Mathematics Books
Princeton University Press The Mathematics of Shock ReflectionDiffraction
Book SynopsisThis book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann''s conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation lawsPDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlin
£63.75
Princeton University Press Introduction to Computational Science
Book SynopsisComputational science is an exciting new field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. This book provides students with a versatile and accessible introduction to the subject.Trade Review"The first edition of this book had received very positive feedback and was warmly welcomed by the mathematical community. It is very good news for all us is that the second revised edition is even better!"--Svitlana P. Rogovchenko, Zentralblatt MATH Praise for the previous edition: "The heart of Introduction to Computational Science is a collection of modules. Each module is either a discussion of a general computational issue or an investigation of an application... [This book] has been carefully and thoughtfully written with students clearly in mind."--William J. Satzer, MAA Reviews Praise for the previous edition: "Introduction to Computational Science is useful for students and others who want to obtain some of the basic skills of the field. Its impressive collection of projects allows readers to quickly enjoy the power of modern computing as an essential tool in building scientific understanding."--Wouter van Joolingen, Physics Today Praise for the previous edition: "A masterpiece. I know of nothing comparable. I give it five stars."--James M. Cargal, UMAP Journal Praise for the previous edition: "This is an important book with a wonderful collection of examples, models, and references."--Robert M. Panoff, Shodor Education Foundation Praise for the previous edition: "This is a very good introduction to the field of computational science."--Peter Turner, Clarkson University "Despite its substantial weight, the book is extremely user friendly... There are many different courses that one could build with this book as foundation, and it is an indispensible resource for anyone seeking to bring modeling projects into their classes."--David M. Bressoud, UMAP Journal
£80.00
Princeton University Press Hangzhou Lectures on Eigenfunctions of the
Book SynopsisBased on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. It shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic.Trade Review"The book is very well written... I would definitely recommend it to anybody who wants to learn spectral geometry."--Leonid Friedlander, Mathematical ReviewsTable of ContentsPreface ix 1A review: The Laplacian and the d'Alembertian 1 1.1 The Laplacian 1 1.2 Fundamental solutions of the d'Alembertian 6 2Geodesics and the Hadamard parametrix 16 2.1 Laplace-Beltrami operators 16 2.2 Some elliptic regularity estimates 20 2.3 Geodesics and normal coordinates|a brief review 24 2.4 The Hadamard parametrix 31 3The sharp Weyl formula 39 3.1 Eigenfunction expansions 39 3.2 Sup-norm estimates for eigenfunctions and spectral clusters 48 3.3 Spectral asymptotics: The sharp Weyl formula 53 3.4 Sharpness: Spherical harmonics 55 3.5 Improved results: The torus 58 3.6 Further improvements: Manifolds with nonpositive curvature 65 4Stationary phase and microlocal analysis 71 4.1 The method of stationary phase 71 4.2 Pseudodifferential operators 86 4.3 Propagation of singularities and Egorov's theorem 103 4.4 The Friedrichs quantization 111 5Improved spectral asymptotics and periodic geodesics 120 5.1 Periodic geodesics and trace regularity 120 5.2 Trace estimates 123 5.3 The Duistermaat-Guillemin theorem 132 5.4 Geodesic loops and improved sup-norm estimates 136 6Classical and quantum ergodicity 141 6.1 Classical ergodicity 141 6.2 Quantum ergodicity 153 Appendix 165 A.1 The Fourier transform and the spaces S( n) and S'( n)) 165 A.2 The spaces D'(OMEGA) and E'(OMEGA) 169 A.3 Homogeneous distributions 173 A.4 Pullbacks of distributions 176 A.5 Convolution of distributions 179 Notes 183 Bibliography 185 Index 191 Symbol Glossary 193
£148.75
Princeton University Press Partial Differential Equations An Introduction
Book SynopsisThis textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serTrade Review"This book is unique in that it provides a very comprehensive introduction to the theory of PDEs embedded in specific relevant applications in the field."--Choice "The authors provide not only a clear and rigorous explanation of the more elementary theoretical aspects of partial differential equations, but they are also concerned with tools of applied mathematics in the setting of partial differential equations... This reviewer warmly recommends this volume to mathematical university libraries."--Vicentiu D. Radulescu, Zentralblatt MATH
£68.00
Princeton University Press Hodge Theory
Book SynopsisProvides an introduction to Hodge theory - one of the central and most vibrant areas of contemporary mathematics - from leading specialists on the subject. This book includes topics that range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps.Trade Review"Charles and Schnell's chapter beautifully surveys the theory of absolute Hodge classes, giving in particular a complete proof of Deligne's theorem on absolute Hodge classes on abelian varieties... A welcome addition to the literature and should be useful to both graduate students and researchers working in Hodge theory."--Dan Petersen, MathSciNetTable of Contents*FrontMatter, pg. i*Contributors, pg. v*Contents, pg. vii*Preface, pg. xv*Chapter One. Introduction to Kahler Manifolds, pg. 1*Chapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem, pg. 70*Chapter Three. Mixed Hodge Structures, pg. 123*Chapter Four. Period Domains and Period Mappings, pg. 217*Chapter Five. The Hodge Theory of Maps, pg. 257*Chapter Six The Hodge Theory of Maps, pg. 273*Chapter Seven. Introduction to Variations of Hodge Structure, pg. 297*Chapter Eight. Variations of Mixed Hodge Structure, pg. 333*Chapter Nine. Lectures on Algebraic Cycles and Chow Groups, pg. 410*Chapter Ten. The Spread Philosophy in the Study of Algebraic Cycles, pg. 449*Chapter Eleven. Notes on Absolute Hodge Classes, pg. 469*Chapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective, pg. 531*Bibliography, pg. 574*Index, pg. 577
£78.20
Princeton University Press PowerUp
Book SynopsisTrade Review"Lane explores secondary, or hidden, mathematical gems that a player might discover upon mature reflection. . . . Just as most car drivers prefer not to inquire how the internal combustion engine works, most video-type users prefer not to ask how computer magic works. For the few who do ask questions, Lane assures us and as his book testifies, 'there's a lot of mathematics under the surface'."---Andrew James Simoson, MathSciNet"Lane explains some pretty technical concepts in an accessible way. . . . A fun survey of interesting maths related through the lens of video games."---Paul Taylor, Aperiodical"The examples [in Power-Up] were carefully chosen from very popular games, so even the most casual player will have heard of the vast majority of the games discussed. In general, Lane's writing is easy to digest, and the use of color and high-quality paper gives the book a nice look and feel." * Choice *"PowerUp is a very readable book based on examples taken from popular video games. . . . It is a pity that too many people are deprived of the pleasure of finding things out via the intellectual game of mathematics. Hopefully, the effort of the likes of Matthew Lane will someday solve the severe marketing problem of mathematics." * Computing Reviews *"Overall the book is excellent. Lane has written a high readable text with colorful illustrations. You won’t regret reading it and maybe Power-Up will add a new level of insight to your computer gaming." * MAA Reviews *"Matthew Lane explores the mathematical underpinning many popular video games in this well-written and very enjoyable book that is pitched at a very broad audience"---Dominic Thorrington, Mathematics TodayTable of ContentsAcknowledgments xi Introduction 1 1. Let's Get Physical 7 1.1 Platforming Perils 7 1.2 Platforming in Three Dimensions 10 1.3 LittleBigPlanet: Exploring Physics through Gameplay 12 1.4 From 2D to 3D: Bending Laws in Portal 14 1.5 Exploring Reality with A Slower Speed of Light 18 1.6 Exploring Alternative Realities 21 1.7 Beyond Physics: Minecraft or Mine Field? 26 1.8 Closing Remarks 27 1.9 Addendum: Describing Distortion 29 2. Repeat Offenders 34 2.1 Let's Play the Feud! 34 2.2 Game Shows and Birthdays 36 2.3 Beyond the First Duplicate 39 2.4 The Draw Something Debacle 41 2.5 Delayed Repetition: Increasing N 46 2.6 Delayed Repetition:Weight Lifting 48 2.7 The Completionist's Dilemma 53 2.8 Closing Remarks 55 2.9 Addendum: In Search of a Minimal k 55 3. Get Out the Voting System 58 3.1 Everybody Votes, but Not for Everything 58 3.2 Plurality Voting: An Example 60 3.3 Ranked-Choice Voting Systems and Arrow's Impossibility Theorem 61 3.4 An Escape from Impossibility? 66 3.5 Is There a "Best" System? 68 3.6 What Game Developers Know that Politicians Don't 71 3.7 The Best of the Rest 76 3.8 Closing Remarks 82 3.9 Addendum: TheWilson Score Confidence Interval 83 4. Knowing the Score 86 4.1 Ranking Players 86 4.2 Orisinal Original 87 4.3 What's in a Score? 91 4.4 Threes! Company 98 4.5 A Mathematical Model of Threes! 100 4.6 Invalid Scores 105 4.7 Lowest of the Low 109 4.8 Highest of the High 116 4.9 Closing Remarks 121 5. The Thrill of the Chase 122 5.1 I'ma GonnaWin! 122 5.2 Shell Games 123 5.3 Green-Shelled Monsters 125 5.4 Generalizations and Limitations 129 5.5 Seeing Red 131 5.6 Apollonius Circle Pursuit 134 5.7 Overview of aWinning Strategy 136 5.8 Pinpointing the Intersections 141 5.9 Blast Radius 145 5.10 The Pursuer and Pursued in Ms. Pac-Man 148 5.11 Concluding Remarks 153 5.12 Addendum: The Pursuit Curve for Red Shells and a Refined Inequality 153 6. Gaming Complexity 158 6.1 From Russia with Fun 158 6.2 P, NP, and Kevin Bacon 160 6.3 Desktop Diversions 165 6.4 Platforming Problems 169 6.5 Fetch Quests: An Overview 170 6.6 Fetch Quests and Traveling Salesmen 175 6.7 Closing Remarks 183 7. The Friendship Realm 184 7.1 Taking It to the Next Level 184 7.2 Friendship as Gameplay: The Sims and Beyond 186 7.3 A Game-Inspired Friendship Model 190 7.4 Approximations to the Model 193 7.5 The Cost of Maintaining a Friendship 195 7.6 From Virtual Friends to Realistic Romance 198 7.7 Modeling Different Personalities 200 7.8 Improving the Model (Again!) 203 7.9 Concluding Remarks 209 8. Order in Chaos 210 8.1 The Essence of Chaos 210 8.2 Love in the Time of Chaos 211 8.3 Shell Games Revisited 216 8.4 How's theWeather? 223 8.5 Concluding Remarks 225 9. The Value of Games 227 9.1 More Important Than Math 227 9.2 Why Games? 230 9.3 What Next? 242 Notes 244 Bibliography 269 Index 273
£25.20
Princeton University Press Chaos and Dynamical Systems
Book SynopsisThe author presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex.Trade Review"Feldman succeeds in introducing the reader to the world of dynamic systems and the, almost mythical, chaos that they can produce."---Adhemar Bultheel, European Mathematical Society"[A] gentle and loving introduction to dynamical systems. . . . Chaos and Dynamical Systems is a book for everyone from the layman to the expert."---David S. Mazel, MAA Reviews
£28.80
Princeton University Press Biomolecular Feedback Systems
Book SynopsisProvides an introduction to the principles and tools for modeling, analyzing, and synthesizing biomolecular systems. This book begins with modeling tools such as reaction-rate equations, reduced-order models, stochastic models, and specific models of important core processes.Trade Review"The authors did superbly in combining the biophysical processes and corresponding mathematics... This book serves both as a primer and a reference for constructing synthetic biological circuits with special focus on biomolecular feedback. It nicely bridges the gap between fields with a concise biological introduction, and approachable mathematics."--Harold Bien and Gabor Balazsi, Quarterly Review of Biology "This book promises much for the reader with a background in both biochemistry and mathematics. Such a reader will not only learn how to analyse models for bioengineered bimolecular systems but they will have the insights to both build these systems and to 'tune' the biochemistry to obtain desired parameter values."--Mark Nelson, Gazette of the Australian Mathematical SocietyTable of ContentsPreface vii 1 Introductory Concepts 1 1.1 Systems biology: Modeling, analysis and role of feedback 1 1.2 The cell as a system 8 1.3 Control and dynamical systems tools 11 1.4 Input/output modeling 18 1.5 From systems to synthetic biology 22 1.6 Further reading 28 2 Dynamic Modeling of Core Processes 29 2.1 Modeling chemical reactions 29 2.2 Transcription and translation 44 2.3 Transcriptional regulation 55 2.4 Post-transcriptional regulation 70 2.5 Cellular subsystems 81 Exercises 86 3 Analysis of Dynamic Behavior 89 3.1 Analysis near equilibria 89 3.2 Robustness 103 3.3 Oscillatory behavior 113 3.4 Bifurcations 124 3.5 Model reduction techniques 127 Exercises 133 4 Stochastic Modeling and Analysis 139 4.1 Stochastic modeling of biochemical systems 139 4.2 Simulation of stochastic systems 154 4.3 Input/output linear stochastic systems 157 Exercises 164 5 Biological Circuit Components 169 5.1 Introduction to biological circuit design 169 5.2 Negative autoregulation 171 5.3 The toggle switch 177 5.4 The repressilator 180 5.5 Activator-repressor clock 184 5.6 An incoherent feedforward loop (IFFL) 189 5.7 Bacterial chemotaxis 191 Exercises 203 6 Interconnecting Components 205 6.1 Input/output modeling and the modularity assumption 205 6.2 Introduction to retroactivity 206 6.3 Retroactivity in gene circuits 209 6.4 Retroactivity in signaling systems 214 6.5 Insulation devices: Retroactivity attenuation 219 6.6 A case study on the use of insulation devices 236 Exercises 239 7 Design Tradeoffs 243 7.1 Competition for shared cellular resources 243 7.2 Stochastic effects: Design tradeoffs in systems with large gains 253 Exercises 257 Bibliography 259 Index 267
