Mathematics Books
World Scientific Publishing Co Pte Ltd Lectures On Algebraic Topology
Book SynopsisAlgebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
£52.25
World Scientific Publishing Co Pte Ltd Problem Based Journey From Elementary Number
Book SynopsisThe book is based on lecture notes of a course 'from elementary number theory to an introduction to matrix theory' given at the Technion to gifted high school students. It is problem based, and covers topics in undergraduate mathematics that can be introduced in high school through solving challenging problems. These topics include Number theory, Set Theory, Group Theory, Matrix Theory, and applications to cryptography and search engines.
£33.25
World Scientific Publishing Co Pte Ltd Introduction To Probability, An: With
Book SynopsisThe main objective of this text is to facilitate a student's smooth learning transition from a course on probability to its applications in various areas. To achieve this goal, students are encouraged to experiment numerically with problems requiring computer solutions.
£52.25
World Scientific Publishing Co Pte Ltd Ordinary Differential Equations With Applications
Book SynopsisWritten in a straightforward and easily accessible style, this volume is suitable as a textbook for advanced undergraduate or first-year graduate students in mathematics, physical sciences, and engineering. The aim is to provide students with a strong background in the theories of Ordinary Differential Equations, Dynamical Systems and Boundary Value Problems, including regular and singular perturbations. It is also a valuable resource for researchers.This volume presents an abundance of examples in physical and biological sciences, and engineering to illustrate the applications of the theorems in the text. Readers are introduced to some important theorems in Nonlinear Analysis, for example, Brouwer fixed point theorem and fundamental theorem of algebras. A chapter on Monotone Dynamical Systems takes care of the new developments in Ordinary Differential Equations and Dynamical Systems.In this third edition, an introduction to Hamiltonian Systems is included to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics.
£58.50
World Scientific Publishing Co Pte Ltd Introduction To Matrix Theory: With Applications
Book SynopsisLinear algebra and matrix theory are among the most important and most frequently applied branches of mathematics. They are especially important in solving engineering and economic models, where either the model is assumed linear, or the nonlinear model is approximated by a linear model, and the resulting linear model is examined.This book is mainly a textbook, that covers a one semester upper division course or a two semester lower division course on the subject.The second edition will be an extended and modernized version of the first edition. We added some new theoretical topics and some new applications from fields other than economics. We also added more difficult exercises at the end of each chapter which require deep understanding of the theoretical issues. We also modernized some proofs in the theoretical discussions which give better overview of the study material. In preparing the manuscript we also corrected the typos and errors, so the second edition will be a corrected, extended and modernized new version of the first edition.
£72.00
World Scientific Publishing Co Pte Ltd Linear Algebra I: Basic Concepts
Book SynopsisThis is the first volume of the two-volume book on linear algebra, in the University of Tokyo (UTokyo) Engineering Course.The objective of this volume is to present, from the engineering viewpoint, the standard mathematical results in linear algebra such as those on systems of equations and eigenvalue problems. In addition to giving mathematical theorems and formulas, it explains how the mathematical concepts such as rank, eigenvalues, and singular values are linked to engineering applications and numerical computations.In particular, the following four aspects are emphasized.
£52.25
World Scientific Publishing Co Pte Ltd Walk Through Combinatorics, A: An Introduction To
Book SynopsisThe first half of the book walks the reader through methods of counting, both direct elementary methods and the more advanced method of generating functions. Then, in the second half of the book, the reader learns how to apply these methods to fascinating objects, such as graphs, designs, random variables, partially ordered sets, and algorithms. In short, the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth, by showing how numerous the applications of our methods are.New to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises — more than a hundred in total — which are located at the end of most subsections. As was the case for all previous editions, the exercises sometimes contain new material that was not discussed in the text, allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory, as well as a chapter on permutation patterns (not often covered in other textbooks), this book is well suited for any undergraduate introductory combinatorics class.
£108.00
Springer Verlag, Singapore Understanding Markov Chains: Examples and
Book SynopsisThis book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.Table of ContentsProbability Background.- Gambling Problems.- Random Walks.- Discrete-Time Markov Chains.- First Step Analysis.- Classification of States.- Long-Run Behavior of Markov Chains.- Branching Processes.- Continuous-Time Markov Chains.- Discrete-Time Martingales.- Spatial Poisson Processes.- Reliability Theory.
£33.24
Springer Verlag, Singapore Mathematical and Computational Studies on
Book SynopsisThis book’s aim is to study the mathematical and computational models to analyze the progress, prognosis, prevention, and panacea of breast cancer. The book discusses application of Markov chains and transient mappings, Charlie–Simpson numerical algorithm, models represented by nonlinear reaction–diffusion-type partial differential equations, and related techniques. The book also attempts to design mathematical model of targeted strategic treatments by using Skilled Killer Drugs (SKD1 and SKD2) to suggest the improvisation of future cancer treatments. Both graduate students and researchers of computational biology and oncologists will benefit by studying this book. Researchers of cancer studies and biological sciences will also find this work helpful.Table of ContentsIntroduction.- Statistics: The Backgrounds & The Basis.- Attacker & Defender Model: The Dynamics of the Immune System.- Mathematical Modeling of Metastatic Cancer.- Mathematical/Computational Modeling of Advanced Immunotherapy.- Mathematical Modeling & Computational Studies On The War Against Breast Cancer.- Gene Therapy.- The Smartest Fighters.- Nutritional Therapy.- The Fateful Code & The Future Course.- Conclusion.
£44.99
Springer Verlag, Singapore Notable Modern Indian Mathematicians and
Book SynopsisThis book provides a comprehensive portrayal of the history of Indian mathematicians and statisticians and uncovers many missing parts of the scientific representation of mathematical and statistical research during the 19th and 20th centuries of Bengal (now West Bengal), India. This book gives a brief historical account about the establishment of the first-two departments in an Indian university, where graduate teaching and research were initiated. This was a unique distinction for the University of Calcutta which was established in 1857. The creation of the world famous Indian Statistical Institute (ISI) in Calcutta (now Kolkata) is also briefly described. The lives and works of the 16 pioneer mathematical scientists who adorned the above mentioned institutions and the first Indian Institute Technology (IIT) of India have been elaborated in lucid language. Some outstanding scholars who were trained at the ISI but left India permanently have also been discussed briefly in a separate chapter. This book fulfils a long-standing gap in the history of modern Indian mathematics, which will make the book very useful to researchers in the history of science and mathematics. Written in very lucid English with little mathematical or statistical jargon makes the book immensely readable even to general readers with interest in scientific history even from non-mathematical, non-statistical background. This book is a clear portrayal of the struggle and success of researchers in mathematical sciences in Bengal (an important part of the colonial India), unveils before the international community of mathematical scientists. The real connoisseurs will appreciate the value of the book, as it will clear up many prevailing misconceptions.Trade Review“The book portrays the lives and works of 16 pioneer mathematical scientists including one woman, closely connected to the University of Calcutta, the Indian Statistical Institute, Calcutta. They worked under difficult circumstances, not having access to modern gadgets. … This book talks of their indomitable courage, hard work, dedication and relentless perseverance. … The author is to be congratulated for her painstaking research work. It is very informative and unique.” (Sita Sundar Ram, zbMATH 1510.01002, 2023)Table of ContentsChapter 1. Historical Prelude and Introduction.- Chapter 2. Sir Asutosh Mookerjee (1864–1924).- Chapter 3. Syamadas Mukhopadhyay (1866–1937).- Chapter 4. Ganesh Prasad (1876–1935).- Chapter 5. Bibhuti Bhusan Datta (1888–1958).- Chapter 6. Prasanta Chandra Mahalanobis (1893–1972).- Chapter 7. Nikhil Ranjan Sen (1894–1963).- Chapter 8. Suddhodan Ghosh (1896–1976).- Chapter 9. Rabindranath Sen (1896–1974).- Chapter 10. Bibhutibhusan Sen (1898–1976).- Chapter 11. Raj Chandra Bose (1901–1987).- Chapter 12. Bhoj Raj Seth (1907–1979).- Chapter 13. . Subodh Kumar Chakrabarty (1909–1987).- Chapter 14. Manindra Chandra Chaki (1913–2007).- Chapter 15. Calyampudi Radhakrishna Rao (b. 10th September 1920).- Chapter 16. Anadi Sankar Gupta (1932–2012).- Chapter 17. Jyoti Das (1937–2015).- Chapter 18. Some Outstanding Minds from the Indian Statistical Institute.
£999.99
Springer Verlag, Singapore Modern Cryptography Volume 2: A Classical
Book SynopsisThis open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random analysis tools, there is a problem of "ambiguity" in both definition and algorithm. The greatest feature of this book is to use probability distribution to carry out rigorous mathematical definition and mathematical demonstration for various unclear or imprecise expressions, so as to make it a rigorous theoretical system for classroom teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic lattice, ideal lattice and generalized NTRU cryptography.This book is used as a professional book for graduate students majoring in mathematics and cryptography, as well as a reference book for scientific and technological personnel engaged in cryptography research.Table of ContentsChapter 1. Gauss lattice theory.- Chapter 2. Reduction principle of Ajtai.- Chapter 3. Learning with errors.- Chapter 4. LWE cryptosystem.- Chapter 5. Cyclic lattice and Ideal lattice.- Chapter 6. Fully Homomorphic Encryption.- Chapter 7. General NTRU cryptosystem.
£40.49
World Scientific Publishing Co Pte Ltd Combinatorial Problems In Mathematical
Book SynopsisThis book focuses on combinatorial problems in mathematical competitions. It provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions. Some enlightening and novel examples and exercises are well chosen in this book.With this book, readers can explore, analyze and summarize the ideas and methods of solving combinatorial problems. Their mathematical culture and ability will be improved remarkably after reading this book.Table of ContentsCounting Principles and Counting Formulas; Pigeonhole Principles and Mean Value Principles; Generating Functions; Recurrence Sequence of Numbers; Classification and Method of Fractional Steps; Corresponding Method; Counting in Two Ways; Recurrence Method; Coloring Method and Evaluation Method; Proof by Contradiction and Extreme Principle; Locally Adjusted Method; Constructive Method; Combinatorial Counting Problems; Existence Problems and the Proof of Inequalities in Combinatorial Problems; Combinatorial Extremum Problems.
