Mathematical logic Books
Cambridge University Press Theories of Computability
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£104.50
Cambridge University Press Computability Enumerability Unsolvability Directions in Recursion Theory 224 London Mathematical Society Lecture Note Series Series Number 224
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£50.99
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.
£45.59
Cambridge University Press Metamaths Machines Godels Proof 38 Cambridge Tracts in Theoretical Computer Science Series Number 38
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£40.84
Cambridge University Press Set Theory 48 London Mathematical Society Student Texts Series Number 48
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£116.85
Cambridge University Press Set Theory for the Working Mathematician 39 London Mathematical Society Student Texts Series Number 39
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£116.85
Cambridge University Press Set Theory for the Working Mathematician
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£43.69
Cambridge University Press LMS 248 Tame Topology ominimal London Mathematical Society Lecture Note Series Series Number 248
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£61.99
Cambridge University Press Stable Groups 240 London Mathematical Society Lecture Note Series Series Number 240
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£65.86
Cambridge University Press Automata Theory with Modern Applications
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£42.74
Cambridge University Press Algorithmic Information Theory
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£45.59
Cambridge University Press Domains and LambdaCalculi 46 Cambridge Tracts in Theoretical Computer Science Series Number 46
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£128.25
Cambridge University Press Principia Mathematica to 56
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£91.19
Cambridge University Press Sets and Proofs 258 London Mathematical Society Lecture Note Series Series Number 258
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£61.71
Cambridge University Press Models and Computability 259 London Mathematical Society Lecture Note Series Series Number 259
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£61.71
Cambridge University Press Dependence Logic A New Approach To Independence Friendly Logic
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£48.44
Cambridge University Press An Introduction to ManyValued and Fuzzy Logic Semantics Algebras and Derivation Systems
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£51.29
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.
£37.99
Cambridge University Press Alfred Tarski Life and Logic
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£25.64
Cambridge University Press Alfred Tarski Life and Logic
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£111.15
Cambridge University Press Continuous Lattices and Domains 93 Encyclopedia of Mathematics and its Applications Series Number 93
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£194.75
Cambridge University Press Rippling MetaLevel Guidance for Mathematical Reasoning 56 Cambridge Tracts in Theoretical Computer Science Series Number 56
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£87.99
Cambridge University Press Automata Theory with Modern Applications
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£76.00
Cambridge University Press An Introduction to NonClassical Logic
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£85.49
Cambridge University Press An Introduction to ManyValued and Fuzzy Logic Semantics Algebras and Derivation Systems
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£85.49
Cambridge University Press The Mathematics of Logic A Guide to Completeness Theorems and their Applications
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£100.70
Cambridge University Press Logic Colloquium 2005
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£105.45
Cambridge University Press Subsystems of Second Order Arithmetic
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£133.95
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
Cambridge University Press Homogeneous Ordered Graphs Metrically Homogeneous Graphs and Beyond
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£90.25
Cambridge University Press Homogeneous Ordered Graphs Metrically Homogeneous Graphs and Beyond Volume 1 Ordered Graphs and Distanced Graphs
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£104.50
Cambridge University Press Topological Duality for Distributive Lattices
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£61.74
Cambridge University Press Equivalents of the Riemann Hypothesis Volume 3 Further Steps towards Resolving the Riemann Hypothesis
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£142.50
Cambridge University Press Philosophical Uses of Categoricity Arguments
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£47.49
Cambridge University Press Lectures on Infinitary Model Theory
Book SynopsisThis book is the first modern introduction to the logic of infinitary languages in forty years, and is aimed at graduate students and researchers in all areas of mathematical logic. Connections between infinitary model theory and other branches of mathematical logic, and applications to algebra and algebraic geometry are both comprehensively explored.Table of ContentsIntroduction; Part I. Classical Results in Infinitary Model Theory: 1. Infinitary languages; 2. Back and forth; 3. The space of countable models; 4. The model existence theorem; 5. Hanf numbers and indiscernibles; Part II. Building Uncountable Models: 6. Elementary chains; 7. Vaught counterexamples; 8. Quasinimal excellence; Part III. Effective Considerations: 9. Effective descriptive set theory; 10. Hyperarithmetic sets; 11. Effective aspects of Lω1,ω; 12. Spectra of Vaught counterexamples; Appendix A. N1-free abelian groups; Appendix B. Admissibility; References; Index.
£105.45
Cambridge University Press Formal Languages in Logic A Philosophical And Cognitive Analysis
Book SynopsisFormal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science.Trade Review'Since the rise of logical empiricism, formal languages have become essential tools of doing philosophy. But why does formalization work? And what are its limitations? This book fills a crucial gap in the literature by addressing these questions from a cognitive, historical, and logical point of view. I recommend it to formal philosophers, critics of formal philosophy, and everyone with an interest in the techniques of conceptual engineering per se.' Hannes Leitgeb, Ludwig Maximilians Universität MunichTable of ContentsIntroduction; 1. Two notions of formality; 2. On the very notion of a formal language; 3. The history, purposes and limitations of formal languages; 4. How we do reason, and the need for counterbalance in science; 5. Formal languages and extended cognition; 6. De-semantification; 7. The debiasing effect of formalization; Conclusion.