£74.80
Princeton University Press NonArchimedean Tame Topology and Stably Dominated
Book SynopsisOver the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedTrade Review"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215
£130.40
Princeton University Press NonArchimedean Tame Topology and Stably Dominated
Book SynopsisTrade Review"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215
£999.99
Princeton University Press Zombies and Calculus
Book SynopsisHow can calculus help you survive the zombie apocalypse? Colin Adams, humor columnist for the Mathematical Intelligencer and one of today's most outlandish and entertaining popular math writers, demonstrates how in this zombie adventure novel. Zombies and Calculus is the account of Craig Williams, a math professor at a small liberal arts college iTrade Review"Romance! Danger! Calculus! Zombies! Adams (How to Ace Calculus), professor of mathematics at Williams College and humor columnist for The Mathematical Intelligencer, takes readers on an apocalyptic and educational adventure that's also a Spielbergian sci-fi thriller... Adams keeps the in-story math both appropriate and accessible, saving in-depth discussion for appendices at the end. Calculus fans looking for 'real-world' applications woven into a nail-biter of a story, chock-full of narrow escapes, betrayals, some plucky kids, the family dog, and even a romantic subplot, will delight in this fun, and funny pop-math book."--Publishers Weekly starred review "The author didn't intend to write a classic horror novel, he intended to write one that explained the ideas of calculus and differential equations (particularly the latter) in a humorous and unusual setting. He has succeeded admirably. This is a book that can be enjoyed by both students and by faculty members seeking a way to spice up their lectures."--Mark Hunacek, MAA Reviews "You'll laugh! You'll cry! You'll use calculus! So much for kids who say, 'When am I ever going to use calculus?' When you're trying to survive the zombie apocalypse, that's when."--Nancy Szokan, Washington Post "A fun idea, quite well realized."--M.A.Orthofer, Complete Review "The book well deserves attention from not squeamish math instructors and a wider audience of intelligent readers, curious of a new literary genre that mixes storytelling with gentle mathematical instruction."--Alexander Bogomolny, CTK Insights "Whether you agree or disagree with the idea of mixing zombies with calculus, Adams is a craftsman of the first order. Zombies and Calculus has everything: calculus, calculation of force, statistics, normal deviation, word play, heroics, romance, slapstick, and zombies. Two bloody thumbs up!"--Robert Schaefer, New York Journal of Books "The unusual and clearly explained mathematical set-pieces are appealing... I will be recommending this book to colleagues. Let's hope they're not squeamish."--Noel-Ann Bradshaw, Times Higher Education "Adams combines mathematics and zombies in an exciting, humorous way... Zombies and Calculus would be a helpful supplemental text for a student currently studying calculus as it applies the concepts in a situation--however unrealistic--that makes it easier to understand."--Tara Creel, Deseret News "I have never met a novel in which the hero is actually teaching calculus to the ones he just rescued in between blowing out the little bit of brains from zombie heads, and smashing cars with a snow plough. Quite a reading experience."--Adhemar Bultheel, European Mathematical Society "Adams is clever to employ a zombie apocalypse scenario to demonstrate the usefulness of calculus and mathematics more broadly."--Carrie Bengston, Science Book A Day "Highly recommended for those just being introduced to calculus, or those who need a user-friendly recap of the basics. It may just help them survive--their education, that is, rather than a zombie attack!"--Rob Ashmore, Mathematics Today "Adams tells his tale with gore and humor. If you are a fan of zombies and enjoy offbeat applications of mathematics, this book is for you."--Joseph Bettina, Mathematics Teacher "I think that the book is very successful at doing what it was intended to do, namely to demonstrate the usefulness and relevance of what may seem at the first glance to be very abstract maths while teaching it in an engaging way. I would struggle to name another book that manages to couch the process of solving ODEs in quite so entertaining and humorous a manner."--Andrew Simmons, Mathematical GazetteTable of ContentsIntroduction 1 CHAPTER 1 Hour 6 3 CHAPTER 2 Hour 7 19 CHAPTER 3 Hour 7 1/2 32 CHAPTER 4 Hour 7 3/4 48 CHAPTER 5 Hour 8 63 CHAPTER 6 Hour 9 80 CHAPTER 7 Hour 10 95 CHAPTER 8 Hour 18 111 CHAPTER 9 Hour 24 137 Epilogue 152 APPENDIX A Continuing the Conversations 155 APPENDIX B A Brief Review of Calculus as Explained to Connor by Ellie 191 Acknowledgments 223 Bibliography 225 Index 227
£18.00
Princeton University Press Whos 1
Book SynopsisA website's ranking on Google can spell the difference between success and failure for a new business. NCAA football ratings determine which schools get to play for the big money in postseason bowl games. Product ratings influence everything from the clothes we wear to the movies we select on Netflix. Ratings and rankings are everywhere, but how exTrade Review"[A] thorough exploration of the methods and applications of ranking for an audience ranging from computer scientists and engineers to high-school teachers to 'people interested in wagering on just about anything'."--Nature Physics "Who's #1 provides a fascinating tour through the world of rankings and is highly recommended."--Richard J. Wilders, MAA Reviews "[T]he book ... provide[s] an excellent, accessible, and stimulating discussion of the material it does cover. Overall, the book makes a valuable addition to the canon of rating and ranking."--David J. Hand, Journal of Applied Statistics "This book provides an interesting overview of ranking various sports teams, chess players, politicians, and the like in real-life circumstances, which typically involve serious constraints on the time available to find the optimal ranking."--Choice "The book could be used to supplement a course on linear algebra and/or numerical linear algebra... The book could also be used as the basis for a short topics course or undergraduate research project on ranking, or it could be used in a modeling class as an example of how mathematical modeling is done. In addition to describing the mathematics of ranking, the book is full of interesting tidbits that add to the pleasure of its reading."--James Keener, SIAM Review "When I started this book I knew very little about American football. I was little the wiser after finishing it, but I had an excellent understanding of various methods used in the obtaining of the ranking of teams and their interrelationships. Langville and Meyer are to be commended for this collection, and anyone who is more conversant with North American sports than I am will most certainly be stimulated by reading Who's #1?"--Andrew I. Dale, Notices of the AMS "Readers will find many interesting ideas as they grapple with the complexities of the science of rating and ranking."--Bob Horton, Mathematics Teacher "[T]his book is a call to consciousness on the relevance of rating and ranking as well as an enjoyable start-up guide from the point of view of algebraic methods."--Francisco Grimaldo Moreno, JASSS "This book is a great introduction to the field (including its constituent parts in linear algebra and data mining) and contains enough depth to be used as a supplemental book in a data mining course or as a jumping off point for an interested researcher... Overall this is a very nice, well written book that could be use in multiple ways by a wide variety of audiences."--Nicholas Mattei, SigAct News "The profit the scientometrics community can gain from this book is an indirect one: an attitude how to compile a systematic collection of potential methods, how to select carefully using theoretical tests and empirical examples and how to combine methods to get a comprehensive, multidimensional rating and ranking system. In this sense, it is a highly recommended reading for all readers of the journal Scientometrics."--Andras Schubert, Scientometrics "This book is an excellent read for everyone; readers might be sports enthusiasts, social choice theorists, mathematicians, computer scientists, engineers, and college and high school teachers. Teachers will find quite an easy way to extract material for a short module."--Valentina Dagiene, Zentralblatt MATHTable of ContentsPreface xiii Purpose xiii Audience xiii Prerequisites xiii Teaching from This Book xiv Acknowledgments xiv Chapter 1. Introduction to Ranking 1 Social Choice and Arrow's Impossibility Theorem 3 Arrow's Impossibility Theorem 4 Small Running Example 4 Chapter 2. Massey's Method 9 Initial Massey Rating Method 9 Massey's Main Idea 9 The Running Example Using the Massey Rating Method 11 Advanced Features of the Massey Rating Method 11 The Running Example: Advanced Massey Rating Method 12 Summary of the Massey Rating Method 13 Chapter 3. Colley's Method 21 The Running Example 23 Summary of the Colley Rating Method 24 Connection between Massey and Colley Methods 24 Chapter 4. Keener's Method 29 Strength and Rating Stipulations 29 Selecting Strength Attributes 29 Laplace's Rule of Succession 30 To Skew or Not to Skew? 31 Normalization 32 Chicken or Egg? 33 Ratings 33 Strength 33 The Keystone Equation 34 Constraints 35 Perron-Frobenius 36 Important Properties 37 Computing the Ratings Vector 37 Forcing Irreducibility and Primitivity 39 Summary 40 The 2009-2010 NFL Season 42 Jim Keener vs. Bill James 45 Back to the Future 48 Can Keener Make You Rich? 49 Conclusion 50 Chapter 5. Elo's System 53 Elegant Wisdom 55 The K-Factor 55 The Logistic Parameter ? 56 Constant Sums 56 Elo in the NFL 57 Hindsight Accuracy 58 Foresight Accuracy 59 Incorporating Game Scores 59 Hindsight and Foresight with ? = 1000, K = 32, H = 15 60 Using Variable K-Factors with NFL Scores 60 Hindsight and Foresight Using Scores and Variable K-Factors 62 Game-by-Game Analysis 62 Conclusion 64 Chapter 6. The Markov Method 67 The Markov Method 67 Voting with Losses 68 Losers Vote with Point Differentials 69 Winners and Losers Vote with Points 70 Beyond Game Scores 71 Handling Undefeated Teams 73 Summary of the Markov Rating Method 75 Connection between the Markov and Massey Methods 76 Chapter 7. The Offense-Defense Rating Method 79 OD Objective 79 OD Premise 79 But Which Comes First? 80 Alternating Refinement Process 81 The Divorce 81 Combining the OD Ratings 82 Our Recurring Example 82 Scoring vs. Yardage 83 The 2009-2010 NFL OD Ratings 84 Mathematical Analysis of the OD Method 87 Diagonals 88 Sinkhorn-Knopp 89 OD Matrices 89 The OD Ratings and Sinkhorn-Knopp 90 Cheating a Bit 91 Chapter 8. Ranking by Reordering Methods 97 Rank Differentials 98 The Running Example 99 Solving the Optimization Problem 101 The Relaxed Problem 103 An Evolutionary Approach 103 Advanced Rank-Differential Models 105 Summary of the Rank-Differential Method 106 Properties of the Rank-Differential Method 106 Rating Differentials 107 The Running Example 109 Solving the Reordering Problem 110 Summary of the Rating-Differential Method 111 Chapter 9. Point Spreads 113 What It Is (and Isn't) 113 The Vig (or Juice) 114 Why Not Just Offer Odds? 114 How Spread Betting Works 114 Beating the Spread 115 Over/Under Betting 115 Why Is It Difficult for Ratings to Predict Spreads? 116 Using Spreads to Build Ratings (to Predict Spreads?) 117 NFL 2009-2010 Spread Ratings 120 Some Shootouts 121 Other Pair-wise Comparisons 124 Conclusion 125 Chapter 10. User Preference Ratings 127 Direct Comparisons 129 Direct Comparisons, Preference Graphs, and Markov Chains 130 Centroids vs. Markov Chains 132 Conclusion 133 Chapter 11. Handling Ties 135 Input Ties vs. Output Ties 136 Incorporating Ties 136 The Colley Method 136 The Massey Method 137 The Markov Method 137 The OD, Keener, and Elo Methods 138 Theoretical Results from Perturbation Analysis 139 Results from Real Datasets 140 Ranking Movies 140 Ranking NHL Hockey Teams 141 Induced Ties 142 Summary 144 Chapter 12. Incorporating Weights 147 Four Basic Weighting Schemes 147 Weighted Massey 149 Weighted Colley 150 Weighted Keener 150 Weighted Elo 150 Weighted Markov 150 Weighted OD 151 Weighted Differential Methods 151 Chapter 13. "What If ..." Scenarios and Sensitivity 155 The Impact of a Rank-One Update 155 Sensitivity 156 Chapter 14. Rank Aggregation-Part 1 159 Arrow's Criteria Revisited 160 Rank-Aggregation Methods 163 Borda Count 165 Average Rank 166 Simulated Game Data 167 Graph Theory Method of Rank Aggregation 172 A Refinement Step after Rank Aggregation 175 Rating Aggregation 176 Producing Rating Vectors from Rating Aggregation-Matrices 178 Summary of Aggregation Methods 181 Chapter 15. Rank Aggregation-Part 2 183 The Running Example 185 Solving the BILP 186 Multiple Optimal Solutions for the BILP 187 The LP Relaxation of the BILP 188 Constraint Relaxation 190 Sensitivity Analysis 191 Bounding 191 Summary of the Rank-Aggregation (by Optimization) Method 193 Revisiting the Rating-Differential Method 194 Rating Differential vs. Rank Aggregation 194 The Running Example 196 Chapter 16. Methods of Comparison 201 Qualitative Deviation between Two Ranked Lists 201 Kendall's Tau 203 Kendall's Tau on Full Lists 204 Kendall's Tau on Partial Lists 205 Spearman's Weighted Footrule on Full Lists 206 Spearman's Weighted Footrule on Partial Lists 207 Partial Lists of Varying Length 210 Yardsticks: Comparing to a Known Standard 211 Yardsticks: Comparing to an Aggregated List 211 Retroactive Scoring 212 Future Predictions 212 Learning Curve 214 Distance to Hillside Form 214 Chapter 17. Data 217 Massey's Sports Data Server 217 Pomeroy's College Basketball Data 218 Scraping Your Own Data 218 Creating Pair-wise Comparison Matrices 220 Chapter 18. Epilogue 223 Analytic Hierarchy Process (AHP) 223 The Redmond Method 223 The Park-Newman Method 224 Logistic Regression/Markov Chain Method (LRMC) 224 Hochbaum Methods 224 Monte Carlo Simulations 224 Hard Core Statistical Analysis 225 And So Many Others 225 Glossary 231 Bibliography 235 Index 241