£26.60
World Scientific Publishing Co Pte Ltd Infinite Group Theory: From The Past To The
Book SynopsisThe development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest.
£72.90
World Scientific Publishing Co Pte Ltd Walk Through Combinatorics, A: An Introduction To
Book SynopsisThis is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them.The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity.The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading.The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com.The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.
£54.00
World Scientific Publishing Co Pte Ltd Principles And Techniques In Combinatorics -
Book SynopsisThe solutions to each problem are written from a first principles approach, which would further augment the understanding of the important and recurring concepts in each chapter. Moreover, the solutions are written in a relatively self-contained manner, with very little knowledge of undergraduate mathematics assumed. In that regard, the solutions manual appeals to a wide range of readers, from secondary school and junior college students, undergraduates, to teachers and professors.
£38.00
World Scientific Publishing Co Pte Ltd Theories Of Integration: The Integrals Of
Book SynopsisThe book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and could be used separately in teaching a portion of an introductory real analysis course. There is a sufficient supply of exercises to make this book useful as a textbook.Table of ContentsIntroduction: Areas; Exercises; Riemann Integral: Riemann's Definition; Basic Properties; Cauchy Criterion; Darboux's Definition; Fundamental Theorem of Calculus; Characterizations of Integrability; Improper Integrals; Exercises; Convergence Theorems and the Lebesgue Integral: Lebesgue's Descriptive Definition of the Integral; Measure; Lebesgue Measure in ℝn; Measurable Functions; Lebesgue Integral; Riemann and Lebesgue Integrals; Mikusinski's Characterization of the Lebesgue Integral; Fubini's Theorem; The Space of Lebesgue Integrable Functions; Exercises; Fundamental Theorem of Calculus and the Henstock - Kurzweil Integral: Denjoy and Perron Integrals; A General Fundamental Theorem of Calculus; Basic Properties; Unbounded Intervals; Henstock's Lemma; Absolute Integrability; Convergence Theorems; Henstock - Kurzweil and Lebesgue Integrals; Differentiating Indefinite Integrals; Characterizations of Indefinite Integrals; The Space of Henstock - Kurzweil Integrable Functions; Henstock - Kurzweil Integrals on ℝn; Exercises; Absolute Integrability and the McShane Integral: Defintions; Basic Properties; Absolute Integrability; Convergence Theorems; The McShane Integral as a Set Function; The Space of McShane Integrable Functions; McShane, Henstock - Kurzweil and Lebesgue Integrals; McShane Integrals on ℝn; Fubini and Tonelli Theorems; McShane, Henstock - Kurzweil and Lebesgue Integrals in ℝn; Exercises.
£66.60
World Scientific Publishing Co Pte Ltd Course In Analysis, A - Volume I: Introductory
Book SynopsisPart 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis.Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions.Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers. Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions.Table of ContentsIntroductory Calculus: Numbers - Revision; The Absolute Value, Inequalities and Intervals; Mathematical Induction; Functions and Mappings; Functions and Mappings Continued; Derivatives; Derivatives Continued; The Derivative as a Tool to Investigate Functions; The Exponential and Logarithmic Functions; Trigonometric Functions and Their Inverses; Investigating Functions; Integrating Functions; Rules for Integration; Analysis in One Dimension: Problems with the Real Line; Sequences and their Limits; A First Encounter with Series; The Completeness of the Real Numbers; Convergence Criteria for Series, b-adic Fractions; Point Sets in Continuous Functions; Differentiation; Applications of the Derivative; Convex Functions and some Norms on n; Uniform Convergence and Interchanging Limits; The Riemann Integral; The Fundamental Theorem of Calculus; A First Encounter with Differential Equations; Improper Integrals and the GAMMA-Function; Power Series and Taylor Series; Infinite Products and the Gauss Integral; More on the GAMMA-Function; Selected Topics on Functions of a Real Variable;
£100.80
World Scientific Publishing Co Pte Ltd Methods And Techniques For Proving Inequalities:
Book SynopsisIn China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year.The authors are coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book explains many basic techniques for proving inequalities such as direct comparison, method of magnifying and reducing, substitution method, construction method, and so on.
£25.65
Springer Exploring the Beauty of Fascinating Numbers
Book SynopsisChapter 1. Digital Root Wonders.- Chapter 2. Elegance of Squares, Cubes, and Higher Powers.- Chapter 3. Triangular Numbers.- Chapter 4. Smith Numbers.- Chapter 5. Amicable Numbers.- Chapter 6. Perfect, Multiply Perfect, and Sociable Numbers.- Chapter 7. Happy Numbers.- Chapter 8. Fabulous Fibonacci Numbers, Lucas Numbers, and Golden Ratio.- Chapter 9. On Some Marvellous Numbers of Kaprekar.- Chapter 10. Amazing Number 108.- Chapter 11. Repunit Numbers.- Chapter 12. Equal?Product?of?Reversible?Numbers (EPRN).- Chapter 13. Unlucky Thirteen.- Chapter 14. Rare Numbers.- Chapter 15. Beauty of Number 153.- Chapter 16. Fascinating Factorials.- Chapter 17. The Number of the Beast 666.- Chapter 18. Ulam Numbers.- Chapter 19. Mystery of p.- Chapter 20. Cab and Vampire Numbers.- Chapter 21. Digital Invariants and Narcissistic Numbers.-Chapter 22. On some special Numbers.-Chapter 23. Number Curiosities.
£37.99
Springer Introduction to Group Theory
Book SynopsisGroups and subgroups.- Normal subgroups.- Finite groups.- Series groups.
£49.49
Springer Verlag, Singapore Machine Learning Methods
Book SynopsisThis book provides a comprehensive and systematic introduction to the principal machine learning methods, covering both supervised and unsupervised learning methods. It discusses essential methods of classification and regression in supervised learning, such as decision trees, perceptrons, support vector machines, maximum entropy models, logistic regression models and multiclass classification, as well as methods applied in supervised learning, like the hidden Markov model and conditional random fields. In the context of unsupervised learning, it examines clustering and other problems as well as methods such as singular value decomposition, principal component analysis and latent semantic analysis. As a fundamental book on machine learning, it addresses the needs of researchers and students who apply machine learning as an important tool in their research, especially those in fields such as information retrieval, natural language processing and text data mining. In order to understand the concepts and methods discussed, readers are expected to have an elementary knowledge of advanced mathematics, linear algebra and probability statistics. The detailed explanations of basic principles, underlying concepts and algorithms enable readers to grasp basic techniques, while the rigorous mathematical derivations and specific examples included offer valuable insights into machine learning. Table of ContentsChapter 1 Introduction to Machine learning and Supervised Learning.- Chapter 2 Perceptron.- Chapter 3 K-Nearest-Neighbor.- Chapter 4 The Naïve Bayes Method.- Chapter 5 Decision Tree.- Chapter 6 Logistic Regression and Maximum Entropy Model.- Chapter 7 Support Vector Machine.- Chapter 8 Boosting.- Chapter 9 EM Algorithm and Its Extensions.- Chapter 10 Hidden Markov Model.- Chapter 11 Conditional Random Field.
£75.99
Cengage Learning Mathematics for Machine Technology
£101.25
Linear Algebra A Modern Introduction Cengage
Book Synopsis
£75.99
Dover Publications Introduction to Topology
Book SynopsisThis volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. Two chapters consider metric space and point-set topology; the other 2 chapters discuss algebraic topological material. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
£15.29
Dover Publications Inc. Elements of the Theory of Functions and
Book SynopsisAdvanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.
£17.84
Dover Publications Inc. Handbook of Mathematical Functions With Formulas
Book SynopsisA classic resource for working with special functions, standard trig, and exponential logarithmic definitions and extensions, it features 29 sets of tables, some to as high as 20 places.
£69.53
Quercus Publishing How to Expect the Unexpected: The Science of
Book SynopsisA Waterstones Best Popular Science Book of 2023'Delightfully clear and vivid to read...A splendid book! Philip Pullman'Absolutely fascinating' James O'Brien'An exceptional book - readable, funny and more needed than ever' Dr Chris van Tulleken, bestselling author of Ultra-Processed PeopleAre you more likely to become a professional footballer if your surname is Ball?· How can you be one hundred per cent sure you will win a bet?· Why did so many Pompeiians stay put while Mount Vesuvius was erupting?· How do you prevent a nuclear war?Ever since the dawn of human civilisation, we have been trying to make predictions about what's in store for us. We do this on a personal level, so that we can get on with our lives efficiently (should I hang my laundry out to dry, or will it rain?). But we also have to predict on a much larger scale, often for the good of our broader society (how can we spot economic downturns or prevent terrorist attacks?). For just as long, we have been getting it wrong. From religious oracles to weather forecasters, and from politicians to economists, we are subjected to poor predictions all the time. Our job is to separate the good from the bad. Unfortunately, the foibles of our own biology - the biases that ultimately make us human - can let us down when it comes to making rational inferences about the world around us. And that can have disastrous consequences.How to Expect the Unexpected will teach you how and why predictions go wrong, help you to spot phony forecasts and give you a better chance of getting your own predictions correct.Trade ReviewA vivid, wide-ranging and delightful guide to the light and the dark side of prediction * Tim Harford, bestselling author of How to Make the World Add Up *Kit Yates presents maths as it should be taught to everyone: accessible, fun, stimulating, and deeply relevant to our lives. Spend some time with this book and you're likely to make better judgements and decisions, to see through the charlatans and snake-oil salespeople - and perhaps even to fool yourself a little less. * Philip Ball, author of the award-winning Critical Mass *Fascinating and fun. From the everyday to global challenges, Kit Yates explores how changing your mind - so often thought to be a weakness - is the best life skill we can all acquire. A brilliant book * Professor Alice Roberts *Yates' writing is a beacon of clarity sorely needed in a complicated and confusing world. How do we overcome our biases, understand coincidences or tackle the unreliability of our intuition? With bountiful familiar examples, he effortlessly overturns so many of our deep-rooted wrong-headed notions gently and persuasively. I'll be quoting from this book * Jim Al-Khalili *I'm a Yates fan. His style is all-clarity-no-bullshit * Aperiodical *Seriously good * Caroline Lucas MP *Absolutely fascinating * James O'Brien *An exceptional book - readable, funny and more needed than ever * Dr Chris van Tulleken, bestselling author of Ultra-Processed People *Yates' writing style imbues the subjects covered with an infectious enthusiasm, artfully dispelling the dry, stuffy perceptions many people have of maths * Physics World *HOW TO EXPECT THE UNEXPECTED is fascinating and (very much to the point) delightfully clear and vivid to read. Like many people, I like reading about maths without actually knowing how to do it, and part of the pleasure of reading this came from its many examples from everyday life. A splendid book! * Philip Pullman *
£18.75
Tarquin Publications Artful Maths Teacher Book
Book Synopsis
£18.99
MIT Press Causal Inference The MIT Press Essential
Book SynopsisA nontechnical guide to the basic ideas of modern causal inference, with illustrations from health, the economy, and public policy.Which of two antiviral drugs does the most to save people infected with Ebola virus? Does a daily glass of wine prolong or shorten life? Does winning the lottery make you more or less likely to go bankrupt? How do you identify genes that cause disease? Do unions raise wages? Do some antibiotics have lethal side effects? Does the Earned Income Tax Credit help people enter the workforce? Causal Inference provides a brief and nontechnical introduction to randomized experiments, propensity scores, natural experiments, instrumental variables, sensitivity analysis, and quasi-experimental devices. Ideas are illustrated with examples from medicine, epidemiology, economics and business, the social sciences, and public policy.
