Applied mathematics Books

Book SynopsisSoccer is the most mathematical of sports--riddled with numbers, patterns, and shapes. How to make sense of them? The answer lies in mathematical modeling, a science with applications in a host of biological systems. Soccermatics brings the two together in a fascinating, mind-bending synthesis. What''s the connection between an ant colony and Total Football, Dutch-style? How is the Barcelona midfield linked geometrically? And how can we relate the mechanics of a Mexican Wave to the singing of cicadas in an Australian valley? Welcome to the world of mathematical modeling, expressed brilliantly by David Sumpter through the prism of soccer. Soccer is indeed more than a game and this book is packed with game theory. After reading it, you will forever watch the game with new eyes.Trade ReviewSumpter's deconstruction of formations proved why maths and football can't live without each other. It's every football nerd's dream. * FourFourTwo *A fascinating and entertaining dive into the mathematics of the beautiful game. * The Guardian *...Highly readable... * The Irish Times *...You will love this book. * The Tribune *This is football looked at in a very different way. David Sumpter is mining a rich and deep seam here in Soccermatics, one that will become an increasingly important part of the game. -- Pat Nevin, former Chelsea and Everton star and football media analystA fascinating study of the structures and patterns that underpin football matches, with revealing and surprising conclusions. -- Michael Cox, editor of Zonal Marking and Guardian SportsSoccermatics provides fresh insight into a game we've been watching all of our lives. But it's more than a book about football and is all the better for it. -- Adam Bate, football features writer for Sky SportsDavid Sumpter brings together his two passions, mathematics and football, in a highly original and entertaining way. The beautiful game illustrated through the beauty of mathematics. -- Philip Maini FRS, Professor of Mathematical Biology, University of OxfordTable of ContentsPreface: The Kick-off Part I: On the Pitch Chapter 1: I Never Predict Anything and I Never Will Chapter 2: How Slime Moulds Built Barcelona Chapter 3: Check My Flow Chapter 4: Statistical Brilliance Chapter 5: Zlatan Ibrah Rocket Science Part II: In the Dugout Chapter 6: Three Points for the Bird-brained Manager Chapter 7: The Tactical Map CHapter 8: Total Cyber Dynamo Chapter 9: The World in Motion Part III: From the Crowd Chapter 10: You'll Never Walk Alone Chapter 11: Bet Against the Masses Chapter 12: Putting My Money Where My Mouth Is Chapter 13: The Results Are In The Full-Time Whistle Notes Acknowledgements Index

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Book SynopsisHugh Barker is a non-fiction author and editor; as the latter he has edited several successful popular maths books, including A Slice of Pi. Hugh is a keen amateur mathematician and was accepted to study maths at Cambridge University aged 16.

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Book SynopsisThis resource has been developed to fully cover unit AS 2: Applied Mathematics of the CCEA specification, addressing both mechanics and statistics.For each topic, the book begins with a logical explanation of the theory, examples to reinforce the explanation, and any key words and definitions that are required. Examples and definitions are clearly differentiated to ease revision and progression through the book. The material then flows into exercises, before introducing the next topic. In this way, the student is guided through the subject.The book contains a large number of exercises in order to provide teachers with as much flexibility as possible for their students. Answers to the questions are included at the back of the book. Contents: 1 Concepts in Mechanics; 2 Kinematics; Constant Acceleration; 3 Motion Graphs; 4 Forces; 5 Newton's Laws; 6 Friction; 7 Connected Bodies; 8 Statistical Sampling; 9 Data Presentation and Interpretation; 10 Central Tendency and Variation; 11 Correlation and Regression; 12 Data Cleaning; 13 Probability; 14 Binomial Distribution

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Book SynopsisWritten by bestselling author Stephen Doyle, this student book will engage and motivate you throughout the course. // Endorsed by WJEC offering high quality support you can trust. // Thorough coverage of all the topics in the AS Level Applied specification. // Extra support for the problem solving and unstructured questions in the specification. // Plenty of examples with worked answers throughout to enable you to check your understanding as you progress through the course. // Answers to questions are provided in order to check your work.Table of ContentsHow to use this book, Revision checklist, Section A Statistics, Topic 1 Statistical sampling, Topic 2 Data presentation and interpretation, Topic 3 Probability, Topic 4 Statistical distributions, Topic 5 Statistical hypothesis testing, Section B: Mechanics, Topic 1 Quantities and units in mechanics, Topic 2 Kinematics, Topic 3 Dynamics of a particle, Topic 4 Vectors, Formulae given in the examination, Formulae that need to be remembered, Test yourself answers

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Book SynopsisA must-read book on the quantitative value investment strategy Warren Buffett and Ed Thorp represent two spectrums of investing: one value driven, one quantitative. Where they align is in their belief that the market is beatable. This book seeks to take the best aspects of value investing and quantitative investing as disciplines and apply them to a completely unique approach to stock selection. Such an approach has several advantages over pure value or pure quantitative investing. This new investing strategy framed by the book is known as quantitative value, a superior, market-beating method to investing in stocks. Quantitative Value provides practical insights into an investment strategy that links the fundamental value investing philosophy of Warren Buffett with the quantitative value approach of Ed Thorp. It skillfully combines the best of Buffett and Ed Thorpweaving their investment philosophies into a winning, market-beating investment strategy. Table of ContentsPreface xi Acknowledgments xiii PART ONE The Foundation of Quantitative Value 1 CHAPTER 1 The Paradox of Dumb Money 3 Value Strategies Beat the Market 9 How Quantitative Investing Protects against Behavioral Errors 23 The Power of Quantitative Value Investing 30 Notes 32 CHAPTER 2 A Blueprint to a Better Quantitative Value Strategy 35 Greenblatt’s Magic Formula 36 It’s All Academic: Improving Quality and Price 45 Strategy Implementation: Investors Behaving Badly 54 Notes 59 PART TWO Margin of Safety—How to Avoid a Permanent Loss of Capital 61 CHAPTER 3 Hornswoggled! Eliminating Earnings Manipulators and Outright Frauds 63 Accruals and the Art of Earnings Manipulation 64 Predicting PROBMs 72 Notes 79 CHAPTER 4 Measuring the Risk of Financial Distress: How to Avoid the Sick Men of the Stock Market 81 A Brief History of Bankruptcy Prediction 83 Improving Bankruptcy Prediction 85 How We Calculate the Risk of Financial Distress 86 Scrubbing the Universe 89 Notes 91 PART THREE Quality—How to Find a Wonderful Business 93 CHAPTER 5 Franchises—The Archetype of High Quality 95 The Chairman’s Secret Recipe 96 How to Find a Franchise 99 Notes 112 CHAPTER 6 Financial Strength: Foundations Built on Rock 113 The Piotroski Fundamentals Score (F_SCORE) 114 Our Financial Strength Score (FS_SCORE) 119 Comparing the Performance of Piotroski’s F_SCORE and Our FS_SCORE 122 Case Study: Lubrizol Corporation 123 Notes 126 PART FOUR The Secret to Finding Bargain Prices 127 CHAPTER 7 Price Ratios: A Horse Race 129 The Horses in the Race 130 Rules of the Race 133 The Race Call 134 A Price Ratio for All Seasons 141 The Offi cial Winner 142 Notes 143 CHAPTER 8 Alternative Price Measures—Normalized Earning Power and Composite Ratios 145 Normalized Earning Power 147 Compound Price Ratios: Is the Whole Greater than the Sum of Its Parts? 150 Notes 163 PART FIVE Corroborative Signals 165 CHAPTER 9 Blue Horseshoe Loves Anacott Steel: Follow the Signals from the Smart Money 167 Stock Buybacks, Issuance, and Announcements 169 Insider Traders Beat the Market 173 Activism and Cloning 176 Short Money Is Smart Money 179 Notes 182 PART SIX Building and Testing the Model 185 CHAPTER 10 Bangladeshi Butter Production Predicts the S&P 500 Close 187 Sustainable Alpha: A Framework for Assessing Past Results 189 What’s the Big Idea? 191 Rigorously Test the Big Idea 196 The Parameters of the Universe 206 Notes 208 CHAPTER 11 Problems with the Magic Formula 211 Glamour Is Always a Bad Bet 216 Improving the Structure of a Quantitative Value Strategy 218 Our Final Quantitative Value Checklist 222 Notes 228 CHAPTER 12 Quantitative Value Beats the Market 229 Risk and Return 231 Robustness 239 A Peek Inside the Black Box 249 Man versus Machine 257 Beating the Market with Quantitative Value 262 Notes 264 Appendix: Analysis Legend 265 About the Authors 267 About the Companion Website 269 Index 271

