world that actually askes the public for assistance in this matter. This book explains why and identifies for the first time the alien and the methods to contact it. The final book in this series will be The Bermuda Proof that deals with the misinformation fed by the authorities.< Less The book guides the reader through a series of worked examples in integral calculus and ordinary differential equations. It is aimed to enhance the skill of manipulating analytic expressions and... More > casting them in suitable forms. Selection of techniques helps to develop a specific style in dealing with analytical problems and leaves room for personal preference in choosing a particular method. The book will be useful for students doing a course in calculus or differential equations and for those who want to refresh their knowledge in this field.< Less no asana no pranayama no Dyana(meditation) no rajayoga no hathayoga no kriyayoga no karma yoga path to god no bhakth iyoga path no gyanayoga path to realization yoga can not taught ... More > cannot learned certificates no make anybody yogis this is an analysis of yoga from a different angle touching the feet of yogis presenting real yoga<This book describes a requirements lifecycle based on the Rational Unified Process (RUP) framework, from business modeling through to analysis and design. The process utilizes a subset of the Unified... More > Modeling Language (UML) to describe this process with 'real' examples, which demonstrate an effective method for software development in almost any situation. It includes some of the most useful software development practices and the most common UML notations. (Version 3 corrects grammar, reorganizes some content and fixes cross-references in version 2.)< Less
Calculus Help In this section you'll find study materials for calculus help. Use the links below to find the area of calculus you're looking for help with. Each study guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn calculus. Study Guides Trigonometric Values of Angles Some very interesting and important functions are formed by dividing the length of one side of a right triangle by the length of another side. These functions are called trigonometric because they come from the geometry of a ... Calculus and Limits Mathematicians, just like children, like to see what happens when we push limits. We are told not to divide by zero, so the temptation overwhelms us to see what happens when we divide by almost zero. The process of using ... Derivatives Straight lines may be ideal to human beings, but most functions have curved graphs. This does not stop us from projecting straight lines on them! For example, at the point marked x on the graph in Figure 6.1, the function is clearly ... Basic Rules of Differentiation Using the limit definition to find derivatives can be very tedious. Luckily, there are many shortcuts available. For example, if function f is a constant, like f (x) = 5 or f ... Rates of Change It is useful to contemplate slopes in practical situations. For example, suppose the following graph in Figure 8.1 is for y = f(x), a function that gives the price y for various amounts x of cheese. ... The Product Rule When a function consists of parts that are added together, it is easy to take its derivative: Simply take the derivative of each part and add them together. We are inclined to try the same trick when the parts are multiplied together, but it does ... Calculus and Chain Rule We have found how to take derivatives of functions that are added, subtracted, multiplied, and divided. Next, we will cover how to work with a function that is put inside another simply by composition. For example, it would be ... Differentiate Both Sides of the Equation Once you have gotten the hang of implicit differentiation, it should not be difficult to take the derivative of both sides with respect to the variable t. This enables us to see how x and y vary ... Limits at Infinity This lesson will serve as a preparation for the graphing in the next lesson. Here, we will work on ways to identify asymptotes from the formula of a rational function. Rational functions are quotients, with a clear numerator and ...
Gain the skills needed for managerial roles in the hospitality and tourism industry. Learn about percentages, menu pricing, yield and price factors, profit and loss statements, algebra, simple and compound interest, hospitality and tourism statistics and weight/volume conversions between the imperial and metric systems. Equivalent: MATH 1102 Prerequisites: You must have completed MATH 1080 (Math Essentials) . If you do not meet this requirement, you must complete the General Math Assessment and score high enough to be assigned to Hospitality Mathematics. You must present proof at the first class.
Introductory Algebra : A Real-World Algebra prepares students for Intermediate Algebra by covering fundamental algebra concepts and key concepts needed for further study. Students of all backgrounds will be delighted to find a refreshing book that appeals to every learning style and reaches out to diverse demographics. Through down-to-earth explanations, patient skill-building, and exceptionally interesting and realistic applications, this worktext will empower students to learn and master algebra in the real world.
Book Description: Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982
Intermediate Algebra - 8th edition ISBN13:978-0495117940 ISBN10: 0495117943 This edition has also been released as: ISBN13: 978-0495118022 ISBN10: 0495118028 Summary: Easy to understand, filled with relevant applications, and focused on helping students develop problem-solving skills, INTERMEDIATE ALGEBRA is unparalleled in its ability to engage students in mathematics and prepare them for higher-level courses. Gustafson and Frisk's accessible style combines with drill problems, detailed examples, and careful explanations to help students overcome any mathematics anxiety. Their proven five-step problem-solving strategy helps break ea...show morech problem down into manageable segments: analyze the problem, form an equation, solve the equation, state the conclusion, and check the result. Examples and problems use real-life data to make the text more relevant to students and to show how mathematics is used in a wide variety of vocations. Plus, the text features plentiful real-world application problems that help build the strong mathematical foundation necessary for students to feel confident in applying their newly acquired skills in further mathematics courses, at home or on117943
All these workshops are suitable for Secondary 3 Maths students this year and it involves teaching and hands-on practice in a step-by-step manner, structured to increase your understanding and confidence upon completion. Ai Ling has taught me the formulas for Maths in an easier way. She also showed me different techniques that can be applied to the Maths question and how to look out for certain things in questions, to be able to apply the formulas learn. That has made it easier for me to do questions and I can now do the questions with much ease. Thank you, Annabelle, CHIJ – Toa Payoh This programme has been very helpful to me for my Maths. Through this programme, I have fully understand certain topics that I was unsure of, for example Trigonometry. This has helped my A-Maths improve greatly and I passed my CA2 A-Maths. It was the first time I passed in this year! Also, I find Ai Ling very interactive and engaging , easy to understand what she's saying. This has helped me alot and I will continue with this programme. Gabriel, Maris Stella High School Out of the many updates this student shared was to 'Start Preparation Early!' He just completed his GCE 'O' Level examinations last month. He wrote to Sean to share his suggestion with all our students. From his experience, he felt that his Sec 4 passed too fast, with time spent on CCAs (he was a student leader) and completion of syllabus. By then, it was just 3 months left to 'O' Levels. As I always talk to students and parents, 'O' Levels consist of the examination of the entire Sec 1 to Sec 4 (or 5) work. This is especially true for Elementary Mathematics. For Additional Mathematics, students are required to be good with 2 years of knowledge. If you are willing to take this student advice seriously of 'Start Preparation Early!', I would like to invite you to join me starting in mid-Jan 2011 in my Ultimate Leap Programme – Weekly Coaching Classes. Click here to read more. Here are the topics discussed for Sec 3 and Sec 4(or 5) and do note that the sequence is subjected to changes. I look forward in meeting some of you and Happy 2011! Oh, did I mention that I've something for all of you next year. wink wink Subscribe to the blog to be updated later in January!
