Mathematical logic Books
Oxford University Press, USA Taking Sudoku Seriously
Book SynopsisPacked with more than a hundred color illustrations and a wide variety of puzzles and brainteasers, Taking Sudoku 2eriously uses this popular craze as the starting point for a fun-filled introduction to higher mathematics. How many Sudoku solution squares are there? What shapes other than three-by-three blocks can serve as acceptable Sudoku regions? What is the fewest number of starting clues a sound Sudoku puzzle can have? Does solving Sudoku require mathematics? Jason Rosenhouse and Laura Taalman show that answering these questions opens the door to a wealth of interesting mathematics. Indeed, they show that Sudoku puzzles and their variants are a gateway into mathematical thinking generally. Among many topics, the authors look at the notion of a Latin square--an object of long-standing interest to mathematicians--of which Sudoku squares are a special case; discuss how one finds interesting Sudoku puzzles; explore the connections between Sudoku, graph theory, and polynomials; and cTrade ReviewThis well-written book would be of interest to anyone, mathematician or not, who likes solving Sudoku puzzles. * Donald Keedwell, Mathematical Gazette *This is an interesting book. The style is conversational and east to read ... * John Sykes, Mathematics in School *I thoroughly enjoyed this book and do not have any criticisms to make. The authors have produced a lovely addition to any budding or practiced mathematicians bookcase. Well-presented and readable for both the novice and the maths expert, which is an admirable feat, this book is for anyone with an interest, no matter how vague or intense, in Sudoku. * Angie Wade, Significance *A beautiful book. * Paul Levrie, Karel de Grote University College *Table of Contents1. Playing the Game ; Mathematics as Applied Puzzle-Solving ; 2. Latin Squares ; What Do Mathematicians Do? ; 3. Greco-Latin Squares ; The Problem of the Thirty-Six Officers ; 4. Counting ; It's Harder Than it Looks ; 5. Equivalence Classes ; The Importance of Being Essentially Identical ; 6. Searching ; The Art of Finding Needles in Haystacks ; 7. Graphs ; Dots, Lines and Sudoku ; 8. Polynomials ; We Finally Found a Use For Algebra ; 9. Extremes ; Sudoku Pushed to its Limits ; 10. Epilogue ; You Can Never Have Too Many Puzzles ; Solutions to Puzzles
£28.89
Oxford University Press Seduced by Logic
Book SynopsisThis is the fascinating story of two women who lives were guided by a passion for mathematics and an insatiable curiosity to know and understand the world around them -- the beautiful, outrageous Émilie du Châtelet and the charmingly subversive Mary Somerville. Against great odds, Émilie and Mary taught themselves mathematics, and did it so well that they each became a world authority on Newtonian mathematical physics.Seduced by Logic begins with Émilie du Châtelet, an 18th-century French aristocrat, intellectual, and Voltaire''s lover, whose true ambition was to be a mathematician. She strove not only to further Newton''s ideas in France, but to prove that they had French connections, including to the work of Descartes, whom Newton had read. She translated the great Principia Mathematica into French, in what became the accepted French version of Newton''s work, and was instrumental in bringing Newton''s revolutionary opus to a Continental audience. A century later, in Scotland, Mary STrade Review...timely reminder of how little things have changed since the 19th century and how much women of science can accomplish. * Wall Street Journal *Table of ContentsIntroduction ; 1 Madame Newton du Chatelet ; 2 Creating the theory of gravity: the Newtonian controversy ; 3 Learning mathematics and fighting for freedom ; 4 Emilie and Voltaire's Academy of Free Thought ; 5 Testing Newton: the'New Argonauts' ; 6 The danger in Newton: life, love and politics ; 7 The nature of light: Emilie takes on Newton ; 8 Searching for 'energy': Emilie discovers Leibniz ; 9 Mathematics and free will ; 10 The re-emergence of Madame Newton du Chatelet ; 11 Love letters to Saint-Lambert ; 12 Mourning Emilie ; 13 Mary Fairfax Somerville ; 14 The long road to fame ; 15 Mechanism of the Heavens ; 16 Mary's second book: popular science in the nineteenth century ; 17 Finding light waves: the 'Newtonian Revolution' comes of age ; 18 Mary Somerville: a fortunate life ; Epilogue: Declaring a point of view
£38.39
Indiana University Press The Puzzle Instinct
Book SynopsisWhat is the necessary raison d'etre that puzzles serve? Why did they emerge at the same time in history as myth, magic and the occult arts? And why can't we put them down? This book presents an exploration of the philosophical implications of the puzzle instinct.Trade Review"Danesi, a professor of semiotics and anthropology (Univ. of Toronto), explores why puzzles, having arisen in earliest human history at the same time as mystery cults, are an intrinsic part of human life. Will Shortz, crossword puzzle editor of the New York Times, has suggested enigmatology as the study of the relationship between puzzles and culture. This book, which explores the puzzle genres that have survived over the years, is a contribution to that rubric. After first asking the question Why puzzles? (and developing several possible answers, among which is that they provide comic relief from unanswerable larger questions), Danesi devotes chapters to each of several types of puzzle. These include language puzzles (e.g., riddles and anagrams); pictures (e.g., optical illusions and mazes); logic (e.g., deductions and paradoxes); numbers (e.g., mathematical recreations); and games (e.g., chess). A final chapter synopsizes the discussion. A detailed list of references is included, as are solutions to the specific puzzles posed. The book is well written, has no mathematical prerequisites, and is quite suitable for a general audience as well as lower- and upper-division undergraduates." —D. Robbins, Trinity College (CT), Choice, December 2002Table of ContentsPreface 1. Why Puzzles? 2. Puzzling Language: Riddles, Anagrams, and Other Verbal Perplexities 3. Puzzling Pictures: Optical Illusions, Mazes, and Other Visual Mind-Bogglers 4. Puzzling Logic: Deductions, Paradoxes, and Other Forms of Mind Play 5. Puzzling Numbers: Magic Squares, Cryptarithms, and Other Mathematical Recreations 6. Puzzling Games: Chess, Checkers, and Other Games 7. The Puzzle of Life Solutions Bibliography and General Reading List Index
£16.14
MIT Press Ltd Essential Logic for Computer Science The MIT
Book SynopsisAn introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory.Computer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science. Topics covered include predicate logic, equation-based software, automated testing and theorem proving, and large-scale computation. Formalism is emphasized, and the book employs three formal notations: traditional algebraic formulas of propositional and predicate logic; digital circuit diagrams; and the widely used partially automated theorem prover, ACL2, which provides an accessible introduction to mechanized formalism
£43.20
MIT Press Ltd Natural Language Semantics Formation and
Book SynopsisAn introduction to natural language semantics that offers an overview of the empirical domain and an explanation of the mathematical concepts that underpin the discipline.This textbook offers a comprehensive introduction to the fundamentals of those approaches to natural language semantics that use the insights of logic. Many other texts on the subject focus on presenting a particular theory of natural language semantics. This text instead offers an overview of the empirical domain (drawn largely from standard descriptive grammars of English) as well as the mathematical tools that are applied to it. Readers are shown where the concepts of logic apply, where they fail to apply, and where they might apply, if suitably adjusted. The presentation of logic is completely self-contained, with concepts of logic used in the book presented in all the necessary detail. This includes propositional logic, first order predicate logic, generalized quantifier theory, and the Lambek an
£72.20
Elsevier Science & Technology The Nuts and Bolts of Proofs
Book SynopsisTable of Contents1. Getting Started 2. Basic Techniques to Prove If/Then Statements 3. Special Kinds of Theorems 4. Some Mathematical Topics on Which to Practice Proof Techniques 5. Review Exercises
£41.36
Taylor & Francis Nondeductive Inference 2 Routledge Library
Book SynopsisOriginally published in 1966. An introduction to current studies of kinds of inference in which validity cannot be determined by ordinary deductive models. In particular, inductive inference, predictive inference, statistical inference, and decision making are examined in some detail. The last chapter discusses the relationship of these forms of inference to philosophical notions of rationality. Special features of the monograph include a discussion of the legitimacy of various criteria for successful predictive inference, the development of an intuitive model which exhibits the difficulties of choosing probability measures over infinite sets, and a comparison of rival views on the foundations of probability in terms of the amount of information which the members of these schools believe suitable for fruitful formalization. The bibliographies include articles by statisticians accessible to students of symbolic logic. Table of Contents1. Inductive and Predictive Inference 2. Hypothesis and Predictive Inference 3. Probability and Predictive Inference 4. Statistical Inference 5. Bayesian Statistical Inference 6. Statistical Decision and Utility 7. Theories and Rationality 8. Bibliography
£87.39
Taylor & Francis Ltd The Equation of Knowledge
Book SynopsisThe Equation of Knowledge: From Bayes'' Rule to a Unified Philosophy of Science introduces readers to the Bayesian approach to science: teasing out the link between probability and knowledge. The author strives to make this book accessible to a very broad audience, suitable for professionals, students, and academics, as well as the enthusiastic amateur scientist/mathematician. This book also shows how Bayesianism sheds new light on nearly all areas of knowledge, from philosophy to mathematics, science and engineering, but also law, politics and everyday decision-making.Bayesian thinking is an important topic for research, which has seen dramatic progress in the recent years, and has a significant role to play in the understanding and development of AI and Machine Learning, among many other things. This book seeks to act as a tool for proselytising the benefits and limits of Bayesianism to a wider public. Features Trade ReviewLê Nguyên Hoang takes us on a fascinating intellectual journey into Bayesianism, cutting across many social and natural sciences. The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science is a real page turner.—George Zaccour, HEC Montréal and co-author of Handbook of Dynamic Game Theory"Each chapter is opened with a fascinating epigraph quoting famous persons, and is completed by the most recent references. There are multiple illustrations, and the Bayes’ formulae are many times presented via various funny symbols of emoji kind. The book is addressed to a wide audience of students, professionals, and actually any reader interested to be better acquainted with modern ideas in various sciences and philosophy of science, and their Bayesian statistical description and interpretation."— Stan Lipovetsky, Technometrics (Volume 63, 2021 - Issue 1)"[. . . ] Trained in the hard school of online videos, Le Nguyen Hoang has found a new tone to talk about science, a tone that is both rigorous and narrative, where examples illuminate the most abstract questions."— From the Foreword by Gilles Dowek, Professor at École Polytechnique and researcher at the Laboratoire d'Informatique de l'École Polytechnique and the Institut National de Recherche en Informatique et en Automatique (INRIA).Lê Nguyên Hoang takes us on a fascinating intellectual journey into Bayesianism, cutting across many social and natural sciences. The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science is a real page turner.— George Zaccour, HEC Montréal and co-author of Handbook of Dynamic Game Theory"Making math accessible to everyone, showing its connections with dozens of different domains, narrating scientific discovery as a personal human adventure, and sharing impressive enthusiasm: there is definitely something of Greg Chaitin's Meta Math! in Lê Nguyên Hoang's book!" — Rémi Peyre, École des Mines de Nancy"A remarkable piece of work, broad and insightful at the same time. This book is unique in that it gives an accessible journey from subtle probabilistic puzzles to the most advanced concepts at the heart of the machine learning revolution; with unrivalled clarity, it exposes deep ideas that have remained very confidential outside of specialized circles, and that yet are becoming fundamental in the way we understand our world."— Clément Hongler, Associate Professor and Chair of Statistical Field Theory, EPFL "As someone who practices research and publishes academic papers, it is frustrating to note how little we, scientists, are trained in epistemology. ‘How do we know that we know?’ This question is often neglected or taken for granted. The recent controversies about reproducibility of scientific publishing might be one of the tips of a larger iceberg. This book will, in my opinion, be remembered as one of those that helped melt the iceberg." — El Mahdi El Mhamdi, École Polytechnique Fédérale de Lausanne."The book has a lively writing style, rather like you are listening to an inspiring lecturer. Indeed the author has a French YouTube channel and is clearly enthusiastic about exposition. It is overtly an account of what the author personally finds interesting. [. . .] In teaching a basic college course, focused on the mathematical setup and on the analysis of data, I often find there is one student who comes to office hours and is interested in seeing connections with broad scientific fields, or in conceptual issues of the philosophy of science. I could certainly recommend this book to such a student. Similarly, for the MAA community it could be an innovative basis for an undergraduate seminar course, in which students would choose a topic from the book and delve deeper into it."— David Aldous, Mathematical Association of AmericaTable of ContentsSction I. Pure Bayesianism. 1. On A Transformative Journey. 2. Bayes Theorem. 3. Logically Speaking... 4. Let’s Generalize! 5. All Hail Prejudices. 6. The Bayesian Prophets. 7. Solomonoff’s Demon. Section II. Applied Bayesianism. 8. Can You Keep A Secret? 9. Game, Set and Math. 10. Will Darwin Select Bayes? 11. Exponentially Counter-Intuitive. 12. Ockham Cuts to the Chase. 13. Facts Are Misleading. Section III. Pragmatic Bayesianism. 14. Quick And Not Too Dirty. 15. Wish Me Luck. 16. Down Memory Lane. 17. Let’s Sleep On It. 18. The Unreasonable Effectiveness of Abstraction. 19. The Bayesian Brain. Section IV. Beyond Bayesianism. 20. It’s All Fiction. 21. Exploring The Origins Of Beliefs. 22. Beyond Bayesianism.