£19.00
Princeton University Press X and the City
Book SynopsisX and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow throughTrade Review"[Adam's] writing is fun and accessible... College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets."--Library Journal "For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."--Choice "Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!"--Sandra L. Arlinghaus, Mathematical Reviews Clippings "It goes without saying that the exposition is very friendly and lucid: this makes the vast majority of material accessible to a general audience interested in mathematical modeling and real life applications. This excellent book may well complement standard texts on engineering mathematics, mathematical modeling, applied mathematics, differential equations; it is a delightful and entertaining reading itself. Thank you, Vickie Kearn, the editor of A Mathematical Nature Walk, for suggesting the idea of this book to Professor Adam--your idea has been delightfully implemented!"--Svitlana P. Rogovchenko, Zentralblatt MATH "[Y]ou'll find this book quite extensive in how many different areas you can apply mathematics in the city and just how revealing even a simple model can be... A Mathematical Nature Walk opened my eyes to nature and now Adam has done the same for cities."--David S. Mazel, MAA Reviews "The author has an entertaining style, interweaving clever stories with the process of mathematical modeling. This book is not designed as a textbook, although it could certainly be used as an interesting source of real-world problems and examples for advanced high school mathematics courses."--Theresa Jorgensen, Mathematics TeacherTable of ContentsPreface xiii Acknowledgments xvii Chapter 1 Introduction: Cancer, Princess Dido, and the city 1 Chapter 2 Getting to the city 7 Chapter 3 Living in the city 15 Chapter 4 Eating in the city 35 Chapter 5 Gardening in the city 41 Chapter 6 Summer in the city 47 Chapter 7 Not driving in the city! 63 Chapter 8 Driving in the city 73 Chapter 9 Probability in the city 89 Chapter 10 Traffic in the city 97 Chapter 11 Car following in the city--I 107 Chapter 12 Car following in the city--II 113 Chapter 13 Congestion in the city 121 Chapter 14 Roads in the city 129 Chapter 15 Sex and the city 135 Chapter 16 Growth and the city 149 Chapter 17 The axiomatic city 159 Chapter 18 Scaling in the city 167 Chapter 19 Air pollution in the city 179 Chapter 20 Light in the city 191 Chapter 21 Nighttime in the city--I 209 Chapter 22 Nighttime in the city--II 221 Chapter 23 Lighthouses in the city? 233 Chapter 24 Disaster in the city? 247 Chapter 25 Getting away from the city 255 Appendix 1 Theorems for Princess Dido 261 Appendix 2 Dido and the sinc function 263 Appendix 3 Taxicab geometry 269 Appendix 4 The Poisson distribution 273 Appendix 5 The method of Lagrange multipliers 277 Appendix 6 A spiral braking path 279 Appendix 7 The average distance between two random points in a circle 281 Appendix 8 Informal "derivation" of the logistic differential equation 283 Appendix 9 A miniscule introduction to fractals 287 Appendix 10 Random walks and the diffusion equation 291 Appendix 11 Rainbow/halo details 297 Appendix 12 The Earth as vacuum cleaner? 303 Annotated references and notes 309 Index 317
£18.00
Princeton University Press Multiparameter Singular Integrals Volume I
Book SynopsisThis book develops a new theory of multi-parameter singular integrals associated with Carnot-Caratheodory balls. Brian Street first details the classical theory of Calderon-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Caratheodory geometry, where the mainTable of Contents*FrontMatter, pg. i*Contents, pg. v*Preface, pg. ix*1. The Calderon-Zygmund Theory I: Ellipticity, pg. 1*2. The Calderon-Zygmund Theory II: Maximal Hypoellipticity, pg. 39*3. Multi-parameter Carnot-Caratheodory Geometry, pg. 198*4. Multi-parameter Singular Integrals I: Examples, pg. 223*5. Multi-parameter Singular Integrals II: General Theory, pg. 268*Appendix A. Functional Analysis, pg. 363*Appendix B. Three Results from Calculus, pg. 376*Appendix C. Notation, pg. 380*Bibliography, pg. 383*Index, pg. 393
£999.99
Princeton University Press An Introduction to Benfords Law
Book SynopsisThis book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the law'Trade Review"This is a marvelous and excellent introduction."--Adhemar Bultheel, European Mathematical Society Bulletin "A must-read for novices and experts alike. It can be used for a graduate-level topics course or as a reference text for researchers in the field. The exposition is outstanding, with hundreds of carefully chosen examples, figures and diagrams to illustrate the theory. For those who are up for a challenge, the book contains several open problems as well. An Introduction to Benford's Law will surely be the go-to text on the subject for years to come."--Pieter C. Allaart, Mathematical ReviewsTable of ContentsPreface vii 1 Introduction 1 1.1 History 3 1.2 Empirical evidence 4 1.3 Early explanations 6 1.4 Mathematical framework 7 2 Significant Digits and the Significand 11 2.1 Significant digits 11 2.2 The significand 12 2.3 The significand sigma-algebra 14 3 The Benford Property 22 3.1 Benford sequences 23 3.2 Benford functions 28 3.3 Benford distributions and random variables 29 4 The Uniform Distribution and Benford's Law 43 4.1 Uniform distribution characterization of Benford's law 43 4.2 Uniform distribution of sequences and functions 46 4.3 Uniform distribution of random variables 54 5 Scale-, Base-, and Sum-Invariance 63 5.1 The scale-invariance property 63 5.2 The base-invariance property 74 5.3 The sum-invariance property 80 6 Real-valued Deterministic Processes 90 6.1 Iteration of functions 90 6.2 Sequences with polynomial growth 93 6.3 Sequences with exponential growth 97 6.4 Sequences with super-exponential growth 101 6.5 An application to Newton's method 111 6.6 Time-varying systems 116 6.7 Chaotic systems: Two examples 124 6.8 Differential equations 127 7 Multi-dimensional Linear Processes 135 7.1 Linear processes, observables, and difference equations 135 7.2 Nonnegative matrices 139 7.3 General matrices 145 7.4 An application to Markov chains 162 7.5 Linear difference equations 165 7.6 Linear differential equations 170 8 Real-valued Random Processes 180 8.1 Convergence of random variables to Benford's law 180 8.2 Powers, products, and sums of random variables 182 8.3 Mixtures of distributions 202 8.4 Random maps 213 9 Finitely Additive Probability and Benford's Law 216 9.1 Finitely additive probabilities 217 9.2 Finitely additive Benford probabilities 219 10 Applications of Benford's Law 223 10.1 Fraud detection 224 10.2 Detection of natural phenomena 225 10.3 Diagnostics and design 226 10.4 Computations and Computer Science 228 10.5 Pedagogical tool 230 List of Symbols 231 Bibliography 234 Index 245
£63.75
Princeton University Press In Pursuit of the Travelling Salesman
Book SynopsisWhat is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics--and it has defied solution to this day. In this book, William Cook takes reaTrade Review"Fascinating ... describes the history, personalities, challenges, applications and techniques used to find solutions of the famous 'Traveling Salesman Problem' and related problems."--Pradeep Mutalik, Wordplay blog at New York Times "The Traveling Salesman Problem, or TSP, might seem to be of purely recreational interest ... but in fact, as William J. Cook's In Pursuit of the Traveling Salesman ably shows, the problem remains a topic of hot interest... [This book is] an excellent place for an interested amateur to get the gist of these big ideas in a down-to-earth discussion... Mr. Cook's affable style means that you're never too far from an enjoyable historical anecdote or an offbeat application of a problem that has interested some of the best minds in applied math for most of a century and that shows no signs of getting stale."--Jordan Ellenberg, Wall Street Journal "The author, William Cook, writes in an easy to understand style and explores the various algorithms and branches of mathematics used to solve TSP, including the branch of mathematics known as linear programming, which is known to most of us through grade school algebra and word problems... In Pursuit of the Traveling Salesman is a thoroughly entertaining nerd-fest for the science minded reader."--Robert Schaefer, New York Journal of Books "Along with a heady dose of algorithms, Cook also offers a diverting survey of the lore and history of the TSP... The new volume addresses a wider audience [than The Traveling Salesman Problem: A Computational Study], with more pictures and fewer equations, explaining how things are done rather than how to do them, but it covers all the same territory as the larger book. The path through that territory seems reasonably close to optimal."--Brian Hayes, American Scientist "In Pursuit of the Traveling Salesman is a first-hand and a first-class introduction into the evolution of TSP, with chapters devoted to related mathematics and algorithmic topics. TSP is really at the heart of much of the research and development of modern computer science, so the author leads the reader through the past and emerging landscape of relevant research up to the very end of the mapped territory. Reading the book looks like an exciting adventure, with the itinerary mapped for the reader by a master story-teller whose work squarely places him in the forefront of the TSP research."--Alexander Bogomolny, Cut the Knot Insights blog "Bill takes his readers down a beautiful path covering the history, applications, and algorithms associated with the TSP. It is a fascinating story, and one that shows a researcher who truly loves his research area... Through this book, you'll learn all about the Traveling Salesman Problem and, more broadly, about the different research directions in combinatorial optimization."--Michael Trick's Operations Research Blog "In his new book, aptly titled In Pursuit of the Traveling Salesman, William Cook enlists us to join him on a personal journey through all-things past and present regarding this mammoth of a mathematical problem... I would highly recommend this book to interested readers and high school mathematics teachers, especially those of upper-level coursework. A great deal of mathematics is covered here and the TSP can easily spark debate and inquiry in the classroom."--Christopher Thompson, Loci: Convergence "In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation, does a wonderful job presenting the history and significance of the TSP and an overview of cutting-edge research. It's a beautiful, visually rich book, full of color photographs and diagrams that enliven both the narrative and mathematical presentation. And it includes a wealth of information."--Math Less Traveled "This book introduces the TSP, its applications, and computational methods for its solution to a general audience."--Choice "Cook is spot-on in his delivery of what could be considered by most as an arcane mathematical problem to be solved by only those in the engineering world but like Hawking, peaks interest in a field in which lowly MIT professors could only dream... His witty commentary complements his own casual insertion into the mathematical world and drive to solve the greatest of mathematics' problems. This book is proof that good science writing and mathematics add up."--Robert Terpstra, Business Today Egypt "The technical details are described with precision, but the inherent mathematical concepts are explained in an informal way so that readers without a deep mathematical background can also follow the story... The book is full of examples, real applications and historical anecdotes, making it really enjoyable to read."--Gregorio Tirado Dominguez, European Mathematical Society "The book is highly recommended to any one with a mathematical curiosity and interest in the development of ideas."--Haris Aziz, ACM SIGACT News "[T]here is sufficient mathematical detail to provide a good start to readers interested in a more technical treatment. The style is congenial, breezy, and entertaining; many anecdotes and pop culture references are included. Even seasoned researchers will find the book a truly enjoyable read, and it can serve as an ideal basis for a college level freshman seminar."--Gabor Pataki, INFORMS Journal on Computing "The author has a solid understanding of the material and tries to present it in an accessible and sometimes entertaining way... I recommend it to anyone interested in gaining a deeper understanding of the TSP and modern developments in solving TSP-like problems."--S. Leigh Nataro, Mathematics Teacher "[T]his book presents the history and significance of the TSP, and provides an overview of this cutting-edge research in a wonderful way. I recommend it to anybody who is interested in a down-to-earth discussion that provides the most current information on the TSP."--Roberto Baldacci, Interfaces "This book covers all facets of the TSP and ventures into some very deep theory of complexity and computability. It is written for the general mathematician or scientist but would also be useful to the OR specialist. Overall it is entertaining, richly illustrated and well-referenced. It tells us much about general problem solving as well as the TSP."--Francis McGonigal, Mathematics TodayTable of ContentsPreface xi Chapter 1: Challenges 1 Tour of the United States 2 An Impossible Task? 6 One Problem at a Time 10 Road Map of the Book 16 Chapter 2: Origins of the Problem 19 Before the Mathematicians 19 Euler and Hamilton 27 Vienna to Harvard to Princeton 35 And on to the RAND Corporation 38 A Statistical View 39 Chapter 3: The Salesman in Action 44 Road Trips 44 Mapping Genomes 49 Aiming Telescopes, X-rays, and Lasers 51 Guiding Industrial Machines 53 Organizing Data 56 Tests for Microprocessors 59 Scheduling Jobs 60 And More 60 Chapter 4: Searching for a Tour 62 The 48-States Problem 62 Growing Trees and Tours 65 AlterationsWhile You Wait 75 Borrowing from Physics and Biology 84 The DIMACS Challenge 91 Tour Champions 92 Chapter 5: Linear Programming 94 General-Purpose Model 94 The Simplex Algorithm 99 Two for the Price of One: LP Duality 105 The Degree LP Relaxation of the TSP 108 Eliminating Subtours 113 A Perfect Relaxation 118 Integer Programming 122 Operations Research 125 Chapter 6: Cutting Planes 127 The Cutting-Plane Method 127 A Catalog of TSP Inequalities 131 The Separation Problem 137 Edmonds's Glimpse of Heaven 142 Cutting Planes for Integer Programming 144 Chapter 7: Branching 146 Breaking Up 146 The Search Party 148 Branch-and-bound for Integer Programming 151 Chapter 8: Big Computing 153 World Records 153 The TSP on a Grand Scale 163 Chapter 9: Complexity 168 A Model of Computation 169 The Campaign of Jack Edmonds 171 Cook's Theorem and Karp's List 174 State of the TSP 178 Do We Need Computers? 184 Chapter 10: The Human Touch 191 Humans versus Computers 191 Tour-finding Strategies 192 The TSP in Neuroscience 196 Animals Solving the TSP 197 Chapter 11: Aesthetics 199 Julian Lethbridge 199 Jordan Curves 201 Continuous Lines 205 Art and Mathematics 207 Chapter 12: Pushing the Limits 211 Notes 213 Bibliography 223 Index 225