examine common algebra-related misconceptions and errors of middle school students. In recent years, success in Algebra I is often considered the mathematics gateway to graduation from high school and success... The number of refugees being uprooted from their homes to seek refuge and resettlement in countries like the United States continues to grow, with large numbers being children. While each refugee group has its own set of challenges when adjustingWith the increasing computational power and the decreasing cost of high bandwidth networks resulted in Distibuted Systems. Distributed Data Mining is being used to analyze and monitor data in distributed systems. In the past, distributedAntibiotic resistance is a problem causing growing concern in the medical community, leading some to speculate that a return to the preantibiotic era is imminent. The problem of antibiotic resistance is particularly significant in the intensive...
Mathematics 101: Introductory Finite Mathematics I, 8th WNCP Edition This text was developed specifically for use in the Mathematics 101 course at the University of Regina. This is a required course for the K-8 Education program for teacher training in Saskatchewan, and also meets the critical thinking requirements for U of R programs in Arts or Fine Arts. The 8th Edition was especially revised with the new 2008 Western and Northern Canadian Protol Mathematics Curriculum in mind. It It includes sections that are intended to reflect the WNCP curriculum's increased focus on logical thinking, multiple strategies for arithmetic calculations - including training in right-to-left computation styles, and probability, at a level suitable for the training of teachers. It features units on 1) Problem Solving Strategies and Logic, 2) Arithmetic and Numeration Systems, 3) Modular, Clock, and Calendar Arithmetic, 4) Number Theory, and 5) Ratios, Percent, Proportion, and Probability. A wide range of problems and exercises accompanies each section, each unit concludes with a comprehensive list of unit review exercises. Mathematics 101: Introductory Finite Mathematics I, 8th WNCP Edition is available electronically in .pdf form, under the condition that these free electronic copies are for personal use only and not for resale. Printed copies of the text are available to Educational institutions or individuals. These can be ordered directly from the University of Regina bookstore. The 2013 price of a coil-bound black-and-white copy is around $30 Cdn + shipping + taxes. Book-bound colour copies are also available on request. A separate Answer Book for Unit Review Exercises is available electronically by request for course instructors. Enquiries can be directed by email to Dr. Allen Herman in the Department of Mathematics and Statistics at the University of Regina.
Links Math Glossary specializes in math terms. This niche sub-dictionary will allow individuals, whether starters in the math field or long time experts to research the exact meaning of terms they encounter
like the enthusiasm, but I fear there may be a bit of mathematical machismo creeping in when he says:A budding mathematician is well-advised to always search for motivation. A major problem with higher mathematical education is the lack of emphasis on motivation--it's something we need to fix, not embrace. Look how much Feynman struggles to motivate things in his lectures on physicsAgain we have some machismo on display. The book Calculus by Spivak is very well-respected in the mathematical community, and yet it commits several of the sins listed here. Rudin's approach is fine for analysis students who are willing to "just do it" without seeing the bigger picture (until they make it to the end), but students who first want to know why they are doing it will be better served by a pedagogical approach that puts more emphasis on motivation. the author didn't say that anyone that hands you a calculus book that doesn't cover compactness and metrics before limits is doing you no favors - he said someone that hands you an analysis book that does these things isn't. for the record many of the problems are applications of the theorems proven in the chapters e.g. fixed point theorem, newton's method, even heisenberg uncertainty principle in the chapter on limits of functions. EDIT: Copy available [Here]. The text is as follows (a.k.a. BIG FAT MIRROR!): Book should be called "Tada! You're a mathematican!", October 26, 2005 By Bolzano Bourbaki This review is from: Principles of Mathematical Analysis, Third Edition (Hardcover) OK... Deep breaths everybody... It is not possible to overstate how good this book is. I tried to give it uncountably many stars but they only have five. Five is an insult. I'm sorry Dr. Rudin... This book is a good reference but let me tell you what its really good for. You have taken all the lower division courses. You have taken that "transition to proof writing" class in number theory, or linear algebra, or logic, or discrete math, or whatever they do at your institution of higher learning. You can tell a contrapositive from a proof by contradiction. You can explain to your grandma why there are more real numbers than rationals. Now its time to get serious. Get this book. Start at page one. Read until you come to the word Theorem. Do not read the proof. Prove it yourself. Or at least try. If you get stuck read a line or two until you see what to do. Thrust, repeat. If you make it through the first six or seven chaptors like this then there shall be no power in the verse that can stop you. Enjoy graduate school. You half way there. Now some people complain about this book being too hard. Don't listen to them. They are just trying to pull you down and keep you from your true destiny. They are the same people who try to sell you TV's and lobodemies.Finally, some people complain about the level of abstraction, which let me just say is not that high. If you want to see abstraction grab a copy of Spanier's 'Algebraic Topology' and stare at it for about an hour. Then open 'Baby Rudin' up again. I promise you the feeling you get when you sit in a hottub for like twenty minutes and then jump back in the pool. InvigoratingAnyway, if this review comes off a combative that's because it is. It's unethical to use another text for an undergraduate real analysis class. It insults and short changes the students. Sure it was OK before Rudin wrote the thing, but now? Why spit on your luck? And if you'r a student and find the book too hard? Try harder. That's the point. If you did not crave intellectual work why are you sitting in an analysis course? Dig in. It will make you a better person. Trust me. Or you could just change your major back to engineering. It's more money and the books always have lots of nice pictures. In conclusion: Thank you Dr. Rudin for your wonderfull book on analysis. You made a man of me. When I was in engineering and taking extra math courses (mainly in pure math and statistics), certain math profs delighted in taking cheap shots at engineers. The first time it's funny, the tenth time it's just annoying. As a group, we