£32.29
Taylor & Francis Ltd PCI Compliance
Book SynopsisThe Payment Card Industry Data Security Standard (PCI DSS) is now in its 18th year, and it is continuing to dominate corporate security budgets and resources. If you accept, process, transmit, or store payment card data branded by Visa, MasterCard, American Express, Discover, or JCB (or their affiliates and partners), you must comply with this lengthy standard.Personal data theft is at the top of the list of likely cybercrimes that modern-day corporations must defend against. In particular, credit or debit card data is preferred by cybercriminals as they can find ways to monetize it quickly from anywhere in the world. Is your payment processing secure and compliant? The new Fifth Edition of PCI Compliance has been revised to follow the new PCI DSS version 4.0, which is a complete overhaul to the standard. Also new to the Fifth Edition are: additional case studies and clear guidelines and instructions for maintaining PCI compliance globally, including coverage of technoTable of ContentsForeword. Acknowledgments. Authors. Chapter 1 About PCI DSS and This Book. Chapter 2 Introduction to Fraud, Identity Theft, and Related Regulatory Mandates. Chapter 3 Why Is PCI Here? Chapter 4 Determining and Reducing Your PCI Scope. Chapter 5 Building and Maintaining a Secure Network. Chapter 6 Strong Access Controls. Chapter 7 Protecting Cardholder Data. Chapter 8 Using Wireless Networking. Chapter 9 Vulnerability Management. Chapter 10 Logging Events and Monitoring the Cardholder Data Environment. Chapter 11 Cloud and Virtualization. Chapter 12 Mobile. Chapter 13 PCI for the Small Business. Chapter 14 PCI DSS for the Service Provider. Chapter 15 Managing a PCI DSS Project to Achieve Compliance. Chapter 16 Don’t Fear the Assessor. Chapter 17 The Art of Compensating Control. Chapter 18 You’re Compliant, Now What? Chapter 19 Emerging Technology and Alternative Payment Schemes. Chapter 20 PCI DSS Myths and Misconceptions. Chapter 21 Final Thoughts. Index by Requirement. Alphabetical Index.
£40.84
Taylor & Francis Ltd Advanced Smart Computing Technologies in
Book SynopsisThis book addresses the topics related to artificial intelligence, the Internet of Things, blockchain technology, and machine learning. It brings together researchers, developers, practitioners, and users interested in cybersecurity and forensics. The first objective is to learn and understand the need for and impact of advanced cybersecurity and forensics and its implementation with multiple smart computational technologies. This objective answers why and how cybersecurity and forensics have evolved as one of the most promising and widely-accepted technologies globally and has widely-accepted applications. The second objective is to learn how to use advanced cybersecurity and forensics practices to answer computational problems where confidentiality, integrity, and availability are essential aspects to handle and answer. This book is structured in such a way so that the field of study is relevant to each readerâs major or interests. It aims to help each reader see the relevance of cybersecurity and forensics to their career or interests. This book intends to encourage researchers to develop novel theories to enrich their scholarly knowledge to achieve sustainable development and foster sustainability. Readers will gain valuable knowledge and insights about smart computing technologies using this exciting book.This book:â Includes detailed applications of cybersecurity and forensics for real-life problemsâ Addresses the challenges and solutions related to implementing cybersecurity in multiple domains of smart computational technologies â Includes the latest trends and areas of research in cybersecurity and forensicsâ Offers both quantitative and qualitative assessments of the topics Includes case studies that will be helpful for the researchersProf. Keshav Kaushik is Assistant Professor in the Department of Systemics, School of Computer Science at the University of Petroleum and Energy Studies, Dehradun, India.Dr. Shubham Tayal is Assistant Professor at SR University, Warangal, India.Dr. Akashdeep Bhardwaj is Professor (Cyber Security & Digital Forensics) at the University of Petroleum & Energy Studies (UPES), Dehradun, India.Dr. Manoj Kumar is Assistant Professor (SG) (SoCS) at the University of Petroleum and Energy Studies, Dehradun, India.Table of Contents1. Detection of Cross-Site Scripting and Phishing Website Vulnerabilities Using Machine Learning. 2. A Review: Security and Privacy Defensive Techniques for Cyber Security Using Deep Neural Networks (DNNs). 3. DNA-Based Cryptosystem for Connected Objects and IoT Security. 4. A Role of Digital Evidence: Mobile Forensics Data. 5. Analysis of Kernel Vulnerabilities Using Machine Learning. 6. Cyber Threat Exploitation and Growth during COVID-19 Times. 7. An Overview of the Cybersecurity in Smart Cities in the Modern Digital Age. 8. The Fundamentals and Potential for Cyber Security of Machine Learning in the Modern World. 9. Qualitative and Quantitative Evaluation of Encryption Algorithms. 10. Analysis and Investigation of Advanced Malware Forensics. 11. Network Intrusion Detection System Using Naïve Bayes Classification Technique for Anomaly Detection. 12. Data Security Analysis in Mobile Cloud Computing for Cyber Security. 13. A Comprehensive Review of Investigations of Suspects of Cyber Crimes. 14. Fault Analysis Techniques in Lightweight Ciphers for IoT Devices.
£87.39
Springer Naive Set Theory
1 The Axiom of Extension.- 2 The Axiom of Specification.- 3 Unordered Pairs.- 4 Unions and Intersections.- 5 Complements and Powers.- 6 Ordered Pairs.- 7 Relations.- 8 Functions.- 9 Families.- 10 Inverses and Composites.- 11 Numbers.- 12 The Peano Axioms.- 13 Arithmetic.- 14 Order.- 15 The Axiom of Choice.- 16 Zorn's Lemma.- 17 Well Ordering.- 18 Transfinite Recursion.- 19 Ordinal Numbers.- 20 Sets of Ordinal Numbers.- 21 Ordinal Arithmetic.- 22 The Schröder-Bernstein Theorem.- 23 Countable Sets.- 24 Cardinal Arithmetic.- 25 Cardinal Numbers.
£71.24
Springer The Joy of Sets
Book Synopsis1 Naive Set Theory.- 1.1 What is a Set?.- 1.2 Operations on Sets.- 1.3 Notation for Sets.- 1.4 Sets of Sets.- 1.5 Relations.- 1.6 Functions.- 1.7 Well-Or der ings and Ordinals.- 1.8 Problems.- 2 The ZermeloFraenkel Axioms.- 2.1 The Language of Set Theory.- 2.2 The Cumulative Hierarchy of Sets.- 2.3 The ZermeloFraenkel Axioms.- 2.4 Classes.- 2.5 Set Theory as an Axiomatic Theory.- 2.6 The Recursion Principle.- 2.7 The Axiom of Choice.- 2.8 Problems.- 3 Ordinal and Cardinal Numbers.- 3.1 Ordinal Numbers.- 3.2 Addition of Ordinals.- 3.3 Multiplication of Ordinals.- 3.4 Sequences of Ordinals.- 3.5 Ordinal Exponentiation.- 3.6 Cardinality, Cardinal Numbers.- 3.7 Arithmetic of Cardinal Numbers.- 3.8 Regular and Singular Cardinals.- 3.9 Cardinal Exponentiation.- 3.10 Inaccessible Cardinals.- 3.11 Problems.- 4 Topics in Pure Set Theory.- 4.1 The Borel Hierarchy.- 4.2 Closed Unbounded Sets.- 4.3 Stationary Sets and Regressive Functions.- 4.4 Trees.- 4.5 Extensions of Lebesgue Measure.- 4.6 A ReTable of ContentsPreface; 1. Naïve Set Theory; 2. The Zermelo-Fraenkel Axioms; 3. Ordinal and Cardinal Numbers; 4. Topics in Pure Set Theory; 5. The Axiom of Constructibility; 6. Independence Proofs in Set Theory; 7. Non-Well-Founded Set Theory; Bibliography; Glossary of Symbols; Index
£48.44
Springer Mathematical Logic
Book SynopsisA.- I Introduction.- II Syntax of First-Order Languages.- III Semantics of First-Order Languages.- IV A Sequent Calculus.- V The Completeness Theorem.- VI The Löwenheim-Skolem and the Compactness Theorem.- VII The Scope of First-Order Logic.- VIII Syntactic Interpretations and Normal Forms.- B.- IX Extensions of First-Order Logic.- X Limitations of the Formal Method.- XI Free Models and Logic Programming.- XII An Algebraic Characterization of Elementary Equivalence.- XIII Lindström's Theorems.- References.- Symbol Index.Trade Review“…the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level.” – Journal of Symbolic LogicTable of ContentsPreface; Part A: 1. Introduction; 2. Syntax of First-Order Languages; 3. Semantics of first-Order Languages; 4. A Sequent Calculus; 5. The Completeness Theorem; 6. The Lowenheim-Skolem and the Compactness Theorem; 7. The Scope of First-Order Logic; 8. Syntactic Interpretations and Normal Forms; Part B: 9. Extensions of First-Order Logic; 10. Limitations of the Formal Method; 11. Free Models and Logic Programming; 12. An Algebraic Characterization of Elementary Equivalence; 13. Lindstroem's Theorems; References; Symbol Index; Subject Index
£51.29
Springer-Verlag New York Inc. Sheaves in Geometry and Logic
Book SynopsisSheaves also appear in logic as carriers for models of set theory. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.Trade ReviewFrom the reviews: "A beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. … authors have a rare gift for conveying an insider’s view of the subject from the start. This book is written in the best Mac Lane style, very clear and very well organized. … it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field." (Wordtrade, 2008)Table of ContentsPreface; Prologue; Categorical Preliminaries; 1. Categories of Functors; 2. Sheaves of Sets; 3. Grothendieck Topologies and Sheaves; 4. First Properties of Elementary Topoi; 5. Basic Constructions of Topoi; 6. Topoi and Logic; 7. Geometric Morphisms; 8. Classifying Topoi; 9. Localic Topoi; 10. Geometric Logic and Classifying Topoi; Appendix: Sites for Topoi; Epilogue; Bibliography; Index of Notations; Index
£58.49
Springer New York Complexity and Real Computation
Book SynopsisThe later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.Table of Contents1 Introduction.- 2 Definitions and First Properties of Computation.- 3 Computation over a Ring.- 4 Decision Problems and Complexity over a Ring.- 5 The Class NP and NP-Complete Problems.- 6 Integer Machines.- 7 Algebraic Settings for the Problem “P ? NP?”.- 8 Newton’s Method.- 9 Fundamental Theorem of Algebra: Complexity Aspects.- 10 Bézout’s Theorem.- 11 Condition Numbers and the Loss of Precision of Linear Equations.- 12 The Condition Number for Nonlinear Problems.- 13 The Condition Number in ?(H(d).- 14 Complexity and the Condition Number.- 15 Linear Programming.- 16 Deterministic Lower Bounds.- 17 Probabilistic Machines.- 18 Parallel Computations.- 19 Some Separations of Complexity Classes.- 20 Weak Machines.- 21 Additive Machines.- 22 Nonuniform Complexity Classes.- 23 Descriptive Complexity.- References.
