Mathematical logic Books
Springer Introduction to Mathematical Structures and Proofs
Book SynopsisPreface to the Second Edition.- Preface to the First Edition.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets.- 5. Combinatorics.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index.Table of Contents-Preface.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets. - 5. Permutations and Combinations.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index
£38.94
Birkhauser Boston Theory of Finite and Infinite Graphs
Book SynopsisCommentary.- Theory of Finite and Infinite Graphs.- Dénes König: A Biographical Sketch.Table of ContentsCommentary.- Theory of Finite and Infinite Graphs.- Dénes König: A Biographical Sketch.
£42.74
MP-AMM American Mathematical Gallery of the Infinite
Book SynopsisGallery of the Infinite is a mathematician's unique view of the infinitely many sizes of infinity. Written in a playful yet informative style, it introduces important concepts from set theory (including the Cantor Diagonalization Method and the Cantor-Bernstein Theorem) using colourful pictures, with little text and almost no formulas.Trade ReviewThis is a beautiful book. The pictures keep the reader engaged in a colourful mathematical journey. It is written in an engaging style suitable for over 11’s but also contains ideas that are likely to interest most adults (without the need for a refresher course, since the book does a good job of being self-contained). [...] Although a mathematician would likely be aware of many of the concepts the book presents, I would still recommend it both as a tool to intrigue others (it makes a great ‘coffee table’ book) and also since it contains many imaginative explanations and original arguments. The illustrations and narrative keep the reader entertained and make the book hard to put down." - London Mathematical Society Newsletter"This is a lovely book… Although a certain affinity with mathematical reasoning is needed the book can be read by almost anyone." - Teun Koetsier, Zentralblatt Math
£24.65
MP-AMM American Mathematical Hilberts Tenth Problem
Book SynopsisHilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900. It asked for a general algorithm to determine if a given Diophantine equation has a solution in integers. It was finally resolved by Julia Robinson, Martin Davis, Hilary Putnam, and finally Yuri Matiyasevich in 1970. This book is an exposition of their achievement.Table of Contents Introduction Cantor and infinity Axiomatic set theory Elementary number theory Computability and provability Hilbert's tenth problem Applications of Hilbert's tenth problem Hilbert's tenth problem over number fields Background material Bibliography Index
£47.70
MP-AMM American Mathematical Set Theory
Book SynopsisPresents various theorems of the theory of sets along with complete proofs. This book discusses strengthening of theorems, the simplification of proofs, and the removal of unnecessary hypotheses.Trade ReviewAn indispensible book for all those interested in the theory of sets and the allied branches of real variable theory."" — Bulletin of the AMSTable of Contents Sets and the Combining of Sets: 1.1 Sets 1.2 Functions 1.3 Sum and intersection 1.4 Product and power Cardinal Numbers: 2.5 Comparison of sets 2.6 Sum, product, and power 2.7 The scale of cardinal numbers 2.8 The elementary cardinal numbers Order Types: 3.9 Order 3.10 Sum and product 3.11 The types $\aleph_0$ and $\aleph$ Ordinal Numbers: 4.12 The well-ordering theorem 4.13 The comparability of ordinal numbers 4.14 The combining of ordinal numbers 4.15 The alefs 4.16 The general concept of product Systems of Sets: 5.17 Rings and fields 5.18 Borel systems 5.19 Suslin sets Point Sets: 6.20 Distance 6.21 Convergence 6.22 Interior points and border points 6.23 The $\alpha, \beta$, and $\gamma$ points 6.24 Relative and absolute concepts 6.25 Separable spaces 6.26 Complete spaces 6.27 Sets of the first and second categories 6.28 Spaces of sets 6.29 Connectedness Point Sets and Ordinal Numbers: 7.30 Hulls and kernels 7.31 Further applications of ordinal numbers 7.32 Borel and Suslin sets 7.33 Existence proofs 7.34 Criteria for Borel sets Mappings of Two Spaces: 8.35 Continuous mappings 8.36 Interval-images 8.37 Images of Suslin sets 8.38 Homeomorphism 8.39 Simple curves 8.40 Topological spaces Real Functions: 9.41 Functions and inverse image sets 9.42 Functions of the first class 9.43 Baire functions 9.44 Sets of convergence Supplement: 10.45 The Baire condition 10.46 Half-schlicht mappings Appendixes Bibliography Further references Index
£54.90
MP-AMM American Mathematical Algebras Lattices Varieties Volume II
Book SynopsisThe second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices.Table of Contents The classification of varieties Equational logic Rudiments of model theory Bibliography Index
£98.10
MP-AMM American Mathematical Algebras Lattices Varieties Volume III
Book SynopsisThe third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices.Table of Contents Finite algebras and their clones Abstract clone theory Commutator theory Bibliography Index
£98.10
CRC Press Multilevel Modeling of Secure Systems in QoPML
Book SynopsisIn order to perform effective analysis of todayâs information security systems, numerous components must be taken into consideration. This book presents a well-organized, consistent solution created by the author, which allows for precise multilevel analysis of information security systems and accounts for all of the significant details. Enabling the multilevel modeling of secure systems, the quality of protection modeling language (QoP-ML) approach provides for the abstraction of security systems while maintaining an emphasis on quality protection. This book introduces the basis of the QoP modeling language along with all the advanced analysis modules, syntax, and semantics. It delineates the steps used in cryptographic protocols and introduces a multilevel protocol analysis that expands current understanding. Introduces quality of protection evaluation of IT Systems Covers the financial, economic, and CO2 emission analysis phase Table of ContentsIntroduction to Multilevel Modeling of Secure Systems. Basis of QoP-ML. Quality of Protection Evaluation of Security Mechanisms. Advanced Communication and Energy Efficiency Modeling. Environmental Impact and Financial Costs Analysis. Reputation Analysis in QoP-ML. Security Metrics – Methodology. Tool Support. Functionality and Usability of QoP-ML. Appendix.
