Mathematics Books

Book SynopsisA Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Third Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the second edition.New to the Third Edition 40% more content with more explanation and examples throughout New chapter on sampling featuring simulation-based methods Model assessment methods discussed Explanation chapter expanded to include introductory ideas about causation Model interpretation in the presence of transformation Crossvalidation for model s

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Book SynopsisDeveloped in cooperation with the International Baccalaureate®Enable students to construct mathematical models by exploring challenging problems and the use of technology. - Engage and excite students with examples and photos of maths in the real world, plus inquisitive starter activities to encourage their problem-solving skills. - Build mathematical thinking with our 'Toolkit' and mathematical exploration chapter, along with our new toolkit feature of questions, investigations and activities. - Develop understanding with key concepts and applications integrated throughout, along with TOK links for every topic. - Prepare your students for assessment with worked examples, extended essay support and colour-coded questions to highlight the level of difficulty and the different types of questions. - Check understanding with review exercise midway and at the end of the textbook. Follows the new 2019 IB Guide for Mathematics: applications and interpretation Standard LevelAvailable in the seriesMathematics for the IB Diploma: Applications and interpretation SLStudent Book ISBN: 9781510462380Student Book Boost eBook ISBN: 9781398334359Exam Practice Workbook SL: 9781398321892Exam Practice Workbook SL Boost eBook: 9781398342323Mathematics for the IB Diploma: Applications and interpretation HLStudent Book ISBN: 9781510462373Student Book Boost eBook ISBN: 9781398334366Exam Practice Workbook HL: 9781398321885Exam Practice Workbook HL Boost eBook: 9781398342354SL & HL Boost Subscription: 9781398341272Trade ReviewAs a teacher and workshop leader I have worked with many textbooks, and this is one of the best IB Mathematics book I have come across. I like the way the topics are sequenced. I like the way the questions are scaffolded. I like how on the pages you have references to TOK and more elements of the Core. In summary: I like the book very much. -- Pedro Monsalve Correa

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Book SynopsisThis book provides in-depth coverage of Pure Mathematics 1 for Cambridge International AS and A Level Mathematics 9709, for examination from 2020 onwards. With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of careers and further study.Exam Board: Cambridge Assessment International EducationFirst teaching: 2018 First examination: 2020This student book is part of a series of nine books covering the complete syllabus for Cambridge International AS and A Level Mathematics (9709) and Further Mathematics (9231), for first teaching from September 2018 first examination from 2020. This title is endorsed by Cambridge Assessment International Education.Written by expert authors, this Student Book: covers all the content of Pure Mathematics 1 with clear references to what you will learn at the start of each chapter, and coverage that clearly and directly matches the Cambridge syllabus sets mathematics in re

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Book SynopsisThis book provides in-depth coverage of Mechanics for Cambridge International AS and A Level Mathematics 9709, for examination from 2020 onwards. With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of careers and further study.Exam Board: Cambridge Assessment International EducationFirst teaching: 2018 First examination: 2020This student book is part of a series of nine books covering the complete syllabus for Cambridge International AS and A Level Mathematics (9709) and Further Mathematics (9231), for first teaching from September 2018 and first examination from 2020. This title is endorsed by Cambridge Assessment International Education.Written by expert authors, this Student Book: covers the complete content of Mechanics (formerly Mechanics 1) with clear references to what you will learn at the start of each chapter, and coverage that clearly and directly matches the Cambridge syllabus sets mat

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Book SynopsisThis book provides in-depth coverage of Probability & Statistics 1 for Cambridge International AS and A Level Mathematics 9709, for examination from 2020 onwards. With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of careers and further study.Exam Board: Cambridge Assessment International EducationFirst teaching: 2018 First examination: 2020This student book is part of a series of nine books covering the complete syllabus for Cambridge International AS and A Level Mathematics (9709) and Further Mathematics (9231), for first teaching from September 2018 and examination from 2020. This title is endorsed by Cambridge Assessment International Education.Written by expert authors, this Student Book: covers the complete content of Probability & Statistics 1 with clear references to what you will learn at the start of each chapter, and coverage that clearly and directly matches the Cambridge syllabus set

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Book SynopsisExam board: EdexcelLevel: AS / A-level Year 1Subject: MathsSuitable for the 2024 examsComplete revision and practice to fully prepare for the A-level examClear and accessible explanations of all the A-level AS / Year 1 content, with lots of practice opportunities for each topic throughout the book.Based on research that proves repeated practice is more effective than repeated study, this book is guaranteed to help you achieve the best results.There are clear and concise revision notes for every topic covered in the curriculum, plus seven practice opportunities to ensure the best results.Includes:quick tests to check understandingend-of-topic practice questionstopic review questions later in the bookmixed practice questions at the end of the bookfree Q&A flashcards to download onlinean ebook version of the revision guidemore topic-by-topic practice and a complete exam-style paper in the added workbook

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Book SynopsisChallenge yourself at home with word and number puzzlesThese are previously unpublished quality Su Doku grids from The Times, and help to develop you to take on Extreme Su Doku.The 200 puzzles in this collection of treacherously difficult puzzles will stretch even the most advanced Su Doku enthusiast. You will need to use all of your best solving techniques to get to the end of this testing challenge.The puzzles in the collection are of the highest quality and are perfect for the advanced solver in need of a constant supply of ultra-difficult puzzles.Guaranteed to provide hours of mind-stretching entertainment.

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Book SynopsisCollins International Primary Maths supports best practice in primary maths teaching, whilst encouraging teacher professionalism and autonomy. A wealth of supporting digital assets are provided for every lesson, including slideshows, tools and games to ensure they are rich, lively and engaging.Each Workbook page has three levels of challenge which allow learners to practise and consolidate their newly acquired knowledge, skills and understanding of the mathematics they are learning. Questions throughout the course develops learners' Thinking and Working Mathematically skills, and each lesson offers an opportunity for personal reflection on progress. The series also supports Cambridge Global Perspectives with activities that develop and practise key skills.Provides learner support as part of a set of resources for the Cambridge Primary curriculum framework (0096) from 2020.This series is endorsed by Cambridge Assessment International Education to support the new curriculum framework 009

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Book SynopsisMaster linear algebra with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests Study quickly and more effectively Learn the best strategies for solving tough problems in step-by-step detail Review what you've learned in class by solving thousands of relevant problems that test your skill Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so compleTable of ContentsVectors in R and C.Matrix Algebra.Systems of Linear Equations.Square Matrices.Determinants.Algebraic Structures.Vector Spaces and Subspaces.Linear Dependence, Basis, Dimension.Mappings.Linear Mappings.Spaces of Linear Mappings.Matrices and Linear Mappings.Change of Basis, Similarity.Inner Product Spaces, Orthogonality.Polynomials Over A Field.Eigenvalues and Eigenvectors.Diagonalization.Canonical Forms.Linear Functional and the Dual Space.Bilinear, Quadratic, and Hermitian Forms.Linear Operators on Inner Product Spaces.Applications to Geometry and Calculus.

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Book SynopsisThe ideal review for your logic courseMore than 40 million students have trusted Schaumâs Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaumâs Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice. 500 solved problems Includes non-classical logics Covers the probability calculus Complements or supplements the major Logic textbooks Appropriate for the following courses: Introduction to Formal Logic, Informal Logic, Logic Programming, Algebra Complete course content in easy-to-follow outline form Hundreds of solved problems for effective test preparation Table of Contents1. Argument Structure2. Argument Evaluation3. Propositional Logic4. The Propositional Calculus5. The Logic of Categorical Statements6. Predicate Logic7. The Predicate Calculus8. Fallacies9. Induction10. The Probability Calculus11. Further Developments in Formal Logic

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Book SynopsisTrade Review"Both textbook and practical guide, this work is an accessible account of Bayesian data analysis starting from the basics…This edition is truly an expanded work and includes all new programs in JAGS and Stan designed to be easier to use than the scripts of the first edition, including when running the programs on your own data sets." --MAA Reviews "fills a gaping hole in what is currently available, and will serve to create its own market" --Prof. Michael Lee, U. of Cal., Irvine; pres. Society for Mathematical Psych "has the potential to change the way most cognitive scientists and experimental psychologists approach the planning and analysis of their experiments" --Prof. Geoffrey Iverson, U. of Cal., Irvine; past pres. Society for Mathematical Psych. "better than others for reasons stylistic.... buy it -- it’s truly amazin’!" --James L. (Jay) McClelland, Lucie Stern Prof. & Chair, Dept. of Psych., Stanford U. "the best introductory textbook on Bayesian MCMC techniques" --J. of Mathematical Psych. "potential to change the methodological toolbox of a new generation of social scientists" --J. of Economic Psych. "revolutionary" --British J. of Mathematical and Statistical Psych. "writing for real people with real data. From the very first chapter, the engaging writing style will get readers excited about this topic" --PsycCritiquesTable of Contents1. What’s in This Book (Read This First!) PART I The Basics: Models, Probability, Bayes’ Rule, and R 2. Introduction: Credibility, Models, and Parameters 3. The R Programming Language 4. What Is This Stuff Called Probability? 5. Bayes’ Rule PART II All the Fundamentals Applied to Inferring a Binomial Probability 6. Inferring a Binomial Probability via Exact Mathematical Analysis 7. Markov Chain Monte Carlo 8. JAGS 9. Hierarchical Models 10. Model Comparison and Hierarchical Modeling 11. Null Hypothesis Significance Testing 12. Bayesian Approaches to Testing a Point ("Null") Hypothesis 13. Goals, Power, and Sample Size 14. Stan PART III The Generalized Linear Model 15. Overview of the Generalized Linear Model 16. Metric-Predicted Variable on One or Two Groups 17. Metric Predicted Variable with One Metric Predictor 18. Metric Predicted Variable with Multiple Metric Predictors 19. Metric Predicted Variable with One Nominal Predictor 20. Metric Predicted Variable with Multiple Nominal Predictors 21. Dichotomous Predicted Variable 22. Nominal Predicted Variable 23. Ordinal Predicted Variable 24. Count Predicted Variable 25. Tools in the Trunk

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Book SynopsisTable of ContentsCHAPTER 1 Introduction to statistics CHAPTER 2 Descriptive statistics CHAPTER 3 Elements of probability CHAPTER 4 Random variables and expectation CHAPTER 5 Special random variables CHAPTER 6 Distributions of sampling statistics CHAPTER 7 Parameter estimation CHAPTER 8 Hypothesis testing CHAPTER 9 Regression CHAPTER 10 Analysis of variance CHAPTER 11 Goodness of fit tests and categorical data analysis CHAPTER 12 Nonparametric hypothesis tests CHAPTER 13 Quality control CHAPTER 14 Life testing CHAPTER 15 Simulation, bootstrap statistical methods, and permutation tests CHAPTER 16 Machine learning and big data