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Book SynopsisVery Short Introductions: Brilliant, Sharp, Inspiring Fluid mechanics is an important branch of physics concerned with the way in which fluids, such as liquids and gases, behave when in motion and at rest. A quintessential interdisciplinary field of science, it interacts with many other scientific disciplines, from chemistry and biology to mathematics and engineering.This Very Short Introduction presents the field of fluid mechanics by focusing on the underlying physical ideas and using everyday phenomena to demonstrate them, from dripping taps to swimming ducks. Eric Lauga shows how this set of fundamental physical concepts can be applied to a wide range of flow behaviours and highlights the role of fluid motion in both the natural and industrial worlds. This book also considers future applications of fluid mechanics in science.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 ReviewOverall, the book should definitely be an individual's go-to source when seeking an authoritative perspective on the field of fluid mechanics. * Anita T. Layton, Society for Industrial and Applied Mathematics Vol 65.4 *Table of Contents1: Fluids 2: Viscosity 3: Pipes 4: Dimensions 5: Boundary layers 6: Vortices 7: Instabilities 8: Researching fluids and flows Further Reading Index

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Book SynopsisOther refinements in the new edition include an enlarged biography of Emmy Noether's life and work, parallels drawn between the present approach and Noether's original 1918 paper, and a summary of the logic behind Noether's theorem.Trade ReviewAs this book is well written and contains a very good set of exercises, it can serve as the primary text for a special topics course.—ChoiceNadis gives no technical details, but Neuenschwander does, in a book for physics majors with a strong background in mathematics; the book does not shy away from Lie groups and the study of invariants. This new edition delves into distinctions between two Noether theorems and adds more exercises, references, and details.—Mathematics MagazineNeuenschwander sets out from the beginning to help the reader who must be familiar with calculus and a few other standard topics, but who is not yet fluent in these areas... His role is to be the teacher on the side, prompting the reader with interesting observations and questions... He anticipates problems, guides you yet also makes you think things through... Not only a very worthwhile read for its content but also for its style.—Ken Zetie, St. Paul's School, Mathematical GazetteWell-written... Throughout there is reference to the life of Emmy Noether, including the many difficulties related to being a woman in a man's world... I am glad her story is given an airing here as she fails to be as famous as she undoubtedly should be.—Phil Dyke, FIMA, Mathematics TodayTechnical and yet ultimately poetic book on Emmy Neother's wonderful theorems... Neuenschwander's work is recommended for anyone who wants to gain a deeper understanding and appreciation of the physics and mathematics behind Emmy Noether's work, as well as the particular challenges she faced in her life.—Miriam R. Aczel, Centre for Environmental Policy, Imperial College London, Contemporary PhysicsTable of ContentsPrefaceAcknowledgmentsQuestionsPart I. When Functionals Are External 1. Symmetry1.1. Symmetry, Invariances, and Conservation Laws1.2. Meet Emmy Noether2. Functionals2.1. Single-Integral Functionals2.2. Formal Definition of a Functional3. Extremals3.1. The Euler-Lagrange Equation3.2. Conservation Laws as Corollariesto the Euler-Lagrange Equation3.3. On the Equivalence of Hamilton's Principleand Newton's Second Law3.4. Where Do Functional Extremal PrinciplesCome From?3.5. Why Kinetic Minus Potential Energy?3.6. Extremals with External ConstraintsPart II. When Functionals Are Invariant 4. Invariance4.1. Formal Definition of Invariance4.2. The Invariance Identity4.3. A More Liberal Definition of Invariance5. Emmy Noether's Elegant (First) Theorem5.1. Invariance + Extremal = Noether's Theorem5.2. Executive Summary of Noether's Theorem5.3. "Extremal" or "Stationary"?5.4. An Inverse Problem5.5. Adiabatic Invariance in Noether's TheoremPart III. The Invariance of Fields6. Noether's Theorem and Fields6.1. Multiple-Integral Functionals6.2. Euler-Lagrange Equations for Fields6.3. Canonical Momentum and the HamiltonianTensor for Fields6.4. Equations of Continuity6.5. The Invariance Identity for Fields6.6. Noether's Theorem for Fields6.7. Complex Fields6.8. Global Gauge Transformations7. Local Gauge Transformations of Fields7.1. Local Gauge Invariance and Minimal Coupling7.2. Electrodynamics as a Gauge Theory,Part 17.3. Pure Electrodynamics, Spacetime Invariances,and Conservation Laws7.4. Electrodynamics as a Gauge Theory,Part 27.5. Local Gauge Invariance and Noether Currents7.6. Internal Degrees of Freedom7.7. Noether's Theorem and GaugedInternal Symmetries8. Emmy Noether's Elegant (Second) Theorem8.1. Two Noether Theorems8.2. Noether's Second Theorem8.3. Parametric Invariance8.4. Free Fall in a Gravitational Field8.5. The Gravitational Field Equations8.6. The Functionals of General Relativity8.7. Gauge Transformations on Spacetime8.8. Noether's Resolution of an Enigma inGeneral RelativityPart IV. Trans-Noether Invariance9. Invariance in Phase Space9.1. Phase Space9.2. Hamilton's Principle in Phase Space9.3. Noether's Theorem and Hamilton's Equations9.4. Hamilton-Jacobi Theory10. The Action as a Generator10.1. Conservation of Probabilityand Continuous Transformations10.2. The Poetry of NatureAppendixesA. Scalars, Vectors, and TensorsB. Special RelativityC. Equations of Motion in Quantum MechanicsD. Conjugate Variables and Legendre TransformationsE. The JacobianF. The Covariant DerivativeBibliographyIndex