£13.29
Princeton University Press The Mathematics of Various Entertaining Subjects
Book SynopsisThe history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books exploring puzzlesTrade ReviewOne of Choice's Outstanding Academic Titles for 2016 "Beineke and Rosenhouse have compiled and edited a fantastic collection of essays dealing with popular mathematics... Anybody who enjoys reading about recreation mathematics should definitely explore these writings."--ChoiceTable of ContentsForeword by Raymond Smullyan vii Preface and Acknowledgments x PART I VIGNETTES 1 Should You Be Happy? 3 Peter Winkler 2 One-Move Puzzles with Mathematical Content 11 Anany Levitin 3 Minimalist Approaches to Figurative Maze Design 29 Robert Bosch, Tim Chartier, and Michael Rowan 4 Some ABCs of Graphs and Games 43 Jennifer Beineke and Lowell Beineke PART II PROBLEMS INSPIRED BY CLASSIC PUZZLES 5 Solving the Tower of Hanoi with Random Moves 65 Max A. Alekseyev and Toby Berger 6 Groups Associated to Tetraflexagons 81 Julie Beier and Carolyn Yackel 7 Parallel Weighings of Coins 95 Tanya Khovanova 8 Analysis of Crossword Puzzle Difficulty Using a Random Graph Process 105 John K. McSweeney 9 From the Outside In: Solving Generalizations of the Slothouber-Graatsma-Conway Puzzle 127 Derek Smith PART III PLAYING CARDS 10 Gallia Est Omnis Divisa in Partes Quattuor 139 Neil Calkin and Colm Mulcahy 11 Heartless Poker 149 Dominic Lanphier and Laura Taalman 12 An Introduction to Gilbreath Numbers 163 Robert W. Vallin PART IV GAMES 13 Tic-tac-toe on Affine Planes 175 Maureen T. Carroll and Steven T. Dougherty 14 Error Detection and Correction Using SET 199 Gary Gordon and Elizabeth McMahon 15 Connection Games and Sperner's Lemma 213 David Molnar PART V FIBONACCI NUMBERS 16 The Cookie Monster Problem 231 Leigh Marie Braswell and Tanya Khovanova 17 Representing Numbers Using Fibonacci Variants 245 Stephen K. Lucas About the Editors 261 About the Contributors 263 Index 269
£38.25
Princeton University Press Actionminimizing Methods in Hamiltonian Dynamics
Book SynopsisJohn Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach--known as Aubry-Mather theory--singles out the existence of special orbits and invariant measures of the system, which posseTable of ContentsPreface vii 1 Tonelli Lagrangians and Hamiltonians on Compact Manifolds 1 1.1 Lagrangian Point of View 1 1.2 Hamiltonian Point of View 4 2 From KAM Theory to Aubry-Mather Theory 8 2.1 Action-Minimizing Properties of Measures and Orbits on KAM Tori 8 3 Action-Minimizing Invariant Measures for Tonelli Lagrangians 18 3.1 Action-Minimizing Measures and Mather Sets 18 3.2 Mather Measures and Rotation Vectors 24 3.3 Mather's a-and B-Functions 28 3.4 The Symplectic Invariance of Mather Sets 35 3.5 An Example: The Simple Pendulum (Part I) 39 3.6 Holonomic Measures and Generic Properties of Tonelli Lagrangians 45 4 Action-Minimizing Curves for Tonelli Lagrangians 48 4.1 Global Action-Minimizing Curves: Aubry and Mane Sets 48 4.2 Some Topological and Symplectic Properties of the Aubry and Mane Sets 66 4.3 An Example: The Simple Pendulum (Part II) 68 4.4 Mather's Approach: Peierls' Barrier 71 5 The Hamilton-Jacobi Equation and Weak KAM Theory 76 5.1 Weak Solutions and Subsolutions of Hamilton-Jacobi and Fathi's Weak KAM theory 76 5.2 Regularity of Critical Subsolutions 85 5.3 Non-Wandering Points of the Mane Set 87 Appendices A On the Existence of Invariant Lagrangian Graphs 89 A.1 Symplectic Geometry of the Phase Space 89 A.2 Existence and Nonexistence of Invariant Lagrangian Graphs 91 B Schwartzman Asymptotic Cycle and Dynamics 97 B.1 Schwartzman Asymptotic Cycle 97 B.2 Dynamical Properties 99 Bibliography 107 Index 113
£37.80
Princeton University Press Mathematics under the Nazis
Book SynopsisContrary to popular belief--and despite the expulsion, emigration, or death of many German mathematicians--substantial mathematics was produced in Germany during 1933-1945. In this landmark social history of the mathematics community in Nazi Germany, Sanford Segal examines how the Nazi years affected the personal and academic lives of those GermanTrade Review"The strength of the book lies in its many individual stories and case histories... [It] offer[s] disturbing and important accounts of the life of science and scientists under the Nazis."--The Economist "The remarkable feature of this book is that in spite of the temptation, the story-telling never succumbs to simplistic descriptions of events or people. The analysis avoids the sentimentality and moral superiority that so often accompany descriptions of the Nazi years... Perhaps this is why Mathematicians under the Nazis is so compelling... This is a perceptive analysis of an important era and well worth reading."--John H. Ewing, Mathematical Reviews "A fascinating, well-researched and richly footnoted account of what occurred within a scientific discipline during the Nazi period."--George G. Szpiro, The Jerusalem ReportTable of Contents*Frontmatter, pg. i*Contents, pg. ix*PREFACE, pg. xi*ACKNOWLEDGMENTS, pg. xix*ABBREVIATIONS, pg. xxi*CHAPTER ONE. Why Mathematics?, pg. 1*CHAPTER TWO. The Crisis in Mathematics, pg. 14*CHAPTER THREE. The German Academic Crisis, pg. 42*CHAPTER FOUR. Three Mathematical Case Studies, pg. 85*CHAPTER FIVE. Academic Mathematical Life, pg. 168*CHAPTER SIX. Mathematical Institutions, pg. 229*CHAPTER SEVEN. Ludwig Bieberbach and "Deutsche Mathematik", pg. 334*CHAPTER EIGHT. Germans and Jews, pg. 419*APPENDIX, pg. 493*BIBLIOGRAPHY, pg. 509*INDEX, pg. 523
£37.80
Princeton University Press Alan Turings Systems of Logic
Book SynopsisBetween inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912-1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt GodeTrade Review"This book presents the story of Turing's work at Princeton University and includes a facsimile of his doctoral dissertation, 'Systems of Logic Based on Ordinals,' which he completed in 1936. The author includes a detailed history of Turing's work in computer science and the attempts to ground the field in formal logic."--Mathematics Teacher "This book is not for the faint hearted, as with the great masters of painting it will insist that some thought goes into appreciating it... I love the book as a book. It is a collectors item and after all what better pursuit can one have than collecting books!"--Patrick Fogarty, Mathematics TodayTable of ContentsPreface ix The Birth of Computer Science at Princeton in the 1930s Andrew W. Appel 1 Turing's Thesis Solomon Feferman 13 Notes on the Manuscript 27 Systems of Logic Based on Ordinals Alan Turing 31 A Remarkable Bibliography 141 Contributors 143
£12.34
Princeton University Press The Proof and the Pudding
Book SynopsisTantalizing math puzzles and cooking recipes that show how mathematical thinking is like the culinary artsTie on your apron and step into Jim Henle''s kitchen as he demonstrates how two equally savory pursuitscooking and mathematicshave more in common than you realize. A tasty dish for gourmets of popular math, The Proof and the Pudding offers a witty and flavorful blend of mathematical treats and gastronomic delights that reveal how life in the mathematical world is tantalizingly similar to life in the kitchen.Take a tricky Sudoku puzzle and a cake that fell. Henle shows you that the best way to deal with cooking disasters is also the best way to solve math problems. Or take an L-shaped billiard table and a sudden desire for Italian potstickers. He explains how preferring geometry over algebra (or algebra over geometry) is just like preferring a California roll to chicken tikka masala. Do you want to know why playfulness is rampant in math and cooking? Or how to turn stinky cheese into an awesome ice cream treat? It's all here: original math and original recipes plus the mathematical equivalents of vegetarianism, Asian fusion, and celebrity chefs.Pleasurable and lighthearted, The Proof and the Pudding is a feast for the intellect as well as the palate.Trade ReviewShortlisted for the 2016 Gourmand World Cookbook Awards, in Digital E-Books "[D]elightful... [The Proof and the Pudding] can inspire any of us who have been stuck on a math problem not to see our struggle as failure... Henle helps us have fun in those dead ends."-- Evelyn Lamb, Scientific American "[The Proof and the Pudding] serves an excellent guide for a novice at both cooking and doing mathematics... [Henle] appears to be having a lot of fun--cooking and doing mathematics; his enjoyment is contagious."--Alexander Bogomolny, Cut the Knot blog "Henle had my mouth watering...and my brain neurons firing from the math puzzles that are reminiscent of Martin Gardner columns. Any fan of Gardner's recreational math...will enjoy the mathy excursions throughout this small volume... [T]his book is a charmer."--Math Tango blog "[D]elightful... [T]he reader will want to grab a pencil and some mixing bowls and play along."--Joel Haack, MAA Reviews "Although he does not mention it so explicitly, there is one thing Henle does extremely well: he transfers an attitude that is a proper one to become a good professional mathematician or a proper chef, or that is apt to any challenging profession for that matter."--Adhemar Bultheel, European Mathematical Society "A thoroughly enjoyable read... Henle does a masterful job of connecting math and cooking, demonstrating that math does not always include numbers and that it can be fun!"--Laura Steward, NCTM "Henle has produced a book that can be enjoyed by a wide variety of audiences... He has given mathematicians another field with which to compare their subject when seeking to explain its interest and value to those who have no qualms about defending the usefulness of food."--Thomas Drucker, London Mathematical Society "Henle finds amazing similarities in both math and cooking."--Sudhirendar Sharma, Current ScienceTable of ContentsPreface vii Acknowledgments ix 1 The Mad Scientist 1 2 The Arrogant Chef 11 3 Simple Tastes 21 4 Complex Flavors 30 5 The Discriminating Eater 40 6 The Persistent Cook 44 7 Gluttony 54 8 Vanity, Sloth, Parsimony, and Lust 62 9 On the Edge, and Over 70 10 Thinking Globally 79 11 Eating Locally 87 12 The Humble Cook 92 13 The Clueless Geek 99 14 Elegant Dishes 103 15 Food for the Masses 110 16 Good Food for the Masses 111 17 Just for Fun 112 18 Just to Be Weird 117 19 Celebrity Chefs 124 20 Economy 128 21 Ethics 135 22 Fusion 138 23 It All Comes Together 149 24 It All Falls Apart 151 25 A Proof and a Pudding 161 Index 163
£19.80
Princeton University Press Mathematical Methods in Elasticity Imaging
Book SynopsisThis book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolutiTrade Review"This timely book that is devoted to a topic of paramount importance is very well written and it contains useful and interesting material. I strongly believe that it will be a valuable resource for researchers in elasticity imaging and related areas of nondestructive testing and inverse problems."--Akhtar A. Khan, MathSciNetTable of ContentsIntroduction 1 1 Layer Potential Techniques 4 1.1 Sobolev Spaces 4 1.2 Elasticity Equations 6 1.3 Radiation Condition 10 1.4 Integral Representation of Solutions to the Lame System 11 1.5 Helmholtz-Kirchhoff Identities 21 1.6 Eigenvalue Characterizations and Neumann and Dirichlet Functions 27 1.7 A Regularity Result 32 2 Elasticity Equations with High Contrast Parameters 33 2.1 Problem Setting 34 2.2 Incompressible Limit 34 2.3 Limiting Cases of Holes and Hard Inclusions 36 2.4 Energy Estimates 38 2.5 Convergence of Potentials and Solutions 42 2.6 Boundary Value Problems 45 3 Small-Volume Expansions of the Displacement Fields 48 3.1 Elastic Moment Tensor 48 3.2 Small-Volume Expansions 55 4 Boundary Perturbations due to the Presence of Small Cracks 66 4.1 A Representation Formula 66 4.2 Derivation of an Explicit Integral Equation 69 4.3 Asymptotic Expansion 71 4.4 Topological Derivative of the Potential Energy 75 4.5 Derivation of the Representation Formula 76 4.6 Time-Harmonic Regime 79 5 Backpropagation and Multiple Signal Classification Imaging of Small Inclusions 80 5.1 A Newton-Type Search Method 80 5.2 A MUSIC-Type Method in the Static Regime 82 5.3 A MUSIC-Type Method in the Time-Harmonic Regime 82 5.4 Reverse-TimeMigration and Kirchhoff Imaging in the Time-Harmonic Regime 84 5.5 Numerical Illustrations 86 6 Topological Derivative Based Imaging of Small Inclusions in the Time-Harmonic Regime 91 6.1 Topological Derivative Based Imaging 91 6.2 Modified Imaging Framework 102 7 Stability of Topological Derivative Based Imaging Functionals 112 7.1 Statistical Stability with Measurement Noise 112 7.2 Statistical Stability with Medium Noise 118 8 Time-Reversal Imaging of Extended Source Terms 125 8.1 Analysis of the Time-Reversal Imaging Functionals 127 8.2 Time-Reversal Algorithm for Viscoelastic Media 129 8.3 Numerical Illustrations 137 9 Optimal Control Imaging of Extended Inclusions 148 9.1 Imaging of Shape Perturbations 149 9.2 Imaging of an Extended Inclusion 152 10 Imaging from Internal Data 160 10.1 Inclusion Model Problem 160 10.2 Binary Level Set Algorithm 162 10.3 Imaging Shear Modulus Distributions 164 10.4 Numerical Illustrations 165 11 Vibration Testing 168 11.1 Small-Volume Expansions of the Perturbations in the Eigenvalues 169 11.2 Eigenvalue Perturbations due to Shape Deformations 181 11.3 Splitting of Multiple Eigenvalues 192 11.4 Reconstruction of Inclusions 193 11.5 Numerical Illustrations 195 A Introduction to Random Processes 201 A.1 Random Variables 201 A.2 Random Vectors 202 A.3 Gaussian Random Vectors 203 A.4 Conditioning 204 A.5 Random Processes 205 A.6 Gaussian Processes 206 A.7 Stationary Gaussian Random Processes 208 A.8 Multi-valued Gaussian Processes 208 B Asymptotics of the Attenuation Operator 210 B.1 Stationary Phase Theorem 210 B.2 Derivation of the Asymptotics 211 C The Generalized Argument Principle and Rouche's Theorem 213 C.1 Notation and Definitions 213 C.2 Generalized Argument Principle 214 C.3 Generalization of Rouche's Theorem 214 References 217 Index 229