engineers are worse at that sort of us-versus-them thing, though. Interesting, that's never been the case for me; professors I've had usually stuck to fairly self-deprecating humor. But I think they secretly hate the statistics department (which I don't really blame them for). The only problem with this book, aka "Little Rudin", is that "Big Rudin" (Real and Complex Analysis) exists. At least, I find that book to be one very nicely written book, although it sadly isn't as approachable as this one (to the extent that anything by Rudin is approachable). They're they same people that complain about a class being too hard, wake up call people, a subject is as hard as it is, if you can't handle that switch into something easier. I think it's that kind of mindset that has actually led to somewhat of a reduction in the quality of grade school mathematical education in the last 20 or so years. (I'm 21, final year undergrad and I think this). no, it was just to illustrate by analogy that someone not understanding insert random field is not necessarily a result of them not trying, or not being smart but could be just a matter of their background and other more complex factors. Hopefully this is obvious now. It's not that the top 1/3 are just 'smarter' necessarily, just that they have the background/knowledge to get it done. Definitely, if universities could get a net increase in their target market (and hence net profits) by dumbing down the material being taught, then I don't doubt that they would do it (or already have done it). Have you seen anything to suggest that this happened though? this is exactly the point of the book, which the review alludes to. it is meant to teach you to struggle (albeit at the same time as teach you basic real analysis); it is meant to make you into a mathematician. And if you're a student and find the book too hard? Try harder. That's the point. If you did not crave intellectual work why are you sitting in an analysis course? Dig in. It will make you a better person. Trust me. Ah, my emphasis is on unnecessary, in the sense of "not fruitful". Rudin does simple things in an overcomplicated manner, at least from a didactic point of view. The effort on learning it that way is not well-spent; it's much more efficient to build intuition first and then fill in the details. Of course you have to struggle with proofs to become a mathematician; I'm contesting the style and choice of proofs. You become a mathematician by drawing a picture that makes the proof intuitive, trivial and superfluous. pure bs. how many journal articles have picture proofs??? i think you're confusing with what you believe/wish math is/was with what math really is. Rudin does simple things in an overcomplicated manner, at least from a didactic point of view. you're not getting it. first go look at any published article - it will assume relatively more from you. note i said relatively which means it will expect and even bigger portion of the steps to be supplied by you. second you cannot teach or provide intuition. one develops intuition through struggle with baffling shit. you have to sit there and literally try tons of techniques just to figure it what he's saying (not even the problems) e.g. do i need to draw a picture or do i need to plot a graph or do i need to try some cases or do i need to weaken the hypotheses or do i need examine this structure in a different context (wtf is an algebra of sets???). this work is what gives you intuition - what really makes a "strong" mathematician. finally there's a reason why the schools use this book and shitty schools use "understanding analysis" by abbott. It sounds like there's a lot of trust placed in the reader to 'figure it out', where only the very intelligent or very determined will get to the point of real understanding. It's not always a matter of intelligence/determination either...sometimes you just don't get something without it being explained a little differently, even if you have both of the things mentioned above. Though I haven't read the book or anything by the author so this might not be my place...though I do enjoy material that's to the point. overpriced - yes. kolmogorov's 'introductory real analysis' certainly trumps this book regarding price. as for the overrated comment, not really. if you would like a lighter treatment of analysis i recommend 'applied analysis' by hunter and nachtergaele, or 'mathematical analysis' by apostol. anyone that thinks applied mathematics cannot retain purity should consider looking into the analysis of stochastic partial differential equations. Agreed. I've been self-studying analysis from it and it has problems with motivation and intuition. However, I don't think it's as bad as some of its detractors make it out to be in terms of 'gaps' in the proofs. Most of the time when I'm stuck on one, I realize that something is almost 'obvious' after some thought. I can see why professors like it so much. If you already know the material, he presents it in an extremely organized, structured and elegant way. I found this to be so for the first chapter which I knew most of already. The book is definitely overpriced. And I agree that the logical flow of ideas that tends to go by the term "motivation" is a bit broken up. I couldn't agree less with the rest of your post. I worked through this book on my own, without any "support." So there aren't many examples--make up your own examples! The exercises aren't sadistic; they're thoughtful and relevant. The reader should be able to complete most of them (and attempt all of them). Hm, maybe I'm wrong, but you don't seem to get the reference to Bourbaki. Albeit I'm all for abstract formal proofs, but they should come with pretty pictures and fancy explanations, tons and tons of them. I can skip 3 pages of explanation if I get the 3 lines of hieroglyphs it's explaining, but if there's no how-to for the naked proofs, that's almost as worthless as the Rosetta stone in 3 pieces. I have found that mathematics self study made me write sloppy proofs in the sense that I frequently omitted things because I thought they were obvious. Several times I would get homework back all marked up with teacher comments saying I needed to qualify my statements more. It wad frustrating because I would copy the proof style from the books I had read from and I thought I was doing it correctly. I guess not! You are right, but your proof is wrong. !B => B is not a contradiction although intuitively it seems like it should be. Consider the case where B is true. Then !T => T, so F => T which is T. Thus not a contradiction. A => B Suppose !(!B => !A) !(B or !A)by Implication from 2 !B and Aby De Morgan from 3 !Bfrom 4 Afrom 4 Bfrom Modus Ponens on 1 and 6 !B and Bfrom 5 and 7 Contradiction on 8 Thus !B => !A There might be a shorter way to do it. Actually a truth table is far simpler than this method. Turns out the problem is that I'm horrible at writing proofs in the 'logic' style, after writing so many in paragraphs. One of my precepts needs to be that B is false; then I prove that that gives A is false. How is this?