£80.74
Taylor & Francis Inc Introduction to Certificateless Cryptography
Book SynopsisAs an intermediate model between conventional PKC and ID-PKC, CL-PKC can avoid the heavy overhead of certificate management in traditional PKC as well as the key escrow problem in ID-PKC altogether. Since the introduction of CL-PKC, many concrete constructions, security models, and applications have been proposed during the last decade. Differing from the other books on the market, this one provides rigorous treatment of CL-PKC.Definitions, precise assumptions, and rigorous proofs of security are provided in a manner that makes them easy to understand. Table of ContentsSetting the Stage. Avoiding key escrow Mathematical concepts and properties. CL-PKC without Random Oracles. Concrete constructions of CLE Generic construction of CLE. CLS secure in the standard model. CL-PKC in the Random Oracle Models. The random oracle model. CLE, CLS and CL-AKE secure in the random oracle model. CL-PKC without parings. Applications, Extensions and Related Primitives. Applications of CL-PKC. Extensions of CL-PKC. Comparisons between CL-PKC and SGC-PKC, Certificate-based PKC. Future Directions. Perspectives.
£80.74
Taylor & Francis Inc Elements of Quasigroup Theory and Applications
Book SynopsisUnderstanding Interaction is a book that explores the interaction between people and technology, in the broader context of the relations between the human made and the natural environments.It is not just about digital technologies our computers, smart phones, the Internet but all our technologies such as mechanical, electrical and electronic. Our ancestors started creating mechanical tools and shaping their environments millions of years ago, developing cultures and languages, which in turn influenced our evolution. Volume 1 of Understanding Interaction looks into this deep history starting from the tool creating period (the longest and most influential on our physical and mental capacities), to the settlement period (agriculture, domestication, villages and cities, written language), the industrial period (science, engineering, reformation and renaissance), and finally the communication period (mass media, digital technologies, global networks).VolumeTable of Contents Preface introduction, overview of chapters of Vol I & II 1. Interacting - overview of design and research for interaction 2. Evolving - technocultural periods, and technology categories 3. Creating - dedicated tool making, and the emergence of language 4. Settling - agriculture, mechanical tools, and writing 5. Industrialising - science, enlightenment, reformation, and renaissance 6. Communicating - information, representation, semiotics Interface - preliminary frameworks and directions References
£147.25
Quercus Publishing How to Expect the Unexpected: The Science of
Book SynopsisA Waterstones Best Popular Science Book of 2023'Delightfully clear and vivid to read...A splendid book! Philip Pullman'Absolutely fascinating' James O'Brien'An exceptional book - readable, funny and more needed than ever' Dr Chris van Tulleken, bestselling author of Ultra-Processed PeopleAre you more likely to become a professional footballer if your surname is Ball?· How can you be one hundred per cent sure you will win a bet?· Why did so many Pompeiians stay put while Mount Vesuvius was erupting?· How do you prevent a nuclear war?Ever since the dawn of human civilisation, we have been trying to make predictions about what's in store for us. We do this on a personal level, so that we can get on with our lives efficiently (should I hang my laundry out to dry, or will it rain?). But we also have to predict on a much larger scale, often for the good of our broader society (how can we spot economic downturns or prevent terrorist attacks?). For just as long, we have been getting it wrong. From religious oracles to weather forecasters, and from politicians to economists, we are subjected to poor predictions all the time. Our job is to separate the good from the bad. Unfortunately, the foibles of our own biology - the biases that ultimately make us human - can let us down when it comes to making rational inferences about the world around us. And that can have disastrous consequences.How to Expect the Unexpected will teach you how and why predictions go wrong, help you to spot phony forecasts and give you a better chance of getting your own predictions correct.Trade ReviewA vivid, wide-ranging and delightful guide to the light and the dark side of prediction * Tim Harford, bestselling author of How to Make the World Add Up *Kit Yates presents maths as it should be taught to everyone: accessible, fun, stimulating, and deeply relevant to our lives. Spend some time with this book and you're likely to make better judgements and decisions, to see through the charlatans and snake-oil salespeople - and perhaps even to fool yourself a little less. * Philip Ball, author of the award-winning Critical Mass *Fascinating and fun. From the everyday to global challenges, Kit Yates explores how changing your mind - so often thought to be a weakness - is the best life skill we can all acquire. A brilliant book * Professor Alice Roberts *Yates' writing is a beacon of clarity sorely needed in a complicated and confusing world. How do we overcome our biases, understand coincidences or tackle the unreliability of our intuition? With bountiful familiar examples, he effortlessly overturns so many of our deep-rooted wrong-headed notions gently and persuasively. I'll be quoting from this book * Jim Al-Khalili *I'm a Yates fan. His style is all-clarity-no-bullshit * Aperiodical *Seriously good * Caroline Lucas MP *Absolutely fascinating * James O'Brien *An exceptional book - readable, funny and more needed than ever * Dr Chris van Tulleken, bestselling author of Ultra-Processed People *Yates' writing style imbues the subjects covered with an infectious enthusiasm, artfully dispelling the dry, stuffy perceptions many people have of maths * Physics World *HOW TO EXPECT THE UNEXPECTED is fascinating and (very much to the point) delightfully clear and vivid to read. Like many people, I like reading about maths without actually knowing how to do it, and part of the pleasure of reading this came from its many examples from everyday life. A splendid book! * Philip Pullman *