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Book SynopsisAbout our author Richard A. Brualdi is Bascom Professor of Mathematics, Emeritus at the University of Wisconsin - Madison. He served as Chair of the Department of Mathematics from 1993-1999. His research interests lie in matrix theory and combinatorics/graph theory. Professor Brualdi is the author or co-author of 6 books, and has published extensively. He is one of the editors-in-chief of the journal Linear Algebra and its Applications and of the journal Electronic Journal of Combinatorics. He is a member of the American Mathematical Society, the Mathematical Association of America, the International Linear Algebra Society, and the Institute for Combinatorics and its Applications. He is also a Fellow of the Society for Industrial and Applied Mathematics.Table of Contents 1. What is Combinatorics? 2. The Pigeonhole Principle 3. Permutations and Combinations 4. Generating Permutations and Combinations 5. The Binomial Coefficients 6. The Inclusion-Exclusion Principle and Applications 7. Recurrence Relations and Generating Functions 8. Special Counting Sequences 9. Systems of Distinct Representatives 10. Combinatorial Designs 11. Introduction to Graph Theory 12. More on Graph Theory 13. Digraphs and Networks 14. Pólya Counting

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Book SynopsisDonal O'Shea is professor of mathematics and dean of faculty at Mount Holyoke College. He has written scholarly books and monographs, and his research articles have appeared in numerous journals and collections. He lives in South Hadley, Massachusetts.Trade ReviewConveys topology's mind-bending contortions with great flair * New Scientist *One can't read The Poincaré Conjecture without an overwhelming awe at the infinite depths and richness of a mathematical realm not made by us * Martin Gardner, author of The Annotated Alice *Reveals the human story behind the challenge of the conjecture, and gives us a glimpse of the weird world inhabited by mathematicians * BBC Focus *Beautifully written * American Scientist *Intriguing * The Times *A truly marvellous book * Martin Gardner *One can't read The Poincaré Conjecture without an overwhelming awe at the infinite depths and richness of a mathematical realm not made by us * Martin Gardner, author of The Annotated Alice *

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Book SynopsisTHE INTERNATIONAL BESTSELLER''An entertaining tour that will change how you see the world'' Sean Carroll, author of Something Deeply HiddenIs there a secret formula for improving your life? For making something a viral hit? For deciding how long to stick with your current job, Netflix series, or even relationship?This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthily and see through scaremongering. They are known only by mathematicians - until now.With wit and clarity, mathematician David Sumpter shows that it isn''t the technical details which make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone cTrade ReviewSometimes books about numbers come along and we're so ecstatic that we just pop with delight. One such book is The Ten Equations that Rule The World -- Tim Harford * More or Less BBC4 *Hugely entertaining, erudite and at times genuinely witty . . . it's nice to be spoken to in grown-up language by a genius. You will come away from Sumpter's book with a much clearer idea of why the world is less messy than it appears * E&T Magazine *These aren't the equations of Newton or Einstein -- crisp relations describing the evolution of a clockwork universe. These are the equations of randomness, expectation, and imperfect information. The equations, in other words, of the real world. David Sumpter provides an entertaining tour that will change how you see the world -- Sean Carroll author of Something Deeply HiddenSumpter writes fascinatingly about his experiences as a consulting mathematician. . . I will encourage my mathematics undergraduates to read this book since it will inspire them by showing the relevance of mathematics to today's world and make them think about the moral issues they will face as mathematicians * Times Higher Education *

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Book SynopsisThis textbook uses insight from differential equations to analyse fundamental subjects of modern theoretical physics, including classical and quantum mechanics, thermodynamics, electromagnetism, superconductivity, gravitational physics, and quantum field theories.Table of ContentsPreface Notation and Convention 1: Hamiltonian Systems and Applications 2: Schrödinger Equation and Quantum Mechanics 3: Maxwell Equations, Dirac Monopole, and Gauge Fields 4: Special Relativity 5: Abelian Gauge Field Equations 6: Dirac Equations 7: GinzburgDSLandau Equations for Superconductivity 8: Magnetic Vortices in Abelian Higgs Theory 9: Non-Abelian Gauge Field Equations 10: Einstein Equations and Related Topics 11: Charged Vortices and ChernDSSimons Equations 12: Skyrme Model and Related Topics 13: Strings and Branes 14: BornDSInfeld Theory of Electromagnetism 15: Canonical Quantization of Fields Appendices Bibliography Index

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Book SynopsisThis book uses Big Allied and Dangerous (BAAD) as the dataset for a modern and comprehensive exploration of why insurgent groups attack civilians, even though their existence depends on public support. The book examines this phenomenon in specific contexts, including schools, news media, and nonmilitary/nongovernment spaces designed for the general public.Trade ReviewIn this compelling book, Asal, Phillips, and Rethemeyer provide a much-needed investigation into why armed militant organizations target civilians during conflicts. The authors use both original quantitative data and numerous case references to construct a comprehensive picture of militant group targeting behavior that considers group relations with civilians, state counter-insurgency strategy, inter-group competition, group criminal activity, group ideology and ethnic ties and a host of other factors. The end result is a book that will inform both scholarly and policy audiences alike. A must-read for anyone interested in insurgent group behavior. * James Piazza, Liberal Arts Professor of Political Science, The Pennsylvania State University *By honing in on relational explanations, this book makes a major contribution to our understanding of why insurgent organizations sometimes kill civilians and other times not. The concept of insurgent embeddedness provides a compelling and novel theoretical lens to explain this variation. Combined with a rich qualitative and quantitative empirical material, it generates profound insights that will inform and inspire students of insurgent violence in years to come. * Hanne Fjelde, Associate Professor, Uppsala University *Insurgent Terrorism is a thought-provoking, provocative investigation by three leading scholars on why insurgent groups may target civilians in pursuit of political goals. This is an important question of increasing relevance for sub-Saharan Africa and the Middle East and North Africa. The book supports its theses with data-driven, careful empirical analysis based on insurgent attacks, goals, and inter-organization linkages. * Todd Sandler, Emeritus Chair, University of Texas at Dallas *This book provides a fresh look at organizations' choices to engage in terrorist attacks against civilians. Advancing a theory of embeddedness, the authors examine complex relationships between insurgent organizations, the state, other insurgents, and the civilian population. They find a diverse set of factors impact different types of terrorism, advancing our understanding of this phenomena. * Kathleen Gallagher Cunningham, Cunningham, Professor, University of Maryland *Insurgent Terrorism is an important book that presents detailed cross-national data and analyses of civilian targeting by insurgent groups in civil conflict. Asal, Phillips, and Rethemeyer persuasively argue that the embeddedness of insurgent groups - that is, their relations with the state, the public, and each other - explains variation in civilian victimization. This relational account produces novel and intriguing findings, such as that both alignment and rivalry with other groups lead to more frequent civilian targeting. Marked by empirical richness, the book advances knowledge on the behavior of insurgent groups, civilian victimization, and civil conflict. * Ursula Daxecker, Associate Professor, University of Amsterdam *Table of ContentsSECTION I. Introduction, Theory, and Initial Testing Chapter 1. Introduction Chapter 2. The Embeddedness Theory of Civilian Targeting by Insurgent Groups Chapter 3. Describing the BAAD2 Insurgency Data and Other Data Sources Chapter 4. Testing Primary Hypotheses SECTION II. Empirical Extensions: Types of Civilian Targeting Chapter 5. Why Do Some Insurgent Groups Attack Schools? Chapter 6. Why Do Some Insurgent Groups Attack Journalists? Chapter 7. Why Do Some Insurgent Groups Mostly Attack the General Public? SECTION III. Further Analysis of Inter-Group Relationships Chapter 8. Longitudinal Modelling of Insurgent Alliances Chapter 9. Understanding Insurgent Rivalry Chapter 10. Conclusion

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Book SynopsisPlease note this title is suitable for any student studying:Exam Board: AQALevel/Subject: AQA Level 3 Certificate in Mathematical StudiesFirst teaching: September 2014First exams: June 2016Developed specifically for the new AQA Mathematical Studies qualification, AQA Mathematical Studies (Level 3 Certificate) Student Book builds students'' confidence and fluency in applying and extending their GCSE Maths knowledge to new and unfamiliar scenarios, and can also support the numerical demands of their other studies. The resource is linked to MyMaths, to offer students further valuable support.

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Book SynopsisHow fast can you calculate? Would you like to be faster? This book presents the time honored tricks and tips of calculation, from a fresh perspective, to boost the speed at which you can add whether a couple of numbers, or columns so long an accountant may faint. Find out how to subtract, multiply, divide, and find square roots more quickly.Trade ReviewIf you think mental arithmetic is out of date in the 21st century, think again. This engaging book is about insight and interestingness beyond the simple utility of quicker calculations. The general style is original and characterful, and makes the book distinctive. * Prasenjit Saha, University of Zurich *This book is about very elementary concepts that ought to be read by sophisticated people who appreciate that elementary does not mean trivial. The author's erudite scholarship shines in the prose, along with just the right level of dry wit. It's serious stuff he's writing about (without numbers and arithmetic, our modern world simply vanishes into the ancient past where numbers were limited to none, one, and many), but in such a way that the reader does not slowly nod-off into a coma. * Paul J. Nahin, University of New Hampshire *Lipscombe's book is unusual, being, as it is, an expansive view of a small subject. The text he presents here is excellent, and is a model of everything a writer strives for: concision, simplicity, directness, accuracy, and surprise. * Don S. Lemons, Bethel College, Kansas *Table of ContentsPreface Introduction Challenge 1: Arithmetical Advice 2: Speedier Sums and Subtractions Interlude I: The Magic of 111,111 3: Accounting for Taste -- Adding Columns Quickly Interlude II: Checking, Check Digits, and Casting out Nines 4: Quicker Quotients and Pleasing Products -- Multiply and Divide by Specific Numbers Interlude III: Doomsday 5: Calculations with Constraints -- Multiply and Divide by Numbers with Specific Properties Interlude IV: Multicultural Multiplication 6: Super Powers -- Calculate Squares, Square Roots, Cube Roots, and More 7: Close-Enough Calculations -- Quick and Accurate Approximations Interlude V: Approximating the Number of Space Aliens 8: Multiplying Irrationally The Grand Finale Further Reading Appendix I: Calculating Doomsday Appendix II: The Squares from 1 to 100