£68.40
Penguin Random House LLC The Puzzlers Dilemma
£22.80
Elsevier Science The Many Valued and Nonmonotonic Turn in Logic
£212.00
Basic Books How to Bake Pi
Book SynopsisA Publishers Weekly best book of 2015Trade Review"Quirky recipes, personal anecdotes and a large dollop of equations are the key ingredients in this alternative guide to maths and the scientific process. You should find it as easy as cooking a pie." --The Observer, Tech Monthly (UK) "A curious cookbook for the mathematical omnivore." --The Irish Times (Ireland) "Eugenia Cheng's charming new book embeds math in a casing of wry, homespun metaphors: math is like vegan brownies, math is like a subway map, math is like a messy desk. Cheng is at home with math the way you're at home with brownies, maps, and desks, and by the end of How to Bake Pi, you might be, too." --Jordan Ellenberg, Professor of Mathematics, University of Wisconsin-Madison, and author of How Not to Be Wrong "What a charming and original book! The central analogy -- math is like cooking -- turns out to be surprisingly apt and often funny. Light and tasty, yet so, so good for you, How to Bake Pi is a real treat." --Steven Strogatz, Professor of Mathematics, Cornell University and author of The Joy of x "Cheng is exceptional at translating the abstract concepts of mathematics into ordinary language, a strength aided by a writing style that showcases the workings of her curious, sometimes whimsical mind. This combination allows her to demystify how mathematicians think and work, and makes her love for mathematics contagious." --Publishers Weekly, starred review "An original book using recipes to explain sophisticated math concepts to students and even the math-phobic... [Cheng] is a gifted teacher... A sharp, witty book to press on students and even the teachers of math teachers." --Kirkus Reviews "[A] well-written, easy-to-read book." --Library Journal "[T]his book was fun and covered some cool maths, using some nice analogies, and would serve as a good intro for someone getting into category theory." --The Aperiodical (UK) "Eugenia Cheng offers an entertaining introduction to the beauty of mathematics by drawing on insights from the kitchen. She explains why baking a flourless cake is like geometry and offers puzzles to whet the appetites of maths fans." --Times Educational Supplement (UK) "Cheng never quite overeggs her metaphor of the mathematician as chef...and her tone is clear, clever and friendly. Even at her most whimsical she is rigorous and insightful. Potentially confusing ideas are expressed with a matter-of-fact simplicity... How to Bake Pi is a welcome addition to the popular-math shelf, unusual not only because of its quirky premise but also because Cheng is a woman, a lucid and nimble expositor, and unashamedly proud of her domestic obsessions... It would be wonderful if this book attracted a new audience to the field. And there's no better ambassador (or dinner-party host, I'd wager) than Eugenia Cheng." --Alex Bellos, New York Times Book Review "Invoking plenty of examples from cooking and baking, as well as other everyday-life situations such as calculating a taxi fare, searching for love through online dating services and training for a marathon, [Cheng] explains abstract mathematical ideas--including topology and logic--in understandable ways... Her lively, accessible book demonstrates how important and intriguing such a pursuit can be." --Scientific American "[A] funny and engaging new book." --Simon Worrall, National Geographic News "Why go to all the trouble to write a book to help people understand mathematics? Because, as Cheng observes, 'understanding is power, and if you help someone understand something, you're giving them power.' Read How to Bake Pi and you will, indeed, go away feeling empowered." --Marc Merlin, Medium "In her new book, How to Bake Pi, mathematician/baker Eugenia Cheng offers a novel, mathematical approach to cooking... How to Bake Pi is more than a mathematically-minded cookbook. It is just as much a book about mathematical theory and how we learn it. The premise at the heart of the book is that the problem that stops a cookbook from teaching us how to cook is the same problem that makes math classes so bad at actually teaching us to do math." --Ria Misra, io9 "[Cheng] masterfully describes what mathematics is. This includes careful and motivated descriptions of the ideas and methods of abstractions, generalization, logic, and axiomatization... This book is entertaining, insightful, deep and accessible." --Mathematical Reviews "Through an enthusiasm for cooking and zest for life, the author, a math professor, provides a new way to think about a field we thought we knew." --Chemical Engineering Progress "With this delightfully surprising book, Eugenia Cheng reveals the hidden beauty of mathematics with passion and simplicity. After reading How to Bake Pi, you won't look at math (nor porridge!) in the same way ever again." --Roberto Trotta, Astrophysicist, Imperial College London and author of The Edge of the Sky "Math is a lot like cooking. We start with the ingredients we have at hand, try to cook up something tasty, and are sometimes surprised by the results. Does this seem odd? Maybe in school all you got was stale leftovers! Try something better: Eugenia Cheng is not only an excellent mathematician and pastry chef, but a great writer, too." --John Baez, Professor of Math at the University of California, Riverside "From clotted cream to category theory, neither cookery nor math are what you thought they were. But deep down they're remarkably similar. A brilliant gourmet feast of what math is really about." --Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick, and author of Visions of Infinity and Professor Stewart's Incredible Numbers "[O]ften entertaining...frequently illuminating... [How to Bake Pi] offers enough nourishment for the brain to chew on for a long time." --Columbus Dispatch "This is the best book imaginable to introduce someone who doesn't think they are interested in mathematics at all to some of the deep ideas of category theory, especially if they like to bake." --MAA Reviews "Beginning each chapter with a recipe, Cheng converts the making of lasagna, pudding, cookies, and other comestibles into analogies illuminating the mathematical enterprise. Though these culinary analogies teach readers about particular mathematical principles and processes, they ultimately point toward the fundamental character of mathematics as a system of logic, a system presenting daunting difficulties yet offering rare power to make life easier. Despite her zeal for mathematical logic, Cheng recognizes that such logic begins in faith -- irrational faith -- and ultimately requires poetry and art to complement its findings. A singular humanization of the mathematical project." --Booklist, starred review PRAISE FOR HOW TO BAKE PI: "Cheng demystifies math by using recipes to explain mathematical concepts. Her two passions have a good deal in common: Baking and math are centered on similar principles, Cheng notes here, and her clever guide offers tangible examples of abstract ideas." --New York Times Book Review, Paperback Row "Dr. Cheng...has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board. She is a theoretical mathematician who works in a rarefied field called category theory, which is so abstract that 'even some pure mathematicians think it goes too far,' Dr. Cheng said. At the same time, Dr. Cheng is winning fame as a math popularizer, convinced that the pleasures of math can be conveyed to the legions of numbers-averse humanities majors still recovering from high school algebra. She has been featured on shows like Late Night With Stephen Colbert and her online math tutorials have been viewed more than a million times." --Natalie Angier, New York Times "Combined with infectious enthusiasm for cooking and a zest for life, Cheng's perspective on math becomes this singular book: a funny, lively, and clear journey no popular book on math has explored before. How to Bake Pi...will dazzle, amuse, and enlighten." --Gambit Weekly "[Cheng's] book, a very gentle introduction to the main ideas of mathematics in general and category theory in particular, exudes enthusiasm for mathematics, teaching, and creative recipes. Category theory is dangerously abstract, but Cheng's writing is down-to-earth and friendly. She's the kind of person you'd want to talk to at a party, whether about math, food, music, or just the weather... Cheng's cheerful, accessible writing and colorful examples make How to Bake Pi an entertaining introduction to the fundamentals of abstract mathematical thinking." --Evelyn Lamb, Scientific American's Roots of Unity blog "[A] slyly illuminating dispatch on the deep meaning of mathematics... Cheng manages to do for us what the mathematician Keith Devlin has said mathematicians do for themselves: she compels us to see numbers and symbols as vivid characters in an ongoing drama, a narrative in which we are alternately observers and participants." --Natalie Angier, The American Scholar
£17.99
John Wiley & Sons Inc Transform Methods in Applied Mathematics
Book SynopsisTransform theory and methods are useful to many professionals from various mathematical backgrounds. This introduction to the theory and practice of continuous and discrete transforms integrates knowledge from many branches of mathematics. It combines heuristic argument and discussion with careful, defensible mathematical statements, frequently in the form of theorems without proof.Table of ContentsThe Laplace Transform. Elementary Functions of a Complex Variable. Fourier Series and the Discrete Fourier Transformation. Complex Integrals and Power Series. The z-Transform and Discrete Filters. The Fourier Transform and Continuous Filters. Wavelets. Appendices. Bibliography. Index.
£163.76
John Wiley & Sons Inc Optimization Methods for Logical Inference
Book SynopsisLogic has recently become a basic modelling tool alongside mathematics, and the two styles of modelling are beginning to combine. This volume exploits the similarity of certain logical and optimization problems to solve inference problems more rapidly than with traditional AI techniques.Trade Review"...the first monograph devoted to a new interesting research area combining logic with optimization methods." (Mathematical Reviews, Issue 2001j)Table of ContentsPropositional Logic: Special Cases. Propositional Logic: The General Case. Probabilistic and Related Logics. Predicate Logic. Nonclassical and Many-Valued Logics. Appendix. Bibliography. Index.
£143.95
John Wiley & Sons Inc Logic For Dummies
Book SynopsisLogic concepts are more mainstream than you may realize. There's logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies.Table of ContentsIntroduction. Part I: Overview of Logic. Chapter 1: What Is This Thing Called Logic? Chapter 2: Logical Developments from Aristotle to the Computer. Chapter 3: Just for the Sake of Argument. Part II: Formal Sentential Logic (SL). Chapter 4: Formal Affairs. Chapter 5: The Value of Evaluation. Chapter 6: Turning the Tables: Evaluating Statements with Truth Tables. Chapter 7: Taking the Easy Way Out: Creating Quick Tables. Chapter 8: Truth Grows on Trees. Part III: Proofs, Syntax, and Semantics in SL. Chapter 9: What Have You Got to Prove? Chapter 10: Equal Opportunities: Putting Equivalence Rules to Work. Chapter 11: Big Assumptions with Conditional and Indirect Proofs. Chapter 12: Putting It All Together: Strategic Moves to Polish Off Any Proof. Chapter 13: One for All and All for One. Chapter 14: Syntactical Maneuvers and Semantic Considerations. Part IV: Quantifier Logic (QL). Chapter 15: Expressing Quantity with Quality: Introducing Quantifier Logic. Chapter 16: QL Translations. Chapter 17: Proving Arguments with QL. Chapter 18: Good Relations and Positive Identities. Chapter 19: Planting a Quantity of Trees. Part V: Modern Developments in Logic. Chapter 20: Computer Logic. Chapter 21: Sporting Propositions: Non-Classical Logic. Chapter 22: Paradox and Axiomatic Systems. Part VI: The Part of Tens. Chapter 23: Ten Quotes about Logic. Chapter 24: Ten Big Names in Logic. Chapter 25: Ten Tips for Passing a Logic Exam. Index.
£17.09
John Wiley & Sons Inc Fuzzy Expert System Tools D3
Book SynopsisFuzzy set theory is a mathematical structure for representing uncertainty. Modern intelligent systems must combine knowledge based on techniques for gathering and processing information with methods of approximate reasoning. This enables an intelligent system to better emulate human decision-making in uncertain environments.Table of ContentsGetting Started. Fuzzy Set Theory. Possibility/Probability Consistency Principle. Knowledge Representation. Imprecision and Fuzzy Logic. Knowledge Processing. Knowledge in FEST. Inference Engine. The Fuzzy Inference Engine. Fuzzy Inference in FEST. References. Index.
£199.76
Dover Publications Inc. An Introduction to Mathematical Logic
Book SynopsisComprehensive overview, suitable for advanced undergraduates and graduate students, covers propositional logic; first-order languages and logic; incompleteness, undecidability, and indefinability; recursive functions; computability; and Hilbert's Tenth Problem. 1995 edition.
£30.39
Dover Publications Inc. First Order Mathematical Logic
Book Synopsis
£11.87
University of California Press Studies in Inductive Logic and Probability Volume I
£85.33
Cambridge University Press Basic Simple Type Theory 42 Cambridge Tracts in Theoretical Computer Science Series Number 42
Book SynopsisType theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for compTrade Review"This is an excellent introduction to type theory. It doesn't bog the reader down in any of the messy details of the proofs and yet it provides many of the most interesting results in the field....Overall, it is a great book for someone who wants to get his feet wet in type theory, but doesn't want to get in over his head." Sigact News"...the book makes useful and stimulating reading and it will be an essential tool for computer scientists working in type theory and related areas." Mathematical ReviewsThe proofs in this book are given in great detail, and still the author succeeds in writing the book in a clear but not too technical style. It is easy and pleasurable to read this book." Journal of Symbolic LogicTable of ContentsIntroduction; 1. The type-free λ-calculus; 2. Assigning types to terms; 3. The principal-type algorithm; 4. Type assignment with equality; 5. A version using typed terms; 6. The correspondence with implication; 7. The converse principal-type algorithm; 8. Counting a type's inhabitants; 9. Technical details; Answers to starred exercises; Bibliography; Table of principal types; Index.
£36.99
Cambridge University Press First Steps in Modal Logic
Book SynopsisThis is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory.Trade Review"This text should appeal to anyone with an interest in model logic...an attractive choice for self-study." J.M. Plotkin, Mathematical Reviews"...offers a distinctive viewpoint and is easy to learn from." D.V. Feldman, ChoiceTable of ContentsIntroduction; Acknowledgements; Part I. Preliminaries: 1. Survey of propositional logic; 2. The modal language; Part II. Transition Structures and Semantics: 3. Labelled transition structures; 4. Valuation and satisfaction; 5. Correspondence theory; 6. The general confluence result; Part III. Proof Theory and Completeness: 7. Some consequence relations; 8. Standard formal systems; 9. The general completeness result; 10. Kripke-completeness; Part IV. Model Constructions: 11. Bismulations; 12. Filtrations; 13. The finite model property; Part V. More Advanced Material: 14. SLL logic; 15. Löb logic; 16. Canonicity without the fmp; 17. Transition structures aren't enough; Part VI. Two Appendices: Bibliography.
£47.99
Cambridge University Press An Introduction to Category Theory
Book SynopsisA crystal clear introduction to category theory that demystifies functors, natural transformations, limits and colimits, adjunctions and more. Any beginning postgraduate mathematician will find all they need in this excellent text to access the subject. Over 200 exercises are provided with solutions available online.Trade Review"This textbook presents a useful introduction to basic category theory, and would be suitable for a first course at the undergraduate level in computer science or mathematics." Steve Awodey, Mathematical ReviewsTable of ContentsPreface; 1. Categories; 2. Basic gadgetry; 3. Functors and natural transformations; 4. Limits and colimits in general; 5. Adjunctions; 6. Posets and monoid sets; Bibliography; Index.