£18.75
Quercus Publishing How to Expect the Unexpected: The Science of
Book SynopsisA Waterstones Best Popular Science Book of 2023'Delightfully clear and vivid to read...A splendid book! Philip Pullman'Absolutely fascinating' James O'Brien'An exceptional book - readable, funny and more needed than ever' Dr Chris van Tulleken, bestselling author of Ultra-Processed PeopleAre you more likely to become a professional footballer if your surname is Ball?· How can you be one hundred per cent sure you will win a bet?· Why did so many Pompeiians stay put while Mount Vesuvius was erupting?· How do you prevent a nuclear war?Ever since the dawn of human civilisation, we have been trying to make predictions about what's in store for us. We do this on a personal level, so that we can get on with our lives efficiently (should I hang my laundry out to dry, or will it rain?). But we also have to predict on a much larger scale, often for the good of our broader society (how can we spot economic downturns or prevent terrorist attacks?). For just as long, we have been getting it wrong. From religious oracles to weather forecasters, and from politicians to economists, we are subjected to poor predictions all the time. Our job is to separate the good from the bad. Unfortunately, the foibles of our own biology - the biases that ultimately make us human - can let us down when it comes to making rational inferences about the world around us. And that can have disastrous consequences.How to Expect the Unexpected will teach you how and why predictions go wrong, help you to spot phony forecasts and give you a better chance of getting your own predictions correct.Trade ReviewA vivid, wide-ranging and delightful guide to the light and the dark side of prediction * Tim Harford, bestselling author of How to Make the World Add Up *Kit Yates presents maths as it should be taught to everyone: accessible, fun, stimulating, and deeply relevant to our lives. Spend some time with this book and you're likely to make better judgements and decisions, to see through the charlatans and snake-oil salespeople - and perhaps even to fool yourself a little less. * Philip Ball, author of the award-winning Critical Mass *Fascinating and fun. From the everyday to global challenges, Kit Yates explores how changing your mind - so often thought to be a weakness - is the best life skill we can all acquire. A brilliant book * Professor Alice Roberts *Yates' writing is a beacon of clarity sorely needed in a complicated and confusing world. How do we overcome our biases, understand coincidences or tackle the unreliability of our intuition? With bountiful familiar examples, he effortlessly overturns so many of our deep-rooted wrong-headed notions gently and persuasively. I'll be quoting from this book * Jim Al-Khalili *I'm a Yates fan. His style is all-clarity-no-bullshit * Aperiodical *Seriously good * Caroline Lucas MP *Absolutely fascinating * James O'Brien *An exceptional book - readable, funny and more needed than ever * Dr Chris van Tulleken, bestselling author of Ultra-Processed People *Yates' writing style imbues the subjects covered with an infectious enthusiasm, artfully dispelling the dry, stuffy perceptions many people have of maths * Physics World *HOW TO EXPECT THE UNEXPECTED is fascinating and (very much to the point) delightfully clear and vivid to read. Like many people, I like reading about maths without actually knowing how to do it, and part of the pleasure of reading this came from its many examples from everyday life. A splendid book! * Philip Pullman *
£15.29
Nova Science Publishers Inc An Introduction to Fuzzy Sets
Book SynopsisAn Introduction to Fuzzy Sets provides a comparison of the quality of life in urban, intermediate and rural NUTS III regions in Portugal, with the main goal of identifying and analysing the necessary and conditions for a high quality of life in those different regions. The authors assess the necessary and sufficient conditions for higher Human Development Index levels, aiming to determine whether the same pattern could be used to explain the happiness index. In order to represent the applications of fuzzy set theory as well as neuro-fuzzy in industry, a literature review of these topics is carried out. As some researchers have efficiently utilized fuzzy logic and neuro-fuzzy, in-depth discussions are provided for stimulating future investigations. Following this, using the L. Zadeh theory of fuzzy sets, the authors consider all types of uncertainties in oil fields and oil production to make a decision as to what model is best in such a fuzzy environment. Additionally, several challenges are explored, such as: the fuzzy random finite difference numerical method, possibilistic uncertainty modelling, and the development of a fuzzy Wilks' theorem to model the hybrid structure of randomness and fuzziness modelling. In closing, a standard fuzzy arithmetic method is used for solving fuzzy equations, as well as for the optimization of fuzzy objectives. The fuzzy variable of the equation is fuzzified using a fuzzy set.Table of ContentsPreface; Quality of Life: Urban versus Rural Analysis Based on Fuzzy Sets Approach; Economically Speaking, Are Happiness and HDI the Same? The Fuzzy-Set Approach; Implementation of Fuzzy Logic and Neuro-Fuzzy in Industry; Lotfi Zadehs Theory of Fuzzy Sets in Decision-Making Process for Oil and Gas Production; Fuzziness-Randomness Modeling of Plasma Disruption in First Wall of Fusion Reactor Using Type I Fuzzy Random Set; Application of a Standard Fuzzy Arithmetic Method; Index.
£58.39
Basic Books The Art of Logic in an Illogical World
Book Synopsis
£20.25
Basic Books The Art of Logic in an Illogical World
Book Synopsis
£16.99
Broadview Press Ltd Formal Logic