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Book SynopsisBlack holes present one of the most fascinating predictions of Einstein''s general theory of relativity. There is strong evidence of their existence through observation of active galactic nuclei, including the centre of our galaxy, observations of gravitational waves, and others.There exists a large scientific literature on black holes, including many excellent textbooks at various levels. However, most of these steer clear from the mathematical niceties needed to make the theory of black holes a mathematical theory. Those which maintain a high mathematical standard are either focused on specific topics, or skip many details. The objective of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject.The book provides a wide background to the current research on all mathematical aspects of the geometry of black hole spacetimes.Trade ReviewWritten with a high standard of rigor and care, with very good treatments of many topics that are hard to find elsewhere. * Robert Wald, University of Chicago *Including some very interesting and unique material, the book is written in a manner that will be accessible for students, and provide a valuable resource for experts working in mathematical general relativity. * Greg Galloway, University of Miami *This text is an excellent research level monograph exploring the detailed and rich structure of black holes in mathematical physics. * Kymani Armstrong-Williams, Physics Book Reviews *Table of ContentsPART I GLOBAL LORENTZIAN GEOMETRY 1: Basic Notions 2: Elements of causality 3: Some applications PART II BLACK HOLES 4: An introduction to black holes 5: Further selected solutions 6: Extensions, conformal diagrams 7: Projection diagrams 8: Dynamical black holes

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Book SynopsisA classic single-volume textbook, popular for its direct and straightforward approach. Understanding Pure Mathematics starts by filling the gap between GCSE and A Level and builds on this base for candidates taking either single-subject of double-subject A Level.Trade Review...clearly presented book with carefully graded questions... worthy of consideration. * Mathematics in Schools *Table of Contents1. Functions ; 2. Vectors ; 3. Coordinate geometry ; 4. Trigonometry ; 5. Algebra I ; 6. Matrices ; 7. Permutations and combinations ; 8. Series and binomial theorem ; 9. Probability ; 10. Calculus I: differentiation ; 11. Sketching functions I ; 12. Calculus II: integration ; 13. Calculus III: further techniques ; 14. Sketching functions II ; 15. Trigonometry II ; 16. Coordinate geometry II ; 17. Three-dimensional work: vectors and matrices ; 18. Algebra II ; 19. Exponential and logarithmic functions ; 20. Calculus IV: further integration ; 21. Numerical methods

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Book SynopsisThis fully updated new edition of Wilson Sutherland's classic text, Introduction to Metric and Topological Spaces, establishes the language of metric and topological spaces with continuity as the motivating concept, before developing its discussion to cover compactness, connectedness, and completeness.Trade ReviewThe presentation, description and explanation throughout the seventeen short chapters are excellent, and the text can be described as self-contained, with many suitably chosen examples and exercises ,.. An interesting innovation for the new edition is having a companion web site in which more useful and relevant materials can be found. * Peter Shiu, The Mathematical Gazette *Table of ContentsPREFACE; REFERENCES; INDEX

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Book SynopsisThe study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof - deductive reasoning from a set of axioms - first arose. To this day geometry remains a very active area of research in mathematics. This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Starting from the basics, Maciej Dunajski proceeds from concrete examples (of mathematical objects like Platonic solids, or theorems like the Pythagorean theorem) to general principles. Throughout, he outlines the role geometry plays in the broader context of science and art. Very Short Introductions: Brilliant, Sharp, Inspiring ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Trade ReviewIt is a lovely little book, to be recommended for sixth-formers or first year undergraduates: it will open their eyes to the amazing beauty and power of this ancient and modern subject. * Stephen Huggett, London Mathematical Society Newsletter, March 2023 *Various geometries are presented, each with particularly engaging examples of problems that are formulated in that particular geometry. * Victor V. Pambuccian, zb Math Open *Table of Contents1: What is geometry? 2: Euclidean geometry 3: Non-Euclidean geometry 4: Geometry of curved spaces 5: Projective geometry 6: Other geometries 7: Geometry of the physical world Further Reading Index

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Book SynopsisThe Nature of Complex Networks provides a systematic introduction to the statistical mechanics of complex networks and the different theoretical achievements in the field that are now finding strands in common.The book presents a wide range of networks and the processes taking place on them, including recently developed directions, methods, and techniques. It assumes a statistical mechanics view of random networks based on the concept of statistical ensembles but also features the approaches and methods of modern random graph theory and their overlaps with statistical physics.This book will appeal to graduate students and researchers in the fields of statistical physics, complex systems, graph theory, applied mathematics, and theoretical epidemiology.Trade ReviewThe current volume by Dorogovtsev and Mendes takes quite a broad view of complex networks to include the analysis of finite and infinite graphs, directed and undirected graphs, multigraphs, hypergraphs, and even simplicial complexes, as networks scale according to increasing N or in some other fashion. The writing style is that of physics and especially statistical mechanics with frequent connections made to physical concepts such as Bose-Einstein condensation...The current volume can especially serve as a useful reference on complex networks from a physics perspective. * Lenwood S. Heath, MathSciNet *Table of ContentsPreface 1: First insight 2: Graphs 3: Classical random graphs 4: Equilibrium networks 5: Evolving networks 6: Connected components 7: Epidemics and spreading phenomena 8: Networks of networks 9: Spectra and communities 10: Walks and search 11: Temporal networks 12: Cooperative systems on networks 13: Inference and reconstruction 14: What's next? Further Reading Appendices A-G References

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Book SynopsisVolume Two of an award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciencesTrade Review“Clear, enthusiastic, and communicating a love of maths, this is a useful, engaging and well-written text.”—Becca Asquith, Professor of Mathematical Immunology, Imperial College London"This is a wonderful book, wise and witty. It would have taught me most of the math I needed for my career in research – if I did all the problems."—Stephen Stearns, author of The Evolution of Life Histories and Evolutionary Medicine“This well-written book covers multivariate calculus and dynamical systems within the context of the biological sciences, providing well-chosen, up-to-date biomedical examples. The Markov chain, along with its many interesting applications, is also introduced.”—Hongyu He, Professor of Mathematics, Louisiana State University

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Book SynopsisTable of Contents1. Getting Started 2. Basic Techniques to Prove If/Then Statements 3. Special Kinds of Theorems 4. Some Mathematical Topics on Which to Practice Proof Techniques 5. Review Exercises

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Book SynopsisThis textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as:Combinations Permutations Graphs Designs Many classical areas are covered as well as new research topics not included in most existing texts, such as: Group algorithms Graph isomorphism Hill-climbing Heuristic search algorithms This work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, Trade Review"Very clear exposition. I jumped right into [the] heuristic methods chapter and understood it almost instantly..." - Dean H. Judson, Ph.D., Nevada State Demographer"…book serves as an introduction to the basic problems and methods…style is clear, transparent…The algorithmic problems are always considered and they are in the center of the discussion…has a fresh approach to combinatorics that is available for readers, students in computer science, electrical engineering without any background in mathematics." - Péter Hajnal, Acta Science Math Table of ContentsStructures and AlgorithmsWhat are Combinatorial Algorithms?What are Combinatorial Structures?What are Combinatorial Problems?O-NotationAnalysis of AlgorithmsComplexity ClassesData StructuresAlgorithm Design TechniquesGenerating Elementary Combinatorial ObjectsCombinatorial GenerationSubsetsk-Element SubsetsPermutationsMore Topics in Combinatorial GenerationInteger PartitionsSet Partitions, Bell and Stirling NumbersLabeled TreesCatalan FamiliesBacktracking AlgorithmsIntroductionA General Backtrack AlgorithmGenerating All CliquesEstimating the Size of a Backtrack TreeExact CoverBounding FunctionsBranch-and-BoundHeuristic SearchIntroduction to Heuristic AlgorithmsDesign Strategies for Heuristic AlgorithmsA Steepest-Ascent Algorithm for Uniform Graph PartitionA Hill-Climbing Algorithm for Steiner Triple SystemsTwo Heuristic Algorithms for the Knapsack ProblemA Genetic Algorithm for the Traveling Salesman ProblemGroups and SymmetryGroupsPermutation GroupsOrbits of SubsetsCoset RepresentativesOrbits of k-tuplesGenerating Objects Having AutomorphismsComputing IsomorphismIntroductionInvariantsComputing CertificatesIsomorphism of Other StructuresBasis ReductionIntroductionTheoretical DevelopmentA Reduced Basis AlgorithmSolving Systems of Integer EquationsThe Merkle-Hellman Knapsack SystemBibliographyAlgorithm IndexProblem IndexIndex

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Book SynopsisThe book provides insights in the decision-making for implementing strategies in various spheres of real-world issues. It integrates optimal policies in various decision­making problems and serves as a reference for researchers and industrial practitioners. Furthermore, the book provides sound knowledge of modelling of real-world problems and solution procedure using the various optimisation and statistical techniques for making optimal decisions. The book is meant for teachers, students, researchers and industrialists who are working in the field of materials science, especially operations research and applied statistics. Table of Contents1. A New Version of the Generalized Rayleigh Distribution with Copula, Properties, Applications and Different Methods of Estimation 2. Expanding the Burr X Model: Properties, Copula, Real Data Modeling and Different Methods of Estimation 3. Transmuted Burr Type X Model with Applications to Life Time Data 4. Monitoring Patients Blood Level through Enhanced Control Chart 5. Goodness of Fit in Parametric and Non-parametric Econometric Models 6. Stochastic Models for Cancer Progression and its Optimal Programming for Control with Chemotherapy 7. A New Unrelated Question Model with Two Questions Per Card 8. Hybrid of Simple Model and a New Unrelated Question Model for Two Sensitive Characteristics 9. Hybrid of Crossed Model and a New Unrelated Question Model for Two Sensitive Characteristics 10. Modified Regression Type Estimator by Ingeniously Utilizing Probabilities for more Efficient Results in Randomized Response Sampling 11. Ratio and Regression Type Estimators for a New Measure of Coefficient of Dispersion Relative to the Empirical Mode 12. Class of Exponential Ratio Type Estimator for Population Mean in Adaptive Cluster Sampling 13. An Inventory Model for Substitutable Deteriorating Products under Fuzzy and Cloud Fuzzy Demand Rate 14. Co-ordinated Selling Price and Replenishment Policies for Duopoly Retailers under Quadratic Demand and Deteriorating Nature of Items15. Quadratic Programming Approach for the Optimal Multi-objective Transportation Problem 16. Analyzing Multi-Objective Fixed-Charge Solid Transportation Problem under Rough and Fuzzy-Rough Environments 17. Overall Shale Gas Water Management: A Neutrosophic Optimization Approach 18. Memory Effect on an EOQ Model with Price Dependant Demand and Deterioration 19. Optimality Conditions of an Unconstrained Imprecise Optimization Problem via Interval Order Relation 20. Power Comparison of Different Goodness of Fit Tests for Beta Generalized Weibull Distribution 21. On the Transmuted Modified Lindley Distribution: Theory and Applications to Lifetime Data 22. Adjusted Bias and Risk for Estimating Treatment Effect after Selection with an Application in Idiopathic Osteoporosis 23. Validity Judgement of an EOQ Model using Phi-coefficient 24. Uncertain Chance-Constrained Multi-Objective Geometric Programming Problem 25. Optimal Decision Making for the Prediction of Diabetic Retinopathy in Type 2 Diabetes Mellitus Patients