£35.14
Cambridge University Press LMS 189 Locally Presentable London Mathematical
Book SynopsisThe concepts of a locally presentable category and an accessible category have turned out to be useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students. Firstly the properties of l-presentable objects, locally l-presentable categories, and l-accessible categories are discussed in detail, and the equivalence of accessible and sketchable categories is proved. The authors go on to study categories of algebras and prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapters they treat some topics in model theory and some set theoretical aspects. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.Trade Review"...the authors have taken the indicated material, organized it effectively, written a very lucid, readable development of it in 280 pages, and added helpful historical remarks to each chapter and a brief appendix on large cardinals. There are some novel results...most notably a significant improvement of the Gabriel-Ulmer theorem on "local generation" of locally presentable categories." J.R. Isbell, Mathematical ReviewsTable of ContentsPreliminaries; 1. Locally presentable categories; 2. Accessible categories; 3. Algebraic categories; 4. Injectivity classes; 5. Categories of models; 6. Vopenka's principle; Appendix: Large cardinals; Open problems.
£87.99
Cambridge University Press Proofs and Computations Perspectives in Logic
Book SynopsisDriven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and GÃdel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Î11âCA0. Ordinal analysis and the (SchwichtenbergâWainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Î11âCA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connTrade Review"Written by two leading practitioners in the area of formal logic, the book provides a panoramic view of the topic. This reference volume is a must for the bookshelf of every practitioner of formal logic and computer science." Prahladavaradan Sampath, Computing ReviewsTable of ContentsPreface; Preliminaries; Part I. Basic Proof Theory and Computability: 1. Logic; 2. Recursion theory; 3. Godel's theorems; Part II. Provable Recursion in Classical Systems: 4. The provably recursive functions of arithmetic; 5. Accessible recursive functions, ID<ω and Π11–CA0; Part III. Constructive Logic and Complexity: 6. Computability in higher types; 7. Extracting computational content from proofs; 8. Linear two-sorted arithmetic; Bibliography; Index.
£71.99
Cambridge University Press Topology via Logic
Book SynopsisThis is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.Table of Contents1. Introduction; 2. Affirmative and refutative assertions; 3. Frames; 4. Frames as algebras; 5. Topology: the definitions; 6. New topologies for old; 7. Point logic; 8. Compactness; 9. Spectral algebraic locales; 10. Domain theory; 11. Power domains; 12. Spectra of rings; Bibliography.
£47.99
Cambridge University Press Proofs and Confirmations
Book SynopsisAn introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses.Trade Review'Proofs and Confirmations is one of the most brilliant examples of mathematical exposition that I have encountered, in many years of reading the same. This is not for the faint-hearted, nor is Proofs and Confirmations a book that can be read in an easy chair, like a novel; it demands active participation by the reader. But Bressoud rewards such readers with a panorama of combinatorics today and with renewed awe at the human ability to penetrate the deeply hidden mysteries of pure mathematics.' Herbert S. Wilf, Science'The unexpected twists and turns will hardly be matched in any novel - this book allows us all to share in the excitement … a brilliant book.' Alun O. Morris'I strongly recommend the book as an account of a remarkable mathematical development.' P. J. Cameron, Proceedings of the Edinburgh Mathematical Society'This is an excellent book which can be recommended without hesitation, not only to specialists in the field, but to any mathematician with time to read something interesting and nicely written.' EMSTable of Contents1. The conjecture; 2. Fundamental structures; 3. Lattice paths and plane partitions; 4. Symmetric functions; 5. Hypergeometric series; 6. Explorations; 7. Square ice.
£37.99
Cambridge University Press An Introduction to NonClassical Logic Second
Book SynopsisThis revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.Trade Review'Priest's Introduction to Non-Classical Logic is my textbook of choice for introducing non-classical logic to undergraduates. It is unique in meeting two almost inconsistent aims. It gives the reader an introduction to a vast range of non-classical logics. No comparable textbook manages to cover modal logics, conditional logics, intuitionistic logic, relevant and paraconsistent logics and fuzzy logic with such clarity and accessibility. Amazingly, it is not merely a catalogue of different logical systems. The distinctive value of this Introduction is that it also tells a coherent story: Priest weaves together these different logics in the one narrative - the search for a logic of conditionals. With the publication of the second volume, this unique combination of breadth and coherence now covers much more ground, and the reader now has an expert guide to much more of the vast field of research in non-classical logics.' Greg Restall, The University of Melbourne'I've used your book (first edition, that is) for years now in my upper level philosophy of logic courses. It is easily the best introduction to non-classical logics. I especially like its coverage of conditionals, and the introduction to relevant logic. Over the years, your book has made my students come to appreciate the variety and scope that exists within in formal logic, I intend to use the new edition so as to carry similar investigations into first order theory.' Jeffry Pelletier, Simon Fraser University'Graham Priest's Introduction to Non-Classical Logic made this fascinating material on alternative logics accessible to my students for the very first time. The very welcome new edition extends the range of what is addressed to include important questions about quantification for modal logic, and the other systems as well.' Tony Roy, California State University, San Bernardino'The first edition of Graham Priest's Introduction to Non-Classical Logic turned out to be an extremely useful and well-written introductory guide to the vast and difficult to survey area of non-classical and philosophical logic. The substantially expanded second edition in two volumes is bound to become a standard reference.' Heinrich Wansing, Dresden University of Technology'Clear, self-contained, generously complete: this is bound to be the classic on non-classical logics for many years to come.' Achille Varzi, Columbia University'This is an excellent introductory book to modern non-classical logics, fully accessible to non-professionals, and useful to professionals too. I have used part of its content in teaching Non-Classical Logic in the past years, and the response from my students shows the great success of the author's intention. The proof system it employs and the meta-proofs it provides are extremely easy to follow, while those followed-up philosophical discussions it summarizes for each logic system are both concise and lucid. It is not only a work introducing modern non-classical logic systems, but also a work full of interesting philosophical discussions on the motivations, advantages and disadvantages of these systems. With one penetrating theme - what a logic of conditionals should be like - in mind, the author has effectively organized a variety of topics into one integrated work. I would recommend it both to logicians and to philosophers, to professionals and to non-professionals.' Wen-fang Wang, National Chung Chen University'The second edition of Graham Priest's book is, like the first, clearly expressed, well thought out for the student and an essential work for all those studying philosophy who want an adequate grounding in non-classical logic. I have used the first edition successfully in my intermediate class for the last five years, and will certainly be adding the second edition to the reading list when it is available.' Steve Read, University of St Andrews'Priest succeeds in offering a marvellously unified treatment of 11 varieties of logic: classical, basic modal, normal modal, non-normal, conditional, intuitionist, many-valued, first-degree entailment, basic relevant, mainstream relevant, and fussy … Excellent references support this concise but clear treatment.' Choice'This book is just what the title says it is … And it is a very good one …' Stewart Shapiro, University of Ohio' … for anyone who wants to explore the non-classical systems, it is the only book of its kind and could not be more highly recommended.' The Times Higher Education Supplement'I've just picked up a copy of the second edition of Graham Preist's An Introduction to Non-Classical Logic from the CUP bookshop. It looks terrific. More than twice the length of the first edition which just covered propositional logics, this covers their extensions with quantifiers and identity too. I thought the fist edition was terrific: so this is a hugely welcome expansion and I'm delighted to report that CUP has published this as a paperback in their Cambridge Introductions to Philosophy Series at just £18.99, which is surely an amazing bargain for a well produced 613 page book. So a must-buy and a must-read!' Logic MattersTable of ContentsPreface to the first edition; Preface to the second edition; Mathematical prolegomenon; Part I. Propositional Logic: 1. Classical logic and the material conditional; 2. Basic modal logic; 3. Normal modal logics; 4. Non-normal modal logics; strict conditionals; 5. Conditional logics; 6. Intuitionist logic; 7. Many-valued logics; 8. First degree entailment; 9. Logics with gaps, gluts, and worlds; 10. Relevant logics; 11. Fuzzy logics; 11a. Appendix: many valued modal logics; Postscript: an historical perspective on conditionals; Part II. Qualification and Identity: 12. Classical logic; 13. Free logic; 14. Constant domain modal logics; 15. Variable domain modal logics; 16. Necessary identity in modal logic; 17. Contingent identity in modal logic; 18. Non-normal modal logics; 19. Conditional logics; 20. Intuitionist logic; 21. Many-valued logics; 22. First degree entailment; 23. Logics with gaps, gluts, and worlds; 24. Relevant logics; 25. Fuzzy logics; Postscript: a methodological coda.
£34.19
Cambridge University Press The Mathematics of Logic A Guide to Completeness Theorems and Their Applications
Book SynopsisThis undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with KÃnig's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theoTrade Review"Kaye (pure mathematics, U. of Birmingham) gives undergraduate and first-year graduates key materials for a first course in logic, including a full mathematical account of the Completeness Theorem for first-order logic. As he builds a series of systems increasing in complexity, and proving and discussing the Completeness Theorem for each, Kaye keeps unfamiliar terminology to a minimum and provides proofs of all the required set theoretical results. He covers K<:o>nig's Lemma (including two ways of looking at mathematics), posets and maximal elements (including order), formal systems (including post systems and compatibility as bonuses), deduction in posets (including proving statements about a poset), Boolean algebras, propositional logic (including a system for proof about propositions), valuations (including semantics for propositional logic), filters and ideals (including the algebraic theory of Boolean algebras), first-order logic, completeness and compactness, model theory (including countable models) and nonstandard analysis (including infinitesimal numbers)." --Book NewsTable of ContentsPreface; How to read this book; 1. König's lemma; 2. Posets and maximal elements; 3. Formal systems; 4. Deductions in posets; 5. Boolean algebras; 6. Propositional logic; 7. Valuations; 8. Filters and ideals; 9. First-order logic; 10. Completeness and compactness; 11. Model theory; 12. Nonstandard analysis; Bibliography; Index.
£39.99
Cambridge University Press Basic Proof Theory 2ed 43 Cambridge Tracts in Theoretical Computer Science Series Number 43
Book SynopsisThis introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selTrade Review'This is a fine book. Any computer scientist with some logical background will benefit from studying it. It is written by two of the experts in the field and comes up to their usual standards of precision and care.' Ray Turner, Computer JournalTable of Contents1. Introduction; 2. N-systems and H-systems; 3. Gentzen systems; 4. Cut elimination with applications; 5. Bounds and permutations; 6. Normalization for natural deduction; 7. Resolution; 8. Categorical logic; 9. Modal and linear logic; 10. Proof theory of arithmetic; 11. Second-order logic; Solutions to selected exercises. Bibliography; Symbols and notation; Index.
£44.99
Cambridge University Press Graph Structure and Monadic SecondOrder Logic A LanguageTheoretic Approach 138 Encyclopedia of Mathematics and its Applications Series Number 138
Book SynopsisThe study of graph structure has advanced with great strides. This book unifies and synthesizes research over the last 25 years, detailing both theory and application. It will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.Trade Review'In its huge breadth and depth the authors manage to provide a comprehensive study of monadic second-order logic on graphs covering almost all aspects of the theory that can be presented from a language theoretical or algebraic point of view. There is currently no other textbook or any other source that matches the range of materials covered in this book. As such it is a fantastic resource for those who to study this area [and] will undoubtedly turn into the standard reference for this area.' Stephan Kreutzer, Mathematical ReviewsTable of ContentsForeword Maurice Nivat; Introduction; 1. Overview; 2. Graph algebras and widths of graphs; 3. Equational and recognizable sets in many-sorted algebras; 4. Equational and recognizable sets of graphs; 5. Monadic second-order logic; 6. Algorithmic applications; 7. Monadic second-order transductions; 8. Transductions of terms and words; 9. Relational structures; Conclusion and open problems; References; Index of notation; Index.