This book offers the sound presentation of mathematics, useful pedagogy, clear and well-constructed writing style, superb problem-solving strategies, and other qualities that have made the Martin-Gay series so successful. Exceptionally interesting and practical real-world applications throughout the book capture readers' interest, while Martin-Gay's streamlined problem-solving process develops and hones their problem-solving skills. New features include Spotlight on Decision-Making applications, revised Chapter Projects, Real-World Chapter Openers, Vocabulary Review sections, video icons, and Study Skills sections. For readers interested in learning or revisiting essential skills in beginning and intermediate algebra through the use of lively and up-to-date applications. Normal 0 false false false KEY BENEFIT: The Bittinger Concepts and Applications Series brings proven pedagogy to a new generation of students, with updates throughout to help today's students learn. ... The BPB team has created a book where the use of the graphing calculator is optional but visualizing the mathematics is not. By creating algebraic-visual side-by-sides, the authors show students the ...
CBD Price: $35.00 ( In Stock ) New Syllabus Additional Mathematics is specially written for students preparing for the GCE "O" level examinations, but will be useful for any students studying in-depth math topics. New concepts and principles are introduced using short, concise explanations which serve to lay the groundwork for advance students; the language used is simple and theoretical explanations are kept to a minimum. Special features include problem solving tips to enhance thinking skills, IT activities, self-assessment to incite active learning and independent thinking, review exercises, real-life problems, problems for different skill levels and interdisciplinary activities. 498 pages, paperback. This textbook covers: Simultaneous Equations, Remainder Theorem and Factor Theorem Quadratic Equations and Functions Partial Fractions Indices, Surds and Logarithms Coordinate Geometry - The Straight Line Trigonometrical Ratios and Equations Graphs and Properties of sin x, cos x and tan x Further Trigonometrical Identities such as Sum and Difference of Two Angles and Equations of the type A cos h + B sin h = C. CBD Price: $15.50 ( In Stock ) This workbook accompanies Singapore Math's "New Syllabus Mathematics Textbook 3" (now out-of-print). A summary of each chapter, practice questions 177 pages, softcover. CBD Price: $35.00 ( In Stock ) 4th in a series of four textbooks, the New Syllabus Mathematics series covers 'O' Level Mathematics. New Syllabus 4 is recommended for students who want a challenging course that will require them to actually apply knowledge to new situations, rather than simply following a procedure. This series integrates pre-algebra, algebra, and geometry and includes some advanced math topics; homeschoolers should be aware that teacher involvement is generally necessary. Explanations of concepts and principles are concise and written in clear language with supportive illustrations and examples. Exercises marked with a * either require more thinking or involve more calculations. Features Include: An interesting introduction at the beginning of each chapter with photographs or graphics. Brief specific instructional objectives for each chapter. "Just for fun" arouses the students' interests in studying mathematics. "Thinking Time" encourages students to think creatively and go even deeper into the topics. "Exploration" provides opportunities for students to learn actively and independently "Problem Solving Tips" provide suggestions to help students in their thinking processes. We also introduce problem solving heuristics and strategies systemically throughout the series. "Your Attention" alerts students to misconceptions. Answers to exercises, reviews, and tests are in the back of the book. There are no answers provided for the investigations and explorations yet. The workbook for this series is sold separately. Grades 7-10. 380 pages, softcover. CBD Price: $15.50 ( In Stock ) This workbook accompanies Singapore Math's sold-separately New Syllabus Math Textbook 4 (New Edition). A summary of each chapter, practice questions, mindmap problems 174 pages, softcover.
MATH 19 is an introduction to limits and differential calculus with a wide variety of applications.Students beginning MATH 19 already have solid algebra and geometry skills.That means students have had two years of high school algebra and one year of high school geometry.Upon successful completion of MATH 19, students are prepared to take MATH 20:Fundamentals of Calculus II, (MATH 20). If you need help, please ask!If you wish to meet with me other than during my office hours, please e-mail me days and times that are convenient for you to meet.I would be happy to make an appointment with you! TEXTBOOK:CALCULUS WITH APPLICATIONS, 10th Edition, by Lial, Greenwell, and Ritchey Final grade for the class is based upon: Quiz Average: 50%, Mid-Term Grade:30%, and Final Examination: 20%. FINAL EXAMINATION will be cumulative. Wednesday, June 26th:5:30 PM until 9:00 PM Make-up quizzes are not given.It is in your best interest to take every quiz, the mid-term, and the final examination. If you miss any of these, you earn a 0% for it.