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Book SynopsisThis book is intended to serve as a bridge in statistics for graduates and business practitioners interested in using their skills in the area of data science and analytics as well as statistical analysis in general. On the one hand, the book is intended to be a refresher for readers who have taken some courses in statistics, but who have not necessarily used it in their day-to-day work. On the other hand, the material can be suitable for readers interested in the subject as a first encounter with statistical work in Python. Statistics and Data Visualisation with Python aims to build statistical knowledge from the ground up by enabling the reader to understand the ideas behind inferential statistics and begin to formulate hypotheses that form the foundations for the applications and algorithms in statistical analysis, business analytics, machine learning, and applied machine learning. This book begins with the basics of programming in Python and data analysTable of Contents1. Data, Stats and Stories - An Introduction 2. Python Programming Primer 3. Snakes, Bears & Other Numerical Beasts: NumPy, SciPy & Pandas 4. The Measure of All Things - Statistics 5. Definitely Maybe: Probability and Distributions 6. Alluring Arguments and Ugly Facts - Statistical Modelling and Hypothesis Testing 7. Delightful Details - Data Visualisation 8. Dazzling Data Designs - Creating Charts A. Variance: Population v Sample B. Sum of First n Integers C. Sum of Squares of the First n Integers D. The Binomial Coefficient E. The Hypergeometric Distribution F. The Poisson Distribution G. The Normal Distribution H. Skewness and Kurtosis I. Kruskal-Wallis Test - No Ties

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Book SynopsisQuantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems.This fully updated new edition addresses many topics not typically found in books at this level, including: Bound state solutions of quantum pendulum Morse oscillator Solutions of classical counterpart of quantum mechanical systems A criterion for bound state Scattering from a locally periodic potential and reflection-less potential Modified Heisenberg relation Wave packet revival and its dynamics An asymptotic method for slowly varying potentials Klein paradox, Einstein-Podolsky-Rosen (EPR) paradox, and Bell's theorem <Table of Contents 1. Why Was Quantum Mechanics Developed? 2. Schrödinger Equation and Wave Function. 3. Operators, Eigenvalues and Eigenfunctions. 4. Exactly Solvable Systems I: Bound States. 5. Exactly Solvable Systems II: Scattering States. 6. Matrix Mechanics. 7. Various Pictures in Quantum Mechanics and Density Matrix. 8. Heisenberg Uncertainty Principle. 9. Momentum Representation. 10. Wave Packet. 11. Theory of Angular Momentum. 12. Hydrogen Atom. 13. Approximation Methods I: Time-Independent Perturbation Theory. 14. Approximation Methods II: Time-Dependent Perturbation Theory. 15. Approximation Methods III: WKB and Asymptotic Methods. 16. Approximation Methods IV: Variational Method. 17. Scattering Theory. 18. Identical Particles. 19. Relativistic Quantum Theory. 20. Mysteries in Quantum Mechanics. 21. Delayed-Choice Experiments. 22. Fractional Quantum Mechanics. 23. Numerical Methods for Quantum Mechanics. Appendices. Index.

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Book Synopsis"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis.Trade Review"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book for classroom use or self-study." --MathSciNetTable of ContentsI. The Complex Number System.- §1. The real numbers.- §2. The field of complex numbers.- §3. The complex plane.- §4. Polar representation and roots of complex numbers.- §5. Lines and half planes in the complex plane.- §6. The extended plane and its spherical representation.- II. Metric Spaces and the Topology of ?.- §1. Definition and examples of metric spaces.- §2. Connectedness.- §3. Sequences and completeness.- §4. Compactness.- §5. Continuity.- §6. Uniform convergence.- III. Elementary Properties and Examples of Analytic Functions.- §1. Power series.- §2. Analytic functions.- §3. Analytic functions as mapping, Möbius transformations.- IV. Complex Integration.- §1. Riemann-Stieltjes integrals.- §2. Power series representation of analytic functions.- §3. Zeros of an analytic function.- §4. The index of a closed curve.- §5. Cauchy’s Theorem and Integral Formula.- §6. The homotopic version of Cauchy’s Theorem and simple connectivity.- §7. Counting zeros; the Open Mapping Theorem.- §8. Goursat’s Theorem.- V. Singularities.- §1. Classification of singularities.- §2. Residues.- §3. The Argument Principle.- VI. The Maximum Modulus Theorem.- §1. The Maximum Principle.- §2. Schwarz’s Lemma.- §3. Convex functions and Hadamard’s Three Circles Theorem.- §4. Phragm>én-Lindel>üf Theorem.- VII. Compactness and Convergence in ihe Space of Analytic Functions.- §1. The space of continuous functions C(G, ?).- §2. Spaccs of analytic functions.- §3. Spaccs of meromorphic functions.- §4. The Riemann Mapping Theorem.- §5. Weierstrass Factorization Theorem.- §6. Factorization of the sine function.- $7. The gamma function.- §8. The Riemann zeta function.- VIII. Runge’s Theorem.- §1. Runge’s Theorem.- §2. Simple connectedness.- §3. Mittag-Leffler’s Theorem.- IX. Analytic Continuation and Riemann Surfaces.- §1. Schwarz Reflection Principle.- $2. Analytic Continuation Along A Path.- §3. Monodromy Theorem.- §4. Topological Spaces and Neighborhood Systems.- $5. The Sheaf of Germs of Analytic Functions on an Open Set.- $6. Analytic Manifolds.- §7. Covering spaccs.- X. Harmonic Functions.- §1. Basic Properties of harmonic functions.- §2. Harmonic functions on a disk.- §3. Subharmonic and superharmonic functions.- §4. The Dirichlet Problem.- §5. Green’s Functions.- XI. Entire Functions.- §1. Jensen’s Formula.- §2. The genus and order of an entire function.- §3. Hadamard Factorization Theorem.- XII. The Range of an Analytic Function.- §1. Bloch’s Theorem.- §2. The Little Picard Theorem.- §3. Schottky’s Theorem.- §4. The Great Picard Theorem.- Appendix A: Calculus for Complex Valued Functions on an Interval.- Appendix B: Suggestions for Further Study and Bibliographical Notes.- References.- List of Symbols.

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Book SynopsisOne Review of Basic Material.- I Numbers and Functions.- II Graphs and Curves.- Two Differentiation and Elementary Functions.- III The Derivative.- IV Sine and Cosine.- V The Mean Value Theorem.- VI Sketching Curves.- VII Inverse Functions.- VIII Exponents and Logarithms.- Three Integration.- IX Integration.- X Properties of the Integral.- XI Techniques of Integration.- XII Applications of Integration.- Four Taylor's Formula and Series.- XIII Taylor's Formula.- XIV Series.- Five Functions of Several Variables.- XV Vectors.- XVI Differentiation of Vectors.- XVII Functions of Several Variables.- XVIII The Chain Rule and the Gradient.- Answer.Table of ContentsI: Review of Basic Material. * Numbers and Functions. * Graphs and Curves. II: Differention and Elementary Functions. * The Derivative. * Sine and Cosine. * The Mean Value Theorem. * Sketching Curves. * Inverse Functions * Exponents and Logarithms. III: Integration. * Integration. * Properties of the Integral. * Techniques of Integration. * Applications of Integration. IV: Taylor's Formula and Series. * Taylor's Formula. * Series. Appendix. V: Functions of Several Variables. * Vectors. * Differention of Vectors. * Functions of Several Variables. * The Chain Rule and the Gradient.