£31.90
Cambridge University Press Mathematical Logic and Computation
Book SynopsisThis book presents mathematical logic from the syntactic point of view, with an emphasis on aspects that are fundamental to computer science. It is an excellent introduction for graduate students and advanced undergraduates interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for professional logicians.Trade Review'Avigad provides a much needed introduction to mathematical logic that foregrounds the role of syntax and computability in our understanding of consistency and inconsistency. The result provides a jumping off point to any of the fields of modern logic, not only teaching the technical groundwork, but also providing a window into how to think like a logician.' Henry Towsner, University of Pennsylvania'This book by one of the most knowledgeable researchers in the field covers a remarkably broad selection of material without sacrificing depth. Its clear organization and unified approach - focused on a syntactic approach and on the role of computation - make it suitable for a wide range of introductory logic sequences at the upper-level undergraduate and graduate level, as well as a valuable resource for background material in more advanced logic courses.' Denis Hirschfeldt, University of Chicago'… an excellent addition to the literature, with plenty more than enough divergences and side-steps from the more well-trodden paths through the material to be consistently interesting … this is most certainly a book to make sure your library gets.' Peter Smith, Logic MattersTable of ContentsPreface; 1. Fundamentals; 2. Propositional Logic; 3. Semantics of Propositional Logic; 4. First-Order Logic; 5. Semantics of First-Order Logic; 6. Cut Elimination; 7. Properties of First-Order Logic; 8. Primitive Recursion; 9. Primitive Recursive Arithmetic; 10. First-Order Arithmetic; 11. Computability 12. Undecidability and Incompleteness; 13. Finite Types; 14. Arithmetic and Computation; 15. Second-Order Logic and Arithmetic; 16. Subsystems of Second-Order Arithmetic; 17. Foundations; Appendix; References; Notation; Index.
£56.99
Cambridge University Press Paradoxes and Inconsistent Mathematics
Book SynopsisContradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses 'dialetheic paraconsistency' a formal framework where some contradictions can be true without absurdity as the basis for developing this idea rigorously, from mathematical foundations up.
£25.64
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
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
£18.99
Penguin Books Ltd A Field Guide to Lies
Book Synopsis
£18.00
John Wiley & Sons Inc Insight into Fuzzy Modeling
Book SynopsisProvides a unique and methodologically consistent treatment of various areas of fuzzy modeling and includes the results of mathematical fuzzy logic and linguistics This book is the result of almost thirty years of research on fuzzy modeling. It provides a unique view of both the theory and various types of applications.Table of ContentsPreface xiii Acknowledgments xv About the Companion Website xvii Part I Fundamentals of Fuzzy Modeling 1 1 What is Fuzzy Modeling 3 2 Overview of Basic Notions 11 3 Fuzzy IF-THEN Rules in Approximation of Functions 49 4 Fuzzy Transform 81 5 Fuzzy Natural Logic and Approximate Reasoning 97 6 Fuzzy Cluster Analysis 137 Part II Selected Applications 149 7 Fuzzy/Linguistic Control and Decision-Making 151 8 F-Transform in Image Processing 189 9 Analysis and Forecasting of Time Series 209
£98.75
John Wiley & Sons Inc Crossing the River with Dogs
Book SynopsisCrossing the River with Dogs: Problem Solving for College Students, 3rd Edition promotes the philosophy that students learn best by working in groups and the skills required for real workplace problem solving are those skills of collaboration. The text aims to improve students' writing, oral communication, and collaboration skills while teaching mathematical problem-solving strategies. Focusing entirely on problem solving and using issues relevant to college students for examples, the authors continue their approach of explaining classic as well as non-traditional strategies through dialogs among fictitious students. This text is appropriate for a problem solving, quantitative reasoning, liberal arts mathematics, mathematics for elementary teachers, or developmental mathematics course.Table of ContentsPreface vii Instructor Resources x Acknowledgments xi Introduction 1 1 Draw a Diagram 11 2 Make a Systematic List 27 3 Eliminate Possibilities 47 4 Use Matrix Logic 73 5 Look for a Pattern 115 6 Guess and Check 145 7 Identify Subproblems 175 8 Analyze the Units 199 9 Solve an Easier Related Problem 233 10 Create a Physical Representation 267 11 Work Backwards 297 12 Draw Venn Diagrams 323 13 Convert to Algebra 351 14 Evaluate Finite Differences 383 15 Organize Information in More Ways 417 16 Change Focus in More Ways 447 17 Visualize Spatial Relationships 473 Appendix 503 Unit Analysis Adding, Subtracting, Multiplying, and Dividing Fractions Area and Volume Formulas Properties of Triangles Properties of Numbers Glossary 511 Bibliography 519 Index of Problem Titles 521 General Index 529 Photo Credits 539 Answers to More Practice Problems 541