£160.55
Penguin Books Ltd A Field Guide to Lies
Book Synopsis
£16.00
John Wiley and Sons Ltd Deduction
Book SynopsisOffers a presentation of classical first-order logic. This book presents a truth tree system based on the work of Jeffrey, as well as a natural deduction system inspired by that of Kalish and Montague.Trade Review“Deduction is the best logic textbook on the market. It is modern, clean, elegant, sharp and direct. It is a perfect accompaniment to the most recent developments in philosophy and logic; in every sense the logic textbook for the twenty-first century.” Rick Benitez, University of SydneyTable of ContentsPreface to the Second Edition viii Acknowledgments x 1 Basic Concepts of Logic 1 1.1 Arguments 1 1.2 Validity 16 1.3 Implication and Equivalence 23 1.4 Logical Properties of Sentences 27 1.5 Satisfiability 31 2 Sentences 36 2.1 The Language of Sentential Logic 36 2.2 Truth Functions 40 2.3 A Sentential Language 46 2.4 Symbolization 49 2.5 Validity 56 2.6 Truth Tables 60 2.7 Truth Tables for Formulas 63 2.8 Truth Tables for Argument Forms 68 2.9 Implication, Equivalence, and Satisfiability 71 3 Truth Trees 76 3.1 Thinking Backwards 76 3.2 Constructing Truth Trees 80 3.3 Negation, Conjunction, and Disjunction 84 3.4 The Conditional and Biconditional 93 3.5 Other Applications 101 4 Natural Deduction 107 4.1 Natural Deduction Systems 107 4.2 Rules for Negation and Conjunction 110 4.3 Rules for the Conditional and Biconditional 118 4.4 Rules for Disjunction 122 4.5 Derivable Rules 125 5 Quantifiers 137 5.1 Constants and Quantifiers 138 5.2 Categorical Sentence Forms 144 5.3 Polyadic Predicates 148 5.4 The Language Q 153 5.5 Symbolization 156 6 Quantified Truth Trees 173 6.1 Rules for Quantifiers 174 6.2 Strategies 178 6.3 Interpretations 189 6.4 Constructing Interpretations from Trees 199 7 Quantified Natural Deduction 206 7.1 Deduction Rules for Quantifiers 206 7.2 Universal Proof 214 7.3 Derived Rules for Quantifiers 220 8 Identity and Function Symbols 225 8.1 Identity 225 8.2 Truth Tree Rules for Identity 231 8.3 Deduction Rules for Identity 235 8.4 Function Symbols 238 9 Necessity 249 9.1 If 249 9.2 Modal Connectives 251 9.3 Symbolization 256 9.4 Modal Truth Trees 261 9.5 Other Tree Rules 265 9.6 World Travelling 268 9.7 Modal Deduction 278 9.8 Other Modal Systems 289 10 Between Truth and Falsehood 295 10.1 Vagueness and Presupposition 295 10.2 Many-Valued Truth Tables 300 10.3 Many-Valued Trees 314 10.4 Many-Valued Deduction 325 10.5 Fuzzy Logic 332 10.6 Intuitionistic Logic 344 11 Obligation 361 11.1 Deontic Connectives 362 11.2 Deontic Truth Trees 370 11.3 Deontic Deduction 381 11.4 Moral and Practical Reasoning 387 12 Counterfactuals 395 12.1 The Meaning of Counterfactuals 399 12.2 Truth Tree Rules for Counterfactuals 402 12.3 Deduction Rules for Counterfactuals 409 12.4 Stalnaker’s Semantics: System CS 418 12.5 Lewis’s Semantics: System CL 423 13 Common-Sense Reasoning 434 13.1 When Good Arguments Go Bad 435 13.2 Truth Trees 439 13.3 Defeasible Deduction 454 13.4 Defeasible Deontic Logic 466 14 Quantifiers and Modality 475 14.1 Quantified S5 475 14.2 Free Logic 487 Bibliography 504 Index 507
£35.96
Harvard University Press Selected Logic Papers
Book SynopsisSelected Logic Papers, long out of print and now reissued with eight additional essays, includes much of the author's important work on mathematical logic and the philosophy of mathematics from the past sixty years.Trade Review[Quine] is at once the most elegant expounder of systematic logic in the older, pre-Gödelian style of Frege and Russell, the most distinguished American recruit to logical empiricism, probably the contemporary American philosopher most admired in the profession, and an original philosophical thinker of the first rank… This is an amazing feat of condensation with something solid to say in its brief scope about every major topic of interest in modern formal logic. * New York Review of Books *What [Quine] is expert in is, of course, logic… What [this book offers] is a view of the expert at work. Selected Logic Papers shows him actually doing logic… Logic is not a guide to life, but then Quine has never maintained that it was. It is a powerful adjunct to empirical inquiry, whose proper use requires prior discipline; its virtue lies in the fact that if we supply it with truth, it will never yield falsehood. Few have shown the manner of its use with more authority. * Partisan Review *This book is of continuing, not just historical interest. Quine is the greatest American philosopher of the twentieth century. His work in logic is inseparable from his work in other parts of philosophy. -- George Boolos, Massachusetts Institute of TechnologyTable of ContentsWhitehead and the Rise of Modern Logic (1941); Logic, Symbolic (1954); A Method of Generating Part of Arithmetic Without Use of Intuitive Logic (1934); Definition of Substitution (1936); Concatenation as a Basis for Arithmetic (1946); Set-theoretic Foundations for Logic (1936); Logic Based on Inclusion and Abstraction (1937); On Ordered Pairs and Relations (1945-46); On w-Inconsistency and a So-called Axiom of Infinity (1952); Element and Number (1941); On an Application of Tarski's Theory of Truth (1952); On Frege's Way Out (1954); Completeness of the Propositional Calculus (1937); On Cores and Prime Implicants of Truth Functions (1958); Two Theorems about Truth Functions (1951); On Boolean Functions (1949); On the Logic of Quantification (1945); A Proof Procedure for Quantification Theory (1954); Interpretations of Sets of Conditions (1953); Church's Theorem on the Decision Problem (1954); Quantification and the Empty Domain (1953); Reduction to a Dyadic Predicate (1953); Variables Explained Away (1960); Truth, Paradox, and Godel's Theorem (1992); Immanence and Validity (1991); MacHale on Boole (1985); Peirce's Logic (1989); Peano as Logician (1982); Free Logic, Description, and Virtual Classes (1994); The Inception of "New Foundations" (1987); Pythagorean Triples and Fermat's Last Theorem (1992).
£29.71
Princeton University Press The Search for Mathematical Roots 18701940
Book SynopsisPresents the history of a critical period in mathematics that includes accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. This work provides surveys of many related topics and figures of the late nineteenth century.Trade Review"Grattan-Guiness's uniformly interesting and valuable account of the interwoven development of logic and related fields of mathematics ... between 1870 and 1940 presents a significantly revised analysis of the history of the period... [His] book is important because it supplies what has been lacking: a full account of the period from a primary mathematical perspective."--James W. Van Evra, IsisTable of ContentsCHAPTER 1 Explanations 1.1 Sallies 3 1.2 Scope and limits of the book 3 1.2.1 An outline history 3 1.2.2 Mathematical aspects 4 1.2.3 Historical presentation 6 1.2.4 Other logics, mathematics and philosophies 7 1.3 Citations, terminology and notations 1.3.1 References and the bibliography 9 1.3.2 Translations, quotations and notations 10 1.4 Permissions and acknowledgements 11 CHAPTER 2 Preludes: Algebraic Logic and Mathematical Analysis up to 1870 2.1 Plan of the chapter 14 2.2 'Logique' and algebras in French mathematics 14 2.2.1 The 'logique' and clarity of 'ideologie' 14 2.2.2 Lagrange's algebraic philosophy 15 2.2.3 The many senses of 'analysis' 17 2.2.4 Two Lagrangian algebras: functional equations and differential operators 17 2.2.5 Autonomy for the new algebras 19 2.3 Some English algebraists and logicians 20 2.3.1 A Cambridge revival: the 'Analytical Society, Lacroix, and the professing of algebras 20 2.3.2 The advocacy of algebras by Babbage, Herschel and Peacock 20 2.3.3 An Oxford movement: Whately and the professing of logic 22 2.4 A London pioneer: De Morgan on algebras and logic 25 2.4.1 Summary of his life 25 2.4.2 De Morgan's philosophies of algebra 25 2.4.3 De Morgan's logical career 26 2.4.4 De Morgan's contributions to the foundations of logic 27 2.4.5 Beyond the syllogism 29 2.4.6 Contretemps over 'the quantification of the predicate' 30 2.4.7 The logic of two place relations, 1860 32 2.4.8 Analogies between logic and mathematics 35 2.4.9 De Morgan's theory of collections 36 2.5 A Lincoln outsider: Boole on logic as applied mathematics 37 2.5.1 Summary of his career 37 2.5.2 Boole's 'general method in analysis' 1844 39 2.5.3 The mathematical analysis of logic, 1847. 'elective symbols' and laws 40 2.5.4 'Nothing' and the 'Universe' 42 2.5.5 Propositions, expansion theorems, and solutions 43 2.5.6 The laws of thought, 1854: modified principles and extended methods 46 2.5.7 Boole's new theory of propositions 49 2.5.8 The character of Boole's system 50 2.5.9 Boole's search for mathematical roots 53 2.6 The semi-followers of Boole 54 2.6.1 Some initial reactions to Boole's theory 54 2.6.2 The reformulation by Jevons 56 2.6.3 Jevons versus Boole 59 2.6.4 Followers of Boole and/or Jevons 60 2.7 Cauchy, Weierstrass and the rise of mathematical analysis 63 2.7.1 Different traditions in the calculus 63 2.7.2 Cauchy and the Ecole Polytechnique 64 2.7.3 The gradual adoption and adaptation of Cauchy's new tradition 67 2.7.4 The refinements of Weierstrass and his followers 68 2.8 Judgement and supplement 70 2.8.1 Mathematical analysis versus algebraic logic 70 2.8.2 The places of Kant and Bolzano 71 CHAPTER 3 Cantor: Mathematics as Mengenlehre 3.1 Prefaces 75 3.1.1 Plan of the chapter 75 3.1.2 Cantor's career 75 3.2 The launching of the Mengenlehre, 1870-1883 79 3.2.1 Riemann's thesis: the realm of discontinuous functions 79 3.2.2 Heine on trigonometric series and the real line, 1870-1872 81 3.2.3 Cantor's extension of Heine's findings, 1870-1872 83 3.2.4 Dedekind on irrational numbers, 1872 85 3.2.5 Cantor on line and plane, 1874-1877 88 3.2.6 Infinite numbers and the topology of linear sets, 1878-1883 89 3.2.7 The Grundlagen, 1883: the construction of number-classes 92 3.2.8 The Grundlagen: the definition of continuity 95 3.2.9 The successor to the Grundlagen, 1884 96 3.3 Cantor's Acta mathematica phase, 1883-1885 97 3.3.1 Mittag-Lefler and the French translations, 1883 97 3.3.2 Unpublished and published 'communications' 1884-1885 98 3.3.3 Order-types and partial derivatives in the 'communications' 100 3.3.4 Commentators on Cantor, 1883-1885 102 3.4 The extension of the Mengenlehre, 1886-1897 103 3.4.1 Dedekind's developing set theory, 1888 103 3.4.2 Dedekind's chains of integers 105 3.4.3 Dedekind's philosophy of arithmetic 107 3.4.4 Cantor's philosophy of the infinite, 1886-1888 109 3.4.5 Cantor's new definitions of numbers 110 3.4.6 Cardinal exponentiation: Cantor's diagonal argument, 1891 110 3.4.7 Transfinite cardinal arithmetic and simply ordered sets, 1895 112 3.4.8 Transfinite ordinal arithmetic and well-ordered sets, 1897 114 3.5 Open and hidden questions in Cantor's Mengenlehre 114 3.5.1 Well-ordering and the axioms of choice 114 3.5.2 What was Cantor's 'Cantor's continuum problem'? 