Book SynopsisFormal Logic is an undergraduate text suitable for introductory, intermediate, and advanced courses in symbolic logic. The book’s nine chapters offer thorough coverage of truth-functional and quantificational logic, as well as the basics of more advanced topics such as set theory and modal logic. Complex ideas are explained in plain language that doesn’t presuppose any background in logic or mathematics, and derivation strategies are illustrated with numerous examples. Translations, tables, trees, natural deduction, and simple meta-proofs are taught through over 400 exercises. A companion website (complimentary for anyone who buys the book) offers supplemental practice software and tutorial videos.Trade Review“Formal Logic is clear, accessible, and intuitive, but it is also precise, explicit, and thorough. Complex and often confusing concepts are rolled out in a no-nonsense and direct manner with funny and demystifying terminology and helpful analogies. It's a pedagogical gem.” — Mary Kate McGowan, Wellesley College“This is an excellent introductory text in symbolic logic. It is accessible, with clear and concise explanations of key concepts, along with many helpful examples and practice problems, but also rigorous enough to prepare students for a second course in logic; indeed, I do not know of any book that better combines these virtues. I am looking forward to using Formal Logic in my courses.” — Kevin Morris, Tulane University“This book makes the ideas of sentential logic, predicate logic, and formal proof easily accessible by getting directly to the point of each in natural, non-technical language. It is concise while never hurried. It gets the details right, not by focusing on them as details, but through clear insight into why they are as they are.” — Colin McLarty, Case Western Reserve University“Paul Gregory’s Formal Logic is worth careful consideration for anyone adopting a new logic text. The inclusion of chapters on set theory and modal logic makes it a valuable resource for students looking to go beyond the standard introduction to logic.” — Michael Hicks, Miami UniversityTable of ContentsI: Informal Notions1: Informal Introduction1.1 Logic: What, Why, How?1.2 Arguments, Forms, and Truth Values1.3 Deductive Criteria1.3.1Quirky Cases of Deductive Validity1.4 Inductive Criteria1.5 Other Deductive Properties1.6 Exercises1.7 Chapter GlossaryII: Truth-Functional Logic2: The Language S2.1 Introducing S2.1.1 Compound Sentences and Truth-Functional Logic 2.1.2 Negation—It is not the case that…2.1.3 Conjunction—Both…and---2.1.4 Disjunction—Either…or---2.1.5 Material Conditional—If …, then---2.1.6 Material Biconditional—…if and only if---2.1.7 Conditionals and Non-Truth-Functionality2.2 Some Technical Bits2.2.1 Object Language and Metalanguage2.2.2 Use and Mention2.2.3 Metavariables2.2.4 Syntax and Semantics 2.3 The Syntax of S2.3.1 Defining the Language2.3.2 Syntactic Concepts and Conventions2.3.3 Exercises2.4 Alternate Symbols and Other Choices2.5 Chapter Glossary3: Formal Semantics for S3.1 Truth Value Assignments and Truth Tables3.2 Semantic Properties of Individual Wffs3.2.1 Exercises3.3 Semantic Properties of Sets of Wffs3.3.1 Exercises3.4 Semantic Properties, Their Interrelations, and Simple Metalogic3.4.1 Exercises3.5 Truth Trees3.5.1 Tests with Truth Trees3.5.2 Exercises3.6 Chapter Glossary4: SD: Natural Deduction in S4.1 The Basic Idea4.1.1 Reiteration4.1.2 Wedge Rules4.1.3 Arrow Rules4.1.4 Hook Rules4.1.5 Vee Rules4.1.6 Double Arrow Rules4.1.7 Exercises4.2 Derivations: Strategies and Notes4.3 Proof Theory in SD4.3.1 Exercises4.4 SDE, an Extension to SD4.4.1 The Inference Rules of SDE4.4.2 Exercises4.4.3 The Replacement Rules of SDE4.4.4 Exercises4.5 Chapter GlossaryIII: Quantificational Logic5: The Language P5.1 Introducing P5.1.1 Quantificational Logic5.1.2 Predicates and Singular Terms5.1.3 Predicate Letters and Individual Constants in P5.1.4 Pronouns and Quantifiers5.1.5 Variables and Quantifiers in P 5.2 The Syntax of P5.2.1 Defining the Language5.2.2 Syntactic Concepts and Conventions5.2.3 Exercises5.3 Simple Symbolizations5.3.1 Non-categorical Claims5.3.2 Exercises5.3.3 Categorical Claims5.3.4 Exercises5.4 Complex Symbolizations5.4.1 Basics of Overlapping Quantifiers5.4.2 Exercises5.4.3 Identity, Numerical Quantification, and Definite Descriptions5.4.4 Exercises5.5 Chapter Glossary6: Formal Semantics for P6.1 Semantics and Interpretations6.1.1 Basics of Interpretations6.1.2 Interlude: A Little Bit of Set Theory6.1.3 Formal Interpretation of P6.1.4 Constructing Interpretations6.2 Semantic Properties of Individual Wffs6.2.1 Exercises6.3 Semantic Properties of Sets of Wffs6.3.1 Exercises6.4 Quantifier Scope and Distribution6.4.1 Exercises6.5 Properties of Relations6.5.1 Exercises6.6 Chapter Glossary7: PD: Natural Deduction in P7.1 Derivation Rules for the Quantifiers7.1.1 Universal Elimination7.1.2 Existential Introduction7.1.3 Universal Introduction7.1.4 Existential Elimination7.1.5 Exercises7.2 Derivations: Strategies and Notes7.3 Proof Theory in PD7.3.1 Exercises7.4 PDE, an Extension to PD7.4.1 Quantifier Negation7.4.2 Exercises7.4 Chapter GlossaryIV: Advanced Topics8: Basic Set Theory, Paradox, and Infinity8.1 Basics of Sets8.2 Russell’s Paradox8.3 The Axiom Schema of Separation8.4 Subset, Intersection, Union, Difference8.4.1 Exercises8.5 Pairs, Ordered Pairs, Power Sets, Relations, and Functions8.6 Infinite Sets and Cantor’s Proof8.6.1 Exercises8.7 Chapter Glossary9: Modal Logic9.1 Necessity, Possibility, and Impossibility9.1.1 Modalities9.1.2 Logical, Metaphysical, Physical9.1.3 Possible Worlds9.2 The Language S9.2.1 The Syntax of S9.2.2 Exercises9.3 Basic Possible Worlds Semantics for S9.3.1 Semantic Properties of Wffs and Sets of Wffs9.3.2 Exercises9.3.3 Possible Worlds and Trees9.3.4 Exercises9.4 Natural Deduction in S9.4.1 System K9.4.2 System D9.4.3 System T9.4.4 System B9.4.5 System S49.4.6 System S59.4.7 Relations Between Modal Systems9.4.8 Exercises9.5 Chapter GlossaryV: AppendicesA: Answers to ExercisesB: GlossaryC: Truth Tables, Tree Rules, and Derivation RulesC.1 Characteristic Truth TablesC.2 Truth Tree Rules for SC.3 The Derivation System SDC.4 The Derivation System SDEC.5 The Derivation System PD
£51.30
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.
£25.45
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.
£22.00
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.