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Book Synopsis

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Book Synopsis"Arthur Benjamin... joyfully shows you how to make nature's numbers dance. Let his book be your partner for a lifetime of learning."-Bill Nye, Science Educator and CEO, The Planetary SocietyTrade Review"Arthur Benjamin shows you that numbers do more than just keep track of things and solve problems. He joyfully shows you how to make nature's numbers dance. Let his book be your partner for a lifetime of learning."-Bill Nye, science educator and CEO, The Planetary Society "Whether it's been decades since you last took algebra or you're currently dealing with the aches of solving for x, The Magic of Math is a good read. Even though it includes, gasp, equations."-Steve Mirsky, Scientific American "As soon as the reader has absorbed one 'trick', Benjamin is already moving on to the next one - and each is more dazzling than the last."-Physics World "Arthur Benjamin's The Magic of Math is a thoroughly engaging book for readers of many ages and mathematical backgrounds... This is an absolute gem of a book. It contains something of interest for everyone, and the author's lively style and obvious affection for the subject makes this a book to keep, reread, and share." -Mathematical Reviews "[A] fascinating book... The writing style is inviting, and the book is filled with fun examples. Readers can easily jump around and choose from the wide variety of topics or read straight through." -Mathematics Teacher "The book is a fast-paced tour of 12 broad topics ranging from simple arithmetic to the subtleties of infinite sums... Benjamin approaches all of these subjects with the goal of emphasizing the wonder and magic inherent in them, while still giving the reader a sense of the mathematics hiding of the magicians sleeve... The book offers a dizzying array of mathematical delights. But here, once the mathemagician has finished his sleight-of-hand, we have the luxury of peeking behind the curtain to understand how all those tricks are done." -Math Horizons "This excellent book is filled with mathematical magic... Benjamin's writing is very readable and entertaining: his numbers dance. "-Manhattan Book Review "The book delivers on all the promise of both aspects of Benjamin's talent: teacher and performer. Like [Martin] Gardner, Benjamin telegraphs a joy in surprising mathematical stunts... I recommend this book for the math enthusiast embarking on his or her university career, the high school adept in your life intrigued by math yet bored in class, or someone remembering fondly math as their favorite subject yet lacking time to enroll in courses now."-Tom Schulte, MAA Reviews "[Benjamin] use[s] some interesting trickery to draw the reader into the conversation about the importance of math in everyday life... The Magic of Math is a good model for instructional material. It delivers material on a complex nature in a manner that most people will be able to understand, and you get some magic tricks and humor thrown in for the bargain. You will enjoy this book, you can count on that."-Roanoke Times "[The Magic of Math] would be perfect reading for the gifted and talented as a supplement to other course work. Of course, self-motivated individuals interested in mathematics will enjoy the book too. It would be a good resource for mathematics teachers seeking some additional spice for their presentations. The book is well written; graphics are particularly clear; physical format is excellent."-CHOICE "[A] well-written, entertaining volume... This solid reference for teachers seeking interesting classroom examples (and jokes) could easily lure a student into further studies in mathematics."-Library Journal "An enthusiastic celebration of the beauty of mathematics... Benjamin delivers a primer generously filled with insights and intuitions that make math approachable, interesting, and, yes, beautiful."-Kirkus Reviews "[A] positively joyful exploration of mathematics. [Benjamin's] approach is simple and refreshingly practical... Whether figuring out compound interest, using trigonometry to determine the height of a tree, or employing calculus to work out a shortest possible walking route, each topic is presented in the clearest, simplest way possible... [I]ts energy and enthusiasm should charm even the most math-phobic readers."-Publishers Weekly, starred review "A look through Art's book shows there really is something magical about maths - and it can be cool too!"-The Weekly News (UK) "With The Magic of Math, Arthur Benjamin has emerged as the world's foremost math teacher and a national treasure. Parents should get this book for their children...and a second copy for themselves. It's that good. And important. Read it."-Michael Shermer, publisher, Skeptic magazine, and author of The Science of Good and Evil "Prepare to be dazzled and delighted. This is a fun, fast-paced magic show of the greatest treasures of pre-college math, from poker hands to Pascal's triangle, all revealed with the flair of a showman and the clarity of a master teacher. The Magic of Math will leave you smiling, awestruck, and begging for an encore." -Steven Strogatz, professor of Mathematics, Cornell University, and author of The Joy of x "The Magic of Math teaches you cool mathematical facts, theorems, puzzles, and problems from arithmetic to calculus. The book provides problems that are accessible to everyone. Teachers will find many ideas to motivate students and to provide an extra challenge for those who are already into math." -Gail Burrill, president emeritus, National Council of Teachers of Mathematics, and Professor of Mathematics Education, Michigan State University "Conventional magic works because you can't understand how it works. The magic of mathematics comes from that exciting 'aha' moment when you suddenly get what's going on. Arthur Benjamin entertainingly provides readers with an all-access backstage pass to the magical world of mathematics." -Marcus du Sautoy, professor of Mathematics, University of Oxford, and author of The Number Mysteries "They say magicians should never reveal their secrets. Happily, Arthur Benjamin has ignored this silly adage-for in this small volume, Benjamin reveals to his audience the secrets of numbers and other mathematical illusions that have intrigued mathematicians for millennia." -Edward B. Burger, president, Southwestern University, and author of The 5 Elements of Effective Thinking "This book will be magical for my students, as it would have been for me throughout my school days. They'll be able to revisit the book frequently as they learn more math, finding deeper appreciation and discovering new areas to explore with each visit." -Richard Rusczyk, founder, Art of Problem Solving, and director, USA Mathematical Talent Search "In The Magic of Math, Arthur Benjamin has pulled off a seemingly impossible trick. He has made higher mathematics appear so natural and engaging that you will wonder why you were ever bored and confused in math class. There are many books that attempt to popularize mathematics. This is one of the best. On virtually every page I found myself learning new things, or looking at familiar topics in novel ways."-Jason Rosenhouse, professor of Mathematics, James Madison University, and author of The Monty Hall Problem "In The Magic of Math, mathemagician Arthur Benjamin gives us an entertaining and enlightening tour of a wide swath of fundamental mathematical ideas, presented in a way that is accessible to a broad audience. A particularly appealing feature of the book is the frequent use of friendly, down-to-earth explanations of the concepts and connections between them." -Ronald Graham, president emeritus, American Mathematical Society, and co-author of Magical Mathematics "This book is a whirlwind tour of mathematics from arithmetic and algebra all the way to calculus and infinity, and especially the number 9. Arthur Benjamin's enthusiastic and engaging writing style makes The Magic of Math a great addition to any math enthusiast's bag of tricks."-Laura Taalman, professor of Mathematics and Statistics, James Madison University "Mathematics is full of surprisingly beautiful patterns, which Arthur Benjamin's witty personality brings to life in The Magic of Math. You will not only discover many wonderful ideas, but you will also find some fun mathematical magic tricks that you will want to try out on your friends and family. Be prepared to learn that math is more entertaining than you may have thought."-George W. Hart, mathematical sculptor, research professor, Stony Brook University, and cofounder, The Museum of Mathematics "The Magic of Math is a delightful stroll through a garden filled with fascinating examples. Anyone with any interest in magic, puzzles, or math will have many hours of enjoyment in reading this book." -Maria M. Klawe, president, Harvey Mudd College "Arthur Benjamin has created an instant mathematical classic, by combining Isaac Asimov's clarity with Martin Gardner's taste and adding his own sense of fun and adventure. I wish he wrote this book when I was a kid."-Paul A. Zeitz, professor and chair of Mathematics, University of San Francisco, and author of The Art and Craft of Problem Solving "There's a playful joy to be found in this book, for readers at any level. Most magicians don't reveal their secrets, but in The Magic of Math, Arthur Benjamin shows how uncovering the mystery behind beautiful mathematical truths makes math even more marvelous to behold."-Francis Su, president, Mathematical Association of America "The Magic of Math offers an expansive, unforgettable journey through mathematics where numbers dance and mathematical secrets are revealed. Just open the book and start reading; you'll be swept over by the magic of Benjamin's writing. Luckily, there is no magician's code to these secrets as you'll undoubtedly want to share and perform them with family and friends." -Tim Chartier, professor of Mathematics, Davidson College, and author of Math Bytes

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Book SynopsisThis original anthology collects 10 of Weyl''s less-technical writings that address the broader scope and implications of mathematics. Most have been long unavailable or not previously published in book form. Subjects include logic, topology, abstract algebra, relativity theory, and reflections on the work of Weyl''s mentor, David Hilbert. 2012 edition.

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Book SynopsisA thorough first course in linear algebra, this two-part treatment begins with the basic theory of vector spaces and linear maps, including dimension, determinants, eigenvalues, and eigenvectors. The second section addresses more advanced topics such as the study of canonical forms for matrices. Ample examples, applications, and exercises appear throughout the text. 1992 edition.

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Book SynopsisIn their bestselling title MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps you discover the nature of statistics and understand its essential role in scientific research.With the addition of contributor Brendan Ames, MATHEMATICAL STATISTICS WITH APPLICATIONS now includes an enhanced eTextbook. Simulation activities using interactive applets and R embedded within the MindTap Reader help students visualize statistical concepts, and an appendix introducing students to statistical data analysis using R can be found at the end of the eTextbook.Table of Contents1. What Is Statistics? Introduction. Characterizing a Set of Measurements: Graphical Methods. Characterizing a Set of Measurements: Numerical Methods. How Inferences Are Made. Theory and Reality. Summary. 2. Probability. Introduction. Probability and Inference. A Review of Set Notation. A Probabilistic Model for an Experiment: The Discrete Case. Calculating the Probability of an Event: The Sample-Point Method. Tools for Counting Sample Points. Conditional Probability and the Independence of Events. Two Laws of Probability. Calculating the Probability of an Event: The Event-Composition Methods. The Law of Total Probability and Bayes''''s Rule. Numerical Events and Random Variables. Random Sampling. Summary. 3. Discrete Random Variables and Their Probability Distributions. Basic Definition. The Probability Distribution for Discrete Random Variable. The Expected Value of Random Variable or a Function of Random Variable. The Binomial Probability Distribution. The Geometric Probability Distribution. The Negative Binomial Probability Distribution (Optional). The Hypergeometric Probability Distribution. Moments and Moment-Generating Functions. Probability-Generating Functions (Optional). Tchebysheff''''s Theorem. Summary. 4. Continuous Random Variables and Their Probability Distributions. Introduction. The Probability Distribution for Continuous Random Variable. The Expected Value for Continuous Random Variable. The Uniform Probability Distribution. The Normal Probability Distribution. The Gamma Probability Distribution. The Beta Probability Distribution. Some General Comments. Other Expected Values. Tchebysheff''''s Theorem. Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional). Summary. 5. Multivariate Probability Distributions. Introduction. Bivariate and Multivariate Probability Distributions. Independent Random Variables. The Expected Value of a Function of Random Variables. Special Theorems. The Covariance of Two Random Variables. The Expected Value and Variance of Linear Functions of Random Variables. The Multinomial Probability Distribution. The Bivariate Normal Distribution (Optional). Conditional Expectations. Summary. 6. Functions of Random Variables. Introductions. Finding the Probability Distribution of a Function of Random Variables. The Method of Distribution Functions. The Methods of Transformations. Multivariable Transformations Using Jacobians. Order Statistics. Summary. 7. Sampling Distributions and the Central Limit Theorem. Introduction. Sampling Distributions Related to the Normal Distribution. The Central Limit Theorem. A Proof of the Central Limit Theorem (Optional). The Normal Approximation to the Binomial Distributions. Summary. 8. Estimation. Introduction. The Bias and Mean Square Error of Point Estimators. Some Common Unbiased Point Estimators. Evaluating the Goodness of Point Estimator. Confidence Intervals. Large-Sample Confidence Intervals Selecting the Sample Size. Small-Sample Confidence Intervals for u and u1-u2. Confidence Intervals for o2. Summary. 9. Properties of Point Estimators and Methods of Estimation. Introduction. Relative Efficiency. Consistency. Sufficiency. The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation. The Method of Moments. The Method of Maximum Likelihood. Some Large-Sample Properties of MLEs (Optional). Summary. 10. Hypothesis Testing. Introduction. Elements of a Statistical Test. Common Large-Sample Tests. Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test. Relationships Between Hypothesis Testing Procedures and Confidence Intervals. Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values. Some Comments on the Theory of Hypothesis Testing. Small-Sample Hypothesis Testing for u and u1-u2. Testing Hypotheses Concerning Variances. Power of Test and the Neyman-Pearson Lemma. Likelihood Ration Test. Summary. 11. Linear Models and Estimation by Least Squares. Introduction. Linear Statistical Models. The Method of Least Squares. Properties of the Least Squares Estimators for the Simple Linear Regression Model. Inference Concerning the Parameters BI. Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression. Predicting a Particular Value of Y Using Simple Linear Regression. Correlation. Some Practical Examples. Fitting the Linear Model by Using Matrices. Properties of the Least Squares Estimators for the Multiple Linear Regression Model. Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression. Prediction a Particular Value of Y Using Multiple Regression. A Test for H0: Bg+1 + Bg+2 = . = Bk = 0. Summary and Concluding Remarks. 12. Considerations in Designing Experiments. The Elements Affecting the Information in a Sample. Designing Experiment to Increase Accuracy. The Matched Pairs Experiment. Some Elementary Experimental Designs. Summary. 13. The Analysis of Variance. Introduction. The Analysis of Variance Procedure. Comparison of More than Two Means: Analysis of Variance for a One-way Layout. An Analysis of Variance Table for a One-Way Layout. A Statistical Model of the One-Way Layout. Proof of Additivity of the Sums of Squares and E (MST) for a One-Way Layout (Optional). Estimation in the One-Way Layout. A Statistical Model for the Randomized Block Design. The Analysis of Variance for a Randomized Block Design. Estimation in the Randomized Block Design. Selecting the Sample Size. Simultaneous Confidence Intervals for More than One Parameter. Analysis of Variance Using Linear Models. Summary. 14. Analysis of Categorical Data. A Description of the Experiment. The Chi-Square Test. A Test of Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test. Contingency Tables. r x c Tables with Fixed Row or Column Totals. Other Applications. Summary and Concluding Remarks. 15. Nonparametric Statistics. Introduction. A General Two-Sampling Shift Model. A Sign Test for a Matched Pairs Experiment. The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment. The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples. The Mann-Whitney U Test: Independent Random Samples. The Kruskal-Wallis Test for One-Way Layout. The Friedman Test for Randomized Block Designs. The Runs Test: A Test for Randomness. Rank Correlation Coefficient. Some General Comments on Nonparametric Statistical Test. 16. Introduction to Bayesian Methods for Inference. Introduction. Bayesian Priors, Posteriors and Estimators. Bayesian Credible Intervals. Bayesian Tests of Hypotheses. Summary and Additional Comments. Appendix 1. Matrices and Other Useful Mathematical Results. Matrices and Matrix Algebra. Addition of Matrices. Multiplication of a Matrix by a Real Number. Matrix Multiplication. Identity Elements. The Inverse of a Matrix. The Transpose of a Matrix. A Matrix Expression for a System of Simultaneous Linear Equations. Inverting a Matrix. Solving a System of Simultaneous Linear Equations. Other Useful Mathematical Results. Appendix 2. Common Probability Distributions, Means, Variances, and Moment-Generating Functions. Discrete Distributions. Continuous Distributions. Appendix 3. Tables. Binomial Probabilities. Table of e-x. Poisson Probabilities. Normal Curve Areas. Percentage Points of the t Distributions. Percentage Points of the F Distributions. Distribution of Function U. Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test. Distribution of the Total Number of Runs R in Sample Size (n1,n2); P(R < a). Critical Values of Pearman''s Rank Correlation Coefficient. Random Numbers. Answer to Exercises. Index. R Appendix. Students are introduced to statistical data analysis and shown how to use R to conduct all of the major statistical procedures from the textbook.