116 3.5.3 "Paradoxes" and the absolute infinite 117 3.6 Cantor's philosophy of mathematics 119 3.6.1 A mixed position 119 3.6.2 (No) logic and metamathematics 120 3.6.3 The supposed impossibility of infinitesimals 121 3.6.4 A contrast with Kronecker 122 3.7 Concluding comments: the character of Cantor's achievements 124 CHAPTER 4 Parallel Processes in Set Theory, Logics and Axiomatics, 1870s-1900s 4.1 Plans for the chapter 126 4.2 The splitting and selling of Cantor's Mengenlehre 126 4.2.1 National and international support 126 4.2.2 French initiatives, especially from Borel 127 4.2.3 Couturat outlining the infinite, 1896 129 4.2.4 German initiatives from Mein 130 4.2.5 German proofs of the Schroder-Bernstein theorem 132 4.2.6 Publicity from Hilbert, 1900 134 4.2.7 Integral equations and functional analysis 135 4.2.8 Kempe on 'mathematical form' 137 4.2.9 Kempe-who? 139 4.3 American algebraic logic: Peirce and his followers 140 4.3.1 Peirce, published and unpublished 141 4.3.2 Influences on Peirre's logic: father's algebras 142 4.3.3 Peirce's first phase: Boolean logic and the categories, 1867-1868 144 4.3.4 Peirce's virtuoso theory of relatives, 1870 145 4.3.5 Peirce's second phase, 1880: the propositional calculus 147 4.3.6 Peirre's second phase, 1881: finite and infinite 149 4.3.7 Peirce's students, 1883: duality, and 'Quantifying' a proposition 150 4.3.8 Peirre on 'icons' and the order of 'quantifiers; 1885 153 ~~~ 4.3.9 The Peirceans in the 1890s 154 4.4 German algebraic logic: from the Grassmanns to Schr6der 156 4.4.1 The Grassmanns on duality 156 4.4.2 Schroder's Grassmannian phase 159 4.4.3 Schroder's Peirrean 'lectures' on logic 161 4.4.4 Schrrider's first volume, 1890 161 4.4.5 Part of the second volume, 1891 167 4.4.6 Schroder's third volume, 1895: the 'logic of relatives' 170 4.4.7 Peirce on and against Schroder in The monist, 1896-1897 172 4.4.8 Schroder on Cantorian themes, 1898 174 4.4.9 The reception and publication of Schroder in the 1900s 175 4.5 Frege: arithmetic as logic 177 4.5.1 Frege and Frege' 177 4.5.2 The 'concept-script' calculus of Frege's 'pure thought; 1879 179 4.5.3 Frege's arguments for logicising arithmetic, 1884 183 4.5.4 Keny's conception of Fregean concepts in the mid 1880s 187 4.5.5 Important new distinctions in the early 1890s 187 4.5.6 The 'fundamental laws' of logicised arithmetic, 1893 191 4.5.7 Frege's reactions to others in the later 1890s 194 4.5.8 More 'fundamental laws' of arithmetic, 1903 195 4.5.9 Frege, Korselt and Thomae on the foundations of arithmetic 197 4.6 Husserl: logic as phenomenology 199 4.6.1 A follower of Weierstrass and Cantor 199 4.6.2 The phenomenological 'philosophy of arithmetic; 1891 201 4.6.3 Reviews by Frege and others 203 4.6.4 Husserl's 'logical investigations; 1900-1901 204 4.6.5 Husserl's early talks in Gottingen, 1901 206 4.7 Hilbert: early proof and model theory, 1899-1905 207 4.7.1 Hilbert's growing concern with axiomatics 207 4.7.2 Hilbert's diferent axiom systems for Euclidean geometry, 1899-1902 208 4.7.3 From German completeness to American model theory 209 4.7.4 Frege, Hilbert and Korselt on the foundations of geometries 212 4.7.5 Hilbert's logic and proof theory, 1904-1905 213 4.7.6 Zermelo's logic and set theory, 1904-1909 216 CHAPTER 5 Peano: the Formulary of Mathematics 5.1 Prefaces 219 5.1.1 Plan of the chapter 219 5.1.2 Peano's career 219 5.2 Formalising mathematical analysis 221 5.2.1 Improving Genocchi, 1884 221 5.2.2 Developing Grassmann's 'geometrical calculus; 1888 223 5.2.3 The logistic of arithmetic, 1889 225 5.2.4 The logistic of geometry, 1889 229 5.2.5 The logistic of analysis, 1890 230 5.2.6 Bettazzi on magnitudes, 1890 232 5.3 The Rivista: Peano and his school, 1890-1895 232 5.3.1 The 'society of mathematicians' 232 5.3.2 'Mathematical logic, 1891 234 5.3.3 Developing arithmetic, 1891 235 5.3.4 Infinitesimals and limits, 1892-1895 236 5.3.5 Notations and their range, 1894 237 5.3.6 Peano on definition by equivalence classes 239 5.3.7 Burali-Forti's textbook, 1894 240 5.3.8 Burali-Forti's research, 1896-1897 241 5.4 The Formulaire and the Rivista, 1895-1900 242 5.4.1 The first edition of the Formulaire, 1895 242 5.4.2 Towards the second edition of the Formulaire, 1897 244 5.4.3 Peano on the eliminability of 'the' 246 5.4.4 Frege versus Peano on logic and definitions 247 5.4.5 Schroder's steamships versus Peano's sailing boats 249 5.4.6 New presentations of arithmetic, 1898 251 5.4.7 - Padoa on classhoody 1899 253 5.4.8 Peano's new logical summary, 1900 254 5.5 Peanists in Paris, August 1900 255 5.5.1 An Italian Friday morning 255 5.5.2 Peano on definitions 256 5.5.3 Burali-Forti on definitions of numbers 257 5.5.4 Padoa on definability and independence 259 5.5.5 Pieri on the logic of geometry 261 5.6 Concluding comments: the character of Peano's achievements 262 5.6.1 Peano's little dictionary, 1901 262 5.6.2 Partly grasped opportunities 264 5.6.3 Logic without relations 266 CHAPTER 6 Russell's Way In: From Certainty to Paradoxes, 1895-1903 6.1 Prefaces 268 6.1.1 Plans for two chapters 268 6.1.2 Principal sources 269 6.1.3 Russell as a Cambridge undergraduate, 1891-1894 271 6.1.4 Cambridge philosophy in the 1890s 273 6.2 Three philosophical phases in the foundation of mathematics, 1895-1899 274 6.2.1 Russell's idealist axiomatic geometries 275 6.2.2 The importance of axioms and relations 276 6.2.3 A pair of pas de deux with Paris: Couturat and Poincare on geometries 278 6.2.4 The emergence of "itehead, 1898 280 6.2.5 The impact of G. E. Moore, 1899 282 6.2.6 Three attempted books, 1898-1899 283 6.2.7 Russell's progress with Cantor's Mengenlehre, 1896-1899 285 6.3 From neo-Hegelianism towards 'Principles', 1899-1901 286 6.3.1 Changing relations 286 6.3.2 Space and time, absolutely 288 6.3.3 'Principles of Mathematics, 1899-1900 288 6.4 The first impact of Peano 290 6.4.1 The Paris Congress of Philosophy, August 1900: Schroder versus Peano on 'the' 290 6.4.2 Annotating and popularising in the autumn 291 6.4.3 Dating the origins of Russell's logicism 292 6.4.4 Drafting the logic of relations, October 1900 296 6.4.5 Part 3 of The principles, November 1900: quantity and magnitude 298 6.4.6 Part 4, November 1900: order and ordinals 299 6.4.7 Part 5, November 1900: the transfinite and the continuous 300 6.4.8 Part 6, December 1900: geometries in space 301 6.4.9 Whitehead on 'the algebra of symbolic logic, 1900 302 6.5 Convoluting towards logicism, 1900-1901 303 6.5.1 Logicism as generalised metageometry, January 1901 303 6.5.2 The first paper for Peano, February 1901: relations and numbers 305 6.5.3 Cardinal arithmetic with "itehead and Russell, June 1901 307 6.5.4 The second paper for Peano, March August 1901: set theory with series 308 6.6 From 'fallacy' to 'contradiction', 1900-1901 310 6.6.1 Russell on Cantor's 'fallacy; November 1900 310 6.6.2 Russell's switch to a 'contradiction' 311 6.6.3 Other paradoxes: three too large numbers 312 6.6.4 Three passions and three calamities, 1901-1902 314 6.7 Refining logicism, 1901-1902 315 6.7.1 Attempting Part 1 of The principles, May 1901 315 6.7.2 Part 2, June 1901: cardinals and classes 316 6.7.3 Part 1 again, April-May 1902: the implicational logicism 316 6.7.4 Part 1: discussing the indefinables 318 6.7.5 Part 7, June 1902: dynamics without statics; and within logic? 322 6.7.6 Sort-of finishing the book 323 6.7.7 The first impact of Frege, 1902 323 6.7.8 AppendixA on Frege 326 6.7.9 Appendix B: Russell's first attempt to solve the paradoxes 327 6.8 The roots of pure mathematics? Publishing The principles at last, 1903 328 6.8.1 Appearance and appraisal 328 6.8.2 A gradual collaboration with Whitehead 331 CHAPTER 7 Russell and Whitehead Seek the Principia Mathematica, 1903-1913 7.1 Plan of the chapter 333 7.2 Paradoxes and axioms in set theory, 1903-1906 333 7.2.1 Uniting the paradoxes of sets and numbers 333 7.2.2 New paradoxes, mostly of naming 334 7.2.3 The paradox that got away: heterology 336 7.2.4 Russell as cataloguer of the paradoxes 337 7.2.5 Controversies over axioms of choice, 1904 339 7.2.6 Uncovering Russell's 'multiplicative axiom, 1904 340 7.2.7 Keyser versus Russell over infinite classes, 1903-1905 342 7.3 The perplexities of denoting, 1903-1906 342 7.3.1 First attempts at a general system, 1903-1905 342 7.3.2 Propositional functions, reducible and identical 344 7.3.3 The mathematical importance of definite denoting functions 346 7.3.4 'On denoting' and the complex, 1905 348 7.3.5 Denoting, quantification and the mysteries of existence 350 7.3.6 Russell versus MacColl on the possible, 1904-1908 351 7.4 From mathematical induction to logical substitution, 1905-1907 354 7.4.1 Couturat's Russellian principles 354 7.4.2 A second pas de deux with Paris: Boutroux and Poincare on logicism 355 7.4.3 Poincare on the status of mathematical induction 356 7.4.4 Russell's position paper, 1905 357 7.4.5 Poincare and Russell on the vicious circle principle, 1906 358 7.4.6 The rise of the substitutional theory, 1905-1906 360 7.4.7 The fall of the substitutional theory, 1906-1907 362 7.4.8 Russell's substitutional propositional calculus 364 7.5 Reactions to mathematical logic and logicism, 1904-1907 366 7.5.1 The International Congress of Philosophy, 1904 366 7.5.2 German philosophers and mathematicians, especially Schonflies 368 7.5.3 Activities among the Peanists 370 7.5.4 American philosophers: Royce and Dewey 371 7.5.5 American mathematicians on classes 373 7.5.6 Huntington on logic and orders 375 7.5.7 Judgements fiom Shearman 376 7.6 Whitehead's role and activities, 1905-1907 377 7.6.1 Whitehead's construal of the 'material world' 377 7.6.2 The axioms of geometries 379 7.6.3 Whitehead's lecture course, 1906-1907 379 7.7 The sad compromise: logic in tiers 380 7.7.1 Rehabilitating propositional functions, 1906-1907 380 7.7.2 Two reflective pieces in 1907 382 7.7.3 Russell's outline of 'mathematical logic, 1908 383 7.8 The forming of Principia mathematica 384 7.8.1 Completing and funding Principia mathematica 384 7.8.2 The Organisation of Principia mathematica 386 7.8.3 The propositional calculus, and logicism 388 7.8.4 The predicate calculus, and descriptions 391 7.8.5 Classes and relations, relative to propositional functions 392 7.8.6 The multiplicative axiom: some uses and avoidance 395 7.9 Types and the treatment of mathematics in Principia mathematica 396 7.9.1 7~pes in orders 396 7.9.2 Reducing the edifice 397 7.9.3 Individuals, their nature and number 399 7.9.4 Cardinals and their finite arithmetic 401 7.9.5 The generalised ordinals 403 7.9.6 The ordinals and the alephs 404 7.9.7 The odd small ordinals 406 7.9.8 Series and continuity 406 7.9.9 Quantity with ratios 408 CHAPTER 8 The Influence and Place of Logicism, 1910-1930 8.1 Plans for two chapters 411 8.2 Whitehead's and Russell's transitions from logic to philosophy, 1910-1916 412 8.2.1 The educational concerns of "itehead, 1910-1916 412 8.2.2 Whitehead on the principles of geometry in the 1910s 413 8.2.3 British reviews of Principia mathematica 415 8.2.4 Russell and Peano on logic, 1911-1913 416 8.2.5 Russell's initial problems with epistemology, 1911-1912 417 8.2.6 Russell's first interactions with Wittgenstein, 1911-1913 418 8.2.7 Russell's confrontation with Wiener, 1913 419 8.3 Logicism and epistemology in America and with Russell, 1914-1921 421 8.3.1 Russell on logic and epistemology at Harvard, 1914 421 8.3.2 Two long American reviews 424 8.3.3 Reactions from Royce students: Sheffer and Lewis 424 8.3.4 Reactions to logicism in New York 428 8.3.5 OtherAmerican estimations 429 8.3.6 Russell's 'logical atomism' and psychology, 1917-1921 430 8.3.7 Russell's 'introduction'to logicism, 1918-1919 432 8.4 Revising logic and logicism at Cambridge, 1917-1925 434 8.4.1 New Cambridge authors, 1917-1921 434 8.4.2 Wittgenstein's 'Abhandlung' and Tractatus, 1921-1922 436 8.4.3 The limitations of Wittgenstein's logic 437 8.4.4 Towards extensional logicism: Russell's revision of Principia mathematica, 1923-1924 440 8.4.5 Ramsey's entry into logic and philosophy, 1920-1923 443 8.4.6 Ramsey's recasting of the theory of types, 1926 444 8.4.7 Ramsey on identity and comprehensive extensionality 446 8.5 Logicism and epistemology in Britain and America, 1921-1930 448 8.5.1 Johnson on logic, 1921-1924 448 8.5.2 Other Cambridge authors, 1923-1929 450 8.5.3 American reactions to logicism in mid decade 452 8.5.4 Groping towards metalogic 454 8.5.5 Reactions in and around Columbia 456 8.6 Peripherals: Italy and France 458 8.6.1 The occasional Italian survey 458 8.6.2 New French attitudes in the Revue 459 8.6.3 Commentaries in French, 1918-1930 461 8.7 German-speaking reactions to logicism, 1910-1928 463 8.7.1 (Neo-)Kantians in the 1910s 463 8.7.2 Phenomenologists in the 1910s 467 8.7.3 Frege's positive and then negative thoughts 468 8.7.4 Hilbert's definitive 'metamathematics; 1917-1930 470 8.7.5 Orders of logic and models of set theory: Lowenheim and Skolem, 1915-1923 475 8.7.6 Set theory and Mengenlehre in various forms 476 8.7.7 Intuitionistic set theory and logic: Brouwer and Weyl, 1910-1928 480 8.7.8 (Neo-)Kantians in the 1920s 484 8.7.9 Phenomenologists in the 1920s 487 8.8 The rise of Poland in the 1920s: the Lvnv-Warsaw school 489 8.8.1 From Lv6v to Warsaw: students of Twardowski 489 8.8.2 Logics with Lukasiewicz and Tarski 490 8.8.3 Russell's paradox and Lesniewski's three systems 492 8.8.4 Pole apart: Chwistek's 'semantic' logicism at Cracov 495 8.9 The rise of Austria in the 1920s: the Schlick circle 497 8.9.1 Formation and influence 497 8.9.2 The impact of Russell, especially upon Camap 499 8.9.3 'Logicism ' in Camap's Abriss, 1929 500 8.9.4 Epistemology in Camap's Aufbau, 1928 502 8.9.5 Intuitionism and proof theory: Brouwer and Godel, 1928-1930 504 CHAPTER 9 Postludes: Mathematical Logic and Logicism in the 1930s 9.1 Plan of the chapter 506 9.2 Godel's incompletability theorem and its immediate reception 507 9.2.1 The consolidation of Schlick's 'Vienna' Circle 507 9.2.2 News from G6del: the Konigsberg lectures, September 1930 508 9.2.3 G6del's incompletability theorem, 1931 509 9.2.4 Effects and reviews of G6del's theorem 511 9.2.5 Zermelo against Godeb the Bad Elster lectures, September 1931 512 9.3 Logic(ism) and epistemology in and around Vienna 513 9.3.1 Carnap for 'metalogic' and against metaphysics 513 9.3.2 Carnap's transformed metalogic: the 'logical syntax of language; 1934 515 9.3.3 Carnap on incompleteness and truth in mathematical theories, 1934-1935 517 9.3.4 Dubislav on definitions and the competing philosophies of mathematics 519 9.3.5 Behmann's new diagnosis of the paradoxes 520 9.3.6 Kaufmann and Waismann on the philosophy of mathematics 521 9.4 Logic(ism) in the U.S.A. 523 9.4.1 Mainly Eaton and Lewis 523 9.4.2 Mainly Weiss and Langer 525 9.4.3 Whitehead's new attempt to ground logicism, 1934 527 9.4.4 The debut of Quine 529 9.4.5 Two journals and an encyclopaedia, 1934-1938 531 9.4.6 Carnap's acceptance of the autonomy of semantics 533 9.5 The battle of Britain 535 9.5.1 The campaign of Stebbing for Russell and Carnap 535 9.5.2 Commentary from Black and Ayer 538 9.5.3 Mathematicians-and biologists 539 9.5.4 Retiring into philosophy: Russell's return, 1936-1937 542 9.6 European, mostly northern 543 9.6.1 Dingler and Burkamp again 543 9.6.2 German proof theory after Godel 544 9.6.3 Scholz's little circle at Munster 546 9.6.4 Historical studies, especially by Jorgensen 547 9.6.5 History philosophy, especially Cavailles 548 9.6.6 Other Francophone figures, especially Herbrand 549 9.6.7 Polish logicians, especially Tarski 551 9.6.8 Southern Europe and its former colonies 553 CHAPTER 10 The Fate of the Search 10.1 Influences on Russell, negative and positive 556 10.1.1 Symbolic logics: living together and living apart 556 10.1.2 The timing and origins of Russell's logicism 557 10.1.3 (Why) was Frege (so) little read in his lifetime? 