£14.39
W. W. Norton & Company Origins Fourteen Billion Years of Cosmic
Book SynopsisDrawing on the current cross-pollination of geology, biology and astrophysics, Origins brings to life the thrilling astronomical discoveries of recent years.Trade Review"This is the book for anyone who wants to see how much we know about our surroundings and how we got here. But it is even more worthwhile for its sense of adventure and for showing just what science-imagination constrained by evidence-can tell us." -- Martin Ince - Times Higher Education "Neil deGrasse Tyson and Donald Goldsmith dip into astronomy, physics, geology, biology and chemistry with a racy and non-mathematical style. They encourage us to search for answers that could overturn much of what we think we already know. The task is daunting, but the excitement glows from every page." -- David Hughes - New Scientist
£15.19
Springer-Verlag New York Inc. Understanding Analysis
Book SynopsisAcutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition.Trade Review“The choice of topics is a happy combination of the essential and the interesting, all truly leading to an understanding of what analysis is and what questions it addresses, aided by the author’s extraordinarily lucid exposition. … Summing Up: Highly recommended. Upper-division undergraduates.” (D. Robbins, Choice, Vol. 53 (2), October, 2015)“This is the second edition of a text for an undergraduate course in single-variable real analysis. … The topics covered in this book are the ones that have, by now, become standard for a one-semester undergraduate real analysis course … . Overall, this book represents, to my mind, the gold standard among single-variable undergraduate analysis texts.” (Mark Hunacek, MAA Reviews, June, 2015)“This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks. … Understanding Analysis is perfectly titled; if your students read it, that’s what’s going to happen. This terrific book will become the text of choice for the single-variable introductory analysis course; take a look at it next time you’re preparing that class.”— Steve Kennedy, MAA Reviews“Each chapter begins with a discussion section and ends with an epilogue. The discussion serves to motivate the content of the chapter while the epilogue points tantalisingly to more advanced topics. … I wish I had written this book! The development of the subject follows the tried-and-true path, but the presentation is engaging and challenging. Abbott focuses attention immediately on the topics which make analysis fascinating … and makes them accessible to an inexperienced audience.”— Scott Sciffer, The Australian Mathematical Society Gazette Table of ContentsPreface.- 1 The Real Numbers.- 2 Sequences and Series.- 3 Basic Topology of R.- 4 Functional Limits and Continuity.- 5 The Derivative.- 6 Sequences and Series of Functions.- 7 The Riemann Integral.- 8 Additional Topics.- Bibliography.- Index.
£31.49
Profile Books Ltd Professor Stewart's Hoard of Mathematical
Book SynopsisIan Stewart, author of the bestselling Professor Stewart's Cabinet of Mathematical Curiosities, presents a new and magical mix of games, puzzles, paradoxes, brainteasers, and riddles. He mingles these with forays into ancient and modern mathematical thought, appallingly hilarious mathematical jokes, and enquiries into the great mathematical challenges of the present and past. Amongst a host of arcane and astonishing facts about every kind of number from irrational or imaginary to complex or cuneiform, we find out: how to organise chaos; how matter balances anti-matter; how to turn a sphere inside out (without creasing it...); why you can't comb a hairy ball; how to calculate pi by observing the stars. And we get some tantalising glimpses of the maths of life and the universe.Mind-stretching, enlightening and endlessly amusing, Professor Stewart's new entertainment will stimulate, delight, and enthral.Trade ReviewPitched at the perfect difficulty level ... clearly and intelligently written ... Anyone with a slight geeky bent to them, whether they be adult or teenager, will find plenty to edify, tickle and tantalise them. It'd make a wonderful present ... I can't wait for the next volume. Highly recommended. * Bookbag *There are jokes, puns, hints on code-breaking and a dollop of the unexpected. You won't have learned any of this in school but if you have a mathematical bent and a logical mind you will soon be teasing out the answers. * Good Book Guide *An ideal present for anyone addicted to Sudoku-like puzzles and beginning to wonder what might lie beyond * Spectator *This is not pure maths. It is maths contaminated with whit, wisdom, and wonder. Ian really is unsurpassed as raconteur of the world of numbers. He guides us on a mind-boggling journey from the ultra trivial to the profound. -- Jeremy Webb * New Scientist *A perfect gift for a clever child * Daily Telegraph *As the professor darts randomly from 'digital cubes' to 'the hairy ball theorem' with boundless playful curiosity, even those with only a sluggish interest in maths will find something to amuse and amaze * Sunday Telegraph *
£8.99
MIT Press Fundamentals of Probability and Statistics for Machine Learning
a huge range and FREE tracked UK delivery on ALL orders.
£76.50
MIT Press The Price of Cake
Book Synopsis
£20.00
MIT Press Ltd Beautiful Math
Book SynopsisFrom the bestselling author of Quantum Computing for Everyone, a concise, accessible, and elegant approach to mathematics that not only illustrates concepts but also conveys the surprising nature of the digital information age.
£20.80
Cambridge University Press Inverse Problems and Data Assimilation
Book SynopsisThis concise introduction covers inverse problems and data assimilation, before exploring their inter-relations. Suitable for both classroom teaching and self-guided study, it is aimed at advanced undergraduates and beginning graduate students in mathematical sciences, together with researchers in science and engineering.Table of ContentsIntroduction; Part I. Inverse Problems: 1. Bayesian inverse problems and well-posedness; 2. The linear-Gaussian setting; 3. Optimization perspective; 4. Gaussian approximation; 5. Monte Carlo sampling and importance sampling; 6. Markov chain Monte Carlo; Exercises for Part I; Part II. Data Assimilation: 7. Filtering and smoothing problems and well-posedness; 8. The Kalman filter and smoother; 9. Optimization for filtering and smoothing: 3DVAR and 4DVAR; 10. The extended and ensemble Kalman filters; 11. Particle filter; 12. Optimal particle filter; Exercises for Part II; Part III. Kalman Inversion: 13. Blending inverse problems and data assimilation; References; Index.
£28.49
Pearson Education Limited Precalculus Global Edition
Book SynopsisMike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago's South Side and currently resides in Oak Lawn, Illinois. Mike has four children; the two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son, Mike Sullivan III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than 10 books. He owns a travel agency, and splits his time between a condo in Naples, Florida, and a home in Oak Lawn, where he enjoys gardening. Mike Sullivan III is Professor of Mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more tTable of Contents1. Graphs 1.1 The Distance and Midpoint Formulas 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 1.3 Lines 1.4 Circles Chapter 1 Review, Test, and Projects 2. Functions and Their Graphs 2.1 Functions 2.2 The Graph of a Function 2.3 Properties of Functions 2.4 Library of Functions; Piecewise-defined Functions 2.5 Graphing Techniques: Transformations 2.6 Mathematical Models: Building Functions Chapter 2 Review, Test, and Projects 3. Linear and Quadratic Functions 3.1 Properties of Linear Functions and Linear Models 3.2 Building Linear Models from Data 3.3 Quadratic Functions and Their Properties 3.4 Build Quadratic Models from Verbal Descriptions and from Data 3.5 Inequalities Involving Quadratic Functions Chapter 3 Review, Test, and Projects 4. Polynomial and Rational Functions 4.1 Polynomial Functions 4.2 Graphing Polynomial Functions; Models 4.3 Properties of Rational Functions 4.4 The Graph of a Rational Function 4.5 Polynomial and Rational Inequalities 4.6 The Real Zeros of a Polynomial Function Chapter 4 Review, Test, and Projects 5. Exponential and Logarithmic Functions 5.1 Composite Functions 5.2 One-to-One Functions; Inverse Functions 5.3 Exponential Functions 5.4 Logarithmic Functions 5.5 Properties of Logarithms 5.6 Logarithmic and Exponential Equations 5.7 Financial Models 5.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models 5.9 Building Exponential, Logarithmic, and Logistic Models from Data Chapter 5 Review, Test, and Projects 6. Trigonometric Functions 6.1 Angles, Arc, Length, and Circular Motion 6.2 Trigonometric Functions: Unit Circle Approach 6.3 Properties of the Trigonometric Functions 6.4 Graphs of the Sine and Cosine Functions 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 6.6 Phase Shift; Sinusoidal Curve Fitting Chapter 6 Review, Test, and Projects 7. Analytic Trigonometry 7.1 The Inverse Sine, Cosine, and Tangent Functions 7.2 The Inverse Trigonometric Functions (Continued) 7.3 Trigonometric Equations 7.4 Trigonometric Identities 7.5 Sum and Difference Formulas 7.6 Double-angle and Half-angle Formulas 7.7 Product-to-Sum and Sum-to-Product Formulas Chapter 7 Review, Test, and Projects 8. Applications of Trigonometric Functions 8.1 Right Triangle Trigonometry; Applications 8.2 The Law of Sines 8.3 The Law of Cosines 8.4 Area of a Triangle 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves Chapter 8 Review, Test, and Projects 9. Polar Coordinates; Vectors 9.1 Polar Coordinates 9.2 Polar Equations and Graphs 9.3 The Complex Plane; De Moivre's Theorem 9.4 Vectors 9.5 The Dot Product 9.6 Vectors in Space 9.7 The Cross Product Chapter 9 Review, Test, and Projects 10. Analytic Geometry 10.1 Conics 10.2 The Parabola 10.3 The Ellipse 10.4 The Hyperbola 10.5 Rotation of Axes; General Form of a Conic 10.6 Polar Equations of Conics 10.7 Plane Curves and Parametric Equations Chapter 10 Review, Test, and Projects 11. Systems of Equations and Inequalities 11.1 Systems of Linear Equations: Substitution and Elimination 11.2 Systems of Linear Equations: Matrices 11.3 Systems of Linear Equations: Determinants 11.4 Matrix Algebra 11.5 Partial