£65.24
Centre for the Study of Language & Information Selected Papers on Discrete Mathematics
Book SynopsisDonald Knuth's influence in computer science ranges from the invention of literate programming to the development of the TeX programming language. One of the foremost figures in the field of mathematical sciences, his papers are widely referenced and stand as milestones of development over a wide range of topics. This volume assembles more than three dozen of Professor Knuth's pioneering contributions to discrete mathematics. It includes a variety of topics in combinatorial mathematics (finite geometries, graph theory, enumeration, partitions, tableaux, matroids, codes); discrete algebra (finite fields, groupoids, closure operators, inequalities, convolutions, Pfaffians); and concrete mathematics (recurrence relations, special numbers and notations, identities, discrete probability). Of particular interest are two fundamental papers in which the evolution of random graphs is studied by means of generating functions.Table of Contents1. Discussion of Mr. Riordan's paper 'Abel identities and inverse relations'; 2. Duality in addition chains; 3. Combinatorial analysis and computers; 4. Tables of finite fields; 5. Finite semifields and projective planes; 6. A class of projective planes; 7. Construction of a random sequence; 8. Oriented subtrees of an arc digraph; 9. Another enumeration of trees; 10. Notes on central groupoids; 11. Permutations, matrices, and generalized Young tableaux; 12. A note on solid partitions; 13. Subspaces, subsets, and partitions; 14. Enumeration of plane partitions; 15. Complements and transitive closures; 16. Permutations with nonnegative partial sums; 17. Wheels within wheels; 18. The asymptotic number of geometries; 19. Random matroids; 20. Identities from partition involutions; 21. Huffman's algorithm via algebra; 22. A permanent inequality; 23. Efficient balanced codes; 24. The power of a prime that divides a generalized binomial coefficient; 25. The first cycles in an evolving graph; 26. The birth of the giant component; 27. Polynomials involving the floor function; 28. The sandwich theorem; 29. Aztec diamonds, checkerboard graphs, and spanning trees.
£30.40
Centre for the Study of Language & Information Universal Logic
Book SynopsisUniversal Logic conceptualizes a new logic, where the main inference connective is understood as 'meaning containment'. Classical logic plays a restricted role, applying to 'classical sentences', while the new logic is studied in depth with chapters on semantics, proof theory, and properties. Based on this logic, simple consistency is proved for naive class theory, also in conjunction with 'classical theories' such as a Z-F-style set theory. This book shows how the main set-theoretic and semantic paradoxes can be solved in a systematic way, which is conceptualized independently of the paradoxes themselves.
£34.53
Centre for the Study of Language & Information Advances in Modal Logic, Volume 2
Book SynopsisModal logic originated in philosophy as the logic of necessity and possibility. Now it has reached a high level of mathematical sophistication and has many applications in a variety of disciplines, ranging from artificial intelligence, computer science and mathematics via natural language syntax and semantics to philosophy. It is the main source of formal languages aimed at analyzing complex notions such as common knowlwdge and formal provability. This volume presents a broad, contemporary view of the field, with contributions covering the foundations of modal logic as well as its many application areas.
£32.67
Wolfram Media Inc Twenty Years of a New Kind of Science
Book Synopsis
£34.36
Taylor & Francis Inc Inverse Problems and Related Topics
Book SynopsisInverse problems arise in many disciplines and hold great importance to practical applications. However, sound new methods are needed to solve these problems. Over the past few years, Japanese and Korean mathematicians have obtained a number of very interesting and unique results in inverse problems.Inverse Problems and Related Topics compiles papers authored by some of the top researchers in Korea and Japan. It presents a number of original and useful results and offers a unique opportunity to explore the current trends of research in inverse problems in these countries. Highlighting the existence and active work of several Japanese and Korean groups, it also serves as a guide to those seeking future scientific exchange with researchers in these countries.Trade Review"The aim of this book is to fill the gap between high-school mathematics and mathematics taught at university…the reader is shown what it means to prove something rigourously…This book is easy to read for anyone with a high-school mathematics background." - European Mathematical Society NewsletterTable of ContentsA Finite Difference Model for Calderón's Boundary Inverse Problem. Inverse Problems for Equations with Memory. Parameter Estimation of Elastic Media. The Probe Method and its Applications. Recent Progress in the Inverse Conductivity Problem with Single Measurement. A Moment Method on Inverse Problems for the Heat Equation. Some Remarks on Free Boundaries of Recirculation Euler Flows with Constant Vorticity. Algorithms for the Identification of Spatially Varying/Invariant Stiffness and Dampings in Flexible Beams. Numerical Solutions of the Cauchy Problem in Potential and Elastostatics. Inverse Source Problems in the Helmholtz Equations. A Numerical Method for a Magnetostatic Inverse Problem using the Edge Element. Exact Controllability Method and Multidimensional Linear Inverse Problems. Impedance Computed Tomo-Electrocardiography. An Inverse Problem for Free Channel Scattering. Surface Impedance Tensor and Boundary Value Problem. Aysmptotics for the Spectral and Weyl Functions of the Operator-Value Sturm-Liouville Problem. Exact Controllability Method and Multidimensional Linear Inverse Problems
£161.50
Cosimo Classics An Investigation of the Laws of Thought
£16.70
Nova Science Publishers Inc Mathematics & Mathematical Logic: New Research
Book SynopsisA computational model is a mathematical structure which is constructed in an easy way and is useful in performing certain computations on the structure. This book discusses how the idea of "computational model" has been formalised by connecting the domain theory with the theory of metric spaces and related topological spaces. The nature of number is also examined, from a synthetic, holistic and interdisciplinary point-of-view, which is mostly mathematical but also encompasses respective psychological, neuro-physiological and philosophical views. Reversible logic circuits are discussed, which are beneficial to both classical and quantum computer design. Three experimental prototypes are used to illustrate how, in the near future, reversible computers will outperform conventional computers, in terms of power dissipation and heat generation. In quantum mechanics and field theory, Schroedinger equation for a single particle in one-dimensional imaginary potential represents one of the most popular schematic non-Hermitian models. Via a solvable square-well approximation technique, this book examines the problems in both the co-ordinate and momentum representations. The optimisation problem is also looked at, which in traditional designs, is stated in precise mathematical terms but in real life, are stated in vague and linguistic terms.