£55.25
Princeton University Press Flatland
Book SynopsisReprint. Originally published: 6th ed. New York: Dover Publications, 1953.Trade Review"One of the most imaginative, delightful and, yes, touching works of mathematics, this slender 1884 book purports to be the memoir of A. Square, a citizen of an entirely two-dimensional world."--The Washington Post Book World "Flatland has remained of interest for over a century precisely because of its ability to engage its readers on so many different planes in so many different dimensions."--Victorian Studies "This reprint of Abbott's Flatland adventures contains an Introduction by Thomas Banchoff which is worth reading on its own. So if you don't have yet this book at home, go ahead and buy this edition."--Zentralblatt MATHTable of ContentsPreface to the Second and Revised Edition ix Introduction xiii Part I This World Section 1 Of the Nature of Flatland 3 2 Of the Climate and Houses in Flatland 4 3 Concerning the Inhabitants of Flatland 6 4 Concerning the Women 8 5 Of our Methods of Recognizing one another 12 6 Of Recognition by Sight 16 7 Concerning Irregular Figures 20 8 Of the Ancient Practice of Painting 22 9 Of the Universal Colour Bill 24 10 Of the Suppression of the Chromatic Sedition 27 11 Concerning our Priests 30 12 Of the Doctrine of our Priests 32 Part II Other Worlds 13 How I had a Vision of Lineland 39 14 How in my Vision I endeavoured to explain the nature of Flatland, but could not 42 15 Concerning a Stranger from Spaceland 46 16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland 49 17 How the Sphere, having in vain tried words, resorted to deeds 55 18 How I came to Spaceland and what I saw there 57 19 How, though the Sphere showed me other mysteries of Spaceland, I still desired more; and what came of it 61 20 How the Sphere encouraged me in a Vision 66 21 How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success 68 22 How I then tried to diff use the Theory of Three Dimensions by other means, and the result 70
£11.99
Princeton University Press The Joy of SET
Book SynopsisHave you ever played the addictive card game SET? Have you ever wondered about the connections between games and mathematics? If the answer to either question is yes, then The Joy of SET is the book for you! The Joy of SET takes readers on a fascinating journey into this seemingly simple card game and reveals its surprisingly deep and diverse matTrade Review"[A] model of mathematical exposition. The quality of writing is consistently high: clear but not condescending, humorous, chatty, and a genuine pleasure to read... I doubt it will be very long before I find something from [The Joy of SET] to use in one of my classes."--Mark Hunacek, MAA Reviews "[The Joy of SET] shows how budding interest in mathematics can be fostered and developed... If [middle and high school teachers] ever try to enliven their classes or just interaction with curious students, this book is one they may depend on."--Alexander Bogomolny, Cut the Knot blog "[A]mazing... What I love about The Joy of SET is that it is written in such a way that it can be read and enjoyed by both SET enthusiasts and someone that has never played SET before... Really and truly, there is enough math in this book to keep you busy for a lifetime! ... I definitely recommend this book."--Sarah Carter, Math Equals Love blog "[The Joy of SET] takes readers on a fascinating journey into this seemingly simple card game... The book is in my view just the right way to talk about math as fun, and intellectually challenging."--Robert Harington, Scholarly Kitchen "[A]s the authors convincingly demonstrate ... the mathematics behind SET actually goes very deep... [The Joy of SET] would make a fantastic resource for a middle school, high school, or undergraduate math club."--Brent Yorgey, Math Less Traveled blog "This book, written by a mathematically inclined family, is the first and only work to explore the connection between the game and mathematics... [The Joy of SET] will attract those who play SET and those who want to explore mathematically related subjects."--ChoiceTable of ContentsPreface vii 1 SET and You 1 2 Counting Fun! 27 3 Probability! 52 4 SET and Modular Arithmetic 72 5 SET and Geometry 98 Interlude: How to Improve at SET 136 6 More Combinatorics 149 7 Probability and Statistics 171 8 Vectors and Linear Algebra 197 9 Affine Geometry Plus 229 10 Computing and Simulations 256 Conclusion 288 Solutions to Exercises 289 Bibliography 303 Index 307
£22.50
Princeton University Press Descent in Buildings
Book SynopsisDescent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fTrade Review"An impressive tour de force."--Bertrand Remy, Jahresbericht der DMVTable of ContentsPreface xi PART 1. MOUFANG QUADRANGLES 1 Chapter 1. Buildings 3 Chapter 2. Quadratic Forms 13 Chapter 3. Moufang Polygons 23 Chapter 4. Moufang Quadrangles 31 Chapter 5. Linked Tori, I 41 Chapter 6. Linked Tori, II 47 Chapter 7. Quadratic Forms over a Local Field 57 Chapter 8. Quadratic Forms of Type E6, E7 and E8 69 Chapter 9. Quadratic Forms of Type F4 79 PART 2. RESIDUES IN BRUHAT-TITS BUILDINGS 83 Chapter 10. Residues 85 Chapter 11. Unramified Quadrangles of Type E6, E7 and E8 91 Chapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8 93 Chapter 13. Ramified Quadrangles of Type E6, E7 and E8 101 Chapter 14. Quadrangles of Type E6, E7 and E8: Summary 109 Chapter 15. Totally Wild Quadratic Forms of Type E7 115 Chapter 16. Existence 119 Chapter 17. Quadrangles of Type F4 129 Chapter 18. The Other Bruhat-Tits Buildings 137 PART 3. DESCENT 141 Chapter 19. Coxeter Groups 143 Chapter 20. Tits Indices 153 Chapter 21. Parallel Residues 165 Chapter 22. Fixed Point Buildings 181 Chapter 23. Subbuildings 195 Chapter 24. Moufang Structures 205 Chapter 25. Fixed Apartments 217 Chapter 26. The Standard Metric 221 Chapter 27. Affine Fixed Point Buildings 233 PART 4. GALOIS INVOLUTIONS 241 Chapter 28. Pseudo-Split Buildings 243 Chapter 29. Linear Automorphisms 251 Chapter 30. Strictly Semi-linear Automorphisms 259 Chapter 31. Galois Involutions 271 Chapter 32. Unramified Galois Involutions 275 PART 5. EXCEPTIONAL TITS INDICES 285 Chapter 33. Residually Pseudo-Split Buildings 287 Chapter 34. Forms of Residually Pseudo-Split Buildings 297 Chapter 35. Orthogonal Buildings 303 Chapter 36. Indices for the Exceptional Bruhat-Tits Buildings 309 Bibliography 327 Index 333
£63.75
Princeton University Press Mathematical Knowledge and the Interplay of
Book SynopsisThis book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, Jose Ferreiros uses the crucial idea of a continuum to provide an account of the development of mathematical knowledgTrade Review"Both philosophers and mathematicians can find ample food for thought in this study."--Choice "Ferreiros has published a fascinating book which consists of an impressive combination of thought-provoking philosophical ideas and mathematical material. As such, it can be interesting for philosophers of mathematics, mathematicians, and other people interested in the topics of mathematical knowledge and mathematical practice."--Joachim Frans, MathScieNetTable of ContentsList of Illustrations ix Foreword xi 1 On Knowledge and Practices: A Manifesto 1 2 The Web of Practices 17 2.1. Historical Work on Practices 18 2.2. Philosophers Working on Practices 22 2.3. What Is Mathematical Practice, Then? 28 2.4. The Multiplicity of Practices 34 2.5. The Interplay of Practices and Its Basis 39 3 Agents and Frameworks 44 3.1. Frameworks and Related Matters 45 3.2. Interlude on Examplars 55 3.3. On Agents 59 3.4. Counting Practices and Cognitive Abilities 65 3.5. Further Remarks on Mathematics and Cognition 74 3.6. Agents and "Metamathematical" Views 79 3.7. On Systematic Links 83 4 Complementarity in Mathematics 89 4.1. Formula and Meaning 89 4.2. Formal Systems and Intended Models 94 4.3. Meaning in Mathematics: A Tentative Approach 99 4.4. The Case of Complex Numbers 104 5 Ancient Greek Mathematics: A Role for Diagrams 112 5.1. From the Technical to the Mathematical 113 5.2. The Elements: Getting Started 117 5.3. On the Euclidean Postulates: Ruling Diagrams (and Their Reading) 127 5.4. Diagram-Based Mathematics and Proofs 131 5.5. Agents, Idealization, and Abstractness 137 5.6. A Look at the Future-Our Past 147 6 Advanced Math: The Hypothetical Conception 153 6.1. The Hypothetical Conception: An Introduction 154 6.2. On Certainty and Objectivity 159 6.3. Elementary vs. Advanced: Geometry and the Continuum 163 6.4. Talking about Objects 170 6.5. Working with Hypotheses: AC and the Riemann Conjecture 176 7 Arithmetic Certainty 182 7.1. Basic Arithmetic 182 7.2. Counting Practices, Again 184 7.3. The Certainty of Basic Arithmetic 189 7.4. Further Clarifications 195 7.5. Model Theory of Arithmetic 198 7.6. Logical Issues: Classical or Intuitionistic Math? 200 8 Mathematics Developed: The Case of the Reals 206 8.1. Inventing the Reals 207 8.2. "Tenths" to the Infinite: Lambert and Newton 215 8.3. The Number Continuum 221 8.4. The Reinvention of the Reals 227 8.5. Simple Infinity and Arbitrary Infinity 231 8.6. Developing Mathematics 236 8.7. Mathematical Hypotheses and Scientific Practices 241 9 Objectivity in Mathematical Knowledge 247 9.1. Objectivity and Mathematical Hypotheses: A Simple Case 249 9.2. Cantor's "Purely Arithmetical" Proofs 253 9.3. Objectivity and Hypotheses, II: The Case of p() 257 9.4. Arbitrary Sets and Choice 261 9.5. What about Cantor's Ordinal Numbers? 265 9.6. Objectivity and the Continuum Problem 273 10 The Problem of Conceptual Understanding 281 10.1. The Universe of Sets 283 10.2. A "Web-of- Practices" Look at the Cumulative Picture 290 10.3. Conceptual Understanding 296 10.4. Justifying Set Theory: Arguments Based on the Real-Number Continuum 305 10.5. By Way of Conclusion 310 References 315 Index 331
£37.80
Princeton University Press Game Theory in Action An Introduction to
Book SynopsisGame Theory in Action is a textbook about using game theory across a range of real-life scenarios. From traffic accidents to the sex lives of lizards, Stephen Schecter and Herbert Gintis show students how game theory can be applied in diverse areas including animal behavior, political science, and economics. The book's examples and problems look aTrade Review"Though not an advanced treatment mathematically speaking, readers become sophisticated consumers of game theories."--Choice "A welcome addition to the existing collection of introductory game theory texts... A very satisfying book."--Jennifer M. Wilson, MathSciNet "[A] wonderful introduction to game theory... I found almost all the games and examples fun to read and fun to work through the decisions and matrices. Whether the games were about politics, wine merchants and connoisseurs, or simply how to view sex ratios in society, you will find something of interest in this book."--David S. Mazel, MAA ReviewsTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface and acknowledgments, pg. xi*Chapter 1. Backward induction, pg. 1*Chapter 2. Eliminating dominated strategies, pg. 37*Chapter 3. Nash equilibria, pg. 61*Chapter 4. Games in extensive form with incomplete information, pg. 88*Chapter 5. Mixed strategy Nash equilibria, pg. 114*Chapter 5. Mixed strategy Nash equilibria, pg. 151*Chapter 7. Symmetries of games, pg. 186*Chapter 8. Alternatives to the Nash equilibrium, pg. 203*Chapter 9. Differential equations, pg. 217*Chapter 10. Evolutionary dynamics, pg. 232*Appendix. Sources for examples and problems, pg. 265*References, pg. 269*Index, pg. 271
£66.30
Princeton University Press Game Theory in Action
Book SynopsisGame Theory in Action is a textbook about using game theory across a range of real-life scenarios. From traffic accidents to the sex lives of lizards, Stephen Schecter and Herbert Gintis show students how game theory can be applied in diverse areas including animal behavior, political science, and economics. The book's examples and problems look aTrade Review"Though not an advanced treatment mathematically speaking, readers become sophisticated consumers of game theories."--Choice "A welcome addition to the existing collection of introductory game theory texts... A very satisfying book."--Jennifer M. Wilson, MathSciNet "[A] wonderful introduction to game theory... I found almost all the games and examples fun to read and fun to work through the decisions and matrices. Whether the games were about politics, wine merchants and connoisseurs, or simply how to view sex ratios in society, you will find something of interest in this book."--David S. Mazel, MAA ReviewsTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface and acknowledgments, pg. xi*Chapter 1. Backward induction, pg. 1*Chapter 2. Eliminating dominated strategies, pg. 37*Chapter 3. Nash equilibria, pg. 61*Chapter 4. Games in extensive form with incomplete information, pg. 88*Chapter 5. Mixed strategy Nash equilibria, pg. 114*Chapter 5. Mixed strategy Nash equilibria, pg. 151*Chapter 7. Symmetries of games, pg. 186*Chapter 8. Alternatives to the Nash equilibrium, pg. 203*Chapter 9. Differential equations, pg. 217*Chapter 10. Evolutionary dynamics, pg. 232*Appendix. Sources for examples and problems, pg. 265*References, pg. 269*Index, pg. 271
£999.99
Princeton University Press Whats Next The Mathematical Legacy of William P.