Fraction Decomposition 11.6 Systems of Nonlinear Equations 11.7 Systems of Inequalities 11.8 Linear Programming Chapter 11 Review, Test, and Projects 12. Sequences; Induction; the Binomial Theorem 12.1 Sequences 12.2 Arithmetic Sequences 12.3 Geometric Sequences; Geometric Series 12.4 Mathematical Induction 12.5 The Binomial Theorem Chapter 12 Review, Test, and Projects 13. Counting and Probability 13.1 Counting 13.2 Permutations and Combinations 13.3 Probability Chapter 13 Review, Test, and Projects 14. A Preview of Calculus: The Limit, Derivative, and Integral of a Function 14.1 Finding Limits Using Tables and Graphs 14.2 Algebra Techniques for Finding Limits 14.3 One-sided Limits; Continuous Functions 14.4 The Tangent Problem; The Derivative 14.5 The Area Problem; The Integral Chapter 14 Review, Test, and Projects Appendix A: Review A.1 Algebra Essentials A.2 Geometry Essentials A.3 Polynomials A.4 Synthetic Division A.5 Rational Expressions A.6 Solving Equations A.7 Complex Numbers; Quadratic Equations in the Complex Number System A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications A.9 Interval Notation; Solving Inequalities A.10 nth Roots; Rational Exponents Appendix B: Graphing Utilities B.1 The Viewing Rectangle B.2 Using a Graphing Utility to Graph Equations B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry B.4 Using a Graphing Utility to Solve Equations B.5 Square Screens B.6 Using a Graphing Utility to Graph Inequalities B.7 Using a Graphing Utility to Solve Systems of Linear Equations B.8 Using a Graphing Utility to Graph a Polar Equation B.9 Using a Graphing Utility to Graph Parametric Equations Answers Credits Index
£61.74
Hodder Education STEP MAT TMUA Skills for success in University
Book SynopsisStand out, showcase your ability and succeed in your university admissions test. Whether you''re taking STEP, MAT or TMUA, this essential guide reveals tried-and-tested strategies for building the problem-solving skills you need to secure a high score.Containing expert advice and worked examples, followed by multiple-choice and extended questions that replicate the exams, this guide is designed to improve your understanding of the admissions tests and help to build the skills universities are looking for.- Learn to think like a university student - detailed guidance, thought-provoking questions and worked solutions show you how to advance your mathematical thinking- Improve your mathematical reasoning - practise the problem-solving skills you need with ''Try it out'' activities throughout the book and end-of-chapter exercises to track progress- Build a path through every problem - our authors guide you through each t
£31.92
Hodder Education OCR A Level Further Mathematics Core Year 2
Book SynopsisExam Board: OCRLevel: A-levelSubject: MathematicsFirst Teaching: September 2017First Exam: June 2018An OCR endorsed textbookGrow your students'' confidence in applying mathematical techniques to solving problems with resources developed specifically for the OCR specification subject experts and in conjunction with MEI (Mathematics in Education and Industry).- Develop reasoning and problem-solving skills with practice questions and differentiated exercises that build mathematical techniques.- Help students to overcome misconceptions and develop insight into problem-solving with annotated worked examples.- Build connections between topics with points of interest and things to notice such as links to real world examples and noticing patterns in the mathematics.- Enhance individual understanding with discussion points designed for the classroom.- Consolidate understanding with end of chapter summaries of the key points.
£999.99
Basic Books The Model Thinker: What You Need to Know to Make
Book SynopsisFrom the stock market to covid-19, census figures to marketing email blasts, we are awash with data. But as anyone who has ever opened up a spreadsheet packed with seemingly infinite lines of data knows, numbers aren't enough: we need to know how to make those numbers talk. In The Model Thinker, social scientist Scott E. Page shows us the mathematical, statistical, and computational models-from linear regression to random walks and far beyond-that can turn anyone into a genius. At the core of the book is Page's "many-model paradigm," which shows the reader how to apply multiple models to organize the data, leading to wiser choices, more accurate predictions, and more robust designs. Now culminating in an examination of how to use the multi-model approach to think about pandemics like covid-19, The Model Thinker provides a toolkit for business people, students, scientists, pollsters, and bloggers to make them better, clearer thinkers, able to leverage data and information to their advantage.
£15.29
Wolfram Media Inc Metamathematics: Foundations & Physicalization
Book Synopsis
£34.36
Harvard University Press Game Theory and the Law
Book SynopsisThis book promises to be the definitive guide to the field. It provides a highly sophisticated yet exceptionally clear explanation of game theory, with a host of applications to legal issues.Trade ReviewGame Theory and the Law promises to be the definitive guide to the field. It provides a highly sophisticated yet exceptionally clear explanation of game theory, with a host of applications to legal issues. The authors have not only synthesized the existing scholarship, but also created the foundation for the next generation of research in law and economics. -- Daniel A. Farber, University of Minnesota Law SchoolThe most comprehensive and encompassing treatment of this approach… [This] is the first nontechnical, modern introduction to how (noncooperative) game theory can be applied specifically to legal analysis… Game Theory and the Law is a user-friendly analysis of concrete, numerical examples, rather than a theoretical presentation of abstract concepts. The authors introduce and explain, with actual legal cases or hypotheticals, the salient issues of modern game theory. This breadth of coverage is remarkable. This is not just a textbook; it is also something of a research monograph, introducing many new models attributable to the authors alone. -- Peter H. Huang * Jurimetrics Journal *Game Theory and the Law is an important book. It is important in the sense that it will serve as a catalyst for an expanded use of game-theoretic models in the study of law. It will be a book that people will one day recognize as having had a considerable influence on its field. And it will receive the praise that accompanies such influence. Happily, such influence will be beneficial to the field of law and such praise will be richly deserved, because Game Theory and the Law is an extremely intelligent and thoughtful text… One of the features of the book that is most striking (and, for my part, most welcome) is the thoughtful and sensible manner in which they approach the use of game theory. Unlike many proponents of game-theoretic analysis, they do not present it as the only legitimate approach to social-scientific analysis. The authors present game theory as a powerful tool that can be used along with other approaches to enhance our understanding of the role of law in social life… The persuasiveness of their general argument for the utility of game theory derives from a combination of the power of their insights along with the sensibility of their analysis. The book is written in a clear, concise and interesting manner. Its bibliographic references render it a source book for additional research in both game theory and law. This is a book that should be read by scholars of law in particular and scholars of political behavior in particular. -- Jack Knight * Law and Politics Book Review *Table of ContentsPreface Introduction: Understanding Strategic Behavior Bibliographic Notes Simultaneous Decisionmaking and the Normal Form Game The Normal Form Game Using Different Games to Compare Legal Regimes The Nash Equilibrium Civil Liability, Accident Law, and Strategic Behavior Legal Rules and the Idea of Strict Dominance Collective Action Problems and the Two-by-Two Game The Problem of Multiple Nash Equilibria Summary Bibliographic Notes Dynamic Interaction and the Extensive Form Game The Extensive Form Game and Backwards Induction A Dynamic Model of Preemption and Strategic Commitment Subgame Perfection Summary Bibliographic Notes Information Revelation, Disclosure Laws, and Renegotiation Incorporating Beliefs into the Solution Concept The Perfect Bayesian Equilibrium Solution Concept Verifiable Information, Voluntary Disclosure, and the Unraveling Result Disclosure Laws and the Limits of Unraveling Observable Information, Norms, and the Problem of Renegotiation Optimal Incentives and the Need for Renegotiation Limiting the Ability of Parties to Renegotiate Summary Bibliographic Notes Signaling, Screening, and Nonverifiable Information Signaling and Screening Modeling Nonverifiable Information Signals and the Effects of Legal Rules Information Revelation and Contract Default Rules Screening and the Role of Legal Rules Summary Bibliographic Notes Reputation and Repeated Games Backwards Induction and Its Limits Infinitely Repeated Games, Tacit Collusion, and Folk Theorems Reputation, Predation, and Cooperation Summary Bibliographic Notes Collective Action, Embedded Games, and the Limits of Simple Models Collective Action and the Role of Law Embedded Games Understanding the Structure of Large Games Collective Action and Private Information Collective Action Problems in Sequential Decisionmaking Herd Behavior Summary Bibliographic Notes Noncooperative Bargaining Modeling the Division of Gains from Trade Legal Rules as Exit Options Bargaining and Corporate Reorganizations Collective Bargaining and Exit Options Summary Bibliographic Notes Bargaining and Information Basic Models of the Litigation Process Modeling Separate Trials for Liability and Damages Information and Selection Bias Discovery Rules and Verifiable Information Summary Bibliographic Notes Conclusion: Information and the Limits of Law Notes References Glossary Index
£34.81
Princeton University Press Real Analysis