558 10.2 The content and impact of logicism 559 10.2.1 Russell's obsession with reductionist logic and epistemology 560 10.2.2 The logic and its metalogic 562 10.2.3 The fate of logicism 563 10.2.4 Educational aspects, especially Piaget 566 10.2.5 The role of the U.S.A.: judgements in the Schi1pp series 567 10.3 The panoply of foundations 569 10.4 Sallies 573 CHAPTER 11 Transcription of Manuscripts 11.1 Couturat to Russell, 18 December 1904 574 11.2 Veblen to Russell, 13 May 1906 577 11.3 Russell to Hawtrey, 22 January 1907 (or 1909?) 579 11.4 Jourdain's notes on Wittgenstein's first views on Russell's paradox, April 1909 580 11.5 The application of Whitehead and Russell to the Royal Society, late 1909 581 11.6 Whitehead to Russell, 19 January 1911 584 11.7 Oliver Strachey to Russell, 4 January 1912 585 11.8 Quine and Russell, June-July 1935 586 11.8.1 Russell to Quine, 6 June 1935 587 11.8.2 Quine to Russell, 4 July 1935 588 11.9 Russell to Henkin, 1 April 1963 592 BIBLIOGRAPHY 594 INDEX 671
£103.70
Princeton University Press Computers Rigidity and Moduli
Book SynopsisPresents an area of mathematical research that combines topology, geometry, and logic. This book seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity.Trade Review"This is a terrific book. It does no less than introduce an entire new field of mathematics - a truly astounding development. It will be widely read, I think, as much because of the masterful exposition as for the beautiful mathematics. Weinberger gives very clear and accessible descriptions of all the relevant tools from computability, topology, and geometry, in a friendly and engaging style. He has done the mathematical community a great service indeed." - Robin Forman, Rice University; "This book represents a very exciting new area of research at the interface of topology and logic. Written in a quite readable style, and presenting the more accessible cases in detail while giving references for the more involved results, it is a book whose methods and ideas will surely have many more significant applications over the next several years." - Kevin M. Whtye, University of Illinois at Chicago"
£62.40
Princeton University Press Fixing Frege
Book SynopsisSurveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. This work considers every proposed fix, each with its distinctive philosophical advantages and drawbacks.Trade ReviewCo-Winner of the 2007 Shoenfield Prize, Association for Symbolic Logic "Fixing Frege fills a serious gap in the Frege's literature (always increasing but perhaps with an excessive attention paid to semantics and the philosophy of language) and should remain for a long time a necessary reference for scholars in the field."--Ignacio Angelelli, Review of Modern LogicTable of ContentsAcknowledgments ix CHAPTER 1: Frege, Russell, and After 1 CHAPTER 2: Predicative Theories 86 CHAPTER 3: Impredicative Theories 146 Tables 215 Notes 227 References 241 Index 249
£59.50
Princeton University Press Enlightening Symbols A Short History of
Book SynopsisWhat did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? This book explains the history behind the development of our mathematical notation system.Trade Review"Mazur (Euclid in the Rainforest) gives readers the fascinating history behind the mathematical symbols we use, and completely take for granted, every day. Mathematical notation turns numbers into sentences--or, to the uninitiated, a mysterious and impenetrable code. Mazur says the story of math symbols begins some 3,700 years ago, in ancient Babylon, where merchants incised tallies of goods on cuneiform tablets, along with the first place holder--a blank space. Many early cultures used letters for both numbers and an alphabet, but convenient objects like rods, fingers, and abacus beads, also proved popular. Mazur shows how our 'modern' system began in India, picking up the numeral 'zero' on its way to Europe, where it came into common use in the 16th century, thanks to travelers and merchants as well as mathematicians like Fibonacci. Signs for addition, subtraction, roots, and equivalence followed, but only became standardized through the influence of scientists and mathematicians like Rene Descartes and Gottfried Leibniz. Mazur's lively and accessible writing makes what could otherwise be a dry, arcane history as entertaining as it is informative."--Publishers Weekly "[A] fascinating narrative... This is a nuanced, intelligently framed chronicle packed with nuggets--such as the fact that Hindus, not Arabs, introduced Arabic numerals. In a word: enlightening."--George Szpiro, Nature "Mazur begins by illustrating how the ancient Incas and Mayans managed to write specific, huge numbers. Then, for more than 200 pages, he traces the history of division signs, square roots, pi, exponents, graph axes and other symbols in the context of cognition, communication, and analysis."--Washington Post "Mazur delivers a solid exposition of an element of mathematics that is fundamental to its history."--Library Journal "Mazur treats only a subset of F. Cajori's monumental A History of Mathematical Notation (Dover, 1993 first edition 1922) and there is overlap with many other mathematical history books, but Mazur adds new findings and insights and it is so much more entertaining ... and these features make it an interesting addition to the existing literature for anybody with only a slight interest in mathematics or its history."--European Mathematical Society "Symbols like '+' and '=' are so ingrained that it's hard to conceive of math without them. But a new book, Enlightening Symbols: A Short History of Mathematical Notation and its Hidden Power, offers a surprising reminder: Until the early 16th century, math contained no symbols at all."--Kevin Hartnett, Boston Globe "Enlightening Symbols retraces the winding road that has led to the way we now teach, study, and conceive mathematics... Thanks to Mazur's playful approach to the subject, Enlightening Symbols offers an enjoyable read."--Gaia Donati, Science "If you enjoy reading about history, languages and science, then you'll enjoy this book... The best part is the writing is compelling enough that you don't have to be a mathematician to enjoy this informative book."--Guardian.com's GrrlScientist blog "[I]nformative, highly readable and scholarly."--Brian Rotman, Literary Review "[T]his insightful account of the historical development of a highly characteristic feature of the mathematical enterprise also represents a valuable contribution to our understanding of the nature of mathematics."--Eduard Glas, Mathematical Reviews Clippings "Joseph Mazur's beautiful book Enlightening Symbols tells the story of human civilization through the development of mathematical notation. Surprises abound... The book is visually exquisite, great care having been taken with illustrations and figures. Mazur's discussion of the emergence of particular symbols affords the reader an overview of the often difficult primary literature."--Donal O'Shea, Sarasota Herald-Tribune "At whatever depth one chooses to read it, Enlightening Symbols has something for everyone. It is entertaining and eclectic, and Mazur's personal and easy style helps connect us with those who led the long and winding search for the best ways to quantify and analyze our world. Their success has liberated us from 'the shackles of our physical impressions of space'--and of the particular and the concrete--'enabling imagination to wander far beyond the tangible world we live in, and into the marvels of generality.'"--Robyn Arianrhod, Notices of the Notices of the American Mathematical Society "Mazur introduces the reader to major characters, weaves in relevant aspects of wider culture and gives a feel for the breadth of mathematical history. It is a useful book for both student and interested layperson alike."--Mark McCartney, London Mathematical Society "[T]his is a good book. It is well written by an experienced author and is full of interesting facts about how the symbols used in mathematics have arisen. It would certainly interest anyone who studies the history of mathematics."--Phil Dyke, Leonardo "Mazur is a master story teller."--John Stillwell, Bulletin of the American Mathematical SocietyTable of ContentsIntroduction ix Definitions xxi Note on the Illustrations xxiii Part 1 Numerals 1 1. Curious Beginnings 3 2. Certain Ancient Number Systems 10 3. Silk and Royal Roads 26 4. The Indian Gift 35 5. Arrival in Europe 51 6. The Arab Gift 60 7. Liber Abbaci 64 8. Refuting Origins 73 Part 2 Algebra 81 9. Sans Symbols 85 10. Diophantus's Arithmetica 93 11. The Great Art 109 12. Symbol Infancy 116 13. The Timid Symbol 127 14. Hierarchies of Dignity 133 15. Vowels and Consonants 141 16. The Explosion 150 17. A Catalogue of Symbols 160 18. The Symbol Master 165 19. The Last of the Magicians 169 Part 3 The Power of Symbols 177 20. Rendezvous in the Mind 179 21. The Good Symbol 189 22. Invisible Gorillas 192 23. Mental Pictures 210 24. Conclusion 216 Appendix A Leibniz's Notation 221 Appendix B Newton's Fluxion of xn 223 Appendix C Experiment 224 Appendix D Visualizing Complex Numbers 228 Appendix E Quaternions 230 Acknowledgments 233 Notes 235 Index 269
£29.75
Princeton University Press AgentZero
Book SynopsisIntroduces a theoretical entity: Agent_Zero. This title weaves a computational tapestry with threads from Plato, Hume, Darwin, Pavlov, Smith, Tolstoy, Marx, James, and Dostoevsky, among others.Trade Review"Agent Zero offers a solution to some of social science's great puzzles. Its behavioral basis is the interplay of emotion, cognition, and network contagion effects. It elegantly explains why so many human actions are so manifestly dysfunctional, and why some are downright evil."—George Akerlof, Nobel Laureate in Economics"Rarely has a book stimulated me intellectually as much as this one. Particularly exciting is the incorporation of agents who feel (affect) and deliberate, as well as influence one another through social interaction. Epstein is a brilliantly creative scholar and the range of applications showcased here is stunning. In sum, this is a pathbreaking book."—Paul Slovic, University of Oregon"Joshua Epstein proposes a parsimonious but powerful model of individual behavior that can generate an extraordinary range of group behaviors, including mob violence, manias and financial panics, rebellions, network dynamics, and a host of other complex social phenomena. This is a highly original, beautifully conceived, and important book."—Peyton Young, University of Oxford"In social science generally and most notably in economics, the rational actor model has long been the benchmark for policy analysis and institutional design. Epstein now offers a worthy alternative: Agent_Zero, a mathematically and computationally tractable agent whose inner workings are grounded in neuroscience. Much like you and me, Agent_Zero is influenced by emotion, reason, and social pressures. Epstein demonstrates that collections of Agent Zeros perform amazingly like real groups, teams, and societies and can therefore serve as the fundamental building blocks for what he calls Generative Social Science. The rational actor now has a true competitor. Agent_Zero is a major advance."—Scott Page, University of Michigan"This is social science based on how our brains actually work. Epstein's computerized 'agents' can feel passion and fear, and can influence each other emotionally. And when they interact, we see many of the realities of social life, from the dynamics of juries to racist violence to Arab springs. A remarkable and original piece of work."