Latest Mathematics education Stories SAN ANTONIO, Feb. 2, 2012 /PRNewswire/ -- With many states requiring Algebra I to graduate from high school, algebra has become one of the gateway courses to school and career success. Yet upwards of 60 to 70 percent of students struggle with algebra or fail to pass state-mandated proficiency exams. PCI Education, the premier provider of resources for students with specialized instructional needs, introduces Algebra City(TM),( )a blended intervention program focusing on the 28 most common... Two Wrong Angles Do Not Make a Right Mountain View, CA (PRWEB) January 05, 2012 When many students hear the word "algebra," their heads begin swimming with thoughts of long, complex equations chock-full of variables, coefficients, exponents, fractions and square roots. It´s true - there is indeed plenty of that. However, many of the fundamental ideas that need to be mastered before moving on to more advanced algebraic concepts involve a branch of mathematics generally... LINCOLN, Neb., Jan. 3, 2012 /PRNewswire/ -- A recent Institute of Education Sciences at the U.S. Department of Education report found that Class.com's Algebra I course administered through its fully accredited online high school, Lincoln National Academy, increased eighth grade students' algebra skills and caused them to take more challenging math courses in high school. "We know how successful students can be at Lincoln National Academy, and it's exciting to have online learning... Shmoop takes the confusion out of the Pre-Algebra equation Mountain View, CA (PRWEB) December 19, 2011 Shmoop, a publisher of digital curriculum and test prep, announces the launch of its expanded free Pre-Algebra resource at Many studentws might regard math as their sworn enemy. The mere mention of a Cartesian Coordinate System may cause toes to curl. The concept of a box and whisker plot may be nothing more than a plan for keeping litter off the... Effective Way to Broaden Access to Algebra I for Grade 8 Students WASHINGTON, Dec. 13, 2011 /PRNewswire-USNewswire/ -- Eighth-grade students who are "algebra ready" and take an online Algebra I course because their schools do not offer the class, outperform their peers in algebra knowledge and are twice as likely to take advanced mathematics classes in high school. The findings are in a rigorous new federally funded study conducted by the American Institutes for Research (AIR) and... NEW YORK, Nov. 22, 2011 /PRNewswire/ -- Education is the key to the future. Yet in too many cases, American students have been falling behind their global peers, particularly in the critical field of mathematics where the instructional approach has tended to be broad and shallow, with little focus on concept mastery. That challenge has led a growing number of U.S. educators to take a serious look at Singapore - that is, at Singapore Math, an innovative curriculum whose effectiveness has... Success in math takes practice to control fears Using brain-imaging technology for the first time with people experiencing mathematics anxiety, University of Chicago scientists have gained new insights into how some students are able to overcome their fears and succeed in math. For the highly math anxious, researchers found a strong link between math success and activity in a network of brain areas in the frontal and parietal lobes involved in controlling attention and regulating... DALLAS, Oct. 17, 2011 /PRNewswire/ -- Voyager, a member of Cambium Learning Group serving at-risk and special student populations through strategic and intensive comprehensive interventions, will host a complimentary, one-hour webinar featuring education author, John Woodward, Ph.D., on Wednesday, October 19, 2011, at 4:00 p.m. Central Time. The webinar, For Every Student to Succeed, Something Different Has To Happen, will address how to successfully support struggling math students....
student workbook is designed to go with online video tutorials that can be found online at The five minute videos introduce concepts and work through... More > two examples for each concept. Using the free online homework system, WAMAP ( students are allowed to practice each concept before moving on to the next topic. There is a short assignment that follows each set of concepts. The philosophy behind this workbook is simple: Students learn math by doing math, not by listening to someone talk about doing math.< Less This workbook incorporates problem sets necessary to master Pre-Algebra subjects and effectively bridge arithmetic and Algebra I. The practice sheets are designed to work resourcefully with the... More > Pre-Algebra Curriculum but can also provide students with the necessary background to be successful in Algebra I. For curriculum information, contact us at info@ssformath.com< Less This workbook has the entire practice set for the Pre Algebra curriculum, followed by the answer keys. This is a valuable learning aid for teachers and parents who want to supplement classroom... More > instruction. All these books are available from Simplified Solutions for Math on LULU. Contact Simplified at ss4math@gmail.com for more information and a complete set of PowerPoint presentations for each lesson, free with purchase of curriculum. Completely self-contained, ideal for home schooling as well as traditional classrooms.< Less Joseph's 487 questions to Pre-Algebra is focused on math practice. It contains 487 questions, concept explanations, and answer keys. The book is very helpful for classes and for strong math... More > foundation.< Less Keep math skills sharp with this review of Pre-Algebra concepts and skills. Eighteen "short and sweet" lessons review the relevant mathematics so that students will find success in Algebra... More > 1. Included "Thinking Guides" provide not only solutions, but also offer instructional guidance which focuses on deep understanding of algebraic concepts so that parents have the help they need to support their child's learning. Free access to online resources is also available.< Less This is a complete curriculum for the second semester of pre-algebra. It is designed to be used with the first semester book as well as the student workbook with keys. All these books are available... More > from Simplified Solutions for Math on LULU. Contact Simplified at ss4math@gmail.com for more information and a complete set of PowerPoint presentations for each lesson, free with purchase. Completely self-contained, ideal for home schooling as well as traditional classrooms.< Less
PTS Newsletter Booker Profiles in Mathematics - Thinking Mathematically This test was designed to assess and analyse students' capacity to think, reason, and problem solve in mathematics. Forty questions are arranged into four levels of increasing problem complexity, starting with questions where the operations to be used are relatively obvious, and ending with questions where strategic thinking is required in order to determine a solution strategy.