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Book SynopsisThis revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.Trade Review'Priest's Introduction to Non-Classical Logic is my textbook of choice for introducing non-classical logic to undergraduates. It is unique in meeting two almost inconsistent aims. It gives the reader an introduction to a vast range of non-classical logics. No comparable textbook manages to cover modal logics, conditional logics, intuitionistic logic, relevant and paraconsistent logics and fuzzy logic with such clarity and accessibility. Amazingly, it is not merely a catalogue of different logical systems. The distinctive value of this Introduction is that it also tells a coherent story: Priest weaves together these different logics in the one narrative - the search for a logic of conditionals. With the publication of the second volume, this unique combination of breadth and coherence now covers much more ground, and the reader now has an expert guide to much more of the vast field of research in non-classical logics.' Greg Restall, The University of Melbourne'I've used your book (first edition, that is) for years now in my upper level philosophy of logic courses. It is easily the best introduction to non-classical logics. I especially like its coverage of conditionals, and the introduction to relevant logic. Over the years, your book has made my students come to appreciate the variety and scope that exists within in formal logic, I intend to use the new edition so as to carry similar investigations into first order theory.' Jeffry Pelletier, Simon Fraser University'Graham Priest's Introduction to Non-Classical Logic made this fascinating material on alternative logics accessible to my students for the very first time. The very welcome new edition extends the range of what is addressed to include important questions about quantification for modal logic, and the other systems as well.' Tony Roy, California State University, San Bernardino'The first edition of Graham Priest's Introduction to Non-Classical Logic turned out to be an extremely useful and well-written introductory guide to the vast and difficult to survey area of non-classical and philosophical logic. The substantially expanded second edition in two volumes is bound to become a standard reference.' Heinrich Wansing, Dresden University of Technology'Clear, self-contained, generously complete: this is bound to be the classic on non-classical logics for many years to come.' Achille Varzi, Columbia University'This is an excellent introductory book to modern non-classical logics, fully accessible to non-professionals, and useful to professionals too. I have used part of its content in teaching Non-Classical Logic in the past years, and the response from my students shows the great success of the author's intention. The proof system it employs and the meta-proofs it provides are extremely easy to follow, while those followed-up philosophical discussions it summarizes for each logic system are both concise and lucid. It is not only a work introducing modern non-classical logic systems, but also a work full of interesting philosophical discussions on the motivations, advantages and disadvantages of these systems. With one penetrating theme - what a logic of conditionals should be like - in mind, the author has effectively organized a variety of topics into one integrated work. I would recommend it both to logicians and to philosophers, to professionals and to non-professionals.' Wen-fang Wang, National Chung Chen University'The second edition of Graham Priest's book is, like the first, clearly expressed, well thought out for the student and an essential work for all those studying philosophy who want an adequate grounding in non-classical logic. I have used the first edition successfully in my intermediate class for the last five years, and will certainly be adding the second edition to the reading list when it is available.' Steve Read, University of St Andrews'Priest succeeds in offering a marvellously unified treatment of 11 varieties of logic: classical, basic modal, normal modal, non-normal, conditional, intuitionist, many-valued, first-degree entailment, basic relevant, mainstream relevant, and fussy … Excellent references support this concise but clear treatment.' Choice'This book is just what the title says it is … And it is a very good one …' Stewart Shapiro, University of Ohio' … for anyone who wants to explore the non-classical systems, it is the only book of its kind and could not be more highly recommended.' The Times Higher Education Supplement'I've just picked up a copy of the second edition of Graham Preist's An Introduction to Non-Classical Logic from the CUP bookshop. It looks terrific. More than twice the length of the first edition which just covered propositional logics, this covers their extensions with quantifiers and identity too. I thought the fist edition was terrific: so this is a hugely welcome expansion and I'm delighted to report that CUP has published this as a paperback in their Cambridge Introductions to Philosophy Series at just £18.99, which is surely an amazing bargain for a well produced 613 page book. So a must-buy and a must-read!' Logic MattersTable of ContentsPreface to the first edition; Preface to the second edition; Mathematical prolegomenon; Part I. Propositional Logic: 1. Classical logic and the material conditional; 2. Basic modal logic; 3. Normal modal logics; 4. Non-normal modal logics; strict conditionals; 5. Conditional logics; 6. Intuitionist logic; 7. Many-valued logics; 8. First degree entailment; 9. Logics with gaps, gluts, and worlds; 10. Relevant logics; 11. Fuzzy logics; 11a. Appendix: many valued modal logics; Postscript: an historical perspective on conditionals; Part II. Qualification and Identity: 12. Classical logic; 13. Free logic; 14. Constant domain modal logics; 15. Variable domain modal logics; 16. Necessary identity in modal logic; 17. Contingent identity in modal logic; 18. Non-normal modal logics; 19. Conditional logics; 20. Intuitionist logic; 21. Many-valued logics; 22. First degree entailment; 23. Logics with gaps, gluts, and worlds; 24. Relevant logics; 25. Fuzzy logics; Postscript: a methodological coda.

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Book SynopsisAstronomy needs statistical methods to interpret data, but statistics is a many-faceted subject that is difficult for non-specialists to access. This handbook helps astronomers analyze the complex data and models of modern astronomy. This second edition has been revised to feature many more examples using Monte Carlo simulations, and now also includes Bayesian inference, Bayes factors and Markov chain Monte Carlo integration. Chapters cover basic probability, correlation analysis, hypothesis testing, Bayesian modelling, time series analysis, luminosity functions and clustering. Exercises at the end of each chapter guide readers through the techniques and tests necessary for most observational investigations. The data tables, solutions to problems, and other resources are available online at www.cambridge.org/9780521732499. Bringing together the most relevant statistical and probabilistic techniques for use in observational astronomy, this handbook is a practical manual for advanced undTrade Review"Bringing together the most relevant statistical and probabilistic techniques for use in observational astronomy, this handbook is a practical manual for advanced undergraduate and graduate students and professional astronomers." -Mathematical ReviewsTable of Contents1. Decision; 2. Probability; 3. Statistics and expectations; 4. Correlation and association; 5. Hypothesis-testing; 6. Data modelling and parameter-estimation: basics; 7. Data modelling and parameter-estimation: advanced topics; 8. Detection and surveys; 9. Sequential data - 1D statistics; 10. Statistics of large-scale structure; 11. Epilogue: statistics and our Universe; Appendices; References; Index.