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Book SynopsisTable of ContentsBasic Math and Pre-Algebra For Dummies, 2nd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: Playing the Numbers Game 7 CHAPTER 2: It’s All in the Fingers: Numbers and Digits 23 CHAPTER 3: The Big Four: Addition, Subtraction, Multiplication, and Division 29 Part 2: Getting a Handle on Whole Numbers 47 CHAPTER 4: Putting the Big Four Operations to Work 49 CHAPTER 5: A Question of Values: Evaluating Arithmetic Expressions 63 CHAPTER 6: Say What? Turning Words into Numbers 75 CHAPTER 7: Divisibility 87 CHAPTER 8: Fabulous Factors and Marvelous Multiples 95 Part 3: Parts of the Whole: Fractions, Decimals, and Percents 109 CHAPTER 9: Fooling with Fractions 111 CHAPTER 10: Parting Ways: Fractions and the Big Four Operations 125 CHAPTER 11: Dallying with Decimals 149 CHAPTER 12: Playing with Percents 171 CHAPTER 13: Word Problems with Fractions, Decimals, and Percents 183 Part 4: Picturing and Measuring — Graphs, Measures, Stats, and Sets 195 CHAPTER 14: A Perfect Ten: Condensing Numbers with Scientific Notation 197 CHAPTER 15: How Much Have You Got? Weights and Measures 205 CHAPTER 16: Picture This: Basic Geometry 217 CHAPTER 17: Seeing Is Believing: Graphing as a Visual Tool 239 CHAPTER 18: Solving Geometry and Measurement Word Problems 247 CHAPTER 19: Figuring Your Chances: Statistics and Probability 259 CHAPTER 20: Setting Things Up with Basic Set Theory 271 Part 5: The X-Files: Introduction to Algebra 279 CHAPTER 21: Enter Mr X: Algebra and Algebraic Expressions 281 CHAPTER 22: Unmasking Mr X: Algebraic Equations 299 CHAPTER 23: Putting Mr X to Work: Algebra Word Problems 311 Part 6: The Part of Tens 321 CHAPTER 24: Ten Little Math Demons That Trip People Up 323 CHAPTER 25: Ten Important Number Sets to Know 329 Index 337 Basic Math and Pre-Algebra Workbook For Dummies, 3rd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: We've Got Your Numbers 7 CHAPTER 2: Smooth Operators: Working with the Big Four Operations 23 CHAPTER 3: Getting Down with Negative Numbers 37 CHAPTER 4: It's Just an Expression 49 CHAPTER 5: Dividing Attention: Divisibility, Factors, and Multiples 69 Part 2: Slicing Things Up: Fractions, Decimals, and Percents 89 CHAPTER 6: Fractions Are a Piece of Cake 91 CHAPTER 7: Fractions and the Big Four 109 CHAPTER 8: Getting to the Point with Decimals 143 CHAPTER 9: Playing the Percentages 165 Part 3: A Giant Step Forward: Intermediate Topics 177 CHAPTER 10: Seeking a Higher Power through Scientific Notation 179 CHAPTER 11: Weighty Questions on Weights and Measures 189 CHAPTER 12: Shaping Up with Geometry 203 CHAPTER 13: Getting Graphic: Xy-Graphs 223 Part 4: The X Factor: Introducing Algebra 235 CHAPTER 14: Expressing Yourself with Algebraic Expressions 237 CHAPTER 15: Finding the Right Balance: Solving Algebraic Equations 259 Part 5: The Part of Tens 277 CHAPTER 16: Ten Alternative Numeral and Number Systems 279 CHAPTER 17: Ten Curious Types of Numbers 287 Index 293

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Book SynopsisSuitable for students in the fields of mathematics, science, and engineering, this title provides a theoretical approach to dynamical systems and chaos. It helps them to analyze the types of differential equations that arise in their area of study.Table of Contents1. First-Order Equations 2. Planar Linear Systems 3. Phase Portraits 4. Classification of Planar Systems 5. Higher Dimension Linear Algebra 6. Higher Dimension Linear Systems 7. Nonlinear Systems 8. Equilibria in Nonlinear Systems 9. Global Nonlinear Techniques 10. Closed Orbits and Limit Sets 11. Applications in Biology 12. Applications in Circuit Theory 13. Applications in Mechanics 14. The Lorenz System 15. Discrete Dynamical Systems 16. Homoclinic Phenomena 17. Existence and Uniqueness Revisited

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Book SynopsisA graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.

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Book SynopsisIn recent years the finance industry has mushroomed to become an important part of modern economies, and many science and engineering graduates have joined the industry as quantitative analysts, with mathematical and computational skills that are needed to solve complex problems of asset valuation and risk management. An important parallel story exists of scientific endeavour. Between 1965-1995, insightful ideas in economics about asset valuation were turned into a mathematical ''theory of arbitrage'', an enterprise whose first achievement was the famous 1973 Black-Scholes formula, followed by extensive investigations using all the resources of modern analysis and probability. The growth of the finance industry proceeded hand-in-hand with these developments. Now new challenges arise to deal with the fallout from the 2008 financial crisis and to take advantage of new technology, which has revolutionized the practice of trading. This Very Short Introduction introduces readers with no previous background in this area to arbitrage theory and why it works the way it does. Illuminating pricing theory, Mark Davis explains its applications to interest rates, credit trading, fund management and risk management. He concludes with a survey of the most pressing issues in mathematical finance today.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 ReviewOnly a scholar of the highest order could provide the depth, breadth, clarity, precision, and brevity to be found in this work. Enjoy the resulting gem. * Dilip B. Madan, Professor of Finance, Robert H. Smith School of Business *This elegant little book will enthral readers looking for a clear sense of what mathematical finance is all about. Each chapter captures the essential ideas within a different aspect of the subject, without burying readers in abstruse models. Davis knows the subject so well, from both the mathematical and practical viewpoints, that he can make it accessible, relevant, and correct, all at the same time. * Darrell Duffie, Dean Witter Distinguished Professor of Finance, Stanford University *With concise explanations of the most important financial mathematical correlations and the mathematical formulas necessary for them, this book represents a successful very short introduction into this complex topic. * zbMATH *Table of ContentsPreface 1: Money, banking, and financial markets 2: Quantifying risks 3: The classical theory of option pricing 4: Interest rates 5: Credit risk 6: Fund management 7: Risk management 8: The banking crisis and its aftermatch Epilogue Further reading Index

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Book SynopsisFrom ecosystems to Facebook, from the Internet to the global financial market, some of the most important and familiar natural systems and social phenomena are based on a networked structure. It is impossible to understand the spread of an epidemic, a computer virus, large-scale blackouts, or massive extinctions without taking into account the network structure that underlies all these phenomena.In this Very Short Introduction, Guido Caldarelli and Michele Catanzaro discuss the nature and variety of networks, using everyday examples from society, technology, nature, and history to explain and understand the science of network theory. They show the ubiquitous role of networks; how networks self-organize; why the rich get richer; and how networks can spontaneously collapse. They conclude by highlighting how the findings of complex network theory have very wide and important applications in genetics, ecology, communications, economics, and sociology. 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.Table of Contents1. A network point of view on the world ; 2. A fruitful approach ; 3. A world of networks ; 4. Connected and close ; 5. Superconnectors ; 6. Emergence of networks ; 7. Digging deeper into networks ; 8. Perfect storms on networks ; 9. All the world's a net. Or not? ; Further reading

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Book Synopsis1 The Binomial No-Arbitrage Pricing Model.- 1.1 One-Period Binomial Model.- 1.2 Multiperiod Binomial Model.- 1.3 Computational Considerations.- 1.4 Summary.- 1.5 Notes.- 1.6 Exercises.- 2 Probability Theory on Coin Toss Space.- 2.1 Finite Probability Spaces.- 2.2 Random Variables, Distributions, and Expectations.- 2.3 Conditional Expectations.- 2.4 Martingales.- 2.5 Markov Processes.- 2.6 Summary.- 2.7 Notes.- 2.8 Exercises.- 3 State Prices.- 3.1 Change of Measure.- 3.2 Radon-Nikodým Derivative Process.- 3.3 Capital Asset Pricing Model.- 3.4 Summary.- 3.5 Notes.- 3.6 Exercises.- 4 American Derivative Securities.- 4.1 Introduction.- 4.2 Non-Path-Dependent American Derivatives.- 4.3 Stopping Times.- 4.4 General American Derivatives.- 4.5 American Call Options.- 4.6 Summary.- 4.7 Notes.- 4.8 Exercises.- 5 Random Walk.- 5.1 Introduction.- 5.2 First Passage Times.- 5.3 Reflection Principle.- 5.4 Perpetual American Put: An Example.- 5.5 Summary.- 5.6 Notes.- 5.7 Exercises.- 6 Interest-Rate-DTable of Contents1. The Binomial No-Arbitrage Pricing Model 1.1. One-Period Binomial Model 1.2. Multiperiod Binomial Model 1.3. Computational Considerations 1.4. Summary 1.5. Notes 1.6. Exercises 2. Probability Theory on Coin Toss Space 2.1. Finite Probability Spaces 2.2. Random Variables, Distributions, and Expectations 2.3. Conditional Expectations 2.4. Martingales 2.5. Markov Processes 2.6. Summary 2.7. Notes 2.8. Exercises 3. State Prices 3.1. Change of Measure 3.2. Radon-Nikod\'ym Derivative Process 3.3. Capital Asset Pricing Model 3.4. Summary 3.5. Notes 3.6. Exercises 4. American Derivative Securities 4.1. Introduction 4.2. Non-Path-Dependent American Derivatives 4.3. Stopping Times 4.4. General American Derivatives 4.5. American Call Options 4.6. Summary 4.7. Notes 4.8. Exercises 5. Random Walk 5.1. Introduction 5.2. First Passage Times 5.3. Reflection Principle 5.4. Perpetual American Put: An Example 5.5. Summary 5.6. Notes 5.7. Exercises 6. Interest-Rate-Dependent Assets 6.1. Introduction 6.2. Binomial Model for Interest Rates 6.3. Fixed-Income Derivatives 6.4. Forward Measures 6.5. Futures 6.6. Summary 6.7. Notes 6.8. Exercises Proof of Fundamental Properties of Conditional Expectations References Index