Book Synopsis
£130.40
Princeton University Press Whats Next The Mathematical Legacy of William P.
Book Synopsis
£66.30
Princeton University Press Classification of Pseudoreductive Groups
Book SynopsisIn the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the autoTrade Review"This book is beautiful and will be at the origin of many advances in the general theory of arbitrary algebraic groups."--Bertrand Remy, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminary notions, pg. 15*3. Field-theoretic and linear-algebraic invariants, pg. 28*4. Central extensions and groups locally of minimal type, pg. 57*5. Universal smooth k-tame central extension, pg. 66*6. Automorphisms, isomorphisms, and Tits classification, pg. 79*7. Constructions with regular degenerate quadratic forms, pg. 108*8. Constructions when PHI has a double bond, pg. 138*9. Generalization of the standard construction, pg. 171*A. Pseudo-isogenies, pg. 181*B. Clifford constructions, pg. 187*C. Pseudo-split and quasi-split forms, pg. 206*D. Basic exotic groups of type F4 of relative rank 2, pg. 230*Bibliography, pg. 239*Index, pg. 241
£63.75
Princeton University Press Positive Definite Matrices
Book SynopsisThis book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineeTrade Review"Written by an expert in the area, the book presents in an accessible manner a lot of important results from the realm of positive matrices and of their applications... The book can be used for graduate courses in linear algebra, or as supplementary material for courses in operator theory, and as a reference book by engineers and researchers working in the applied field of quantum information."--S. Cobzas, Studia Universitatis Babes-Bolyai, Mathematica "There is no obvious competitor for Bhatia's book, due in part to its focus, but also because it contains some very recent material drawn from research articles. Beautifully written and intelligently organised, Positive Definite Matrices is a welcome addition to the literature. Readers who admired his Matrix Analysis will no doubt appreciate this latest book of Rajendra Bhatia."--Douglas Farenick, Image "This is an outstanding book. Its exposition is both concise and leisurely at the same time."--Jaspal Singh Aujla, Zentralblatt MATHTable of ContentsPreface vii Chapter 1: Positive Matrices 1 1.1 Characterizations 1 1.2 Some Basic Theorems 5 1.3 Block Matrices 12 1.4 Norm of the Schur Product 16 1.5 Monotonicity and Convexity 18 1.6 Supplementary Results and Exercises 23 1.7 Notes and References 29 Chapter 2: Positive Linear Maps 35 2.1 Representations 35 2.2 Positive Maps 36 2.3 Some Basic Properties of Positive Maps 38 2.4 Some Applications 43 2.5 Three Questions 46 2.6 Positive Maps on Operator Systems 49 2.7 Supplementary Results and Exercises 52 2.8 Notes and References 62 Chapter 3: Completely Positive Maps 65 3.1 Some Basic Theorems 66 3.2 Exercises 72 3.3 Schwarz Inequalities 73 3.4 Positive Completions and Schur Products 76 3.5 The Numerical Radius 81 3.6 Supplementary Results and Exercises 85 3.7 Notes and References 94 Chapter 4: Matrix Means 101 4.1 The Harmonic Mean and the Geometric Mean 103 4.2 Some Monotonicity and Convexity Theorems 111 4.3 Some Inequalities for Quantum Entropy 114 4.4 Furuta's Inequality 125 4.5 Supplementary Results and Exercises 129 4.6 Notes and References 136 Chapter 5: Positive Definite Functions 141 5.1 Basic Properties 141 5.2 Examples 144 5.3 Loewner Matrices 153 5.4 Norm Inequalities for Means 160 5.5 Theorems of Herglotz and Bochner 165 5.6 Supplementary Results and Exercises 175 5.7 Notes and References 191 Chapter 6: Geometry of Positive Matrices 201 6.1 The Riemannian Metric 201 6.2 The Metric Space Pn 210 6.3 Center of Mass and Geometric Mean 215 6.4 Related Inequalities 222 6.5 Supplementary Results and Exercises 225 6.6 Notes and References 232 Bibliography 237 Index 247 Notation 253
£999.99
Princeton University Press Approximating Perfection A Mathematicians
Book SynopsisThis is a book for those who enjoy thinking about how and why Nature can be described using mathematical tools. Approximating Perfection considers the background behind mechanics as well as the mathematical ideas that play key roles in mechanical applications. Concentrating on the models of applied mechanics, the book engages the reader in the typeTrade Review"A well-written general-interest introduction to classical mechanics."--ChoiceTable of ContentsPreface vii Chapter 1. The Tools of Calculus 1 1.1 Is Mathematical Proof Necessary? 2 1.2 Abstraction, Understanding, Infinity 6 1.3 Irrational Numbers 8 1.4 What Is a Limit? 11 1.5 Series 15 1.6 Function Continuity 19 1.7 How to Measure Length 21 1.8 Antiderivatives 33 1.9 Definite Integral 35 1.10 The Length of a Curve 42 1.11 Multidimensional Integrals 44 1.12 Approximate Integration 47 1.13 On the Notion of a Function 52 1.14 Differential Equations 53 1.15 Optimization 59 1.16 Petroleum Exploration and Recovery 61 1.17 Complex Variables 63 1.18 Moving On 65 Chapter 2. The Mechanics of Continua 67 2.1 Why Do Ships Float? 67 2.2 The Main Notions of Classical Mechanics 71 2.3 Forces, Vectors, and Objectivity 74 2.4 More on Forces; Statics 76 2.5 Hooke's Law 80 2.6 Bending of a Beam 84 2.7 Stress Tensor 94 2.8 Principal Axes and Invariants of the Stress Tensor 100 2.9 On the Continuum Model and Limit Passages 102 2.10 Equilibrium Equations 104 2.11 The Strain Tensor 108 2.12 Generalized Hooke's Law 113 2.13 Constitutive Laws 114 2.14 Boundary Value Problems 115 2.15 Setup of Boundary Value Problems of Elasticity 118 2.16 Existence and Uniqueness of Solution 120 2.17 Energy; Minimal Principle for a Spring 126 2.18 Energy in Linear Elasticity 128 2.19 Dynamic Problems of Elasticity 132 2.20 Oscillations of a String 134 2.21 Lagrangian and Eulerian Descriptions of Continuum Media 137 2.22 The Equations of Hydrodynamics 140 2.23 D'Alembert-Euler Equation of Continuity 142 2.24 Some Other Models of Hydrodynamics 144 2.25 Equilibrium of an Ideal Incompressible Liquid 145 2.26 Force on an Obstacle 148 Chapter 3. Elements of the Strength of Materials 151 3.1 What Are the Problems of the Strength of Materials? 151 3.2 Hooke's Law Revisited 152 3.3 Objectiveness of Quantities in Mechanics Revisited 157 3.4 Plane Elasticity 159 3.5 Saint-Venant's Principle 161 3.6 Stress Concentration 163 3.7 Linearity vs. Nonlinearity 165 3.8 Dislocations, Plasticity, Creep, and Fatigue 166 3.9 Heat Transfer 172 3.10 Thermoelasticity 175 3.11 Thermal Expansion 177 3.12 A Few Words on the History of Thermodynamics 178 3.13 Thermodynamics of an Ideal Gas 180 3.14 Thermodynamics of a Linearly Elastic Rod 182 3.15 Stability 186 3.16 Static Stability of a Straight Beam 188 3.17 Dynamical Tools for Studying Stability 193 3.18 Additional Remarks on Stability 195 3.19 Leak Prevention 198 Chapter 4. Some Questions of Modeling in the Natural Sciences 201 4.1 Modeling and Simulation 201 4.2 Computerization and Modeling 203 4.3 Numerical Methods and Modeling in Mechanics 206 4.4 Complexity in the Real World 208 4.5 The Role of the Cosine in Everyday Measurements 209 4.6 Accuracy and Precision 211 4.7 How Trees Stand Up against the Wind 213 4.8 Why King Kong Cannot Be as Terrible as in the Movies 216 Afterword 219 Recommended Reading 221 Index 223
£22.50
Princeton University Press L.A. Math Romance Crime and Mathematics in the
Book SynopsisMove over, Sherlock and Watson--the detective duo to be reckoned with. In the entertaining short-story collection L.A. Math, freelance investigator Freddy Carmichael and his sidekick, Pete Lennox, show how math smarts can crack even the most perplexing cases. Freddy meets colorful personalities throughout Los Angeles and encounters mysterious circuTrade Review"Fun for any crime-fiction lover who fancies a spot of mathematical adventuring, or vice versa."--Brian Clegg, Popular Science blog "James D Stein ... explains in the preface to the book that entertaining stories set in Los Angeles, with mathematics squeezed painlessly in, was his long cherished dream of a way to teach basic math as fun rather than a chore ... a book to teach math to non-science students at university."--S. Ananthanarayanan, The Statesman "If you liked the Numb3rs TV show: L.A. Math: Romance, Crime, and Mathematics in the City of Angels by James D. Stein."--John Allen Paulos, author of A Numerate Life "A former maths professor has turned detective to demonstrate just how useful--and how entertaining--his subject can be."--Matthew Reiz, Times Higher Education "With tight and engaging plots, the stories in LA Math are neatly written and just the right length to read in around 15 minutes."--Dominic Lenton, Engineering & TechnologyTable of ContentsPREFACE: L.A. Math ix MATHEMATICAL TOPICS BY CHAPTER xv CHAPTER 1. A Change of Scene 1 CHAPTER 2. The Case of the Vanishing Greenbacks 11 CHAPTER 3. A Matter of Time 21 CHAPTER 4. The Worst Forty Days since the Flood 31 CHAPTER 5. The Accidental Guest 40 CHAPTER 6. Message from a Corpse 50 CHAPTER 7. Animal Passions 60 CHAPTER 8. Nothing to Crow About 69 CHAPTER 9. The Winning Streak 78 CHAPTER 10. One Long Season 88 CHAPTER 11. The Great Basketball Fix 97 CHAPTER 12. It's All in the Game 106 CHAPTER 13. Division of Labor 115 CHAPTER 14. The Quarterback Controversy 123 APPENDIXES: Continuing the Investigations 1. Mathematical Logic in "A Change of Scene" 137 2. Percentages in "The Case of the Vanishing Greenbacks" 143 3. Averages and Rates in "A Matter of Time" 148 4. Sequences and Arithmetic Progressions in "The Worst Forty Days since the Flood" 153 5. Algebra, the Language of Quantitative Relationships, in "The Accidental Guest" 161 6. Mathematics of Finance in "Message from a Corpse" 166 7. Set Theory in "Animal Passions" 175 8. The Chinese Restaurant Principle: Combinatorics in "Nothing to Crow About" 184 9. Probability and Expectation in "The Winning Streak" 189 10. Conditional Probability in "One Long Season" 198 11. Statistics in "The Great Basketball Fix" 202 12. Game Theory in "It's All in the Game" 213 13. Elections in "Division of Labor" 219 14. Algorithms, Efficiency, and Complexity in "The Quarterback Controversy" 225 An Introduction to Sports Betting 231 Notes 235 Index 239
£20.90
Princeton University Press e The Story of a Number
Book SynopsisThe interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with oTrade ReviewHonorable Mention for the 1994 Award for Best Professional/Scholarly Book in Mathematics, Association of American Publishers "This is a gently paced, elegantly composed book, and it will bring its readers much pleasure... Maor has written an excellent book that should be in every public and school library."--Ian Stewart, New Scientist "Maor wonderfully tells the story of e. The chronological history allows excursions into the lives of people involved with the development of this fascinating number. Maor hangs his story on a string of people stretching from Archimedes to David Hilbert. And by presenting mathematics in terms of the humans who produced it, he places the subject where it belongs--squarely in the centre of the humanities."--Jerry P. King, Nature "Maor has succeeded in writing a short, readable mathematical story. He has interspersed a variety of anecdotes, excursions, and essays to lighten the flow... [The book] is like the voyages of Columbus as told by the first mate."--Peter Borwein, Science "Maor attempts to give the irrational number e its rightful standing alongside pi as a fundamental constant in science and nature; he succeeds very well... Maor writes so that both mathematical newcomers and long-time professionals alike can thoroughly enjoy his book, learn something new, and witness the ubiquity of mathematical ideas in Western culture."--Choice "It can be recommended to readers who want to learn about mathematics and its history, who want to be inspired and who want to understand important mathematical ideas more deeply."--EMS Newsletter "[A] very interesting story about the history of e, logarithms, and related matters, especially the history of calculus... [A] useful complement to a course in calculus and analysis, shedding light on some fundamental topics."--Mehdi Hassani, MAA ReviewsTable of ContentsPreface1John Napier, 161432Recognition113Financial Matters234To the Limit, If It Exists285Forefathers of the Calculus406Prelude to Breakthrough497Squaring the Hyperbola588The Birth of a New Science709The Great Controversy8310e[superscript x]: The Function That Equals its Own Derivative9811e[superscript theta]: Spira Mirabilis11412(e[superscript x] + e[superscript -x])/2: The Hanging Chain14013e[superscript ix]: "The Most Famous of All Formulas"15314e[superscript x + iy]: The Imaginary Becomes Real16415But What Kind of Number Is It?183App. 1. Some Additional Remarks on Napier's Logarithms195App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches] [infinity]197App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus200App. 4. The Inverse Relation between lim (b[superscript h] - 1)/h = 1 and lim (1 + h)[superscript 1/h] = b as h [approaches] 0202App. 5. An Alternative Definition of the Logarithmic Function203App. 6. Two Properties of the Logarithmic Spiral205App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions208App. 8. e to One Hundred Decimal Places211Bibliography213Index217