This set of tests provides opportunities for assessment and evaluation; a variety of questions will tests students knowledge of what they've learned in the BJU Press Fundamentals of Math Grade 7 curriculum. Product: Fundamentals of Math 7 Tests (2nd Edition) Vendor: BJU Press Edition Number: 2 Binding Type: Other Minimum Grade: 7th Grade Maximum Grade: 7th Grade Weight: 1.112 pounds Length: 11 inches Width: 8.5 inches Height: 0.452 inches Vendor Part Number: 218958 Fundamentals of Math 7 Tests (2nd Edition). Average Rating Parent Rating Comments We used the DVD's for BJU. I have to say my children did not find them easy to watch. They felt the instructor was quite boring. My husband felt that a lot of the lessons should have been simplified for better understanding. He often stopped the DVD to teach them an easier way to work the problems.
series by K A Hesse, published by Longman, was written at the time of decimalisation. The series consists of five books. Each book contains a large number of routine exercises. There is some brief explanation where required. The books are aimed at Key Stage Two students but could be appropriate for routine revision and practice… This resource, published by Schofield & Sims, is the sixth fifth fourth Alpha Mathematics series of text books which were developed for use by more able Alpha Mathematics series of text books which were developed for use by more able students of junior and middle school age. It continues the theme of book one and allows students to review and extend their knowledge of specific topics. Contents include: Number alternatives… The Science in a Topic students'… The Science in a Topic students'… The science in a Topic students'…
Presenting lessons that engage students with interactive resources and stimulating lectures, MA1099 is a two-semester course that guides students through mathematical ideas and techniques, and encourages the development of problem-solving skills.
Monday, January 30, 2012 Stats: Chapter 5 test will be Thursday! Until then students will complete the remainder of page 263 and learn about poisson distributions. Calculus: We started Chapter five today and we are working on LRAM, RRAM and MRAM. Students will be asked to complete lesson 5-1 as homework. Then we will compute defimite integrals and make connections between the computations and what we learned with RAM. Students will be asked to complete lesson 5-2 for an assignment. Monday, January 23, 2012 Statistics: Students will be working on the binomial formula, Pascals' Triangle and the Poisson distribution this week. Students will complete page 263, 2-25 and page 276, 7-12. Calculus: At the start of the week, students will complete their related rates activity. Then, students will be learning how to graph slope fields of functions and how to sketch a curve of a function given information about its derivatives. Students will complete problems given in class. Wednesday, January 18, 2012 Stats: Students will begin working on chapter 5, Probability Distributions. They will complete page 244 #'s 6-25 for homework. Then students will work on finding the mean, variance and standard deviation for probability distributions and complete an assignment on page 253 #'s 1-18. Calculus: Students will begin the week by studying how the amplitude and period of a sinusoidial curve affect sound. Next, they will begin working on related rates and complete page 237 #'s 11, 13, 14, 20 and 22.
Pathways Applied Mathematics for Work Overview This subject offers students the opportunity to formalise mathematical skills they will use in the work place. Each semester will introduce students to the basic concepts involved in mathematics and its impact on their daily life; common examples include department store discounts, credit card costs, mobile phone plans, computations associated with tax returns and other common financial forms. Topical issues such as electricity consumption and costs may be used as contexts for students to study. How much does it cost to operate your television? How much does your refrigerator cost to run? Energy saving light globes, are they a worthwhile investment? A myriad of investigations and opportunities exist in this flexible course structure. Applied Structure Applied Foundation Mathematics is a VCE mathematics is designed to meet the needs of the students undertaking the subject, it is however terminal at year 11.
Since every single physics teacher I've had tells me that the physics learned in class is actually outdated and wind resistance ignored like an annoying sibling I was wondering what we actually used in modern math today? Edit Your Question Please avoid any drastic changes to the overall meaning of your question. For professional physicists: Calculus Analysis-Think of it as an 8th course in Calculus Some Advanced Algebra-After 3 courses in Calculus Differential Equations Linear Algebra Probability Maybe a little Measure Theory: Taken after 5 courses in Calculus Bayesian Statistics Linear Models-Statistics Math is not taught at school so that people can do Physics. It's mainly taught to improve rational thinking skills. If and when you do Physics as a subject at University, say, they'll also teach you the maths you need to know.
Number Theory: A Lively Introduction with Proofs, Applications, and Stories, is a new book that provides a rigorous yet accessible introduction to elementary number theory along with relevant applications.Readable discussions motivate new concepts and theorems before their formal definitions and statements are presented. Many theorems are preceded by Numerical Proof Previews, which are numerical examples that will help give students a concrete understanding of both the statements of the theorems and the ideas behind their proofs, before the statement and proof are formalized in more abstract terms. In addition, many applications of number theory are explained in detail throughout the text, including some that have rarely (if ever) appeared in textbooks.A unique feature of the book is that every chapter includes a math myth, a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exercise sets include in-depth Explorations, in which a series of exercises develop a topic that is related to the material in the section.
ObjectiveGiven the current bridgedimensions, the student will beable to estimate a plan for ahigher bridge to accommodatefuture container ships. 3 Algebra 1 Standards 5.0 Students solve multistep problems, includingword problems, involving linear equations andlinear inequalities in one variable and provide justification for each step. 8.0 Students understand the concepts of parallellines and perpendicular lines and how thoseslopes are related. Students are able to findthe equation of a line perpendicular to a givenline that passes through a given point.