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Book SynopsisFirst Steps in Space-Time: A Brief Introduction to Special Relativity provides an accessible, authentic, and readable introduction to the theory of special relativity. The academic level of the book builds only on skills that would be covered in a GCSE maths course, such as Pythagoras's theorem, and rearranging equations, and no prior knowledge of relativity (or physics) is assumed. The key benefits of the work are to bridge the gap between popular science books and university textbooks, and make the theory of relativity as broadly accessible as physically possible. The book allows the reader to discover and appreciate that relativity is not an intractable esoteric curiosity, but a beautiful and succinct theory that profoundly shaped the course of history and our interpretation of our day-to-day lives. This book is ideal for readers with an interest in physics and a little working knowledge of maths, who have studied mathematics at about A-level standard: professionals such

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Book SynopsisUse TRIZ to unlock creative problem solving Are you new to TRIZ and looking for an easy-to-follow guide on how you can use it to enhance your company's creativity, innovation and problem-solving abilities? Look no further! Written in plain English and packed with tons of accessible and easy-to-follow instruction, TRIZ For Dummies shows you how to use this powerful toolkit to discover all the ways of solving a problem, uncover new concepts and identify previously unseen routes for new product development. An international science that relies on the study of patterns in problems and solutions, TRIZ offers a powerful problem-solving and creativity-generating solution for companies looking to promote innovation, especially in the face of having to do more with less. Inside, you'll find out how to successfully apply this problem-solving toolkit to benefit from the experience of the whole worldnot just the spontaneous and occasional creativity of individuals or groups of engineers with an orTrade ReviewThe book is entertaining and engaging, and reading it may be the first step to changing the way you approach problems forever (Professional Engineering, May 2016)Table of ContentsIntroduction 1 About This Book 2 Foolish Assumptions 3 Icons Used in This Book 3 Beyond the Book 4 Where to Go from Here 4 Part I: Getting Started with TRIZ 5 Chapter 1: Going from Zero to TRIZ 7 Getting to Know TRIZ 8 Increasing Ideality 8 Uncovering patterns in human creativity 10 Learning to think in the abstract 11 Connecting conceptual thinking with your knowledge and experience 13 Going beyond your own experience 14 Thinking functionally 15 Starting Your TRIZ Journey 16 Getting a handle on the TRIZ tools 16 Reapplying proven knowledge to deliver innovative new solutions 17 Modelling problems conceptually 19 Supercharging your thinking 20 Mastering TRIZ 22 Putting the tools together in the TRIZ problem‐solving process 22 Innovating with others by sharing solutions 24 Cultivating the motivation for innovation 24 Being humble and looking like a genius 26 Chapter 2: Understanding the Fundamental TRIZ Philosophy 27 Thinking TRIZ 28 Picturing TRIZ’s beginnings 28 Standing on the shoulders of giants – or reinventing the wheel? 29 Understanding the TRIZ Philosophy 30 Learning to think conceptually 30 Reapplying proven knowledge to solve problems 32 Getting everything you want without changing anything 34 Developing confidence 35 Being Systematic and Creative 36 Using TRIZ processes for understanding and solving problems 36 Thinking freely 37 Challenging assumptions 37 Part II: Opening Your TRIZ Toolbox 39 Chapter 3: Solving Contradictions with the 40 Inventive Principles 41 Uncovering and Understanding Unresolved Conflicts 41 Spotting contradictions and seeing how they’re resolved 42 Understanding the two types of contradiction 44 Reapplying other people’s genius solutions 44 Solving Technical Contradictions 46 Improving imperfect solutions with a little help from your friends 48 Using the Contradiction Matrix 48 Getting to Grips with Physical Contradictions 53 Resolving Physical Contradictions 54 Clever Tricks to Outsmart Contradictions: Using the 40 Inventive Principles 56 Applying the 40 Inventive Principles to real problems 56 Digging for buried treasure in the right places 58 Chapter 4: Applying the Trends of Technical Evolution 61 Looking More Closely at the Trends 62 Discovering the 8 Trends 65 Charting future product directions 69 Achieving a system’s ultimate destiny 73 Applying the Trends 74 Listening to the voice of the product 75 Using the Trends to develop a next‐generation system 76 Moving systems forward and knowing when to go back 78 Applying the Trends More Generally 79 Increasing Ideality 79 Transition to the Super‐System 79 Increasing System Coordination 79 S‐Curves 80 Using the Trends to Create Strong Patents 80 Strengthening and ring‐fencing your own patents 80 Leapfrogging competitors’ technology 81 Chapter 5: Improving Ideality by Using Resources 83 Understanding the Ideality Equation: How TRIZ Defines Value 84 Defining benefits 84 Defining costs 86 Defining downsides 86 Putting the Ideality Equation together 87 Understanding the Links Between Benefits, Functions and Solutions 89 Thinking Resourcefully 90 Understanding resources and where to find them 91 Learning how to hunt for resources 92 Getting what you want using what you have 95 Embedding resource thinking into everyday life 96 Chapter 6: Using the TRIZ Effects Database 99 Thinking Innovatively with the Prism of TRIZ 100 Taking out unnecessary detail 100 Reapplying clever solutions in new and exciting ways 102 Making new connections between existing technologies 104 Using the Database of Scientific Effects 105 Learning to look for what you want 105 Applying the Effects Database to solve problems 106 Strategies for analogous searching 109 Inventing with TRIZ 110 Matching needs and systems 110 Uncovering unmet needs 113 Applying existing technologies to create novel inventions 114 Part III: Thinking Like a Genius 117 Chapter 7: Breaking Psychological Inertia with the TRIZ Creativity Tools 119 Recognising Psychological Inertia 120 Appreciating the Benefits of Psychological Inertia 122 Beating Psychological Inertia 124 Why bad solutions are a good idea 124 Using the 13 TRIZ tools for creative thinking 125 Understanding and Solving Problems Using Smart Little People 127 Modelling problems and solutions conceptually 128 Breaking out of practical thinking 129 Bringing wacky ideas back to reality 130 Stretching Your Thinking with Size–Time–Cost 132 Restructuring your view of what’s possible 133 Finding inventive solutions 134 Chapter 8: Thinking in Time and Scale 137 Stretching Your Thinking in Time and Scale 137 Remembering to stretch yourself 140 Considering whether 9 boxes are really enough 141 Thinking big and thinking small 142 Looking at your situation with new eyes 143 Understanding Problems in Time and Scale 144 Recognising the importance of the big picture 145 Mapping causes of problems and hazards 145 Thinking strategically: Predicting future opportunities and threats 145 Finding Novel Solutions in Time and Scale 148 Locating inventive times and places to solve a problem 148 Covering the waterfront by finding all possible solutions 149 Learning to Think in Time and Scale 151 Chapter 9: Living in Utopia (then Coming Back to Reality) 153 Defining the Ideal Outcome 153 Locating your North Star: Setting your problem‐solving direction 154 Outlining benefits as a team 154 Striving for perfection with the Ideal Outcome, Prime Benefit and Ultimate Goal 156 Setting your constraints 158 Considering stakeholders: Don’t be afraid to ask your customers 159 Taking a Step Towards Reality with Ideal Systems 160 Thinking of what you want and then getting it 160 Using 9 Boxes to define your Ideal System 161 Using divergent thinking with Ideal Functions 162 Making Sensible Decisions by Considering All Benefits, Costs and Harms 163 From perfection to reality: Defining the Ideality you want 164 Learning to compare apples and pears 165 Thinking about the unthinkable: Managing risk 166 Chapter 10: Problem Solving and Being Creative with Others 167 Going for What You Really Want 167 Thinking in Extremes 170 Challenging constraints: Real or imagined? 