Book SynopsisIntended for the students interested in the disciplines of mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels, this third volume in a series of titles focuses on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals.Trade Review"We are all fortunate that a mathematician with the experience and vision of E.M. Stein, together with his energetic young collaborator R. Shakarchi, has given us this series of four books on analysis."--Steven George Krantz, Mathematical Reviews "This series is a result of a radical rethinking of how to introduce graduate students to analysis... This volume lives up to the high standard set up by the previous ones."--Fernando Q. Gouvea, MAA Review "As one would expect from these authors, the exposition is, in general, excellent. The explanations are clear and concise with many well-focused examples as well as an abundance of exercises, covering the full range of difficulty... [I]t certainly must be on the instructor's bookshelf as a first-rate reference book."--William P. Ziemer, SIAM ReviewTable of ContentsForeword vii Introduction xv 1Fourier series: completion xvi Limits of continuous functions xvi 3Length of curves xvii 4Differentiation and integration xviii 5The problem of measure xviii Chapter 1. Measure Theory 1 1Preliminaries 1 The exterior measure 10 3Measurable sets and the Lebesgue measure 16 4Measurable functions 7 4.1 Definition and basic properties 27 4.Approximation by simple functions or step functions 30 4.3 Littlewood's three principles 33 5* The Brunn-Minkowski inequality 34 6Exercises 37 7Problems 46 Chapter 2: Integration Theory 49 1The Lebesgue integral: basic properties and convergence theorems 49 2Thespace L 1 of integrable functions 68 3Fubini's theorem 75 3.1 Statement and proof of the theorem 75 3.Applications of Fubini's theorem 80 4* A Fourier inversion formula 86 5Exercises 89 6Problems 95 Chapter 3: Differentiation and Integration 98 1Differentiation of the integral 99 1.1 The Hardy-Littlewood maximal function 100 1.The Lebesgue differentiation theorem 104 Good kernels and approximations to the identity 108 3Differentiability of functions 114 3.1 Functions of bounded variation 115 3.Absolutely continuous functions 127 3.3 Differentiability of jump functions 131 4Rectifiable curves and the isoperimetric inequality 134 4.1* Minkowski content of a curve 136 4.2* Isoperimetric inequality 143 5Exercises 145 6Problems 152 Chapter 4: Hilbert Spaces: An Introduction 156 1The Hilbert space L 2 156 Hilbert spaces 161 2.1 Orthogonality 164 2.2 Unitary mappings 168 2.3 Pre-Hilbert spaces 169 3Fourier series and Fatou's theorem 170 3.1 Fatou's theorem 173 4Closed subspaces and orthogonal projections 174 5Linear transformations 180 5.1 Linear functionals and the Riesz representation theorem 181 5.Adjoints 183 5.3 Examples 185 6Compact operators 188 7Exercises 193 8Problems 202 Chapter 5: Hilbert Spaces: Several Examples 207 1The Fourier transform on L 2 207 The Hardy space of the upper half-plane 13 3Constant coefficient partial differential equations 221 3.1 Weaksolutions 222 3.The main theorem and key estimate 224 4* The Dirichlet principle 9 4.1 Harmonic functions 234 4.The boundary value problem and Dirichlet's principle 43 5Exercises 253 6Problems 259 Chapter 6: Abstract Measure and Integration Theory 262 1Abstract measure spaces 263 1.1 Exterior measures and Caratheodory's theorem 264 1.Metric exterior measures 266 1.3 The extension theorem 270 Integration on a measure space 273 3Examples 276 3.1 Product measures and a general Fubini theorem 76 3.Integration formula for polar coordinates 279 3.3 Borel measures on R and the Lebesgue-Stieltjes integral 281 4Absolute continuity of measures 285 4.1 Signed measures 285 4.Absolute continuity 288 5* Ergodic theorems 292 5.1 Mean ergodic theorem 294 5.Maximal ergodic theorem 296 5.3 Pointwise ergodic theorem 300 5.4 Ergodic measure-preserving transformations 302 6* Appendix: the spectral theorem 306 6.1 Statement of the theorem 306 6.Positive operators 307 6.3 Proof of the theorem 309 6.4 Spectrum 311 7Exercises 312 8Problems 319 Chapter 7: Hausdorff Measure and Fractals 323 1Hausdorff measure 324 Hausdorff dimension 329 2.1 Examples 330 2.Self-similarity 341 3Space-filling curves 349 3.1 Quartic intervals and dyadic squares 351 3.Dyadic correspondence 353 3.3 Construction of the Peano mapping 355 4* Besicovitch sets and regularity 360 4.1 The Radon transform 363 4.Regularity of sets when d 3 370 4.3 Besicovitch sets have dimension 371 4.4 Construction of a Besicovitch set 374 5Exercises 380 6Problems 385 Notes and References 389 Bibliography 391 Symbol Glossary 395 Index 397
£74.80
Princeton University Press Sacred Mathematics
Book SynopsisPresents excerpts from the travel diary of a Japanese mathematician, Yamaguchi Kanzan, who journeyed on foot throughout Japan to collect temple geometry problems. This book explains the sacred and devotional aspects of sangaku, and reveals how Japanese folk mathematicians discovered many theorems independently of mathematicians in the West.Trade ReviewWinner of the 2008 PROSE Award in Mathematics, Association of American Publishers "Now Fukagawa Hidetoshi, a mathematics teacher, and writer Tony Rothman present a collection of Sangaku problems in their book, Sacred Mathematics. The puzzles range from simple algebra within the grasp of any intermediate-school student, to challenging problems that require graduate-school mathematics to solve. Copious illustrations and many detailed solutions show the scope, complexity, and beauty of what was tackled in Japan during the Tokugawa shogunate."--Peter J. Lu, Nature "Fascinating and beautiful book."--Physics World "This book is the most thorough (and beautiful) account of Japanese temple geometry (sangaku) available."--Paul J. Campbell, Mathematics Magazine "The difficult problems with complete solutions and rich commentary that comprise the heart of this book will interest every mathematics student."--Choice "This is a marvelous book. Good books are not just written or compiled, they are crafted. Sacred Mathematics is a well crafted work that combines mathematics, history and cultural considerations into an intriguing narrative... The writing style is appealing and the organization of material excellent. Princeton University Press must be congratulated on producing this quality publication and offering it at an agreeable price. This book is highly recommended for personal reading and library acquisition. It should be especially appealing to problem solvers."--Frank J. Swetz, Convergence "A unique book in every respect. Sacred Mathematics demonstrates how mathematical thinking can vary by culture yet transcend cultural and geographic boundaries."--International Institute for Asian Studies NewsletterTable of ContentsForeword by Freeman Dyson ix Preface by Fukagawa Hidetoshi xiii Preface by Tony Rothman xv Acknowledg ments xix What Do I Need to Know to Read This Book? xxi Notation xxv Chapter 1: Japan and Temple Geometry 1 Chapter 2: The Chinese Foundation of Japanese Mathematics 27 Chapter 3: Japa nese Mathematics and Mathematicians of the Edo Period 59 Chapter 4: Easier Temple Geometry Problems 89 Chapter 5: Harder Temple Geometry Problems 145 Chapter 6: Still Harder Temple Geometry Problems 191 Chapter 7: The Travel Diary of Mathematician Yamaguchi Kanzan 243 Chapter 8: East and West 283 Chapter 9: The Mysterious Enri 301 Chapter 10: Introduction to Inversion 313 For Further Reading 337 Index 341
£49.30
Princeton University Press Theory of Games and Economic Behavior
Book SynopsisPublished in 1944, "Theory of Games and Economic Behavior" featured a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. This title includes the original text, an introduction by Harold Kuhn, and reviews and articles on the book that appeared at the time of its original publication.Trade ReviewPraise for Princeton's previous edition: "A rich and multifaceted work... [S]ixty years later, the Theory of Games may indeed be viewed as one of the landmarks of twentieth-century social science."--Robert J. Leonard, History of Political Economics Praise for Princeton's previous edition: "Opinions still vary on the success of the project to put economics on a sound mathematical footing, but game theory was eventually hugely influential, especially on mathematics and the study of automata. Every self-respecting library must have one."--Mike Holderness, New Scientist "While the jury is still out on the success or failure of game theory as an attempted palace coup within the economics community, few would deny that interest in the subject--as measured in numbers of journal page--is at or near an all-time high. For that reason alone, this handsome new edition of von Neumann and Morgenstern's still controversial classic should be welcomed by the entire research community."--James Case, SIAM News "The main achievement of the book lies, more than in its concrete results, in its having introduced into economics the tools of modern logic and in using them with an astounding power of generalization."--The Journal of Political Economy "One cannot but admire the audacity of vision, the perseverance in details, and the depth of thought displayed in almost every page of the book... The appearance of a book of [this] calibre ... is indeed a rare event."--The American Economic Review "Posterity may regard this book as one of the major scientific achievements of the first half of the twentieth century. This will undoubtedly be the case if the authors have succeeded in establishing a new exact science--the science of economics. The foundation which they have laid is extremely promising."