£110.66
Springer Reading Writing and Proving
Book Synopsis-Preface.-1. The How, When, and Why of Mathematics.- 2. Logically Speaking.- 3.Introducing the Contrapositive and Converse.- 4. Set Notation and Quantifiers.- 5. Proof Techniques.- 6. Sets.- 7. Operations on Sets.- 8. More on Operations on Sets.- 9. The Power Set and the Cartesian Product.- 10. Relations.- 11. Partitions.- 12. Order in the Reals.- 13. Consequences of the Completeness of (Bbb R).- 14. Functions, Domain, and Range.-15. Functions, One-to-One, and Onto.- 16. Inverses.- 17. Images and Inverse Images.- 18. Mathematical Induction.- 19. Sequences.- 20. Convergence of Sequences of Real Numbers.- 21. Equivalent Sets.- 22. Finite Sets and an Infinite Set.- 23. Countable and Uncountable Sets.- 24. The Cantor-Schröder-Bernstein Theorem.- 25. Metric Spaces.- 26. Getting to Know Open and Closed Sets.- 27. Modular Arithmetic.- 28. Fermat's Little Theorem.- 29. Projects.- Appendix.- References.- Index.Trade ReviewFrom the reviews of the second edition:“The book is written in an informal way, which could please the beginners and not offend the more experienced reader. A reader can find a lot of problems for independent study as well as a lot of illustrations encouraging him/her to draw pictures as an important part of the process of mathematical thinking.”—European Mathematical Society, September 2011"Several areas like sets, functions, sequences and convergence are dealt with and several exercises and projects are provided for deepening the understanding. …It is the impression of the author of this review that the book can be particularly strongly recommended for teacher students to enable them to catch and transfer the “essence” of mathematical thinking to their pupils. But also everybody else interested in mathematics will enjoy this very well written book.—Burkhard Alpers (Aalen), zbMATH“The book is primarily concerned with an exposition of those parts of mathematics in which students need a more thorough grounding before they can work successfully in upper-division undergraduate courses. … a mathematically-conventional but pedagogically-innovative take on transition courses.” —Allen Stenger, The Mathematical Association of America, September, 2011Table of Contents-Preface. -1. The How, When, and Why of Mathematics.- 2. Logically Speaking.- 3.Introducing the Contrapositive and Converse.- 4. Set Notation and Quantifiers.- 5. Proof Techniques.- 6. Sets.- 7. Operations on Sets.- 8. More on Operations on Sets.- 9. The Power Set and the Cartesian Product.- 10. Relations.- 11. Partitions.- 12. Order in the Reals.- 13. Consequences of the Completeness of (\Bbb R).- 14. Functions, Domain, and Range.- 15. Functions, One-to-One, and Onto.- 16. Inverses.- 17. Images and Inverse Images.- 18. Mathematical Induction.- 19. Sequences.- 20. Convergence of Sequences of Real Numbers.- 21. Equivalent Sets.- 22. Finite Sets and an Infinite Set.- 23. Countable and Uncountable Sets.- 24. The Cantor-Schröder-Bernstein Theorem.- 25. Metric Spaces.- 26. Getting to Know Open and Closed Sets.- 27. Modular Arithmetic.- 28. Fermat’s Little Theorem.- 29. Projects.- Appendix.- References.- Index.
£64.55
Centre for the Study of Language & Information Quantifiers, Deduction, and Context
Book SynopsisThis volume is an outgrowth of the second Workshop on Logic, Language and Computation held at Stanford in the spring of 1993. The workshop brought together researchers interested in natural language to discuss the current state of the art at the borderline of logic, linguistics and computer science. The papers in this collection fall into three central research areas of the nineties, namely quantifiers, deduction, and context. Each contribution reflects an ever-growing interest in a more dynamic approach to meaning, which focuses on inference patterns and the interpretation of sentences in the context of a larger discourse. The papers apply either current logical machinery - such as linear logic, generalised quantifier theory, dynamic logic - or formal analyses of the notion of context in discourse to classical linguistic issues, with original and thought-provoking results deserving of a wide audience.Table of Contents1. The Context-Dependency of Implicit Arguments; 2. A Deductive Account of Quantification in LFG; 3. The Sorites Fallacy and the Context-dependence of Vague Predicates; 4. Presuppositions and Information Updating; 5. Indefeasible semantics and Defeasible Pragmatics; 6. Pronoun Interpretation Preferences: an Account; 7. Resumptive Quantifiers in Exception Sentences; 8. (In)definites and genericity.