170 Restructuring problems and solutions 173 Thinking crazily (while being practical) 173 Being Persistent in the Face of Failure 175 Improving imperfect solutions 175 Fixing things when something’s gone wrong 177 Knowing when to stop 178 Sharing and Developing Ideas with Other People 178 Recognising why bad solutions are a good idea 179 Seeing the flaws in your own solutions 180 Learning to love other people’s solutions 181 Capturing, sharing and combining solutions 181 Creating a climate for innovation 182 Part IV: Understanding, Defining and Solving Difficult Problems with TRIZ 185 Chapter 11: Applying the TRIZ Problem‐Solving Process 187 Logically and Systematically Solving Problems 187 Trusting the process (and yourself) 188 Making big leaps by taking small steps 189 Developing your own problem‐solving map 189 Climbing the Problem‐Solving Steps 191 Understanding the overall process 191 Sharpening the axe 193 Knowing your needs and scoping the situation 195 Defining your problem correctly 195 Generating Solutions 196 Expecting the unexpected 196 Applying the TRIZ solution tools 197 Ranking and Developing Solutions 198 Developing solutions further 198 Ranking solutions by Ideality 199 Converging by concept 200 Solving Difficult Problems Effectively in a Team 201 Gaining team understanding and consensus 201 Converging and diverging 201 Thinking fast and thinking slow 202 Putting solutions into practice 203 Chapter 12: Getting to Grips with Your Problems with Function Analysis 205 Making Complex Problems Simple 205 Understanding the building blocks of Function Analysis 207 Defining interactions: The good, the bad and the ugly 208 Charting all parts of your system and beyond 210 Building a Function Analysis Diagram 212 Completing a Function Analysis 212 Listing your components and their interactions 212 Drawing a Function Map 213 Listing, prioritising and solving problems 213 Uncovering Conflicts: Putting Contradictions in Context 214 Understanding How Everything Fits Together 215 Using Function Analysis 216 Modelling difficult problems 217 Gaining the confidence required to change things 218 Achieving clarity in complex situations 220 Communicating effectively 220 Chapter 13: Solving Problems using the TRIZ Standard Solutions 223 Defining a Subject–action–Object 223 Categorising Problems 225 Dealing with Harmful Actions 226 Improving Insufficient Actions 228 Measuring and Detecting 228 Applying the Standard Solutions 231 Developing a well‐formulated problem 231 Solving problems outlined in a Function Analysis 232 Generating innovative solutions 233 Tackling a real problem 235 Improving a solution 237 Chapter 14: Trimming for Elegant, Low‐Cost Solutions 241 Making Things Better and Cheaper 241 Improving systems by removing stuff 242 Clever cost‐cutting: Doing more with less 245 Using resources wisely 247 Creating Elegant Solutions 248 Applying the Trimming Rules 248 Following the process and going off‐piste 252 Trimming to Infinity and Beyond 252 Trimming to Create Strong Intellectual Property 254 Getting round someone else’s patent 254 Developing your own patent further 255 Part V: The Part of Tens 257 Chapter 15: Ten Pitfalls to Avoid 259 Thinking TRIZ Doesn’t Apply to You 259 Waiting for the ‘Right’ Problem 260 Starting Too Big 260 Tackling Problems for Which You Can’t Implement Solutions 261 Tackling Problems without Involving the Problem Owner 261 Trying to Solve Problems When You Don’t Understand the Issue or the Technology 262 Trying to Solve Problems When You Lack Crucial Knowledge 262 Working on a Problem That’s Already Been Solved 263 Undertaking TRIZ by Stealth 263 Giving Up Too Soon 264 Chapter 16: Ten Tips for Getting Started with TRIZ 265 Learn It 265 Use It 266 Start Small 266 Attend a Workshop 266 Think and Talk TRIZ 267 Find a Friend 267 Fail Safely 268 Be Bold 268 Fail Better 269 Reflect 269 Part VI: Appendixes 271 Appendix A: The 40 Inventive Principles 273 Inventive Principle 1: Segmentation 273 Inventive Principle 2: Taking Out 274 Inventive Principle 3: Local Quality 274 Inventive Principle 4: Asymmetry 275 Inventive Principle 5: Merging 275 Inventive Principle 6: Multi‐Function 275 Inventive Principle 7: Nested Doll 276 Inventive Principle 8: Counterweight 276 Inventive Principle 9: Prior Counteraction 276 Inventive Principle 10: Prior Action 277 Inventive Principle 11: Cushion in Advance 277 Inventive Principle 12: Equal Potential 277 Inventive Principle 13: The Other Way Round 278 Inventive Principle 14: Spheres and Curves 278 Inventive Principle 15: Dynamism 279 Inventive Principle 16: Partial or Excessive Action 279 Inventive Principle 17: Another Dimension 279 Inventive Principle 18: Mechanical Vibration 280 Inventive Principle 19: Periodic Action 280 Inventive Principle 20: Continuous Useful Action 281 Inventive Principle 21: Rushing Through 281 Inventive Principle 22: Blessing in Disguise 281 Inventive Principle 23: Feedback 282 Inventive Principle 24: Intermediary 282 Inventive Principle 25: Self‐service 283 Inventive Principle 26: Copying 283 Inventive Principle 27: Cheap, Short‐Living Objects 284 Inventive Principle 28: Replace Mechanical System 284 Inventive Principle 29: Pneumatics and Hydraulics 285 Inventive Principle 30: Flexible Membranes and Thin Films 285 Inventive Principle 31: Porous Materials 285 Inventive Principle 32: Colour Change 286 Inventive Principle 33: Uniform Material 286 Inventive Principle 34: Discarding and Recovering 287 Inventive Principle 35: Parameter Change 287 Inventive Principle 36: Phase Changes 288 Inventive Principle 37: Thermal Expansion 289 Inventive Principle 38: Boosted Interactions 289 Inventive Principle 39: Inert Atmosphere 290 Inventive Principle 40: Composite Structures 290 Appendix B: The Contradiction Matrix 291 Appendix C: The 39 Parameters of the Contradiction Matrix 293 Appendix D: The Separation Principles 299 Appendix E: The Oxford TRIZ Standard Solutions 301 Solutions for Dealing with Harms 302 H1 Trim out the harm 302 H2 Block the harm 303 H3 Turn the harm into good 304 H4 Correct the harm 304 Solutions for Improving Insufficiency 305 i1 Add something to the subject or object 305 i2 Evolve the subject and object 306 i.a Improve the action 307 Solutions for Detection and Measurement 308 M1 Indirect methods 309 M2 Add something 309 M3 Enhance measurement with fields 309 M4 Use additives with fields 310 M5 Evolve the measurement system 310 Index 311