£176.24
Lehigh University Press Logic with a Probability Semantics
Book SynopsisThe present study is an extension of the topic introduced in Dr. Hailperin's Sentential Probability Logic, where the usual true-false semantics for logic is replaced with one based more on probability, and where values ranging from 0 to 1 are subject to probability axioms. Moreover, as the word "sentential" in the title of that work indicates, the language there under consideration was limited to sentences constructed from atomic (not inner logical components) sentences, by use of sentential connectives ("no," "and," "or," etc.) but not including quantifiers ("for all," "there is"). An initial introduction presents an overview of the book. In chapter one, Halperin presents a summary of results from his earlier book, some of which extends into this work. It also contains a novel treatment of the problem of combining evidence: how does one combine two items of interest for a conclusion-each of which separately impart a probability for the conclusion-so as to have a probability for the conclusion based on taking both of the two items of interest as evidence? Chapter two enlarges the Probability Logic from the first chapter in two respects: the language now includes quantifiers ("for all," and "there is") whose variables range over atomic sentences, not entities as with standard quantifier logic. (Hence its designation: ontological neutral logic.) A set of axioms for this logic is presented. A new sentential notion—the suppositional—in essence due to Thomas Bayes, is adjoined to this logic that later becomes the basis for creating a conditional probability logic. Chapter three opens with a set of four postulates for probability on ontologically neutral quantifier language. Many properties are derived and a fundamental theorem is proved, namely, for any probability model (assignment of probability values to all atomic sentences of the language) there will be a unique extension of the probability values to all closed sentences of the language.Trade ReviewThere are some original features in the treatment given to the subject by the author, which make it an interesting reading also for people well acquainted with other work on probabilistic logics. * Mathematical Reviews *Anyone interested in the history and philosophy of logic will find this work intriguing. Amateur logicians will find it challenging but will appreciate the progression toward expressing quantified probability logic in a richer formal structure, thus broadening the book's range of possible applications. * Mathematics Teacher *Table of Contents1 Preface 2 Introduction: An Overview Part 3 1. Sentenial Probability Logic Chapter 4 1.1 Verity logic Chapter 5 1.2 Probability logic for S Chapter 6 1.3 Interval-based probability Chapter 7 1.4 Sentential suppositional logic Chapter 8 1.5 Conditional-probability logic Chapter 9 1.6 Logical consequence for probability logic Chapter 10 1.7 Combining evidence Part 11 2. Logic With Quantifiers Chapter 12 2.0 Ontologically neutral (ON) language Chapter 13 2.1 Syntax and semantics of ON logic Chapter 14 2.2 Axiomatic formalization of ON logic Chapter 15 2.3 Adequacy of ON logic Chapter 16 2.4 Quantification logic with the suppositional Part 17 3. Probability functions on ON languages Chapter 18 3.1 Probability functions on ON languages Chapter 19 3.2 Main Theorem of ON probability logic Chapter 20 3.3 Borel's denumerable probability Chapter 21 3.4 Infinite "events" and probability functions Chapter 22 3.5 Kolmogorov probability spaces Chapter 23 3.6 Logical consequence in probability logic Chapter 24 3.7 Borel's denumerable probability defended Part 25 4. Conditional-Probability and Quantifiers Chapter 26 4.1 Conditional-probability in quantifier logic Chapter 27 4.2 The paradox of confirmation 28 Bibliography 29 Index
£59.40
Martino Fine Books Mathematics and Plausible Reasoning Two Volumes in One
£31.76
Experiment Perilous Problems for Puzzle Lovers: Math, Logic
Book Synopsis
£12.34
Orange Grove Books A Problem Course in Mathematical Logic
Book Synopsis
£29.66
Orange Grove Books Forall X: Introductory Textbook in Formal Logic
Book Synopsis
£24.71
NY Research Press Fuzzy Systems: Theory and Applications
Book Synopsis
£97.02
States Academic Press Fundamentals of Mathematical Logic
Book Synopsis
£108.07
Morgan & Claypool Publishers Logic for Physicists
Book Synopsis
£23.75
Clanrye International Fuzzy Logic: A Practical Approach
Book Synopsis
£107.38
Guardian Faber Publishing So You Think You've Got Problems?: Surprising and
Book SynopsisThought you had it bad? In this book, you will be:Imprisoned by a sadistic logician.Challenged to raise dogs from the dead. Trapped on a burning island.And much more besides . . .Everything is at stake in this compendium of more than 150 ingenious puzzles, selected to reveal the wonderful diversity of brainteasers that have confounded and intrigued solvers for the last thousand years. You'll need to pit your wits against probability problems, wrestle with wordplay, grapple with geometry and scrabble for survival. Along the way you will discover stories of whip-smart thinkers, eccentric novelists and a poodle with allegedly supernatural powers. You will absorb fascinating and important mathematical ideas. Some solutions will rely on ingenuity, some will challenge you to spot hidden patterns, others call for extreme rationality. All will surprise, entertain and stretch your brain. Will you make it out with your puzzling pride intact?