Click each topic to find out more specifically what we will be covering. These topics are from the IBO math studies course guidelines. TOPIC 1 - Introduction to the GDC (graphic display calculator) 1 day We will use this section to introduce you to the numerical, graphical and listing facilities of the GDC and we will make sure that you are familiar with commonly used buttons. TOPIC 2 - Number and Algebra 9 days In this section you will be introduced to some basic elements and concepts of mathematics. You must have a mastery of this section in order to be successful in the work for the rest of the course. TOPIC 3 - Sets, logic and probability 14 days The aim of this section is to enable you to understand the concept of a set and to use appropriate notation, to enable you to translate between verbal and symbolic statements, to introduce the principles of logic to analyse these statements, and to enable you to analyse random events. TOPIC 4 - Functions 17 days In this section you will develop an understanding of some of the functions that can be applied to practical situations. TOPIC 5 - Geometry and trigonometry 14 days This section will be used to develop your ability to draw clear diagrams, represent information given in two dimensions, and develop the ability to apply geometric and trigonometric techniques to problem solving. TOPIC 6 - Statistics 17 days The aims of this section are to introduce you to concepts that will prove useful in further studies of inferential statistics, and develop techniques to describe and analyse sets of data. TOPIC 7 - Introductory differential calculus 10 days This section will be used to introduce the concept of the gradient of the graph of a function, which is fundamental to the study of differential calculus, so that you can apply the concept of the derivative of a function to solving practical problems. TOPIC 8 - Financial mathematics 7 days In this section you will build a firm understanding of the concepts underlying certain financial transactions.
The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math 9780691134932 ISBN: 0691134936 Pub Date: 2009 Publisher: Princeton University Press Summary: Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. His books include the best-selling Sync: The Emerging Science of Spontaneous Order (Hyperion). Strogatz, Steven H. is the author of The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math, published 2009 under ISBN 9780691134932 and 0691134936. Fourteen The Ca...lculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math textbooks are available for sale on ValoreBooks.com, eight used from the cheapest price of $4.59, or buy new starting at $26.73691134932 ISBN:0691134936 Pub Date:2009 Publisher:Princeton University Press Valore Books is the college student's top choice for cheap The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math rentals, or used and new copies that can get to you quickly.
Books Differential Geometry This original text for courses in differential geometry is geared toward advanced undergraduate and graduate majors in math and physics. Based on an advanced class taught by a world-renowned mathematician for more than fifty years, the treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Starting with an introduction to the various curvatures associated to a hypersurface embedded in Euclidean space, the text advances to a brief review of the differential and integral calculus on manifolds. A discussion of the fundamental notions of linear connections and their curvatures follows, along with considerations of Levi-Civita's theorem, bi-invariant metrics on a Lie group, Cartan calculations, Gauss's lemma, and variational formulas. Additional topics include the Hopf-Rinow, Myer's, and Frobenius theorems; special and general relativity; connections on principal and associated bundles; the star operator; superconnections; semi-Riemannian submersions; and Petrov types. Prerequisites include linear algebra and advanced calculus, preferably in the language of differential forms. An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations. This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard's theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences. This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are helpful for a deeper understanding of both classical and modern physics and engineering. It is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. A main addition introduced in this Third Edition is the inclusion of an Overview, which can be read before starting the text. This appears at the beginning of the text, before Chapter 1. Many of the geometric concepts developed in the text are previewed here and these are illustrated by their applications to a single extended problem in engineering, namely the study of the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis. Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text. A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject. Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level. The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.
PAPERBACK New 1401821103This edition of Mathematics for Plumbers and Pipefitters continues to teach the essential math concepts that have made the book the outstanding reference in its field. A collection of modern fitting materials demonstrates the various math concepts, and the book emphasizes a problem-solving methodology that can be applied to both current and future materials and job situations in plumbing and pipefitting. Enhancements to the text include simplified explanations, new drawings, a new unit on calculating partial volumes in odd-shaped tanks, and a reworked unit on heat-loss calculations that has been revised to keep pace with modern heat-loss methods. Related Subjects Meet the Author Lee Smith is a Registered Master Plumber and certified vocational math instructor. His many years of practical and teaching experience in the pipe trades includes domestic and industrial work in the areas of refrigeration and air conditioning, deep sea diving vehicles, and nuclear piping. In addition to several certificates in the trades, Mr. Smith has held Master Plumber credentials for forty years. He earned his A.A.in applied science and technology from Thomas A. Edison State College, and his B.A. and M.A. degrees in education from Temple