£14.24
Princeton University Press The Calculus of Happiness
Book SynopsisTrade Review"There are plenty of books about managing your wealth, but The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love, by Oscar Fernandez of Princeton University Press, sounds intriguing."--Matthew Partridge, Money Week "[E]ngaging... Readers are sure to get a sense of how content from algebra and precalculus can help inform us about important decisions that are almost universally relevant."--Jason M. Graham, MAA Reviews "Brilliant... Where Fernandez's book scores highly is that it goes beyond being a typical self-help manual for the numerate, by presenting example after example of how mathematical topics such as probability, game theory and exponential functions really do make sense of a world that can sometimes seem so subjective. It's also an easy-going analysis of those areas in life that get brushed under the carpet, to be attended to another day. Once you realise it all boils down to maths, you will wake up happier, wealthier and healthier tomorrow morning, and we have Oscar E. Fernandez to thank for that."Nick Smith, Engineering & TechnologyTable of ContentsPreface ix Math Topics Covered by Chapter xiii I: A Healthier You Is Just a Few Equations Away 1 1 How Many Calories Should You Eat Each Day? 3 1.1 The Linear Functions Hidden in Your Diet 4 1.2 The Mathematics of Metabolism 8 1.3 Burn Those Calories! Work Those Quads! 11 1.4 The Calories Required to Digest Food 14 2 Live Longer (and Be Healthier) by Eating the Right Foods 20 2.1 A Game of Macronutrient Musical Chairs 20 2.2 How to Eat More and Be Healthier: Energy Density 29 2.3 Live Long(er) and Prosper with theWaist-Height Ratio 34 II: A Mathematician's Guide to Managing Your Money 41 3 Dissecting Your Monthly Budget 43 3.1 The Return of the King (the Linear Function) 44 3.2 To Expenses, and Beyond! 49 3.3 How Many YearsWill It Take You to Reach Financial Independence? 62 4 How to Beat Wall Street at Its Own Game 69 4.1 How to Make 15% a Year, Guaranteed 70 4.2 The Safest Investments 71 4.3 Quantifying Investment Risk and Return 73 4.4 Stocks, Bonds, and the "All-Weather" Portfolio 77 III: Looking for Love? There May Be an Equation for That 87 5 Finding "The 1" 89 5.1 What the Search for Aliens Can Teach You about FindingYour Soulmate 89 5.2 Why Hiring a Secretary Is Like Dating 92 5.3 The Stable Matching Problem 97 6 Living Happily Ever After with "The 1" 103 6.1 Your Relationship as a Dynamical System 104 6.2 Need Help Making a Joint Decision? There's an Equation for That 108 6.3 How Psychologists Use Math to Predict Divorce 113 Epilogue 118 Acknowledgments 120 Appendix A: Background Content 121 Appendix 1 123 Appendix 2 128 Appendix 3 130 Appendix 4 141 Appendix 5 143 Appendix 6 144 Bibliography 151 Index 157
£22.00
Princeton University Press Undiluted HocusPocus The Autobiography of Martin
Book SynopsisMartin Gardner wrote the Mathematical Games column for Scientific American for twenty-five years and published more than seventy books on topics as diverse as magic, religion, and Alice in Wonderland. Gardner's illuminating autobiography is a candid self-portrait by the man evolutionary theorist Stephen Jay Gould called our "single brightest beaconTrade ReviewOne of American Association for the Advancement of Science's Books for General Audiences and Young Adults 2014 "His radiant self lives on in his massive and luminous literary output and shines at its sweetest, wittiest and most personal in Undiluted Hocus-Pocus."--Teller, New York Times Book Review "For those of us who believe that the sciences and the humanities don't have to be enemies, Martin Gardner is an inspiring model. Undiluted Hocus-Pocus reveals a man immersed in philosophy, religion and literature, even as he makes a career writing about science."--Jordan Ellenberg, Wall Street Journal "Readers who only know Gardner for his math and science writing will be surprised at his focus on religion, and this autobiography demonstrates his passion to explain and understand the world around him."--Publishers Weekly "For half a century, Martin Gardner (1914-2010) was an international scientific treasure... Gardner's passion for writing and his warmth and humour shine forth on every page of this book, making it a memoir of a great human being."--David Singmaster, Nature "Zealously debunking science fads and declaring his bafflement at the human brain, maths writer Martin Gardner was on fine form in this posthumous memoir."--Nature "The style is that of a memoir, conversationally phrased, and not afraid to be sidetracked occasionally by an amusing aside. Gardner paints vividly an inside picture of American intellectual life in the twentieth century, coloured by honest accounts of the many influential figures with whom he came into contact."--Alexander Shannon, Plus magazine "His illuminating autobiography, Undiluted Hocus-Pocus ... offers a rare, intimate look at Gardner's life and work."--Mother Nature Network "In summary, I give this book the highest praise that I can possibly give an autobiography: it was much too short."--Charles Ashbacher, MAA Reviews "[Undiluted Hocus-Pocus] is the most sincere, unadulterated biography I ever read... [D]etails of his life and personality exposed in the book help create a more complete picture of this fascinating person... Martin Gardner had tremendous influence on several generations of young minds; his autobiography will help his fans appreciate how that came about. This is a book no one who ever heard his name would want to miss."--Cut the Knot Insights blog "I only wish his autobiography was twice as long, for I never tire of reading him and feeling enriched... And thank you Martin for this last, final, further peek into your brilliant, fertile, curious, nimble, incisive, probing, captivating life and mind."--Math Tango blog "Undiluted Hocus-Pocus reminds us how Gardner taught many of us how to play the game of mathematics better."--Mathrecreation blog "A case can be made, in purely practical terms, for Martin Gardner as one of the most influential writers of the 20th century. His popularizations of science and mathematical games in Scientific American, over the 25 years he wrote for them, might have helped create more young mathematicians and computer scientists than any other single factor prior to the advent of the personal computer... Gardner was capable of appealing to the literary side of left-brained sorts, and did so with ... taste and restraint... Undiluted Hocus-Pocus, his posthumously published autobiography ... reveals the sort of mentality that shaped itself around his encyclopedic interests."--David Auerbach, Los Angeles Review of Books "[This book] will be an eye-opener knowing that Martin Gardner was active on so many diverse fields."--European Mathematical Society "The book is just a delight to read."--Stephen Hirtle, Pittsburgh Post-Gazette "Here my guru and sage brought together, over the course of two hundred pages, the full range of his interests--math, magic, philosophy, stories, poetry, science, religion, politics--and combined these disparate topics with an account of his private life and intellectual development. I enjoyed every page of this book."--Ted Gioia, Millions "Reading Martin Gardner's autobiography is like spending a pleasant afternoon in the company of a 95-year-old man with sharp memories and a twinkle in his eye. Oh wait, that's what it is."--Science Musings blog "This book describes some of the pivotal moments in the life of prolific author/journalist Martin Gardner (1914-2010), who is best known for his illuminating and entertaining contributions to Scientific American magazine from 1956 to 1981. Fans of Martin Gardner will find this posthumously published autobiography fascinating."--Choice "[H]ighly readable. Even those well familiar with Gardner's writings, although they will be acquainted with much of the ground covered, will still make several new discoveries. The foreword by Persi Diaconis will also interest mathematicians."--Leon Harkleroad, Zentralblatt Math "A delightful book."--Peter E. Blau, Red Circle Society "For all his fame, Gardner was a humble, generous man, always modest about his mathematical achievements. His humanity, humor, and sheer decency shine through every page. Reading this book is like chatting with him about his intellectually adventure-filled life for a whole weekend."--Colm Mulcahy, Math Horizons "At the age of 95 he wrote this ... charming and informative autobiography covering an incredibly prolific and productive life that should inspire anyone who encounters it."--AAAS "Martin Gardner as one of those rare and valuable writers who could venture into the worlds of science and mathematics as an intelligent and interested layman, and then entertain the rest of us with his discoveries."--Jon Wainwright, Skeptic Magazine "A very interesting read."--Christopher Hollings, Mathematics TodayTable of ContentsForeword: Magic, Mathematics, and Mysterians, by Persi Diaconis xi Preface xxiii Prologue: I Am a Mysterian xxv 1 Earliest Memories 1 2 Lee School 10 3 Tulsa Central High, I 21 4 Central High, II 28 5 Hutchins and Adler 40 6 Richard McKeon 47 7 I Lose My Faith 53 8 Chicago, I 62 9 Chicago, II 76 10 I Become a Journalist 88 11 Mother and Dad 98 12 The Navy, I 111 13 The Navy, II 119 PHOTO ESSAY follows page 124 14 Esquire and Humpty 125 15 Scientific American 134 16 Pseudoscience 150 17 Math and Magic Friends 160 18 Charlotte 173 19 Bob and Betty 185 20 God 191 21 My Philosophy 195 Afterword: My Most Elegant Friend ... , by James Randi 209 Index 215
£17.09
Princeton University Press Summing It Up From One Plus One to Modern Number
Book SynopsisTrade Review"Offers a clear and beautiful progression from addition to modern number theory."--Math-Blog "The authors did a remarkable job in making some aspects of modern number theory very accessible to readers with only a minimal knowledge of mathematics, say a student who had a first calculus course. However, also mathematicians who do not have number theory as their main focus will enjoy this book."--Adhemar Bultheel, European Mathematical Society "Ash and Gross do a masterful job of leading students from finite sums to modular forms and to the forefront of modern number theory... This is an excellent piece of mathematical writing."--Choice "[A]n accessible and fun introduction to modular forms... [Summing It Up] is engaging and conversational, without losing accuracy or essential rigor."--Dominic Lanphier, American Mathematical MonthlyTable of Contents*Frontmatter, pg. i*CONTENTS, pg. vii*PREFACE, pg. xi*ACKNOWLEDGMENTS, pg. xv*INTRODUCTION: WHAT THIS BOOK IS ABOUT, pg. 1*CHAPTER 1. PROEM, pg. 11*CHAPTER 2. SUMS OF TWO SQUARES, pg. 22*CHAPTER 3. SUMS OF THREE AND FOUR SQUARES, pg. 32*CHAPTER 4. SUMS OF HIGHER POWERS: WARING'S PROBLEM, pg. 37*CHAPTER 5. SIMPLE SUMS, pg. 42*CHAPTER 6. SUMS OF POWERS, USING LOTS OF ALGEBRA, pg. 50*CHAPTER 7. INFINITE SERIES, pg. 73*CHAPTER 8. CAST OF CHARACTERS, pg. 96*CHAPTER 9. ZETA AND BERNOULLI, pg. 103*CHAPTER 10. COUNT THE WAYS, pg. 110*CHAPTER 11. THE UPPER HALF-PLANE, pg. 127*CHAPTER 12. MODULAR FORMS, pg. 147*CHAPTER 13. HOW MANY MODULAR FORMS ARE THERE?, pg. 160*CHAPTER 14. CONGRUENCE GROUPS, pg. 179*CHAPTER 15. PARTITIONS AND SUMS OF SQUARES REVISITED, pg. 186*CHAPTER 16. MORE THEORY OF MODULAR FORMS, pg. 201*CHAPTER 17. MORE THINGS TO DO WITH MODULAR FORMS: APPLICATIONS, pg. 213*BIBLIOGRAPHY, pg. 225*INDEX, pg. 227
£19.80
Princeton University Press The padic Simpson Correspondence