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Book SynopsisSome people fear and mistrust numbers. Others want to use them for everything. After a long career as a statistician, Paul Goodwin has learned the hard way that the ones who want to use them for everything are a very good reason for the rest of us to fear and mistrust them. Something Doesn't Add Up is a fieldguide to the numbers that rule our world, even though they don't make sense. Wry, witty and humane, Goodwin explains mathematical subtleties so painlessly that you hardly need to think about numbers at all. He demonstrates how statistics that are meant to make life simpler often make it simpler than it actually is, but also reveals some of the ways we really can use maths to make better decisions. Enter the world of fitness tracking, the history of IQ testing, China's social credit system, Effective Altruism, and learn how someone should have noticed that Harold Shipman was killing his patients years before they actually did. In the right hands, maths is a useful tool. It's just a pity there are so many of the wrong hands about.Trade ReviewPraise for Forewarned: A Sceptic's Guide to Prediction The book is awash with entertaining examples of predictions that were astoundingly accurate and others that were spectacularly wrong. * Irish Times *

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Book SynopsisThis book, the second in a two-volume set, provides an introduction to the basics of (mainly) non-relativistic quantum mechanics. While the first volume addresses the basic principles, this second volume discusses applications and extensions to more complex problems. In addition to topics dealt with in traditional quantum mechanics texts, such as symmetries or many-body problems, it also treats issues of current interest such as entanglement, Bell’s inequality, decoherence and various aspects of quantum information in detail. Furthermore, questions concerning the basis of quantum mechanics and epistemological issues which are relevant e.g. to the realism debate are discussed explicitly. A chapter on the interpretations of quantum mechanics rounds out the book. Readers are introduced to the requisite mathematical tools step by step. In the appendix, the most relevant mathematics is compiled in compact form, and more advanced topics such as the Lenz vector, Hardy’s experiment and Shor’s algorithm are treated in more detail. As an essential aid to learning and teaching, 130 exercises are included, most of them with solutions. This revised second edition is expanded by an introduction into some ideas and problems of relativistic quantum mechanics. In this second volume, an overview of quantum field theory is given and basic conceptions of quantum electrodynamics are treated in some detail. Originally written as a course for students of science education, the book addresses all those science students and others who are looking for a reasonably simple, fresh and modern introduction to the field.Trade Review“This book continues the excellent introduction to quantum mechanics of the first volume ... suited for beginners to get first insights which may be deepened reading the appendices. The two volumes can be best recommended generally and especially for self studies.” (K.-E. Hellwig, zbMATH 1445.81002, 2020)Table of ContentsOne-Dimensional Piecewise-Constant Potentials.- Angular Momentum.- The Hydrogen Atom.- The Harmonic Oscillator.- Perturbation Theory.- Entanglement, EPR, Bell.- Symmetries and Conservation Laws.- The Density Operator.- Identical Particles.- Decoherence.- Scattering.- Quantum Information.- Is Quantum Mechanics Complete?.- Interpretations of Quantum Mechanics.

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Book SynopsisOlympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics.In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate number of test questions is available for reader's practice and testing purpose. Their detailed solutions are also conveniently provided.The examples are not very complicated so that readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions are from many countries, e.g. China, Russia, USA, Singapore, etc. In particular, the reader can find many questions from China, if he is interested in understanding mathematical Olympiad in China. This book serves as a useful textbook of mathematical Olympiad courses, or as a reference book for related teachers and researchers.Table of ContentsVolume 1: Operations on Rational Numbers; Linear Equations of Single Variable; Multiplication Formulae; Absolute Value and Its Applications; Congruence of Triangles; Similarity of Triangles; Divisions of Polynomials; Solutions to Testing Questions; Volume 2: Congruence of Integers; Decimal Representation of Integers; Pigeonhole Principle; Viete's Theorem and Its Applications; Linear Inequalities and System of Linear Inequalities; Inequalities with Absolute Values; Geometric Inequalities; Fundamental Properties of Circles; Solutions to Testing Questions; and other chapters.

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Book SynopsisThis book provides a clear understanding of quantum mechanics (QM) by developing it from fundamental postulates in an axiomatic manner, as its central theme. The target audience is physics students at master's level. It avoids historical developments, which are piecemeal, not logically well knitted, and may lead to misconceptions. Instead, in the present approach all of QM and all its rules are developed logically starting from the fundamental postulates only and no other assumptions. Specially noteworthy topics have been developed in a smooth contiguous fashion following the central theme. They provide a new approach to understanding QM. In most other texts, these are presented as disjoint separate topics. Since the reader may not be acquainted with advanced mathematical topics like linear vector space, a number of such topics have been presented as mathematical preliminary. Standard topics, viz. derivation of uncertainty relations, simple harmonic oscillator by operator method,boun

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Book SynopsisThis second edition textbook offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications. Calculus is a prerequisite for understanding the basic concepts, however the book is written with a sensitivity to students’ common difficulties with calculus that does not obscure the thorough treatment of the probability content. The first six chapters of this text neatly and concisely cover the material traditionally required by most undergraduate programs for a first course in probability. The comprehensive text includes a multitude of new examples and exercises, and careful revisions throughout. Particular attention is given to the expansion of the last three chapters of the book with the addition of one entirely new chapter (9) on ’Finding and Comparing Estimators.’ The classroom-tested material presented in this second edition forms the basis for a second course introducing mathematical statistics.Table of ContentsProbability Space.- Conditional probabilities.- Discrete random variables.- Binomial random variables.- Poisson random variables.- Simulations of discrete random variables.- Combinatorics.- Continuous random variables.- The sample average and sample.- Estimating and testing proportions.- Estimating and testing means.- Small samples.- Chi-squared tests.- Design of experiments.- The cumulative distribution function.- Continuous joint distributions.- Covariance and independence.- Conditional distribution and expectation.- The bivariate normal distribution.- Sums of Bernoulli random variables.- Coupling random variables.- The moment generating function.- The chi-squared, Student and F distributions.- Sampling from a normal distribution.- Finding estimators.- Comparing estimators.- Best unbiased estimators.- Bayes’ estimator.- Multiple linear regression.- List of common discrete distributions.- List of common continuous distributions.- Further reading.- Normal table.- Student table.- Chi-squared table.- Index.

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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 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 SynopsisComputerized databases provide a powerful everyday tool for data handling by scientists and engineers. However, the unique nature of many technical tasks requires a specialized approach to make use of the many powerful commercial database tools now available. Using these tools has proved difficult because database technology is often shrouded in layers of jargon. An essential guide for scientists and engineers who use computers to avoid drowning in a flood of data, Database Systems in Science and Engineering dispels the myths associated with database design and breaks the barriers to successful databases. Using the language of scientists and engineers, this book explains concepts and problems, offers practical steps and solutions, and provides new ideas for better data handling. The first part of the book presents an overview of technical databases using examples taken from real applications and the current state of technical databases. The second part covers the computer impleTrade Review"… a valuable resource for scientists … a fine job of presenting the information necessary to plan, design, and use computerized technical databases …The language is clear, the treatment easy to follow, and the presentation is copiously illustrated with realistic diagrams and flow charts … the authors frequently emphasize that the user and his or her needs are the key to successful database design. Chapters on developing an effective user interface and on efficient dissemination of data provide specific suggestions for accomplishing this purpose." -Journal of Chemical Information and Computer SciencesTable of ContentsIntroduction to technical databases. The nature of technical data. Types of technical databases. The use of technical databases. User interfaces. The dissemination of technical databases. Data structures. Architecture of a database. Data models. Database planning. Database design. Expert systems.