Difference in Calculus AB and Calculus BC Calculus AB is designed to be taught over a full high school academic year. Calculus AB can be covered within a year even while spending some time on elementary functions. Adequate preparation for Calculus AB, however, requires dedicated time on topics in differential and integral calculus. AP exams lay special emphasis on these topics. Calculus BC is designed to be offered by schools that are able to complete all the prerequisites before the course. Calculus BC spans one full year in the calculus of functions of a single variable. The course content for Calculus BC has certain additional topics apart from the same for Calculus AB. Prerequisites (for both Calculus AB and Calculus BC) algebra geometry trigonometry analytic geometry elementary functions properties of functions algebra of functions graphs of functions Before studying calculus, all students must complete four years of secondary mathematics designed for college-bound students in topics such as: Topics covered in Calculus AB and Calculus BC Functions, Graphs, and Limits Derivatives Integrals Polynomial Approximations and Series For detailed description of course content under each topic,Click Here. AP Calculus Exam Pattern (AP Calculus AB and AP Calculus BC) Each exam runs 3 hours and 15 minutes and covers topics typically included in about two-thirds of a full-year college level Calculus sequence (Calculus AB) or those included in a full-year, college-level calculus sequence (Calculus BC). Students taking Calculus BC will receive a sub-score grade for the AB portion of the exam in addition to the overall composite grade. Both AP Calculus courses require a similar depth of understanding of common topics, and graphing-calculator use is an integral part of the courses. Both exams contain: 1 hour and 45 minutes of multiple-choice questions that tests proficiency on a wide variety of topics. 1 hour and 30 minutes of free-response questions that allows the students to demonstrate their ability to solve problems using an extended chain of reasoning. Both the multiple-choice and free-response sections contain sections where a graphing calculator is required and parts where calculator use is prohibited. List of AP approved graphing calculators can be seen on collegeboard.com. Section I - Multiple-Choice: This section has two parts - Part A - 55 minutes - 28 questions without calculator Part B - 50 minutes - 17 questions using a graphic calculator Random guessing can hurt the final score of student. While there is nothing to lose for leaving a question blank but one quarter of a point is subtracted for each incorrect answer on the test. Section II - Free Response: This section also has two parts - Part A - 45 minutes - 3 questions using a graphic calculator Part B - 45 minutes - 3 questions without calculator During Part B, one is permitted to continue work on problems in Part A but use of calculators is prohibited during this time. Scoring Scheme: AP Calculus Each section (Multiple choice & free response) accounts for one-half of the final exam grade. It is not expected that all questions will be answered to, since there is full coverage of the subject matter. TransWebTutors.com provides the students an excellent platform to learn about function theory using various existing mathematical techniques and graphing calculator, the rules of differentiation and their applicability, integration techniques their applications. We customize the package based on your availability and performance in the diagnostic test. TransWebTutors.com provides online tutors who are experts in analyzing the student's strengths and weaknesses, and thus design the package so that students can master every section. AP Calculus AB Packages * Fast Track Course for 30 hrs (Price : $ 299) Exhaustive Course for 60 hrs (Price : $ 599) Fast Track Course The duration for this course is 30 hrs. Intensive coverage of each section is carried out. Free Diagnostic test Free Discussion based on the diagnostic test and choosing strong and weak area's 1.0hour Functions, Graphs & Limits Analysis of Graphs 1.0 hour Functions, Graphs & Limits Limits of Functions (incl. one-sided limits) 1.0 hour Functions, Graphs & Limits Asymptotic and Unbounded Behavior 1.0 hour Functions, Graphs & Limits Continuity as a Property of Functions 2.0 hour Derivatives Concept of the Derivative 1.0 hour Derivatives Derivative at a point 2.0 hour Derivatives Derivative as a Function 2.0 hour Derivatives Second Derivatives 2.0 hour Derivatives Applications of Derivatives 2.0 hour Derivatives Computation of Derivatives 2.0 hour Integrals Interpretations and Properties of Definite Integrals 2.0 hour Integrals Applications of Integrals 2.0 hour Integrals Fundamental Theorem of Calculus 2.0 hour Integrals Techniques of Anti-differentiation 2.0 hour Integrals Applications of Anti-differentiation 2.0 hour Integrals Numerical Approximations to Definite Integrals 1.0 hour Full Course 1st Review after Differentiation 1.0 hour Full Course 2nd Review after Integration 1.0 hour Full Course Overall Review in the end Free Final Assessment test Free Detailed discussion on the attempt of AP Calculus AB Exam Exhaustive Course The duration for Exhaustive course for AP Calculus AB preparation in different topics is given below. Each topic and subtopic is exhaustively and comprehensively taught.
Whether you buy it used on Amazon for $39.95 or somewhere else, you can sell it back through our Book Trade-In Program at the current price of $8.58. PBS Teachers provides PreK-12 educational resources and activities for educators tied to PBS programming and correlated to local and national standards and professional ... AGS Pre-Algebra - Revised The bridge to algebra Help your students make a smooth transition from basic math to algebra. Pre-Algebra is written for the needs of the ... math. used teacher resources this page up-dated may 5, 2010. over 2,500 items are now listed, call for pricing and quantities available. 252 244 0728 Gateway - Algebra I . Interactive sites to help students practice skills needed for the Algebra Gateway exam Page last edited 2/24/2009 - (Algebra I new ... Insights Into Algebra 1: Teaching for Learning is an eight-part video, print, and Web-based professional development workshop for middle and high school teachers. Catalog: UWC Materials for Educational Use (12-01-10) All of the materials available are listed here. Please use this reference to fill out the checklist you will ... Materials for Educational Use Catalog 12-01-10.doc Featured Resource: Go! DragonflyTV GPS: Earthquakes Watch as Claire and Nisha take a tour of Lawrence Hall of Science geology exhibit and then walk the fault lines in San ...
More About This Textbook Overview For over fifty years, the Mathematical Association of America (MAA) has been engaged in the construction and administration of challenging contests for students in American and Canadian high schools at every level of ability. This is the ninth book of problems and solutions from the American Mathematics Competitions 12 (AMC), aimed at students of high school age, and featuring 325 problems from the 13 AMC contests held in the years 2001-2007. Graphs and figures have since been redrawn to make them more consistent in form and style, and the solutions to the problems have been both edited and supplemented. The Problem Index contained classifies the problems into the following major subject areas: Algebra and Arithmetic, Sequences and Series, Triangle Geometry, Circle Geometry, Quadrilateral Geometry, Polygon Geometry, Counting Coordinate Geometry, Solid Geometry, Discrete Probability, Statistics, Number Theory, and Logic. These are then broken down into subcategories and cross-referenced for ease of
Mex 1.5 description Use the math expression calculator to quickly evaluate multi variable mathematical expressions. You can type in an expression such as 34+67*sin(23)+log(10) and see the result instantaneously. Mex supports multiple variables, basic operators and trignometric/log functions.
This work provides an alternative for trainee and practising maths teachers at both primary and secondary levels. Based on the DfES and TTA guidelines and requirements, it presents a comprehensive guide to the background, theory and practice of more...

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