Book SynopsisTrade Review"The authors give a very detailed introduction to the theory, smoothing out some difficulties by introducing new concepts."--Gerd Faltings, Zentralblatt MATHTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. ix*Chapter I. Representations of the fundamental group and the torsor of deformations. An overview, pg. 1*Chapter II. Representations of the fundamental group and the torsor of deformations. Local study, pg. 27*Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects, pg. 179*Chapter IV. Cohomology of Higgs isocrystals, pg. 307*Chapter V. Almost etale coverings, pg. 449*Chapter VI. Covanishing topos and generalizations, pg. 485*Facsimile : A p-adic Simpson correspondence, pg. 577*Bibliography, pg. 595*Indexes, pg. 599
£138.55
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£124.00
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£59.50
Princeton University Press Fourier Restriction for Hypersurfaces in Three
Book SynopsisTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Chapter 1. Introduction, pg. 1*Chapter 2. Auxiliary Results, pg. 29*Chapter 3. Reduction to Restriction Estimates near the Principal Root Jet, pg. 50*Chapter 4. Restriction for Surfaces with Linear Height below 2, pg. 57*Chapter 5. Improved Estimates by Means of Airy-Type Analysis, pg. 75*Chapter 6. The Case When hlin(PHI) => 2: Preparatory Results, pg. 105*Chapter 7. How to Go beyond the Case hlin(PHI) => 5, pg. 131*Chapter 8. The Remaining Cases Where m = 2 and B = 3 or B = 4, pg. 181*Chapter 9. Proofs of Propositions 1.7 and 1.17, pg. 244*Bibliography, pg. 251*Index, pg. 257
£130.40
Princeton University Press Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra
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£63.75
Princeton University Press The Calculus of Selfishness
Book SynopsisTrade Review"With collaborators from Vienna, Sigmund has pioneered the development of evolutionary game dynamics. This thought-provoking book is a distillation of his many influential contributions to the field. It is a showcase of clever models and elegant mathematics, replete with sometimes counterintuitive insights."--Nature "In The Calculus of Selfishness, Karl Sigmund provides a comprehensive and accessible mathematical exposition of the evolutionary game theory of selfishness. The book should prove accessible to natural and social scientists as its mathematical arguments employ intuition, geometry, and simulation with a minimum of axiomatic formality. The demands on the reader typically involve little more than linear algebra and calculus."--David Krakauer, Science "Sigmund's mathematical exposition is exemplary. He starts with the presumption that the reader has only rudimentary linear algebra and some notion of what a differential equation is, and he builds up from there, introducing more advanced concepts and results as needed. He avoids formal proofs and bookkeeping in favor of careful explanations of key points and illustrative calculations. As he teaches evolutionary game theory, Sigmund is also demonstrating how to write about applied mathematics."--Cosma Shalizi, American Scientist "Sigmund's writing is admirably clear and historically grounded and he wisely restricts his coverage primarily to a subset of situations... [Sigmund] makes fascinating reading for the interested general reader and provides a good background in game theory which should inoculate readers from being fooled by sloppy or completely incorrect references in the popular media."--Sarah Boslaugh, MAA Reviews "Sigmund has ... done an admirable job of motivating the material and making it accessible for the non-expert who is interested in theories to explain the evolution of cooperation."--Ross Cressman, Mathematical ReviewsTable of ContentsPreface vii Chapter 1: Introduction: Social Traps and Simple Games 1 Chapter 2: Game Dynamics and Social Learning 25 Chapter 3: Direct Reciprocity: The Role of Repetition 49 Chapter 4: Indirect Reciprocity: The Role of Reputation 82 Chapter 5: Fairness and Trust: The Power of Incentives 104 Chapter 6: Public Goods and Joint Efforts: Between Freedom and Enforcement 123 Chapter 7: Cooperation in Structured Populations 145 References 155 Index 169
£999.99
Princeton University Press Complexities
Book SynopsisTrade ReviewWinner of the 2006 Book Award, Mathematics/Computer Science category, Alpha Sigma Nu, and the Association of Jesuit Colleges and Universities "A definitive work, very carefully written, Complexities will inspire a wide range of women mathematicians and scientists for a long period of time... By far this is the most important study of women in mathematics that even a giant amongst men mathematicians will find himself reading with sheer pleasure."--Current Engineering Practice "[T]he variation in [the book's] content and writing styles ... is exactly its strength--it is both an excellent reference for a professor wishing to provide a student with a few inspiring gems and a comprehensive overall picture of the life of women in mathematics. Its lessons are gleaned from the trials and tribulations of a specific group, but the advice is universal."--Lisa DeKeukelaere, MAA Online "The collection documents the complex nature of the conditions women have faced while pursuing their careers in mathematics. It shows the pleasure women had in discovering new mathematics, and energy to do a good job!"--Silke Gobel, Zentralblatt "As a female mathematics student, I found that reading this book increased my appreciation for the courage and determination of the women who entered mathematics before me, while also building my personal confidence in the prospect of finding a rewarding and fulfilling life in the mathematical community."--Gwen Spencer, Math Horizons
£28.80
Princeton University Press Elements of Mathematics
Book SynopsisTrade Review"[Stillwell] writes clearly and engagingly... [Elements of Mathematics] can appeal to various constituencies at different levels of mathematical sophistication."--Mark Hunacek, MAA Reviews "A great exploration of elementary mathematics, its limitations, how infinity complicates things, and how various branches of mathematics fit together."--Antonio Cangiano, Math-Blog "Stillwell is ... One of the better current mathematical authors: he writes clearly and engagingly, and makes more of an effort than most to provide historical detail and a sense of how various mathematical ideas tie in with one another... The features we have learned to expect from Stillwell (including, but not limited to, excellent writing) are present in [Elements of Mathematics] as well."--MAA Reviews "An accessible read... Stillwell breaks down the basics, providing both historical and practical perspectives from arithmetic to infinity."--Gemma Tarlach, Discover "[A] sophisticated treatment of topics usually described as elementary."--John Allen Paulos "[Elements of Mathematics] is quite a tour de force, organized by areas of mathematics--arithmetic, computation, algebra, geometry, calculus, and so on--and in each area Stillwell manages to distill down the big ideas and the connections with other areas. He is a master expositor, and the text manages to be engaging and accessible without watering down the mathematics. I definitely learned new things from the book!"--Brent Yorgey, Math Less Traveled blog "From a lifetime of teaching, Stillwell has distilled some nice examples from the entire gamut of elementary mathematics."--Mathematical Reviews Clippings "[A] wonderful book... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics."--Victor Katz, Bulletin of the American Mathematical Society "Elements of Mathematicsis a fine ... overview of the field of mathematics... The writing is clear, succinct, organized, and the diagrams [and] illustrations excellent... While some of the discussion is introductory or elementary, it always leads to deeper, more challenging ideas... [T]his will make a fine basic addition to most mathematicians' bookshelves."--Math Tango "Stillwell uses his broad and impressive command of mathematics to transport a reader through each topic and to a higher level of understanding and questioning."--Convergence "[A] wonderful book ... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics."--Victor Katz, Bulletin of the American Mathematical Society "[Elements of Mathematics] is a book that everybody should read. You will be the better for it."--Reuben Hersh, American Mathematical MonthlyTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*1. Elementary Topics, pg. 1*2. Arithmetic, pg. 35*3. Computation, pg. 73*4. Algebra, pg. 106*5. Geometry, pg. 148*6. Calculus, pg. 193*7. Combinatorics, pg. 243*8. Probability, pg. 279*9. Logic, pg. 298*10. Some Advanced Mathematics, pg. 336*Bibliography, pg. 395*Index, pg. 405
£999.99
Princeton University Press Making and Breaking Mathematical Sense
Book SynopsisTrade Review"[Making and Breaking Mathematical Sense] offers a substantial and interesting treatment of issues in the philosophy of mathematical practice."--Calvin Jongsma, MAA ReviewsTable of ContentsAcknowledgments xi Introduction 1 What Philosophy of Mathematics Is Today 1 What Else Philosophy of Mathematics Can Be 3 A Vignette: Option Pricing and the Black-Scholes Formula 6 Outline of This Book 10 1: Histories of Philosophies of Mathematics 13 History 1: On What There Is, Which Is a Tension between Natural Order and Conceptual Freedom 14 History 2: The Kantian Matrix, Which Grants Mathematics a Constitutive Intermediary Epistemological Position 22 History 3: Monster Barring, Monster Taming, and Living with Mathematical Monsters 28 History 4: Authority, or Who Gets to Decide What Mathematics Is About 33 The "Yes, Please!" Philosophy of Mathematics 37 2: The New Entities of Abbacus and Renaissance Algebra 39 Abbacus and Renaissance Algebraists 39 The Emergence of the Sign of the Unknown 40 First Intermediary Reflection 45 The Arithmetic of Debited Values 46 Second Intermediary Reflection 51 False and Sophistic Entities 53 Final Reflection and Conclusion 56 3: A Constraints-Based Philosophy of Mathematical Practice 59 Dismotivation 59 The Analytic A Posteriori 63 Consensus 67 Interpretation 72 Reality 81 Constraints 84 Relevance 90 Conclusion 97 4: Two Case Studies of Semiosis in Mathematics 100 Ambiguous Variables in Generating Functions 101 Between Formal Interpretations 101 Models and Applications 107 Openness to Interpretation 109 Gendered Signs in a Combinatorial Problem 112 The Problem 112 Gender Role Stereotypes and Mathematical Results 116 Mathematical Language and Its Reality 120 The Forking Paths of Mathematical Language 122 5: Mathematics and Cognition 128 The Number Sense 129 Mathematical Metaphors 137 Some Challenges to the Theory of Mathematical Metaphors 142 Best Fit for Whom? 143 What Is a Conceptual Domain? 146 In Which Direction Does the Theory Go? 150 So How Should We Think about Mathematical Metaphors? 154 An Alternative Neural Picture 156 Another Vision of Mathematical Cognition 163 From Diagrams to Haptic Vision 164 Haptic Vision in Practice 171 6: Mathematical Metaphors Gone Wild 177 What Passes between Algebra and Geometry 177 Piero della Francesca (Italy, Fifteenth Century) 178 Omar Khayyam (Central Asia, Eleventh Century) 179 Rene Descartes (France, Seventeenth Century) 181 Rafael Bombelli (Italy, Sixteenth Century) 183 Conclusion 187 A Garden of Infinities 188 Limits 189 Infinitesimals and Actual Infinities 194 7: Making a World, Mathematically 199 Fichte 201 Schelling 206 Hermann Cohen 209 The Unreasonable(?) Applicability of Mathematics 213 Bibliography 219 Index 233
£999.99
Princeton University Press The Mathematics of Various Entertaining Subjects
Book SynopsisCopyright 2017 by Princeton University Press.Trade Review"[This book] is beautiful in that just about every problem could be explained to anybody with almost no mathematics background at all, but the methods of solving them take you deeply into many complex areas of mathematics. The books gathers together problems which pop up through what one might consider 'silly' or 'frivolous' questions, but which lead to new ways of thinking and have applications in enormously wide-ranging areas of mathematics."---Jonathan Shock, Mathemafrica"The editors once again have brought together an extraordinary list of authors to produce nineteen engaging papers, split into five groups: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. . . . It is often deeply challenging mathematically and, as a result, all the more fun. Each reader will find chapters that appeal to them." * MAA Reviews *"In the second volume of this engaging series, Beineke . . . and Rosenhouse . . . deliver another fantastic collection of essays dealing with popular mathematics. . . . Anyone who enjoys reading about recreational mathematics will find plenty to enjoy and discover in this second volume." * Choice *
£38.25