£26.37
Centre for the Study of Language & Information Vicious Circles: On the Mathematics of
Book SynopsisCircular analyses of philosophical, linguistic, or computational phenomena have been attacked on the assumption that they conflict with mathematical rigour. Barwise and Moss have undertaken to prove this assumption false. This volume is concerned with extending the modelling capabilities of set theory to provide a uniform treatment of circular phenomena. As a means of guiding the reader through the concrete examples of the theory, the authors have included many exercises and solutions: these exercises range in difficulty and ultimately stimulate the reader to come up with new results. Vicious Circles is intended for use by researchers who want to use hypersets; although some experience in mathematics is necessary, the book is accessible to people with widely differing backgrounds and interests.Trade Review' ... a book to learn from.' L'Enseignement MathématiqueTable of ContentsPart I. Background: 1. Introduction; 2. Background on set theory; Part II. Vicious Circles: 3. Circularity in computer science; 4. Circularity in philosophy; 5. Circularity and paradox; Part III. Basic Theory: 6. The solution dilemma; 7. Bisimulation; Part IV. Elementary applications: 8. Graphs; 9. Modal logic; 10. Streams; 11. Games; 12. Modeling the semantic paradoxes; Part V. Further Theory: 13. Greatest fixed points; 14. Uniform operators; 15. Corecursion; Part VI. Further Applications: 16. Some applications; 17. Modeling partial information; 18. Circularity and the notion of set; 19. Conclusions and future directions.
£66.74
Experiment Perilous Problems for Puzzle Lovers: Math, Logic
Book Synopsis
£12.99
ISTE Ltd and John Wiley & Sons Inc Petri Nets: Fundamental Models, Verification and
Book SynopsisA Petri net is a mathematical representation of a network. This book first introduces the basic models including time and stochastic extensions, in particular place-transition and high level Petri nets. Their modeling and design capabilities are illustrated by a set of representations of interest in operating and communication systems. The volume then addresses the related verification problems and proposes corresponding solutions by introducing the main notions needed to fully understand the behavior and properties behind Petri nets. Particular attention is devoted to how systems can be fully represented and analyzed in terms of their behavioral, time, and stochastic aspects by using the same formal approach and semantic basis. Finally, illustrative examples are presented in the important fields of interoperability in telecommunication services, programming languages, multimedia architectures, manufacturing systems, and communication protocols.Trade Review"We think that this volume should greatly help any designer to build the new forthcoming generation of distributed systems." (Mathematical Reviews, 2011) Table of ContentsPreface xv Introduction xvii PART 1. FUNDAMENTAL MODELS 1 Chapter 1. Basic Semantics 3 Michel DIAZ Chapter 2. Application of Petri Nets to Communication Protocols 27 Michel DIAZ Chapter 3. Analysis Methods for Petri 41 Serge HADDAD and François VERNADAT Chapter 4. Decidability and Complexity of Petri Net Problems 87 Serge HADDAD Chapter 5. Time Petri Nets 123 Bernard BERTHOMIEU, Marc BOYER and Michel DIAZ Chapter 6. Temporal Composition and Time Stream Petri Nets 163 Michel DIAZ and Patrick SÉNAC Chapter 7. High Level Petri Nets 185 Claude GIRAULT and Jean-François PRADAT-PEYRE Chapter 8. Analysis of High Level Petri Nets 221 Claude GIRAULT and Jean-François PRADAT-PEYRE Chapter 9. Stochastic Petri Nets 269 Serge HADDAD and Patrice MOREAUX Chapter 10. Stochastic Well-formed Petri Nets 303 Serge HADDAD and Patrice MOREAUX Chapter 11. Tensor Methods and Stochastic Petri Nets 321 Serge HADDAD and Patrice MOREAUX PART 2. VERIFICATION AND APPLICATION OF PETRI NETS 347 Chapter 12. Verification of Specific Properties 349 Serge HADDAD and François VERNADAT Chapter 13. Petri Net Unfoldings – Properties 415 Jean-Michel COUVREUR and Denis POITRENAUD Chapter 14. Symmetry and Temporal Logic 435 Serge HADDAD and Jean-Michel ILIÉ Chapter 15. Hierarchical Time Stream Petri Nets 461 Patrick SÉNAC and Michel DIAZ Chapter 16. Petri Nets and Linear Logic 481 Brigitte PRADIN, Robert VALETTE and Nicolas RIVIÈRE Chapter 17. Modeling of Multimedia Architectures: the Case of Videoconferencing with Guaranteed Quality of Service 501 Philippe OWEZARSKI and Marc BOYER Chapter 18 Performance Evaluation in Manufacturing Systems 527 Isabel DEMONGODIN, Nathalie SAUER and Laurent TRUFFET Conclusion 577 List of Authors 579 Index 581
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