--The Bulletin of the American Mathematical SocietyTable of ContentsPREFACE v TECHNICAL NOTE v ACKNOWLEDGMENT x CHAPTER I: FORMULATION OF THE ECONOMIC PROBLEM 1.THE MATHEMATICAL METHOD IN ECONOMICS 1 1.1. Introductory remarks 1 1.2. Difficulties of the application of the mathematical method 2 1.3. Necessary limitations of the objectives 6 1.4. Concluding remarks 7 2.QUALITATIVE DISCUSSION OF THE PROBLEM OF RATIONAL BEHAVIOR 8 2.1. The problem of rational behavior 8 2.2. "Robinson Crusoe" economy and social exchange economy 9 2.3. The number of variables and the number of participants 12 2.4. The case of many participants: Free competition 13 2.5. The "Lausanne" theory 15 3.THE NOTION OF UTILITY 15 3.1. Preferences and utilities 15 3.2. Principles of measurement: Preliminaries 16 3.3. Probability and numerical utilities 17 3.4. Principles of measurement: Detailed discussion 20 3.5. Conceptual structure of the axiomatic treatment of numerical utilities 24 3.6. The axioms and their interpretation 26 3.7. General remarks concerning the axioms 28 3.8. The role of the concept of marginal utility 29 4.STRUCTURE OF THE THEORY: SOLUTIONS AND STANDARDS OF BEHAVIOR 31 4.1. The simplest concept of a solution for one participant 31 4.2. Extension to all participants 33 4.3. The solution as a set of imputations 34 4.4. The intransitive notion of "superiority" or "domination" 37 4.5. The precise definition of a solution 39 4.6. Interpretation of our definition in terms of "standards of behavior" 40 4.7. Games and social organizations 43 4.8. Concluding remarks 43 CHAPTER II: GENERAL FORMAL DESCRIPTION OF GAMES OF STRATEGY 5.Introduction 46 5.1. Shift of emphasis from economics to games 46 5.2. General principles of classification and of procedure 46 6.THE SIMPLIFIED CONCEPT OF A GAME 48 6.1. Explanation of the termini technici 48 6.2. The elements of the game 49 6.3. Information and preliminary 51 6.4. Preliminarity, transitivity, and signaling 51 7.THE COMPLETE CONCEPT OF A GAME 55 7.1. Variability of the characteristics of each move 55 7.2. The general description 57 8.SETS AND PARTITIONS 60 8.1. Desirability of a set-theoretical description of a game 60 8.2. Sets, their properties, and their graphical representation 61 8.3. Partitions, their properties, and their graphical representation 63 8.4. Logistic interpretation of sets and partitions 66 *9. THE SET-THEORETICAL DESCRIPTION OF A CAME 67 *9.1. The partitions which describe a game 67 *9.2. Discussion of these partitions and their properties 71 *10. AXIOMATIC FORMULATION 73 *10.1. The axioms and their interpretations 73 *10.2. Logistic discussion of the axioms 76 *10.3. General remarks concerning the axioms 76 *10.4. Graphical representation 77 11.STRATEGIES AND THE FINAL SIMPLIFICATION OF THE DESCRIPTION OF THE GAME 79 11.1. The concept of a strategy and its formalization 79 11.2. The final simplification of the description of a game 81 11.3. The role of strategies in the simplified form of a game 84 11.4. The meaning of the zero-sum restriction 84 CHAPTER III: ZERO-SUM TWO-PERSON GAMES: THEORY 12.PRELIMINARY SURVEY 85 12.1. General viewpoints 85 12.2. The one-person game 85 12.3. Chance afid probability 87 12.4. The next objective 87 13.FUNCTIONAL CALCULUS 88 13.1. Basic definitions 88 13.2. The operations Max and Min 89 13.3. Commutativity questions 91 13.4. The mixed case. Saddle points 93 13.5. Proofs of the main facts 95 14.STRICTLY DETERMINED GAMES 98 141. Formulation of the problem 98 14.2. The minorant and the majorant games 100 14.3. Discussion of the auxiliary games 101 14.4. Conclusions 105 14.5. Analysis of strict determinateness 106 14.6. The interchange of players. Symmetry 109 14.7. Non strictly determined games 110 14.8. Program of a detailed analysis of strict determinateness 111 *15. GAMES WITH PERFECT INFORMATION *15.1. Statement of purpose. Induction 112 *15.2. The exact condition (First step) 114 *15.3. The exact condition (Entire induction) 116 *15.4. Exact discussion of the inductive step 117 *15.5. Exact discussion of the inductive step (Continuation) 120 *15.6. The result in the case of perfect information 123 *15.7. Application to Chess 124 *15.8. The alternative, verbal discussion 126 16.LINEARITY AND CONVEXITY 128 16.1. Geometrical background 128 16.2. Vector operations 129 16.3. The theorem of the supporting hyperplanes 134 16.4. The theorem of the alternative for matrices 138 17.MIXED STRATEGIES. THE SOLUTION FOR ALL GAMES 143 17.1. Discussion of two elementary examples 143 17.2. Generalization of this viewpoint 145 17.3. Justification of the procedure as applied to an individual play 146 17.4. The minorant and the majorant games. (For mixed strategies) 149 17.5. General strict determinateness 150 17.6. Proof of the main theorem 153 17.7. Comparison of the treatment by pure and by mixed strategies 155 17.8. Analysis of general strict determinateness 158 17.9. Further characteristics of good strategies 160 17.10. Mistakes and their consequences. Permanent optimality 162 17.11. The interchange of players. Symmetry 165 CHAPTER IV: ZERO-SUM TWO-PERSON GAMES: EXAMPLES 18.SOME ELEMENTARY GAMES 169 18.1. The simplest games 169 18.2. Detailed quantitative discussion of these games 170 18.3. Qualitative characterizations 173 18.4. Discussion of some specific games. (Generalized forms of Matching Pennies) 175 18.5. Discussion of some slightly more complicated games 178 18.6. Chance and imperfect information 182 18.7. Interpretation of this result 185 *19. POKER AND BLUFFING 186 *19.1. Description of Poker 186 *19.2. Bluffing 188 *19.3. Description of Poker (Continued) 189 *19.4. Exact formulation of the rules 190 *19.5. Description of the strategy 191 *19.6. Statement of the problem 195 *19.7. Passage from the discrete to the continuous problem 196 *19.8. Mathematical determination of the solution 199 *19.9. Detailed analysis of the solution 202 *19.10. Interpretation of the solution 204 *19.11. More general forms of Poker 207 *19.12. Discrete hands 208 *19.13. m possible bids 209 *19.14. Alternate bidding 211 *19.15. Mathematical description of all solutions 216 *19.16. Interpretation of the solutions. Conclusions 218 CHAPTER V: ZERO-SUM THREE-PERSON GAMES 20.PRELIMINARY SURVEY 220 20.1. General viewpoints 220 20.2. Coalitions 221 21.THE SIMPLE MAJORITY GAME OF THREE PERSONS 222 21.1. Definition of the game 222 21.2. Analysis of the game: Necessity of "understandings" 223 21.3. Analysis of the game: Coalitions. The role of symmetry 224 22.FURTHER EXAMPLES 225 22.1. Unsymmetric distributions. Necessity of compensations 225 22.2. Coalitions of different strength. Discussion 227 22.3. An inequality. Formulae 229 23.THE GENERAL CASE 231 23.1. Detailed discussion. Inessential and essential games 231 23.2. Complete formulae 232 24.DISCUSSION OF AN OBJECTION 233 24.1. The case of perfect information and its significance 233 24.2. Detailed discussion. Necessity of compensations between three or more players 235 CHAPTER VI: FORMULATION OF THE GENERAL THEORY: ZERO-SUM n-PERSON GAMES 25.THE CHARACTERISTIC FUNCTION 238 25.1. Motivation and definition 238 25.2. Discussion of the concept 240 25.3. Fundamental properties 241 25.4. Immediate mathematical consequences 242 26.CONSTRUCTION OF A GAME WITH A GIVEN CHARACTERISTIC FUNCTION 243 26.1. The construction 243 26.2. Summary 245 27.STRATEGIC EQUIVALENCE. INESSENTIAL AND ESSENTIAL GAMES 245 27.1. Strategic equivalence. The reduced form 245 27.2. Inequalities. The quantity [gamma] 248 27.3. Inessentiality and essentiality 249 27.4. Various criteria. Non additive utilities 250 27.5. The inequalities in the essential case 252 27.6. Vector operations on characteristic functions 253 28.GROUPS, SYMMETRY AND FAIRNESS 255 28.1. Permutations, their groups and their effect on a game 255 28.2. Symmetry and fairness 258 29.RECONSIDERATION OF THE ZERO-SUM THREE-PERSON GAME 260 29.1. Qualitative discussion 260 29.2. Quantitative discussion 262 30.THE EXACT FORM OF THE GENERAL DEFINITIONS 263 30.1. The definitions 263 30.2. Discussion and recapitulation 265 *30.3. The concept of saturation 266 30.4. Three immediate objectives 271 31.FIRST CONSEQUENCES 272 31.1. Convexity, flatness, and some criteria for domination 272 31.2. The system of all imputations. One element solutions 277 31.3. The isomorphism which corresponds to strategic equivalence 281 32.DETERMINATION OF ALL SOLUTIONS OF THE ESSENTIAL ZERO-SUM THREE-PERSON GAME 282 32.1. Formulation of the mathematical problem. The graphical method 282 32.2. Determination of all solutions 285 33.CONCLUSIONS 288 33.1. The multiplicity of solutions. Discrimination and its meaning 288 33.2. Statics and dynamics 290 CHAPTER VII: ZERO-SUM FOUR-PERSON GAMES 34.PRELIMINARY SURVEY 291 34.1. General viewpoints 291 34.2. Formalism of the essential zero sum four person games 291 34.3. Permutations of the players 294 35.DISCUSSION OF SOME SPECIAL POINTS IN THE CUBE Q 295 35.1. The corner I. (and V., VI., VII.) 295 35.2. The corner VIII. (and II., III., IV.,). The three person game and a "Dummy" 299 35.3. Some remarks concerning the interior of Q 302 36.DISCUSSION OF THE MAIN DIAGONALS 304 36.1. The part adjacent to the corner VIII.: Heuristic discussion 304 36.2. The part adjacent to the corner VIII.: Exact discussion 307 *36.3. Other parts of the main diagonals 312 37.THE CENTER AND ITS ENVIRONS 313 37.1. First orientation about the conditions around the center 313 37.2. The two alternatives and the role of symmetry 315 37.3. The first alternative at the center 316 37.4. The second alternative at the center 317 37.5. Comparison of the two central solutions 318 37.6. Unsymmetrical central solutions 319 *38. A FAMILY OF SOLUTIONS FOR A NEIGHBORHOOD OF THE CENTER 321 *38.1. Transformation of the solution belonging to the first alternative at the center 321 *38.2. Exact discussion 322 *38.3. Interpretation of the solutions 327 CHAPTER VIII: SOME REMARKS CONCERNING n [equal to or greater than] 5 PARTICIPANTS 39.THE NUMBER OF PARAMETERS IN VARIOUS CLASSES OF GAMES 330 39.1. The situation for n = 3, 4 330 39.2. The situation for all n [equal to or greater than] 3 330 40.THE SYMMETRIC FIVE PERSON GAME 332 40.1. Formalism of the symmetric five person game 332 40.2. The two extreme cases 332 40.3. Connection between the symmetric five person game and the 1, 2, 3 symmetric four person game 334 CHAPTER IX: COMPOSITION AND DECOMPOSITION OF GAMES 41.COMPOSITION AND DECOMPOSITION 339 41.1. Search for n-person games for which all solutions can be determined 339 41.2. The first type. Composition and decomposition 340 41.3. Exact definitions 341 41.4. Analysis of decomposability 343 41.5. Desirability of a modification 345 42.MODIFICATION OF THE THEORY 345 42.1. No complete abandonment of the zero sum restriction 345 42.2. Strategic equivalence. Constant sum games 346 42.3. The characteristic function in the new theory 348 42.4. Imputations, domination, solutions in the new theory 350 42.5. Essentiality, inessentiality and decomposability in the new theory 351 43.THE DECOMPOSITION PARTITION 353 43.1. Splitting sets. Constituents 353 43.2. Properties of the system of all splitting sets 353 43.3. Characterization of the system of all splitting sets. The decomposition partition 354 43.4. Properties of the decomposition partition 357 44.DECOMPOSABLE GAMES. FURTHER EXTENSION OF THE THEORY 358 44.1. Solutions of a (decomposable) game and solutions of its constituents 358 44.2. Composition and decomposition of imputations and of sets of imputations 359 44.3. Composition and decomposition of solutions. The main possibilities and surmises 361 44.4. Extension of the theory. Outside sources 363 44.5. The excess 364 44.6. Limitations of the excess. The non-isolated character of a game in the new setup 366 44.7. Discussion of the new setup. E(e0), F(e0) 367 45.LIMITATIONS OF THE EXCESS. STRUCTURE OF THE EXTENDED THEORY 378 45.1. The lower limit of the excess 368 45.2. The upper limit of the excess. Detached and fully detached imputations 369 45.3. Discussion of the two limits, |[Gamma]|1, |[Gamma]|2. Their ratio 372 45.4. Detached imputations and various solutions. The theorem connecting E(e0), F(e0) 375 45.5. Proof of the theorem 376 45.6. Summary and conclusions 380 46.DETERMINATION OF ALL SOLUTIONS OF A DECOMPOSABLE GAME 381 46.1. Elementary properties of decompositions 381 46.2. Decomposition and its relation to the solutions: First results concerning F(e0) 384 46.3. Continuation 386 46.4. Continuation 388 46.5. The complete result in F(e0) 390 46.6. The complete result in E(e0) 393 46.7. Graphical representation of a part of the result 394 46.8. Interpretation: The normal zone. Heredity of various properties 396 46.9. Dummies 397 46.10. Imbedding of a game 398 46.11. Significance of the normal zone 401 46.12. First occurrence of the phenomenon of transfer: n = 6 402 47.THE ESSENTIAL THREE-PERSON GAME IN THE NEW THEORY 403 47.1. Need for this discussion 403 47.2. Preparatory considerations 403 47.3. The six cases of the discussion. Cases (I)-(III) 406 47.4. Case (IV): First part 407 47.5. Case (IV): Second part 409 47.6. Case (V) 413 47.7. Case (VI) 415 47.8. Interpretation of the result: The curves (one dimensional parts) in the solution 416 47.9. Continuation: The areas (two dimensional parts) in the solution 418 CHAPTER X: SIMPLE GAMES 48.WINNING AND LOSING COALITIONS AND GAMES WHERE THEY OCCUR 420 48.1. The second type of 41.1. Decision by coalitions 420 48.2. Winning and Losing Coalitions 421 49.CHARACTERIZATION OF THE SIMPLE GAMES 423 49.1. General concepts of winning and losing coalitions 423 49.2. The special role of one element sets 425 49.3. Characterization of the systems W, L of actual games 426 49.4. Exact definition of simplicity 428 49.5. Some elementary properties of simplicity 428 49.6. Simple games and their W, L. The Minimal winning coalitions: Wm 429 49.7. The solutions of simple games 430 50.THE MAJORITY GAMES AND THE MAIN SOLUTION 431 50.1. Examples of simple games: The majority games 481 50.2. Homogeneity 433 50.3. A more direct use of the concept of imputation in forming solutions 435 50.4. Discussion of this direct approach 436 50.5. Connections with the general theory. Exact formulation 438 50.6. Reformulation of the result 440 50.7. Interpretation of the result 442 50.8. Connection with the Homogeneous Majority game 443 51.METHODS FOR THE ENUMERATION OF ALL SIMPLE GAMES 445 51.1. Preliminary Remarks 445 51.2. The saturation method: Enumeration by means of W 446 51.3. Reasons for passing from W to Wm. Difficulties of using Wm 448 51.4. Changed Approach: Enumeration by means of Wm 450 51.5. Simplicity and decomposition 452 51.6. Inessentiality, Simplicity and Composition. Treatment of the excess 454 51.7. A criterium of decomposability in terms of Wm 455 52.THE SIMPLE GAMES FOR SMALL n 457 52.1. Program. n = 1, 2 play no role. Disposal of n = 3 457 52.2. Procedure for n [equal to or greater than] 4: The two element sets and their role in classify ing the Wm 458 52.3. Decomposability of cases C*, Cn-2, Cn-1 459 52.4. The simple games other than [1, ... , 1, n - 2]h, (with dummies): The Cases Ck, k = 0, 1, ... , n - 3 461 52.5. Disposal of n = 4, 5 462 53.THE NEW POSSIBILITIES OF SIMPLE GAMES FOR n [equal to or greater than] 6 463 53.1. The Regularities observed for n [equal to or greater than] 6 463 53.2. The six main counter examples (for n = 6, 7) 464 54.DETERMINATION OF ALL SOLUTIONS IN SUITABLE GAMES 470 54.1. Reasons to consider other solutions than the main solution in simple games 470 54.2. Enumeration of those games for which all solutions are known 471 54.3. Reasons to consider the simple game [1, ... , 1, n - 2]h, 472 *55. THE SIMPLE GAME [1, ... , 1, n - 2]h 473 *55.1. Preliminary Remarks 473 *55.2. Domination. The chief player. Cases (I) and (11) 473 *55.3. Disposal of Case (I) 475 *55.4. Case (II): Determination of V [above horizontal bar] 478 *55.5. Case (II): Determination of V [below horizontal bar] 481 *55.6. Case (II): [alpha] and S* 484 *55.7. Case (II') and (II"). Disposal of Case (II') 485 *55.8. Case (II"): [alpha] and V'. Domination 488 *55.9. Case (II"): Determination of V' *55.10. Disposal of Case (II") 488 *55.11. Reformulation of the complete result 497 *55.12. Interpretation of the result 499 CHAPTER XI: GENERAL NON-ZERO-SUM GAMES 56.EXTENSION OF THE THEORY 504 56.1. Formulation of the problem 504 56.2. The fictitious player. The zero sum extension [Gamma] 505 56.3. Questions concerning the character of [Gamma below horizontal bar] 506 56.4. Limitations of the use of [Gamma above horizontal bar] 508 56.5. The two possible procedures 510 56.6. The discriminatory solutions 511 56.7. Alternative possibilities 512 56.8. The new setup 514 56.9. Reconsideration of the case when [Gamma] is a zero sum game 516 56.10. Analysis of the concept of domination 520 56.11. Rigorous discussion 523 56.12. The new definition of a solution 526 57.THE CHARACTERISTIC FUNCTION AND RELATED TOPICS 527 57.1. The characteristic function: The extended and the restricted form 527 57.2. Fundamental properties 528 57.3. Determination of all characteristic functions 530 57.4. Removable sets of players 533 57.5. Strategic equivalence. Zero-sum and constant-sum games 535 58.INTERPRETATION OF THE CHARACTERISTIC FUNCTION 538 58.1. Analysis of the definition 538 58.2. The desire to make a gain vs. that to inflict a loss 539 58.3. Discussion 541 59.GENERAL CONSIDERATIONS 542 59.1. Discussion of the program 542 59.2. The reduced forms. The inequalities 543 59.3. Various topics 546 60.THE SOLUTIONS OF ALL GENERAL GAMES WITH n [equal to or less than] 3 548 60.1. The case n = 1 548 60.2. The case n = 2 549 60.3. The case n = 3 550 60.4. Comparison with the zero sum games 554 61.ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 1, 2 555 61.1. The case n = 1 555 61.2. The case n = 2. The two person market 555 61.3. Discussion of the two person market and its characteristic function 557 61.4. Justification of the standpoint of 58 559 61.5. Divisible goods. The "marginal pairs" 560 61.6. The price. Discussion 562 62.ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 3: SPECIAL CASE 564 62.1. The case n = 3, special case. The three person market 564 62.2. Preliminary discussion 566 62.3. The solutions: First subcase 566 62.4. The solutions: General form 569 62.5. Algebraical form of the result 570 62.6. Discussion 571 63.ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 3: GENERAL CASE 573 63.1. Divisible goods 573 63.2. Analysis of the inequalities 575 63.3. Preliminary discussion 577 63.4. The solutions 577 63.5. Algebraical form of the result 580 63.6. Discussion 581 64.THE GENERAL MARKET 583 64.1. Formulation of the problem 583 64.2. Some special properties. Monopoly and monopsony 584 CHAPTER XII: EXTENSION OF THE CONCEPTS OF DOMINATION AND SOLUTION 65.THE EXTENSION. SPECIAL CASES 587 65.1. Formulation of the problem 587 65.2. General remarks 588 65.3. Orderings, transitivity, acyclicity 589 65.4. The solutions: For a symmetric relation. For a complete ordering 591 65.5. The solutions: For a partial ordering 592 65.6. Acyclicity and strict acyclicity 594 65.7. The solutions: For an acyclic relation 597 65.8. Uniqueness of solutions, acyclicity and strict acyclicity 600 65.9. Application to games: Discreteness and continuity 602 66.GENERALIZATION OF THE CONCEPT OF UTILITY 603 66.1. The generalization. The two phases of the theoretical treatment 603 66.2. Discussion of the first phase 604 66.3. Discussion of the second phase 606 66.4. Desirability of unifying the two phases 607 67.DISCUSSION OF AN EXAMPLE 608 67.1. Description of the example 608 67.2. The solution and its interpretation 611 67.3. Generalization: Different discrete utility scales 614 67.4. Conclusions concerning bargaining 616 APPENDIX: THE AXIOMATIC TREATMENT OF UTILITY 617 INDEX OF FIGURES 633 INDEX OF NAMES 634 INDEX OF SUBJECTS 635
£51.00
Princeton University Press Prime Suspects
Book SynopsisThis outrageous graphic novel investigates key concepts in mathematics by taking readers on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics within a thrilling murder mystery.Trade Review"Prime Suspects will appeal to a variety of readers in a variety of venues . . . . For the mathematician who eats, sleeps, and drinks numbers, start on page one and just enjoy the story . . . the book is fun, and interesting, and a challenge on many levels."---Judith Reveal, New York Journal of Books"Prime Suspects blends together the worlds of mathematics and forensic science to give readers both an interesting mystery and an education in numbers."---Anelise Farris, Rogues Portal"A total one-off."---Matthew Reisz, Times Educational Supplement"This is really a great book with so many references to mathematical ideas, that you can read and reread and find every time new details hidden in the graphics."---Adhemar Bultheel, European Mathematical Society"What a spectacular book! I am rather blown away by it."---Jonathan Shock, MathemAfrica"Granville and Granville have performed something of a feat. They've written a graphic detective novel that is both interesting to read and yet simultaneously teaches its readers some deep mathematics . . . . It's very difficult to write a book on an advanced topic in mathematics that's accessible to math students and enthusiasts yet touches on contemporary research that is of interest to a broad swath of practicing mathematicians. Prime Suspects is such a book. And it's entertaining to boot. I recommend it in the strongest terms."---Benjamin Linowitz, MAA Reviews"Bringing in elements from film noir, TV police shows and famous movies, coupled with some amazing art work, subtlemathematical humour and corny science jokes, and what you have is a one-of-a-kind creation – indeed, Prime Suspects has it all from minus to plus infinity."---David Appell, Physics World"Renowned number-theorist Andrew Granville here explores the graphic novel as a format to popularize mathematical discoveries. This absolutely brilliantly illustrated book arose from an earlier play and an accompanying commissioned musical piece. The mathematics too is astonishing—but explained understandably." * Mathematics Magazine *"If you are a mathematician, I definitely recommend reading (and listening to) Prime Suspects. If you are not a mathematician, you might miss a number of references, and some passages might be too mysterious or technical, but still it makes for interesting reading; it might be good for you, too."---Marco Abate, The Mathematical Intelligencer"The artwork and presentation are both well up to the standard of a mainstream graphic novel."---Andrew Ruddle, Mathematics Today"Prime Suspects is a work of art which anyone with a passion for maths will appreciate and enjoy."---Lennie Wells, Mathematical Gazette"I definitely recommend."---Marco Abate, Mathematical Intelligencer