£9.49
Welbeck Publishing Group Limited The Most Difficult Logic Problems Test Your
Book Synopsis
£12.30
Profile Books Ltd x+y: A Mathematician's Manifesto for Rethinking
Book SynopsisFrom imaginary numbers to the fourth dimension and beyond, mathematics has always been about imagining things that seem impossible at first glance. In x+y, Eugenia Cheng draws on the insights of higher-dimensional mathematics to reveal a transformative new way of talking about the patriarchy, mansplaining and sexism: a way that empowers all of us to make the world a better place. Using precise mathematical reasoning to uncover everything from the sexist assumptions that make society a harder place for women to live to the limitations of science and statistics in helping us understand the link between gender and society, Cheng's analysis replaces confusion with clarity, brings original thinking to well worn arguments - and provides a radical, illuminating and liberating new way of thinking about the world and women's place in it.Trade ReviewA way of seeing this exhausting debate from a completely new angle ... bold and optimistic * Guardian *Compelling ... x+y provides useful new tools for change, for those - like me - involved in diversity, equity and inclusion initiatives. For those who are not yet involved, she sets out reasons to become so. And I'm a new fan of pure mathematics. Dr Cheng, can we be friends? * Nature *... a fascinating, disarmingly accessible read and a wonderful example of what academics should in general do much more of * Irish Times *Praise for The Art of Logic: 'Mind-expanding ... a meaningful contribution to creating a better society as well as happier conversations and relationships * Guardian *With humour, grace, and a natural gift for making explanations seem fun, Eugenia Cheng has done it again. You'll think more clearly after reading this book -- Daniel Levitin, bestselling author of The Organised Mind & A Field Guide to Lies and StatisticsRadical and liberating * Emerald Street *A perceptive analysis of logic and its limitations ... Cheng is successful not only in helping readers think more clearly, but in helping them understand why others sometimes appear to be illogical * Times Higher Education *
£9.49
Profile Books Ltd Mathematical Intelligence: What We Have that
Book SynopsisFROM THE PRESENTER OF THE TEDx TALK 'You weren't bad at maths - you just weren't looking at it the right way' 'Compelling and wonderfully readable' - Ian Stewart, bestselling author of Seventeen Equations that Changed the World 'AI is powerful, but human thinking is differently powerful, and Junaid Mubeen deftly shows us how' - Eugenia Cheng, author of How to Bake Pi There's so much talk about the threat posed by intelligent machines that it sometimes seems as though we should surrender to our robot overlords now. But Junaid Mubeen isn't ready to throw in the towel just yet. As far as he is concerned, we have the edge over machines because of a remarkable system of thought developed over the millennia. It's familiar to us all, but often badly taught and misrepresented in popular discourse - maths. Computers are brilliant at totting up sums, pattern-seeking and performing, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical superpowers.Trade Review[An] intelligent analysis * Nature *Insightful * Popular Science *A compelling and wonderfully readable analysis of why computers won't replace mathematicians, but why the two together are superior to either on its own. A rallying-cry for real intelligence in the age of algorithms and artificial intelligence. -- Ian Stewart, author * What's the Use? *Maths needs more demystifiers, and Junaid Mubeen is here to lift back the veil to show the inner workings of maths and mathematicians. This book importantly shows that computers and AI do not make mathematicians redundant - in fact, Mubeen uses the advances and stumbling blocks in AI to illuminate the crucial contribution that human mathematicians continue to make. I recommend this to anyone who thinks - or knows someone who thinks - that AI will make the study of maths redundant. AI is powerful, but human thinking is differently powerful, and Junaid Mubeen deftly shows us how. -- Eugenia Cheng, author * X + Y: A Mathematician's Manifesto for Rethinking Gender *
£19.00
Profile Mathematical Intelligence
Book SynopsisThere's so much talk about the threat posed by intelligent machines that it sometimes seems as though we should surrender to our robot overlords. But Junaid Mubeen isn't ready to throw in the towel just yet. As far as he is concerned, we have the creative edge over machines, because of a remarkable system of thought that humans have developed over the millennia. It's familiar to us all, but often badly taught in schools and misrepresented in popular discourse - maths. Computers are, of course, brilliant at totting up sums, pattern-seeking and performing mindless tasks of, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical superpowers.
£10.44
Taylor & Francis Ltd Mild Cognitive Impairment: International
Book SynopsisMild Cognitive Impairment (MCI) has been identified as an important clinical transition between normal aging and the early stages of Alzheimer's disease (AD). Since treatments for AD are most likely to be most effective early in the course of the disease, MCI has become a topic of great importance and has been investigated in different populations of interest in many countries. This book brings together these differing perspectives on MCI for the first time. This volume provides a comprehensive resource for clinicians, researchers, and students involved in the study, diagnosis, treatment, and rehabilitation of people with MCI. Clinical investigators initially defined mild cognitive impairment (MCI) as a transitional condition between normal aging and the early stages of Alzheimer’s disease (AD). Because the prevalence of AD increases with age and very large numbers of older adults are affected worldwide, these clinicians saw a pressing need to identify AD as early as possible. It is at this very early stage in the disease course that treatments to slow the progress and control symptoms are likely to be most effective.Since the first introduction of MCI, research interest has grown exponentially, and the utility of the concept has been investigated from a variety of perspectives in different populations of interest (e.g., clinical samples, volunteers, population-based screening) in many different countries. Much variability in findings has resulted. Although it has been acknowledged that the differences observed between samples may be ‘legitimate variations’, there has been no attempt to understand what it is we have learned about MCI (i.e., common features and differences) from each of these perspectives.This book brings together information about MCI in different populations from around the world. Mild Cognitive Impairment will be an important resource for any clinician, researcher, or student involved in the study, detection, treatment, and rehabilitation of people with MCI.Trade Review"This valuable volume brings the kind of broad perspective to mild cognitive impairment that has long been needed. Rather than basing conclusions on a single sample or framework, the editors have pulled together articles from leading research groups around the world. This is the kind of comprehensive approach that is needed for developing systematic and valid definitions of MCI and identifying better tools that make it possible to differentiate between benign memory changes in later life and the early signs of pathological processes." - Steven H. Zarit, Department of Human Development and Family Studies, The Pennsylvania State University"This volume provides the most comprehensive overview of mild cognitive impairment currently available. The conceptual and methodological challenges for studying MCI are tackled with rigor, and the complexities of defining the syndrome are not underestimated. This book is certain to become a classic text for those studying or researching cognitive agin, MCI and dementia, and for clinicians seeking an authoritative reference on the