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Book SynopsisThis book developed from the need to teach a linear algebra course to students focused on data science and bioinformatics programs. These students tend not to realize the importance of linear algebra in applied sciences, since traditional linear algebra courses tend to cover mathematical contexts but not the computational aspect of linear algebra or its applications to data science and bioinformatics. The author presents the topics in a traditional course, yet offers lectures as well as lab exercises on simulated and empirical data sets. This textbook provides students a theoretical basis which can then be applied to the practical R and Python problems, providing the tools needed for real-world applications.Each section starts with working examples to demonstrate how tools from linear algebra can help solve problems in applied sciences. These exercises start from easy computations, such as computing determinants of matrices, to practical applications on simulated and e

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resulting applications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities. Table of Contents1. The Middle East, or the Beginning.- 2. The Sages of Ancient Greece.- 3. The Chinese Middle Ages.- 4. India and Persia.- 5. From the Renaissance to the Birth of Calculus.- 6. The Age of Analysis and the French Revolution.- 7. Modern Mathematics, Modern Art.- 8. Abstraction: Mathematics Since the Twentieth Century.

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Book SynopsisThis textbook provides an introduction to the mathematical methods used to analyse deterministic models in life sciences, including population dynamics, epidemiology and ecology.

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Book SynopsisPart 1.How is Music Born?.- Chapter 1.Introduction.- Chapter 2.Intervals, Scales, Tuning and Harmonics.- Chapter 3.Acoustic Basis and Generation of Sound.- Chapter 4.Complexity and Dynamics in Phase Space.- Part 2.Journey across the World.- Chapter 5.Physical and Mathematical Aspects in European Music.- Chapter 6.Music in Other Cultures.- Part 3.Moving beyond.- Chapter 7.Why Do we Know that it is Mozart?.- Chapter 8.Ending without End.

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Book SynopsisThis book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry. Trade Review“This book gives an introduction to financial mathematics. It presents also some background of mathematical facts necessary for understanding modern finance. … For the reader convenience, the book contains a detailed contents, a list of figures, a list of tables, a list of simulations, a list of acronyms and a list of used symbols.” (Jacek Jakubowski, zbMATH 1409.91002, 2019)“This excellent textbook is addressed to undergraduate and graduate students in mathematics and finance who want to study the main tools of stochastic calculus and its application to quantitative finance. Also, it can be used as a reference book for practitioners and professionals from the financial industry who want a better understanding of the theoretical aspects of stochastic calculus, and how it can be used in the pricing of financial derivatives.” (Carlos Vázquez Cendón, Mathematical Reviews, August, 2017)Table of Contents

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Book SynopsisThis book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter.Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments.Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.Trade Review“‘The aim of this book is to provide a rigorous introduction to the theory of stochastic calculus for continuous semi-martingales putting a special emphasis on Brownian motion.’ … If the reader has the background and needs a rigorous treatment of the subject this book would be a good choice. Le Gall writes clearly and gets to the point quickly … .” (Richard Durrett, MAA Reviews, March, 2017) “The purpose of this book is to provide concise but rigorous introduction to the theory of stochastic calculus for continuous semimartingales, putting a special emphasis on Brownian motion. … The book is written very clearly, it is interesting both for its construction and maintenance, mostly it is self-contained. It can be recommended to everybody who wants to study stochastic calculus, including those who is interested to its applications in other fields.” (Yuliya S. Mishura, zbMATH, 2017)Table of ContentsGaussian variables and Gaussian processes.- Brownian motion.- Filtrations and martingales.- Continuous semimartingales.- Stochastic integration.- General theory of Markov processes.- Brownian motion and partial differential equations.- Stochastic differential equations.- Local times.- The monotone class lemma.- Discrete martingales.- References.

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Book SynopsisCovid-19 has shown us the importance of mathematical and statistical models to interpret reality, provide forecasts, and explore future scenarios. Algorithms, artificial neural networks, and machine learning help us discover the opportunities and pitfalls of a world governed by mathematics and artificial intelligence.Trade Review“Alfio Quarteroni invites us to the stage of contemporary science and technology in which multidisciplinarity and transferability are combined to contribute to the construction of the wisdom of life … . A great master. Its access does not present difficulties beyond the decision to satisfy an intellectual and spiritual curiosity with a future edge: a book to be read with ease and understood with great quality.” (Melio Sáenz, ResearchGate, researchgate.net, June, 2023)Table of Contents1 Epidemic.- 2 Retrospective.- 3 Interlude: the revolution that did not happen and the revolution that was unforeseen.- 4 Artificial intelligence, learning computers, artificial neural networks.- 5 A bit of maths (behind artificial intelligence and machine learning).- 6 BIG DATA - BIG BROTHER (or, on the ethical and moral aspects of artificial intelligence).

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Book Synopsis- Part I Modelling Assets and Markets.- Introduction.- The Pricing of Financial Derivatives.- Part II Computational Pricing Methods in the Black-Scholes Framework.- Binomial Tree Methods.- Simulation I: Monte Carlo Methods.- Finite Difference Methods.- Part III Simulation Methods Beyond the Black-Scholes Framework.- Simulation II: Modelling Multivariate Financial Data.- Stochastic Models for Interest Rates.- Simulation III: Numerical Approximation of SDE Models.

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Book Synopsis

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Book SynopsisThis is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; coversTrade Review"The treasures [in the Princeton Companion to Applied Mathematics] go on and on."--Lloyd N. Trefethen, SIAM Review "[An] impressive volume... It has been a major project that eventually resulted in this amazing product."--Adhemar Bultheel, European Mathematical Society "Safe to say there is something for everyone in The Princeton Companion to Applied Mathematics."--Alan Stevens, Mathematics Today "[A] valuable addition to the mathematics library of any university or research institution."--Library Journal "Higham and his associate editors ... have produced an admirably readable and informative volume, which anyone interested in applied mathematics would be well advised to consult or--better still--to own!"--James Case, SIAM News "A unique work full of beautiful and interesting mathematics. It is surely a valuable resource for exposing young mathematicians to possible areas of applied mathematics for research and further study. Without a doubt PCAM is an important contribution to the mathematical literature."--Jason M. Graham, MathSciNet "[A]n excellent reference that successfully compiles into a readable and engaging form the broad range of topics that an applied mathematician might encounter in their career... As a reader, I find myself flipping through the pages and becoming engaged in new and interesting ideas from the world of applied math."--Joanna Bieri, MAA Reviews "A handy one-volume reference for applied mathematics that cuts across several disciplines within an academic framework."--Lesley S.J. Farmer, Reference ReviewsTable of Contents*Frontmatter, pg. i*Contents, pg. v*Preface, pg. ix*Contributors, pg. xiii*Part I. Introduction to Applied Mathematics, pg. 1*Part II. Concepts, pg. 81*Part III. Equations, Laws, and Functions of Applied Mathematics, pg. 135*Part IV. Areas of Applied Mathematics, pg. 173*Part V. Modeling, pg. 591*Part VI. Example Problems, pg. 733*Part VII. Application Areas, pg. 783*Part VIII. Final Perspectives, pg. 897*Index, pg. 963

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Book SynopsisTable of ContentsPart 1 Introduction to Programming Using MATLAB 1. Introduction to MATLAB 2. Vectors and Matrices 3. Introduction to MATLAB Programming 4. Selection Statements 5. Loop Statements and Vectorizing Code 6. MATLAB Programs 7. Text Manipulation 8. Data Structures Part 2 Advanced Topics for Problem Solving with MATLAB 9. Data Transfer 10. Advanced Functions 11. Introduction to Object-Oriented Programming and Graphics 12. Advanced Plotting Techniques 13. Sights and Sounds 14. Advanced Mathematics 15. Introduction to Machine Learning