—W. Brian Arthur, Santa Fe InstituteTable of ContentsForeword xi Preface xiii Acknowledgments xv INTRODUCTION 1 MOTIVATION 1 Generate Social Dynamics 2 A Core Target 2 THE MODEL COMPONENTS 5 Model Overview 6 Skeletal Equation 8 Specific Components 9 ORGANIZATION 10 Part I: Mathematical Model 10 Part II: Agent-Based Model 11 Part III: Extensions 13 Replicability and Research Resources on the Princeton University Press Website 16 Part IV: Future Research and Conclusions 17 PART 1. MATHEMATICAL MODEL 19 I.1. THE PASSIONS: FEAR CONDITIONING 19 Fear Circuitry and the Perils of Fitness 20 Nomenclature of Conditioning 29 The Rescorla-Wagner Model 33 Social Examples 37 Fear Extinction 41 I.2. REASON: THE COGNITIVE COMPONENT 46 I.3. THE SOCIAL COMPONENT 51 Simple Version of the Core Target 55 Examples of Fear Contagion 57 Mechanisms of Fear Contagion 59 Conformist Empirical Estimates 63 Generalizing Rescorla-Wagner 67 The Central Case 69 Tolstoy: The First Agent Modeler 71 A Mathematical Aside on Social Norms as Vector Fields 74 Extinction of Majorities 78 I.4. INTERIM CONCLUSIONS 80 PART II. AGENT-BASED COMPUTATIONAL MODEL 81 Affective Component 84 "Rational" Component 85 Social Component 88 Action 89 Pseudocode 89 II.1. COMPUTATIONAL PARABLES 90 Parable 1: The Slaughter of Innocents through Dispositional Contagion 90 Parable 2: Agent_Zero Initiates: Leadership as Susceptibility to Dispositional Contagion 94 Run 3. Information Cuts Both Ways 96 Run 4. A Day in the Life of Agent_Zero: How Affect and Probability Can Change on Different Time Scales 98 Run 5. Lesion Studies 102 PART III. EXTENSIONS 107 III.1. ENDOGENOUS DESTRUCTIVE RADIUS 107 III.2. AGE AND IMPULSE CONTROL 109 III.3. FIGHT VS. FLIGHT 110 Case 1: Fight 111 Case 2: Flight 112 Capital Flight 114 III.4. REPLICATING THE Latane-DARLEY EXPERIMENT 114 Threshold Imputation 115 The Dialogue 118 III.5. MEMORY 118 III.6. COUPLINGS: ENTANGLEMENT OF PASSION AND REASON 122 Mathematical Treatment 124 III.7.ENDOGENOUS DYNAMICS OF CONNECTION STRENGTH 128 Affective Homophily 128 General Setup 130 Agent-Based Model: Nonequlibrium Dynamics 135 III.8. GROWING THE 2011 ARAB SPRING 138 III.9. JURY PROCESSES 143 Phase 1. Public Phase 143 Phase 2. Courtroom Trial Phase 145 Phase 3. Jury Phase 147 III.10. EMERGENT DYNAMICS OF NETWORK STRUCTURE 152 Network Structure Dynamics as a Poincare Map 153 Relation to Literature 159 III.11. MULTIPLE SOCIAL LEVELS 160 Agent_Zero as Witness to History 161 III.12. THE 18TH BRUMAIRE OF AGENT_ZERO 165 III.13. INTRODUCTION OF PRICES AND SEASONAL ECONOMIC CYCLES 168 Prices 168 A Christmas Story 173 III.14. SPIRALS OF MUTUAL ESCALATION 176 PART IV. FUTURE RESEARCH AND CONCLUSION 181 IV.1. FUTURE RESEARCH 181 IV.2. CONCLUSION 187 Civil Violence 187 Economics 188 Health Behavior 189 Psychology 190 Jury Dynamics 191 The Formation and Dynamics of Networks 191 Mutual Escalation Dynamics 192 Birth and Intergenerational Transmission 192 IV.3. TOWARD NEW GENERATIVE FOUNDATIONS 192 Appendix I. Threshold Imputation Bounds 195 Appendix II. Mathematica Code 197 Appendix III. Agent_Zero NetLogo Source Code 213 Appendix IV. Parameter Settings for Model Runs 221 References 227 Index 243
£44.00
Princeton University Press Math Bytes
Book SynopsisHow can reposting on Twitter kill a movie's opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson's method for disproving Fermat's Last Theorem? This title deals with these questions.Trade ReviewOne of Choice's Outstanding Academic Titles for 2014 "[Math Bytes] manages to fulfill its aim of providing a 'tasty byte of math and computing' while following a clear, concise, and to-the-point format... [P]rovides interesting insights to some of the complex, highly sophisticated algorithms that lie behind some of our most widely used technological resources."--Rachael Skyner, Science "The author's humanistic, sincere enjoyment of communicating his selections permeates and I think defines the book... The choice of topics and exposition details make the book entertainingly relevant."--Alexander Bogomolny, Cut the Knot "Math Bytes is fun and full of puzzles and brainteasers in a mashup of mathematics, social media, and pop culture referencing Beyonce, Google, and Twitter among others... This reviewer is simply a fool for math puzzles (though some readers might stop at simply a fool). Math Bytes scratches that itch quite nicely."--Robert Schaefer, New York Journal of Books "Printed on glossy paper and filled with colourful photographs, illustrations and diagrams on nearly every page, this book discusses mathematical ideas that can help us make sense of the digital world. The author's offbeat viewpoint comes from a truly unusual background; he studied mime with the legendary Marcel Marceau whilst pursuing his doctorate in applied maths."--Devorah Bennu, GrrlScientist, The Guardian "Tim Chartier, a professor of mathematics at Davidson College, has put together a delightful book of recreational mathematics. His presentation of a large array of topics is accompanied by excellent graphics, many in color... In sum, a fun book."--Philip J. Davis, SIAM News "The mathematical topics are interesting and informative; if you teach at the college level, you are likely to find some interesting fodder for your courses here. You also may, as I did, learn some new things yourself... This book, which is filled with photos, drawings, and anecdotes, is a treasure trove of amusing mathematical vignettes. It makes for very pleasant summer reading."--Mark Hunacek, MAA Reviews "The reader is constantly challenged to think about it or answer certain questions and to solve some problems (some solutions are provided at the end). Most of all, it's such a lovely little booklet that does not give you the time to get bored with. The average chapter length, including the many illustrations, is only 10 pages. Just enough to catch your interest and get bitten by the mathematics."--A. Bultheel, European Mathematical Society "For readers who love math, computing and puzzles, Math Bytes will be a welcome gift."--George Erdosh, San Francisco Book Review "[L]ively and entertaining book... All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pace--a bit and a byte at a time."--Zentralblatt MATH "A mathematical Pandora's box released is perhaps the best way to describe this book. It overflows with ideas, flitting from one fascinating topic to the next, often without an apparent connection. The range is impressive... Everyone should find a 'math byte' of interest in this book, and perhaps end up finding other topics of interest as well."--Choice "I definitely learnt a few new things and was entertained as I did so. Furthermore, anything that spreads the message that mathematics is both interesting and useful has to be a good thing, so I wish this book success."--Rob Ashmore, Mathematics Today "A fun collection of mathematical applications that has something for everyone, even mathphobes."--Anne Quinn, National Council of Teachers of MathematicsTable of ContentsPreface ix 1Your First Byte 1 2Deceiving Arithmetic 5 3Two by Two 11 4Infinite Detail 21 5Plot the Course 32 6Doodling into a Labyrinth 42 7Obama-cize Yourself 54 8Painting with M&Ms 61 9Distorting Reality 73 10A Pretty Mathematical Face 86 11March MATHness 98 12Ranking a Googol of Bits 105 13A Byte to Go 124 14Up to the Challenge 125 Bibliography 131 Index 133 Image Credits 135
£18.00
Princeton University Press An Introduction to Benfords Law
Book SynopsisThis book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the law'Trade Review"This is a marvelous and excellent introduction."--Adhemar Bultheel, European Mathematical Society Bulletin "A must-read for novices and experts alike. It can be used for a graduate-level topics course or as a reference text for researchers in the field. The exposition is outstanding, with hundreds of carefully chosen examples, figures and diagrams to illustrate the theory. For those who are up for a challenge, the book contains several open problems as well. An Introduction to Benford's Law will surely be the go-to text on the subject for years to come."--Pieter C. Allaart, Mathematical ReviewsTable of ContentsPreface vii 1 Introduction 1 1.1 History 3 1.2 Empirical evidence 4 1.3 Early explanations 6 1.4 Mathematical framework 7 2 Significant Digits and the Significand 11 2.1 Significant digits 11 2.2 The significand 12 2.3 The significand sigma-algebra 14 3 The Benford Property 22 3.1 Benford sequences 23 3.2 Benford functions 28 3.3 Benford distributions and random variables 29 4 The Uniform Distribution and Benford's Law 43 4.1 Uniform distribution characterization of Benford's law 43 4.2 Uniform distribution of sequences and functions 46 4.3 Uniform distribution of random variables 54 5 Scale-, Base-, and Sum-Invariance 63 5.1 The scale-invariance property 63 5.2 The base-invariance property 74 5.3 The sum-invariance property 80 6 Real-valued Deterministic Processes 90 6.1 Iteration of functions 90 6.2 Sequences with polynomial growth 93 6.3 Sequences with exponential growth 97 6.4 Sequences with super-exponential growth 101 6.5 An application to Newton's method 111 6.6 Time-varying systems 116 6.7 Chaotic systems: Two examples 124 6.8 Differential equations 127 7 Multi-dimensional Linear Processes 135 7.1 Linear processes, observables, and difference equations 135 7.2 Nonnegative matrices 139 7.3 General matrices 145 7.4 An application to Markov chains 162 7.5 Linear difference equations 165 7.6 Linear differential equations 170 8 Real-valued Random Processes 180 8.1 Convergence of random variables to Benford's law 180 8.2 Powers, products, and sums of random variables 182 8.3 Mixtures of distributions 202 8.4 Random maps 213 9 Finitely Additive Probability and Benford's Law 216 9.1 Finitely additive probabilities 217 9.2 Finitely additive Benford probabilities 219 10 Applications of Benford's Law 223 10.1 Fraud detection 224 10.2 Detection of natural phenomena 225 10.3 Diagnostics and design 226 10.4 Computations and Computer Science 228 10.5 Pedagogical tool 230 List of Symbols 231 Bibliography 234 Index 245
£63.75
Princeton University Press Actionminimizing Methods in Hamiltonian Dynamics
Book SynopsisJohn Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach--known as Aubry-Mather theory--singles out the existence of special orbits and invariant measures of the system, which posseTable of ContentsPreface vii 1 Tonelli Lagrangians and Hamiltonians on Compact Manifolds 1 1.1 Lagrangian Point of View 1 1.2 Hamiltonian Point of View 4 2 From KAM Theory to Aubry-Mather Theory 8 2.1 Action-Minimizing Properties of Measures and Orbits on KAM Tori 8 3 Action-Minimizing Invariant Measures for Tonelli Lagrangians 18 3.1 Action-Minimizing Measures and Mather Sets 18 3.2 Mather Measures and Rotation Vectors 24 3.3 Mather's a-and B-Functions 28 3.4 The Symplectic Invariance of Mather Sets 35 3.5 An Example: The Simple Pendulum (Part I) 39 3.6 Holonomic Measures and Generic Properties of Tonelli Lagrangians 45 4 Action-Minimizing Curves for Tonelli Lagrangians 48 4.1 Global Action-Minimizing Curves: Aubry and Mane Sets 48 4.2 Some Topological and Symplectic Properties of the Aubry and Mane Sets 66 4.3 An Example: The Simple Pendulum (Part II) 68 4.4 Mather's Approach: Peierls' Barrier 71 5 The Hamilton-Jacobi Equation and Weak KAM Theory 76 5.1 Weak Solutions and Subsolutions of Hamilton-Jacobi and Fathi's Weak KAM theory 76 5.2 Regularity of Critical Subsolutions 85 5.3 Non-Wandering Points of the Mane Set 87 Appendices A On the Existence of Invariant Lagrangian Graphs 89 A.1 Symplectic Geometry of the Phase Space 89 A.2 Existence and Nonexistence of Invariant Lagrangian Graphs 91 B Schwartzman Asymptotic Cycle and Dynamics 97 B.1 Schwartzman Asymptotic Cycle 97 B.2 Dynamical Properties 99 Bibliography 107 Index 113
£35.70
Princeton University Press Alan Turings Systems of Logic
Book SynopsisBetween inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912-1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt GodeTrade Review"This book presents the story of Turing's work at Princeton University and includes a facsimile of his doctoral dissertation, 'Systems of Logic Based on Ordinals,' which he completed in 1936. The author includes a detailed history of Turing's work in computer science and the attempts to ground the field in formal logic."--Mathematics Teacher "This book is not for the faint hearted, as with the great masters of painting it will insist that some thought goes into appreciating it... I love the book as a book. It is a collectors item and after all what better pursuit can one have than collecting books!"--Patrick Fogarty, Mathematics TodayTable of ContentsPreface ix The Birth of Computer Science at Princeton in the 1930s Andrew W. Appel 1 Turing's Thesis Solomon Feferman 13 Notes on the Manuscript 27 Systems of Logic Based on Ordinals Alan Turing 31 A Remarkable Bibliography 141 Contributors 143
£12.34