clinical manifestations of MCI." - Kaarin J. Anstey, Centre for Mental Health Research, Australian National University"The editors of this book have done a great job. The description of the issues is laid out in a well-written introduction, making the descriptions of the research papers very accessible, even to the less well-informed reader. The conclusion likewise pulled together the various strands, including defining what still needs to be done to further refine the concept of MCI." - Graham A. Jackson, Laverndale Hospital, Scotland. In Dementia, August, 2008"This valuable volume brings the kind of broad perspective to mild cognitive impairment that has long been needed. Rather than basing conclusions on a single sample or framework, the editors have pulled together articles from leading research groups around the world. This is the kind of comprehensive approach that is needed for developing systematic and valid definitions of MCI and identifying better tools that make it possible to differentiate between benign memory changes in later life and the early signs of pathological processes." - Steven H. Zarit, Department of Human Development and Family Studies, The Pennsylvania State University"This volume provides the most comprehensive overview of mild cognitive impairment currently available. The conceptual and methodological challenges for studying MCI are tackled with rigor, and the complexities of defining the syndrome are not underestimated. This book is certain to become a classic text for those studying or researching cognitive agin, MCI and dementia, and for clinicians seeking an authoritative reference on the clinical manifestations of MCI." - Kaarin J. Anstey, Centre for Mental Health Research, Australian National University"The editors of this book have done a great job. The description of the issues is laid out in a well-written introduction, making the descriptions of the research papers very accessible, even to the less well-informed reader. The conclusion likewise pulled together the various strands, including defining what still needs to be done to further refine the concept of MCI." - Graham A. Jackson, Laverndale Hospital, Scotland. In Dementia, August, 2008Table of ContentsPart 1. Introduction. H. Tuokko, I. McDowell, An Overview of Mild Cognitive Impairment. Part 2. General Population Research on MCI. C. Fabrigoule, P. Barberger-Gateau, J.-F. Dartigues, The PAQUID Study. K. Palmer, L. Bäckman, B.J. Small, L. Fratiglioni, Cognitive Impairment in Elderly Persons without Dementia: Findings from the Kungsholmen Project. J. Fleming, F.E. Matthews, M. Chatfield, C. Brayne, Population Levels of Mild Cognitive Impairment in England and Wales. A. Collie, P. Maruff, D.G. Darby, C. Masters, J. Currie, The Melbourne Aging Study. Part 3. Specific Samples. R. Wilson, N.T. Aggarwal, D.A. Bennett, Mild Cognitive Impairment in the Religious Orders Study. G. Smith, M. Machulda, K. Kantarci, A Perspective from the Mayo Clinic. M.C. Tierney, Prediction of Probable Alzheimer's Disease: The Sunnybrook Memory Study. H. Wolf, H.-J. Gertz, Studies in the Leipzig Memory Clinic: Contribution to the Concept of Mild Cognitive Impairment. Part 4. Interventions. H. Chertkow, Emerging Pharmacological Therapies for Mild Cognitive Impairment. B. Woods, L. Clare, Cognition-based Therapies and Mild Cognitive Impairment. K. Peters, G. Winocur, Combined Therapies in Mild Cognitive Impairment. Part 5. Summary and Future Directions. H. Tuokko, D.F. Hultsch, The Future of Mild Cognitive Impairment.
£80.74
Orion Publishing Co Numbers: 10 Things You Should Know
Book SynopsisUncover the language of our universe - numbers - in this wide-ranging whistle-stop tour of the history and majesty of mathematics.Our world simply wouldn't function if we didn't have numbers. But where do they come from? Why do we cut cake the wrong way? How can there be different sizes of infinity?All these questions and more are answered in this engaging romp through the history of numbers by acclaimed science writer, Colin Stuart. From the mathematicians who have (and haven't) shouted 'Eureka!' to the theories that affect and inform our everyday lives; Numbers shows us that maths was never boring - we were just being taught it in the wrong way.Consisting of ten bite-sized essays, there's no better guide to this fundamental science.
£9.49
Atlantic Books Metamaths
Book SynopsisOne of the world's greatest mathematicians explains his revolutionary hypothesis about the enigma at the heart of maths: omega. 'Chaitin comes across as a kind of mathematical Richard Feynman, intuitive and high-spirited, irreverent and plain-spoken.' -- Peter Pesic, TLSMeta Maths is Gregory Chaitin's exuberant account of his discovery of 'omega': the infinitely long, exquisitely complex and utterly incalculable representation of randomness and unknowability in mathematics. From Euclid to Gödel to Turing, Chaitin's infectious narrative guides us on a spellbinding journey through the historical advances in maths and science that led to his breakthrough discovery. Once there he takes us further, to the very frontiers of scientific thinking. Meta Maths shows that mathematics is as much art form as logic, as much science as pure reasoning, and sheds light on what we can ultimately hope to know about the universe and the very nature of life.Trade ReviewMeta Maths is truly idiosyncratic. Informal, chatty and cerebral... it mixes mathematics with Chaitin's outlook on life and philosophy... Great fun. -- Alan Cane * Financial Times *
£16.19
Imperial College Press Meaning, Logic And Ludics
Book SynopsisThis book presents several recent advances in natural language semantics and explores the boundaries between syntax and semantics over the last two decades. It is based on some of the most recent theories in logic, such as linear logic and ludics, first created by Jean-Yves Girard, and it also provides some sharp analyses of computational semantical representations, explaining advanced theories in theoretical computer sciences, such as the lambda-mu and Lambek-Grishin calculi which were applied by Philippe de Groote and Michael Moortgat. The author also looks at Aarne Ranta's ‘proof as meaning’ approach, which was first based on Martin-Löf's Type Theory.Meaning, Logic and Ludics surveys the many solutions which have been proposed for the syntax-semantics interface, taking into account the specifications of linguistic signs (continuous or discontinuous) and the fundamental mechanisms developed by linguists and notable Generativists. This pioneering publication also presents ludics (in a chapter co-authored with Myriam Quatrini), a framework which allows us to characterize meaning as an invariant with regard to interaction between processes. It is an excellent book for advanced students, and academics alike, in the field of computational linguistics.Table of ContentsCompositional Semantics and Generative Grammar; Mathematics of Syntactic Structure; Elements of Proof Theory; Variants of the Lambek Calculus; Grammatical Reasoning; Minimalist Derivations; Continuations and Contexts; Towards Dynamics of Meaning; Interaction and Dialogue.
£113.40
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
£294.45
Icon Books Introducing Infinity: A Graphic Guide
Book SynopsisInfinity is a profoundly counter-intuitive and brain-twisting subject that has inspired some great thinkers - and provoked and shocked others.The ancient Greeks were so horrified by the implications of an endless number that they drowned the man who gave away the secret. And a German mathematician was driven mad by the repercussions of his discovery of transfinite numbers.Brian Clegg and Oliver Pugh's brilliant graphic tour of infinity features a cast of characters ranging from Archimedes and Pythagoras to al-Khwarizmi, Fibonacci, Galileo, Newton, Leibniz, Cantor, Venn, Gödel and Mandelbrot, and shows how infinity has challenged the finest minds of science and mathematics. Prepare to enter a world of paradox.
£8.54
College Publications Studies in Diagrammatology and Diagram Praxis
£17.58
College Publications Passed Over in Silence. On Wittgenstein's Tractatus and Its System
£19.95