£23.40
Princeton University Press A Cooperative Species
Book SynopsisWhy do humans, uniquely among animals, cooperate in large numbers to advance projects for the common good? Contrary to the conventional wisdom in biology and economics, this generous and civic-minded behavior is widespread and cannot be explained simply by far-sighted self-interest or a desire to help close genealogical kin. In A Cooperative SpecieTrade Review"The achievement of Bowles and Gintis is to have put together from the many disparate sources of evidence a story as plausible as any we're likely to get in the present state of behavioural sciences of how human beings came to be as co-operative as they are."--W.G. Runciman, London Review of Books "In A Cooperative Species, economists Samuel Bowles and Herbert Gintis update their ideas on the evolutionary origins of altruism. Containing new data and analysis, their book is a sustained and detailed argument for how genes and culture have together shaped our ability to cooperate... By presenting clear models that are tied tightly to empirically derived parameters, Bowles and Gintis encourage much-needed debate on the origins of human cooperation."--Peter Richerson, Nature "An outstanding book that presents an important contribution and quite simply raises the scientific standard associated with the difficult and contentious problem of how human altruism evolved."--Charles Efferson, Economic Journal "A Cooperative Species: Human Reciprocity and Its Evolution states a clearly articulated gene-culture coevolution explanation for why we are a cooperative species. It is a read that will stretch readers' minds a bit, and I think it is an eminently valuable read... I await with eagerness the next time Bowles and Gintis are out cooperating again."--Jonathan D. Springer, PsycCRITIQUES "[T]he authors' systematic and mathematical approach will appeal to any reader seriously interested in learning about alternative theories of adaptive altruism, and their treatment of cultural inheritance using population-genetic models is first-rate. Although this book will by no means settle the debate surrounding the evolutionary origin of altruism, it is a worthy addition and is well worth reading."--P. William Hughes, Journal of Economic Issues "Bowles and Gintis are clearly not short of ideas. The attention they draw to the role of conflict and coordinated punishment in the evolution of our cooperative and reciprocal species makes the book very much worth reading. Their focus on the evolution of human nature also paints a much richer picture of our behavior than traditional economics tends to do."--Journal of Economic Literature "Bowles and Gintis are not the first to claim that competition, conflict, and war between human groups is the foundation of cooperation and of society. However, their integration of this insight into evolutionary game theory stands to increase the accessibility of this powerful idea to a large number of scholars working in a dominant theoretical perspective that spans the social and biological sciences. This is one reason why I recommend their new book A Cooperative Species: Human Reciprocity and Its Evolution."--Noah Mark, Journal of Artificial Societies and Social Simulation "This book makes a strong case for returning as a discipline to this vexed theme. I can only hope we do so with the analytical ingenuity and empirical humility that Bowles and Gintis display."--Jacob G. Foster, American Journal of Sociology "Cooperative Species: Human Reciprocity and Its Evolution should be of interest to individuals across multiple disciplines. The book provides a compelling argument supported by multiple kinds of theoretical and empirical evidence. Although the book does use some technical language and examples in places, the explanation is sufficiently clear to make the main ideas and arguments of the book accessible to individuals who were not previously familiar with these technicalities."--Christopher M. Caldwell, Metapsychology Online "[This book] makes important contributions to our understanding of the nature and function of emotions in politics, including the evolution of emotion and cognition and their linkages to democratic governance... [It] should become [an] important resource for students of politics who have the requisite background in the behavioral sciences and wish to develop an integrated, life science perspective in their own work."--Michael S. Latner, Politics and the Life SciencesTable of ContentsPreface xi Chapter 1: A Cooperative Species 1 Chapter 2: The Evolution of Altruism in Humans 8 2.1 Preferences, Beliefs, and Constraints 9 2.2 Social Preferences and Social Dilemmas 10 2.3 Genes, Culture, Groups, and Institutions 13 2.4 Preview 18 Chapter 3: Social Preferences 19 3.1 Strong Reciprocity Is Common 20 3.2 Free-Riders Undermine Cooperation 22 3.3 Altruistic Punishment Sustains Cooperation 24 3.4 Effective Punishment Depends on Legitimacy 26 3.5 Purely Symbolic Punishment Is Effective 29 3.6 People Punish Those Who Hurt Others 31 3.7 Social Preferences Are Not Irrational 32 3.8 Culture and InstitutionsMatter 33 3.9 Behavior Is Conditioned on Group Membership 35 3.10 People Enjoy Cooperating and Punishing Free-Riders 38 3.11 Social Preferences in Laboratory and Natural Settings 39 3.12 Competing Explanations 42 Chapter 4: The Sociobiology of Human Cooperation 46 4.1 Inclusive Fitness and Human Cooperation 48 4.2 Modeling Multi-level Selection 52 4.3 EquilibriumSelection 57 4.4 Reciprocal Altruism 59 4.5 Reciprocal Altruism in Large Groups 63 4.6 Reputation: Indirect Reciprocity 68 4.7 Altruism as a Signal of Quality 71 4.8 Positive Assortment 72 4.9 Mechanisms and Motives 75 Chapter 5: Cooperative Homo economicus 79 5.1 Folk Theorems and Evolutionary Dynamics 80 5.2 The Folk Theorem with Imperfect Public Information 83 5.3 The Folk Theorem with Private Information 86 5.4 Evolutionarily Irrelevant Equilibria 87 5.5 Social Norms and Correlated Equilibria 89 5.6 The Missing Choreographer 90 Chapter 6: Ancestral Human Society 93 6.1 Cosmopolitan Ancestors 95 6.2 Genetic Evidence 99 6.3 PrehistoricWarfare 102 6.4 The Foundations of Social Order 106 6.5 The Crucible of Cooperation 110 Chapter 7: The Coevolution of Institutions and Behaviors 111 7.1 Selective Extinction 115 7.2 Reproductive Leveling 117 7.3 Genetic Differentiation between Groups 120 7.4 Deme Extinction and the Evolution of Altruism 121 7.5 The Australian Laboratory 123 7.6 The Coevolution of Institutions and Altruism 124 7.7 Simulating Gene-Culture Coevolution 126 7.8 Levelers and Warriors 130 Chapter 8: Parochialism, Altruism, andWar 133 8.1 Parochial Altruism and War 135 8.2 The Emergence of Parochial Altruism and War 138 8.3 Simulated and Experimental Parochial Altruism 142 8.4 The Legacy of a Past "Red in Tooth and Claw" 146 Chapter 9: The Evolution of Strong Reciprocity 148 9.1 Coordinated Punishment 150 9.2 Altruistic Punishment in a Realistic Demography 156 9.3 The Emergence of Strong Reciprocity 159 9.4 Why Coordinated Punishment Succeeds 163 9.5 A Decentralized Social Order 164 Chapter 10: Socialization 167 10.1 Cultural Transmission 168 10.2 Socialization and the Survival of Fitness-Reducing Norms 171 10.3 Genes, Culture, and the Internalization of Norms 173 10.4 The Internalized Norm as Hitchhiker 176 10.5 The Gene-Culture Coevolution of a Fitness-Reducing Norm 179 10.6 How Can Internalized Norms Be Altruistic? 180 10.7 The Programmable Brain 183 11Social Emotions 186 11.1 Reciprocity, Shame, and Punishment 188 11.2 The Evolution of Social Emotions 191 11.3 The "Great Captains of Our Lives" 192 12Conclusion: Human Cooperation and Its Evolution 195 12.1 The Origins of Human Cooperation 196 12.2 The Future of Cooperation 199 Appendix 201 A1 Altruism Defined 201 A2 Agent-Based Models 202 A3 Game Theory 207 A4 Dynamical Systems 209 A5 The Replicator Dynamic 212 A6 Continuation Probability and Time Discount Factor 213 A7 Alternatives to the Standing Model 214 A8 The Prisoner's Dilemma with Public and Private Signals 215 A9 Student and Nonstudent Experimental Subjects 217 A10 The Price Equation 218 A11 Weak Multi-level Selection 222 A12 Cooperation and Punishment with Quorum Sensing 223 References 225 Subject Index 251 Author Index 255
£25.20
Princeton University Press Games for Your Mind
Book SynopsisTrade Review"Fascinating. . . . Part philosophy, part maths, part activity book; Games for Your Mind is an ingenious thing."---Amy Barrett, BBC Science Focus"Excellent."---Elizabeth Palmer, Christian Century"It’s a serious and at times technical book, specifically about logic puzzles, though beneath its concern with matters such as obversion and epistemic obligations it has an unexpected jauntiness."---Henry Hitchings, Times Literary Supplement"Jason Rosenhouse’s Games for Your Mind is an engaging popular mathematics book written to enlighten the reader on the mathematics and logic behind popular puzzles. . . .overall, the reviewer would recommend this book to all people who want a puzzling challenge. Although the puzzles towards the end of the book feel impossible, the thrill of that ‘ah!’ moment when you work through Rosenhouse’s solution is surely a high for any mathematician out there."---Holly A. J. Middleton-Spencer, London Mathematical Society
£22.50