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Book SynopsisTrade ReviewA fascinating book. -- James Ryerson * New York Times Book Review *Fascinating…This is bold, heady stuff…The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling. He is as much at home describing the niceties of experimental work in cognitive science as he is discussing arcane tribal rituals and the technical details of grammar…It is often poignant, and makes a virtue of the author’s experiences with some of the indigenous peoples he describes, based on a childhood following his missionary parents—in particular his famous father, Daniel Everett—into the Amazon jungle…Numbers is eye-opening, even eye-popping. And it makes a powerful case for language, as a cultural invention, being central to the making of us. -- Vyvyan Evans * New Scientist *Everett buttresses his argument with an impressive array of studies from different fields…It all adds up to a powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans but ‘a creation of the human mind, a cognitive invention that has altered forever how we see and distinguish quantities.’ His argument that numbers played a crucial role in the development of agriculture and the complex societies it supported is equally persuasive. -- Amir Alexander * Wall Street Journal *In this multi-disciplinary investigation, anthropologist Caleb Everett examines the seemingly limitless possibilities and innovations made possible by the evolution of number systems. -- Rachel E. Gross * Smithsonian *Caleb Everett provides a fascinating account of the development of human numeracy, from innate abilities to the complexities of agricultural and trading societies, all viewed against the general background of human cultural evolution. He successfully draws together insights from linguistics, cognitive psychology, anthropology, and archaeology in a way that is accessible to the general reader as well as to specialists. He does not avoid controversy, making this a key contribution to a developing debate. -- Bernard Comrie, University of California, Santa BarbaraIn his journey through the millennia of human evolution, from the forests of Amazonia to the deserts of Australia, ever in search of a better understanding of human diversity, Caleb Everett presents a breathtaking narrative of how the human species developed one of its most distinct cognitive and linguistic achievements: to count and to use concepts of quantity to expand and enrich a wide range of cultural activities. -- Bernd Heine, University of Cologne