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Book SynopsisThis book provides a detailed description of how Python can be used to give insight into the flow of groundwater based on analytic solutions. Starting with simple problems to illustrate the basic principles, complexity is added step by step to show how one-dimensional and two-dimensional models of one or two aquifers can be implemented. Steady and transient flow problems are discussed in confined, semi-confined, and unconfined aquifers that may include wells, rivers, and areal recharge. Special consideration is given to coastal aquifers, including the effect of tides and the simulation of interface flow.Application of Python allows for compact and readable code, and quick visualization of the solutions. Python scripts are provided to reproduce all results. The scripts are also available online so that they can be altered to meet site-specific conditions. This book is intended both as training material for the next generation of university students and as a useful resource forTrade Review 'This is a fantastic addition to the analytical solutions and analytic element modeling canon with a modern approach to programming with Python. I hope readers will use it to learn and explore groundwater theory, and to up their game on making simple reality checks of complex systems to improve all groundwater modeling.''The authors do an excellent job of describing practically important calculations, like determining the critical flowrate at which a pumped well starts to induce flow from a nearby river.'- Michael Fienen, Groundwater - NGWA, Book Review, 7 September 2022'This is a fantastic addition to the analytical solutions and analytic element modeling canon with a modern approach to programming with Python. I hope readers will use it to learn and explore groundwater theory, and to up their game on making simple reality checks of complex systems to improve all groundwater modeling.''The authors do an excellent job of describing practically important calculations, like determining the critical flowrate at which a pumped well starts to induce flow from a nearby river.'- Michael Fienen, Groundwater - NGWA, Book Review, 7 September 2022Table of Contents0. Basics of Groundwater Flow. 1. Steady One-dimensional Flow with Constant Transmissivity. 2. Steady One-dimensional Semi-confined Flow. 3. Steady One-dimensional Unconfined Flow with Variable Saturated Thickness. 4. Steady One-dimensional Flow in Coastal Aquifers. 5. Transient One-dimensional Flow. 6. Steady Two-dimensional Flow to Wells. 7. Steady Two-dimensional Flow to Wells in Uniform Background Flow. 8. Analytic Element Modeling of Steady Two-dimensional Flow. 9. Transient Two-dimensional Flow. 10. Steady Two-dimensional Flow in the Vertical Plane. 11. Appendix - Python Primer

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Book SynopsisThe first edition of this award-winning book attracted a wide audience. This second edition is both a joy to read and a useful classroom tool. Unlike traditional textbooks, it requires no mathematical prerequisites and can be read around the mathematics presented. If used as a textbook, the mathematics can be prioritized, with a book both students and instructors will enjoy reading.Secret History: The Story of Cryptology, Second Edition incorporates new material concerning various eras in the long history of cryptology. Much has happened concerning the political aspects of cryptology since the first edition appeared. The still unfolding story is updated here.The first edition of this book contained chapters devoted to the cracking of German and Japanese systems during World War II. Now the other side of this cipher war is also told, that is, how the United States was able to come up with systems that were never broken.The text is in t

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Book SynopsisLinear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader''s confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading pTrade ReviewThis book gives an introduction to linear algebra for students with limited mathematical preparation. ... The steady pace of the book is so gentle that no student need be left behind. * Peter Macgregor, Mathematical Gazette *Table of Contents1. Linear Equations and Matrices ; 2. Euclidean Space ; 3. General Vector Spaces ; 4. Inner Product Spaces ; 5. Linear Transformation ; 6. Determinants ; 7. Eigenvalues and Eigenvectors

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Book SynopsisEverything You Need to Know about Mathematics for Science and EngineeringUpdated and expanded with new topics, The Mathematics Companion: Mathematical Methods for Physicists and Engineers, 2nd Edition presents the essential core of mathematical principles needed by scientists and engineers. Starting from the basic concepts of trigonometry, the book covers calculus, differential equations, and vector calculus. A new chapter on applications discusses how we see objects mathematically with the eye, how quantum mechanics works, and more.A Convenient, Student-Friendly Format Rich with Diagrams and Clear ExplanationsThe book presents essential mathematics ideas from basic to advanced level in a way that is useful to both students and practicing professionals. It offers a unique and educational approach that is the signature style of the author's companion books. The author explains mathematical concepts clearly, concisely, and visually, ilTrade Review"The book summarizes basic notions of mathematical methods for physicists and engineers in a schematic way. It is aimed both at science students and physicists who need a quick handy reference when they have to solve a specific mathematical problem."—Applications of Mathematics, 60, 2015Praise for the First Edition:"This is an interesting and useful little book … .it is very well done, and everything that might be expected to be there is there … . The book might also be invaluable for those undergraduate students in Mathematics, Science, or Engineering, who need to undertake first- and second-year courses in Mathematics, and it will serve those who wish to have quick access to all those formulae that seem to be so readily forgotten."—Australian Physics, March/April 2006Table of ContentsPart 1 Essential Mathematics: Basic mathematics. Differentiation. Integration. Exponentials and logarithms. Hyperbolic functions. Infinite series. Part 2 Advance Mathematics: Ordinary differential equations. Laplace transforms. Vector analysis. Partial derivatives. Multiple integrals. Fourier series. Special functions. Partial differential equations.

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Book SynopsisHow to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory.Trade ReviewI'd very strongly recommend it to undergraduates studying maths, Sixth formers about to study maths, and anyone who did a maths degree a while ago and wants to revisit groups, rings and fields. I also recommend that any first year pure maths lecturers reading this should add this book to their course's reading list. * Chalkdust *Table of Contents1: What is Abstract Algebra? 2: Axioms and Denitions 3: Theorems and Proofs 4: Studying Abstract Algebra 5: Binary Operations 6: Groups and Subgroups 7: Quotient Groups 8: Isomorphisms and Homomorphisms 9: Rings References

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Book SynopsisTrade Review"...if you use this book frequently it’s definitely worth getting the new edition…" --MAA.org, November 2014 "The integrals are very useful, but this book includes many other features that will be helpful to the reader, especially graduate students. The sections on Hermite and Legendre polynomials are especially helpful for students of Electricity and Magnetism, Quantum Mechanics, and Mathematical physics (they won't have to hunt in several books to find what they need)." --Barry Simon, California Institute of Technology "This book is to the CRC Mathematical Tables as the unabridged Oxford English Dictionary is to Webster's Collegiate. Besides being big, it's easy to find things in, because of the way the integrals are organized into classes...It really helped me through grad school." --Phil Hobbs, Amazon ReviewTable of Contents1. Elementary Functions 2. Indefinite Integrals of Elementary Functions 3. Definite Integrals of Elementary Functions 4. Combinations Involving Trigonometric and Hyperbolic Functions and Power 5. Indefinite Integrals of Special Functions 6. Definite Integrals of Special Functions 7. Associated Legendre Functions 8. Special Functions 9. Hypergeometric Functions 10. Vector Field Theory 11. Algebraic Inequalities 12. Integral Inequalities 13. Matrices and Related Result 14. Determinants 15. Norms 16. Ordinary Differential Equations 17. Fourier, Laplace, and Mellin Transforms 18. The Z-transform

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Book SynopsisTable of Contents1. Properties of the Surface 2. Principles of Tolerancing 3. Principles of Geometrical Tolerancing 4. Profile Tolerancing 5. Tolerancing of Cones 6. Positional Tolerancing 7. Tolerancing of Edges 8. Projected Tolerance Zone 9. Substitute Elements 10. Maximum Material Requirement 11. Envelope Requirement 12. Least Material Requirement 13. Tolerancing of Flexible Parts 14. Tolerance chains (accumulation of tolerances) 15. Statistical Tolerancing 16. Respecting Geometrical Tolerances During Manufacturing 17. General Geometrical Tolerances 18. Inspection of Geometrical Deviations 19. Function Related, Manufacturing Related, Inspection Related Geometrical Tolerancing 20. Examples of Geometrical Tolerancing 21. Differences Between ISO/ANSI/BS and Other Standards 22. Synopsis of ISO-Standards

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