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Book SynopsisFor many students, calculus can be the most mystifying and frustrating course they will ever take. This study guide works as a supplement to any single-variable calculus course or textbook. It includes more than 475 examples (ranging from easy to hard) that provide step-by-step reasoning.Trade Review"Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach, The Calculus Lifesaver is a welcome addition to the arsenal of calculus teaching aids."--MAA Online "This rather lengthy book serves as an excellent resource as well as a text for a refresher course in single-variable calculus, and as a study guide for anyone who needs or is required to know basic calculus concepts...Readers will find this book written for them, as calculus is presented in a very casual conversational tone; certainly, students who are not mathematics majors will benefit greatly."--J.T. Zerger, Choice "Students who are having difficulty in calculus could use it as a resource in addition to their professor and teaching assistant."--Mathematics TeacherTable of ContentsWelcome xviii How to Use This Book to Study for an Exam xix Two all-purpose study tips xx Key sections for exam review (by topic) xx Acknowledgments xxiii Chapter 1: Functions, Graphs, and Lines 1 1.1 Functions 1 1.1.1 Interval notation 3 1.1.2 Finding the domain 4 1.1.3 Finding the range using the graph 5 1.1.4 The vertical line test 6 1.2 Inverse Functions 7 1.2.1 The horizontal line test 8 1.2.2 Finding the inverse 9 1.2.3 Restricting the domain 9 1.2.4 Inverses of inverse functions 11 1.3 Composition of Functions 11 1.4 Odd and Even Functions 14 1.5 Graphs of Linear Functions 17 1.6 Common Functions and Graphs 19 Chapter 2: Review of Trigonometry 25 2.1 The Basics 25 2.2 Extending the Domain of Trig Functions 28 2.2.1 The ASTC method 31 2.2.2 Trig functions outside [0; 2pi] 33 2.3 The Graphs of Trig Functions 35 2.4 Trig Identities 39 Chapter 3: Introduction to Limits 41 3.1 Limits: The Basic Idea 41 3.2 Left-Hand and Right-Hand Limits 43 3.3 When the Limit Does Not Exist 45 3.4 Limits at 1 and - 47 3.4.1 Large numbers and small numbers 48 3.5 Two Common Misconceptions about Asymptotes 50 3.6 The Sandwich Principle 51 3.7 Summary of Basic Types of Limits 54 Chapter 4: How to Solve Limit Problems Involving Polynomials 57 4.1 Limits Involving Rational Functions as chi --> alphaa 57 4.2 Limits Involving Square Roots as chi --> alpha 61 4.3 Limits Involving Rational Functions as chi --> 61 4.3.1 Method and examples 64 4.4 Limits Involving Poly-type Functions as chi --> 66 4.5 Limits Involving Rational Functions as chi --> - 70 4.6 Limits Involving Absolute Values 72 Chapter 5: Continuity and Differentiability 75 5.1 Continuity 75 5.1.1 Continuity at a point 76 5.1.2 Continuity on an interval 77 5.1.3 Examples of continuous functions 77 5.1.4 The Intermediate Value Theorem 80 5.1.5 A harder IVT example 82 5.1.6 Maxima and minima of continuous functions 82 5.2 Differentiability 84 5.2.1 Average speed 84 5.2.2 Displacement and velocity 85 5.2.3 Instantaneous velocity 86 5.2.4 The graphical interpretation of velocity 87 5.2.5 Tangent lines 88 5.2.6 The derivative function 90 5.2.7 The derivative as a limiting ratio 91 5.2.8 The derivative of linear functions 93 5.2.9 Second and higher-order derivatives 94 5.2.10 When the derivative does not exist 94 5.2.11 Differentiability and continuity 96 Chapter 6: How to Solve Differentiation Problems 99 6.1 Finding Derivatives Using the Definition 99 6.2 Finding Derivatives (the Nice Way) 102 6.2.1 Constant multiples of functions 103 6.2.2 Sums and Differences of functions 103 6.2.3 Products of functions via the product rule 104 6.2.4 Quotients of functions via the quotient rule 105 6.2.5 Composition of functions via the chain rule 107 6.2.6 A nasty example 109 6.2.7 Justification of the product rule and the chain rule 111 6.3 Finding the Equation of a Tangent Line 114 6.4 Velocity and Acceleration 114 6.4.1 Constant negative acceleration 115 6.5 Limits Which Are Derivatives in Disguise 117 6.6 Derivatives of Piecewise-Defined Functions 119 6.7 Sketching Derivative Graphs Directly 123 Chapter 7: Trig Limits and Derivatives 127 7.1 Limits Involving Trig Functions 127 7.1.1 The small case 128 7.1.2 Solving problems|the small case 129 7.1.3 The large case 134 7.1.4 The "other" case 137 7.1.5 Proof of an important limit 137 7.2 Derivatives Involving Trig Functions 141 7.2.1 Examples of Differentiating trig functions 143 7.2.2 Simple harmonic motion 145 7.2.3 A curious function 146 Chapter 8: Implicit Differentiation and Related Rates 149 8.1 Implicit Differentiation 149 8.1.1 Techniques and examples 150 8.1.2 Finding the second derivative implicitly 154 8.2 Related Rates 156 8.2.1 A simple example 157 8.2.2 A slightly harder example 159 8.2.3 A much harder example 160 8.2.4 A really hard example 162 Chapter 9: Exponentials and Logarithms 167 9.1 The Basics 167 9.1.1 Review of exponentials 167 9.1.2 Review of logarithms 168 9.1.3 Logarithms, exponentials, and inverses 169 9.1.4 Log rules 170 9.2 Definition of e 173 9.2.1 A question about compound interest 173 9.2.2 The answer to our question 173 9.2.3 More about e and logs 175 9.3 Differentiation of Logs and Exponentials 177 9.3.1 Examples of Differentiating exponentials and logs 179 9.4 How to Solve Limit Problems Involving Exponentials or Logs 180 9.4.1 Limits involving the definition of e 181 9.4.2 Behavior of exponentials near 0 182 9.4.3 Behavior of logarithms near 1 183 9.4.4 Behavior of exponentials near or - 1 184 9.4.5 Behavior of logs near 187 9.4.6 Behavior of logs near 0 188 9.5 Logarithmic Differentiation 189 9.5.1 The derivative of chia 192 9.6 Exponential Growth and Decay 193 9.6.1 Exponential growth 194 9.6.2 Exponential decay 195 9.7 Hyperbolic Functions 198 Chapter 10: Inverse Functions and Inverse Trig Functions 201 10.1 The Derivative and Inverse Functions 201 10.1.1 Using the derivative to show that an inverse exists 201 10.1.2 Derivatives and inverse functions: what can go wrong 203 10.1.3 Finding the derivative of an inverse function 204 10.1.4 A big example 206 10.2 Inverse Trig Functions 208 10.2.1 Inverse sine 208 10.2.2 Inverse cosine 211 10.2.3 Inverse tangent 213 10.2.4 Inverse secant 216 10.2.5 Inverse cosecant and inverse cotangent 217 10.2.6 Computing inverse trig functions 218 10.3 Inverse Hyperbolic Functions 220 10.3.1 The rest of the inverse hyperbolic functions 222 Chapter 11: The Derivative and Graphs 225 11.1 Extrema of Functions 225 11.1.1 Global and local extrema 225 11.1.2 The Extreme Value Theorem 227 11.1.3 How to find global maxima and minima 228 11.2 Rolle's Theorem 230 11.3 The Mean Value Theorem 233 11.3.1 Consequences of the Mean Value Theorem 235 11.4 The Second Derivative and Graphs 237 11.4.1 More about points of inection 238 11.5 Classifying Points Where the Derivative Vanishes 239 11.5.1 Using the first derivative 240 11.5.2 Using the second derivative 242 Chapter 12: Sketching Graphs 245 12.1 How to Construct a Table of Signs 245 12.1.1 Making a table of signs for the derivative 247 12.1.2 Making a table of signs for the second derivative 248 12.2 The Big Method 250 12.3 Examples 252 12.3.1 An example without using derivatives 252 12.3.2 The full method: example 1 254 12.3.3 The full method: example 2 256 12.3.4 The full method: example 3 259 12.3.5 The full method: example 4 262 Chapter 13: Optimization and Linearization 267 13.1 Optimization 267 13.1.1 An easy optimization example 267 13.1.2 Optimization problems: the general method 269 13.1.3 An optimization example 269 13.1.4 Another optimization example 271 13.1.5 Using implicit Differentiation in optimization 274 13.1.6 A difficult optimization example 275 13.2 Linearization 278 13.2.1 Linearization in general 279 13.2.2 The Differential 281 13.2.3 Linearization summary and examples 283 13.2.4 The error in our approximation 285 13.3 Newton's Method 287 Chapter 14: L'Hopital's Rule and Overview of Limits 293 14.1 L'Hopital's Rule 293 14.1.1 Type A: 0/0 case 294 14.1.2 Type A: +- / +- case 296 14.1.3 Type B1 ( - ) 298 14.1.4 Type B2 (0 x +- ) 299 14.1.5 Type C (1+- , 00, or 0) 301 14.1.6 Summary of L'Hopital's Rule types 302 14.2 Overview of Limits 303 Chapter 15: Introduction to Integration 307 15.1 Sigma Notation 307 15.1.1 A nice sum 310 15.1.2 Telescoping series 311 15.2 Displacement and Area 314 15.2.1 Three simple cases 314 15.2.2 A more general journey 317 15.2.3 Signed area 319 15.2.4 Continuous velocity 320 15.2.5 Two special approximations 323 Chapter 16: Definite Integrals 325 16.1 The Basic Idea 325 16.1.1 Some easy examples 327 16.2 Definition of the Definite Integral 330 16.2.1 An example of using the definition 331 16.3 Properties of Definite Integrals 334 16.4 Finding Areas 339 16.4.1 Finding the unsigned area 339 16.4.2 Finding the area between two curves 342 16.4.3 Finding the area between a curve and the y-axis 344 16.5 Estimating Integrals 346 16.5.1 A simple type of estimation 347 16.6 Averages and the Mean Value Theorem for Integrals 350 16.6.1 The Mean Value Theorem for integrals 351 16.7 A Nonintegrable Function 353 Chapter 17: The Fundamental Theorems of Calculus 355 17.1 Functions Based on Integrals of Other Functions 355 17.2 The First Fundamental Theorem 358 17.2.1 Introduction to antiderivatives 361 17.3 The Second Fundamental Theorem 362 17.4 Indefinite Integrals 364 17.5 How to Solve Problems: The First Fundamental Theorem 366 17.5.1 Variation 1: variable left-hand limit of integration 367 17.5.2 Variation 2: one tricky limit of integration 367 17.5.3 Variation 3: two tricky limits of integration 369 17.5.4 Variation 4: limit is a derivative in disguise 370 17.6 How to Solve Problems: The Second Fundamental Theorem 371 17.6.1 Finding indefinite integrals 371 17.6.2 Finding definite integrals 374 17.6.3 Unsigned areas and absolute values 376 17.7 A Technical Point 380 17.8 Proof of the First Fundamental Theorem 381 Chapter 18: Techniques of Integration, Part One 383 18.1 Substitution 383 18.1.1 Substitution and definite integrals 386 18.1.2 How to decide what to substitute 389 18.1.3 Theoretical justification of the substitution method 392 18.2 Integration by Parts 393 18.2.1 Some variations 394 18.3 Partial Fractions 397 18.3.1 The algebra of partial fractions 398 18.3.2 Integrating the pieces 401 18.3.3 The method and a big example 404 Chapter 19: Techniques of Integration, Part Two 409 19.1 Integrals Involving Trig Identities 409 19.2 Integrals Involving Powers of Trig Functions 413 19.2.1 Powers of sin and/or cos 413 19.2.2 Powers of tan 415 19.2.3 Powers of sec 416 19.2.4 Powers of cot 418 19.2.5 Powers of csc 418 19.2.6 Reduction formulas 419 19.3 Integrals Involving Trig Substitutions 421 19.3.1 Type 1: 421 19.3.2 Type 2: 423 19.3.3 Type 3: 424 19.3.4 Completing the square and trig substitutions 426 19.3.5 Summary of trig substitutions 426 19.3.6 Technicalities of square roots and trig substitutions 427 19.4 Overview of Techniques of Integration 429 Chapter 20: Improper Integrals: Basic Concepts 431 20.1 Convergence and Divergence 431 20.1.1 Some examples of improper integrals 433 20.1.2 Other blow-up points 435 20.2 Integrals over Unbounded Regions 437 20.3 The Comparison Test (Theory) 439 20.4 The Limit Comparison Test (Theory) 441 20.4.1 Functions asymptotic to each other 441 20.4.2 The statement of the test 443 20.5 The p-test (Theory) 444 20.6 The Absolute Convergence Test 447 Chapter 21: Improper Integrals: How to Solve Problems 451 21.1 How to Get Started 451 21.1.1 Splitting up the integral 452 21.1.2 How to deal with negative function values 453 21.2 Summary of Integral Tests 454 21.3 Behavior of Common Functions near and - 456 21.3.1 Polynomials and poly-type functions near and - 456 21.3.2 Trig functions near and - 459 21.3.3 Exponentials near and - 461 21.3.4 Logarithms near 465 21.4 Behavior of Common Functions near 0 469 21.4.1 Polynomials and poly-type functions near 0 469 21.4.2 Trig functions near 0 470 21.4.3 Exponentials near 0 472 21.4.4 Logarithms near 0 473 21.4.5 The behavior of more general functions near 0 474 21.5 How to Deal with Problem Spots Not at 0 or 475 Chapter 22: Sequences and Series: Basic Concepts 477 22.1 Convergence and Divergence of Sequences 477 22.1.1 The connection between sequences and functions 478 22.1.2 Two important sequences 480 22.2 Convergence and Divergence of Series 481 22.2.1 Geometric series (theory) 484 22.3 The nth Term Test (Theory) 486 22.4 Properties of Both Infinite Series and Improper Integrals 487 22.4.1 The comparison test (theory) 487 22.4.2 The limit comparison test (theory) 488 22.4.3 The p-test (theory) 489 22.4.4 The absolute convergence test 490 22.5 New Tests for Series 491 22.5.1 The ratio test (theory) 492 22.5.2 The root test (theory) 493 22.5.3 The integral test (theory) 494 22.5.4 The alternating series test (theory) 497 Chapter 23: How to Solve Series Problems 501 23.1 How to Evaluate Geometric Series 502 23.2 How to Use the nth Term Test 503 23.3 How to Use the Ratio Test 504 23.4 How to Use the Root Test 508 23.5 How to Use the Integral Test 509 23.6 Comparison Test, Limit Comparison Test, and p-test 510 23.7 How to Deal with Series with Negative Terms 515 Chapter 24: Taylor Polynomials, Taylor Series, and Power Series 519 24.1 Approximations and Taylor Polynomials 519 24.1.1 Linearization revisited 520 24.1.2 Quadratic approximations 521 24.1.3 Higher-degree approximations 522 24.1.4 Taylor's Theorem 523 24.2 Power Series and Taylor Series 526 24.2.1 Power series in general 527 24.2.2 Taylor series and Maclaurin series 529 24.2.3 Convergence of Taylor series 530 24.3 A Useful Limit 534 Chapter 25: How to Solve Estimation Problems 535 25.1 Summary of Taylor Polynomials and Series 535 25.2 Finding Taylor Polynomials and Series 537 25.3 Estimation Problems Using the Error Term 540 25.3.1 First example 541 25.3.2 Second example 543 25.3.3 Third example 544 25.3.4 Fourth example 546 25.3.5 Fifth example 547 25.3.6 General techniques for estimating the error term 548 25.4 Another Technique for Estimating the Error 548 Chapter 26: Taylor and Power Series: How to Solve Problems 551 26.1 Convergence of Power Series 551 26.1.1 Radius of convergence 551 26.1.2 How to find the radius and region of convergence 554 26.2 Getting New Taylor Series from Old Ones 558 26.2.1 Substitution and Taylor series 560 26.2.2 Differentiating Taylor series 562 26.2.3 Integrating Taylor series 563 26.2.4 Adding and subtracting Taylor series 565 26.2.5 Multiplying Taylor series 566 26.2.6 Dividing Taylor series 567 26.3 Using Power and Taylor Series to Find Derivatives 568 26.4 Using Maclaurin Series to Find Limits 570 Chapter 27: Parametric Equations and Polar Coordinates 575 27.1 Parametric Equations 575 27.1.1 Derivatives of parametric equations 578 27.2 Polar Coordinates 581 27.2.1 Converting to and from polar coordinates 582 27.2.2 Sketching curves in polar coordinates 585 27.2.3 Finding tangents to polar curves 590 27.2.4 Finding areas enclosed by polar curves 591 Chapter 28: Complex Numbers 595 28.1 The Basics 595 28.1.1 Complex exponentials 598 28.2 The Complex Plane 599 28.2.1 Converting to and from polar form 601 28.3 Taking Large Powers of Complex Numbers 603 28.4 Solving zn = w 604 28.4.1 Some variations 608 28.5 Solving ez = w 610 28.6 Some Trigonometric Series 612 28.7 Euler's Identity and Power Series 615 Chapter 29: Volumes, Arc Lengths, and Surface Areas 617 29.1 Volumes of Solids of Revolution 617 29.1.1 The disc method 619 29.1.2 The shell method 620 29.1.3 Summary ... and variations 622 29.1.4 Variation 1: regions between a curve and the y-axis 623 29.1.5 Variation 2: regions between two curves 625 29.1.6 Variation 3: axes parallel to the coordinate axes 628 29.2 Volumes of General Solids 631 29.3 Arc Lengths 637 29.3.1 Parametrization and speed 639 29.4 Surface Areas of Solids of Revolution 640 Chapter 30: Differential Equations 645 30.1 Introduction to Differential Equations 645 30.2 Separable First-order Differential Equations 646 30.3 First-order Linear Equations 648 30.3.1 Why the integrating factor works 652 30.4 Constant-coefficient Differential Equations 653 30.4.1 Solving first-order homogeneous equations 654 30.4.2 Solving second-order homogeneous equations 654 30.4.3 Why the characteristic quadratic method works 655 30.4.4 Nonhomogeneous equations and particular solutions 656 30.4.5 Finding a particular solution 658 30.4.6 Examples of finding particular solutions 660 30.4.7 Resolving conicts between yP and yH 662 30.4.8 Initial value problems (constant-coefficient linear) 663 30.5 Modeling Using Differential Equations 665 Appendix A Limits and Proofs 669 A.1 Formal Definition of a Limit 669 A.1.1 A little game 670 A.1.2 The actual definition 672 A.1.3 Examples of using the definition 672 A.2 Making New Limits from Old Ones 674 A.2.1 Sums and Differences of limits|proofs 674 A.2.2 Products of limits|proof 675 A.2.3 Quotients of limits|proof 676 A.2.4 The sandwich principle|proof 678 A.3 Other Varieties of Limits 678 A.3.1 Inffinite limits 679 A.3.2 Left-hand and right-hand limits 680 A.3.3 Limits at and - 680 A.3.4 Two examples involving trig 682 A.4 Continuity and Limits 684 A.4.1 Composition of continuous functions 684 A.4.2 Proof of the Intermediate Value Theorem 686 A.4.3 Proof of the Max-Min Theorem 687 A.5 Exponentials and Logarithms Revisited 689 A.6 Differentiation and Limits 691 A.6.1 Constant multiples of functions 691 A.6.2 Sums and Differences of functions 691 A.6.3 Proof of the product rule 692 A.6.4 Proof of the quotient rule 693 A.6.5 Proof of the chain rule 693 A.6.6 Proof of the Extreme Value Theorem 694 A.6.7 Proof of Rolle's Theorem 695 A.6.8 Proof of the Mean Value Theorem 695 A.6.9 The error in linearization 696 A.6.10 Derivatives of piecewise-defined functions 697 A.6.11 Proof of L'Hopital's Rule 698 A.7 Proof of the Taylor Approximation Theorem 700 Appendix B Estimating Integrals 703 B.1 Estimating Integrals Using Strips 703 B.1.1 Evenly spaced partitions 705 B.2 The Trapezoidal Rule 706 B.3 Simpson's Rule 709 B.3.1 Proof of Simpson's rule 710 B.4 The Error in Our Approximations 711 B.4.1 Examples of estimating the error 712 B.4.2 Proof of an error term inequality 714 List of Symbols 717 Index 719

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