{"title":"Mathematical logic Books","description":"","products":[{"product_id":"introducing-infinity-a-graphic-guide-9781848314061","title":"Introducing Infinity: A Graphic Guide","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003cb\u003eInfinity is a profoundly counter-intuitive and brain-twisting subject that has inspired some great thinkers - and provoked and shocked others.\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e\u003cbr\u003eThe 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.\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eBrian 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.\u003c\/p\u003e","brand":"Icon Books","offers":[{"title":"Default Title","offer_id":47850703389015,"sku":"9781848314061","price":8.54,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781848314061.jpg?v=1710619619"},{"product_id":"schaums-outline-of-boolean-algebra-and-switching-circuits-9780070414600","title":"Schaums Outline of Boolean Algebra and Switching","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003cb\u003eConfusing Textbooks? Missed Lectures? Not Enough Time?\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eFortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eThis Schaum's Outline gives you\u003c\/b\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ePractice problems with full explanations that reinforce knowledge\u003c\/li\u003e\n\u003cli\u003eCoverage of the most up-to-date developments in your course field\u003c\/li\u003e\n\u003cli\u003eIn-depth review of practices and applications\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eFully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!\u003c\/p\u003e\u003cp\u003eSchaum's Outlines-Problem Solved.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eThe Algebra of LogicThe Algebra of SetsBoolean AlgebrasSwitching Circuits and Logic CircuitsTopics in the Theory of Boolean AlgebrasAppendix","brand":"McGraw-Hill Education - Europe","offers":[{"title":"Default Title","offer_id":48732109799767,"sku":"9780070414600","price":23.39,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780070414600.jpg?v=1791453832"},{"product_id":"an-introduction-to-proof-theory-normalization-cutelimination-and-consistency-proofs-9780192895943","title":"An Introduction to Proof Theory Normalization","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eAn Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface 1 Introduction 2 Axiomatic calculi 3 Natural deduction 4 Normal deductions 5 The sequent calculus 6 The cut-elimination theorem 7 The consistency of arithmetic 8 Constructive ordinals and induction 9 The consistency of arithmetic, continued Appendices: A The Greek alphabet B Set-theoretic notation C Axioms, rules, and theorems of axiomatic calculi D Exercises on axiomatic derivations E Natural deduction F Sequent calculus G Outline of the cut elimination theorem","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732613312855,"sku":"9780192895943","price":29.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192895943.jpg?v=1719997653"},{"product_id":"the-foundations-of-mathematics-9780198706434","title":"The Foundations of Mathematics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years'' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students'' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of ''nonstandard analysis'', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eThe writing is both rigorous and thorough, and the authors use compact presentations to support their explanations and proofs. Highly recommended. * N. W. Schillow, CHOICE *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eI: THE INTUITIVE BACKGROUND; II: THE BEGINNINGS OF FORMALISATION; III: THE DEVELOPMENT OF AXIOMATIC SYSTEMS; IV: USING AXIOMATIC SYSTEMS; V: STRENGTHENING THE FOUNDATIONS","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732766929239,"sku":"9780198706434","price":23.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198706434.jpg?v=1719998308"},{"product_id":"logic-9780198811701","title":"Logic","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eLogic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy. In this new edition Graham Priest expands his discussion to cover the subjects of algorithms and axioms, and proofs in mathematics.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePREFACE TO SECOND EDITION; PREFACE TO FIRST EDITION; GLOSSARY; PROBLEMS; PROBLEM SOLUTIONS; BIBLIOGRAPHY; GENERAL INDEX","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732792717655,"sku":"9780198811701","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198811701.jpg?v=1719998421"},{"product_id":"category-theory-9780199237180","title":"Category Theory","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eCategory theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda''s lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eThe book is well organised and very well written. The presentation of the material is from the concrete to the abstract, proofs are worked out in detail and the examples and the exercises spread throughout the text mark a pleasant rhythm for its reading. In all, Awodey's Category Theory is a very nice and recommendable introduction to the subject. * Pere Pascual, EMS Newsletter *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface ; 1. Categories ; 2. Abstract Structures ; 3. Duality ; 4. Groups and Categories ; 5. Limits and Colimits ; 6. Exponentials ; 7. Naturality ; 8. Categories of Diagrams ; 9. Adjoints ; 10. Monads and Algrebras ; References ; Solutions to Selected Exercises ; Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732837577047,"sku":"9780199237180","price":61.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199237180.jpg?v=1719998611"},{"product_id":"essential-logic-for-computer-science-the-mit-press-9780262039185","title":"Essential Logic for Computer Science The MIT","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cb\u003eAn introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory.\u003c\/b\u003e\u003cp\u003eComputer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science. Topics covered include predicate logic, equation-based software, automated testing and theorem proving, and large-scale computation. \u003c\/p\u003e\u003cp\u003eFormalism is emphasized, and the book employs three formal notations: traditional algebraic formulas of propositional and predicate logic; digital circuit diagrams; and the widely used partially automated theorem prover, ACL2, which provides an accessible introduction to mechanized formalism\u003c\/p\u003e","brand":"MIT Press Ltd","offers":[{"title":"Default Title","offer_id":48733449617751,"sku":"9780262039185","price":43.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780262039185.jpg?v=1720000125"},{"product_id":"sheaves-in-geometry-and-logic-9780387977102","title":"Sheaves in Geometry and Logic","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eSheaves also appear in logic as carriers for models of set theory. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"A beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. … authors have a rare gift for conveying an insider’s view of the subject from the start. This book is written in the best Mac Lane style, very clear and very well organized. … it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field.\" (Wordtrade, 2008)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; Prologue; Categorical Preliminaries; 1. Categories of Functors; 2. Sheaves of Sets; 3. Grothendieck Topologies and Sheaves; 4. First Properties of Elementary Topoi; 5. Basic Constructions of Topoi; 6. Topoi and Logic; 7. Geometric Morphisms; 8. Classifying Topoi; 9. Localic Topoi; 10. Geometric Logic and Classifying Topoi; Appendix: Sites for Topoi; Epilogue; Bibliography; Index of Notations; Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727916375,"sku":"9780387977102","price":61.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387977102.jpg?v=1720001409"},{"product_id":"foundations-and-fundamental-concepts-of-mathematics-dover-books-on-mathematics-9780486696096","title":"Foundations and Fundamental Concepts of","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThird edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48733800595799,"sku":"9780486696096","price":13.04,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486696096.jpg?v=1720001754"},{"product_id":"geometry-9781071602973","title":"Geometry","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cdiv\u003eThis text is the fifth and final in the series of educational books written by Israel Gelfand with his colleagues for high school students. These books cover the basics of mathematics in a clear and simple format - the style Gelfand was known for internationally. Gelfand prepared these materials so as to be suitable for independent studies, thus allowing students to learn and practice the material at their own pace without a class.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e\n\u003ci\u003eGeometry\u003c\/i\u003e takes a different approach to presenting basic geometry for high-school students and others new to the subject.  Rather than following the traditional axiomatic method that emphasizes formulae and logical deduction, it focuses on geometric constructions. Illustrations and problems are abundant throughout, and readers are encouraged to draw figures and move them in the plane, allowing them to develop and enhance their geometrical vision, imagination, and creativity. Chapters are structured so that only certai\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\n\u003cp\u003e“This book is intended to engage the reader visually, tactilely, and kinesthetically. … It has a good set of material to enliven more traditional geometry instruction. … There are problems and exercises throughout. The exercises are accompanied by solutions.” (MAA Reviews, October 10, 2020)\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePoints and Lines: A Look at Projective Geometry.- Parallel Lines: A Look at Affine Geometry.- Area: A Look at Symplectic Geometry.- Circles: A Look at Euclidean Geometry.\u003c\/div\u003e","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48738192687447,"sku":"9781071602973","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781071602973.jpg?v=1723811807"},{"product_id":"the-joy-of-abstraction-9781108477222","title":"The Joy of Abstraction","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eJourney through the world of abstract mathematics into category theory with popular science author Eugenia Cheng. Featuring humanizing examples and demystification of mathematical thought processes, this book is for fans of How to Bake Pi who want to dig deeper into mathematical concepts and build their mathematical background.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'This book is an educational tour de force that presents mathematical thinking as a right-brained activity. Most 'left brain\/right brain' education-talk is at best a crude metaphor; but by putting the main focus on the process of (mathematical) abstraction, Eugenia Cheng supplies the reader (whatever their 'brain-type') with the mental tools to make that distinction precise and potentially useful. The book takes the reader along in small steps; but make no mistake, this is a major intellectual journey. Starting not with numbers, but everyday experiences, it develops what is regarded as a very advanced branch of abstract mathematics (category theory, though Cheng really uses this as a proxy for mathematical thinking generally). This is not watered-down math; it's the real thing. And it challenges the reader to think-deeply at times. We 'left-brainers' can learn plenty from it too.' Keith Devlin, Stanford University (Emeritus), author of The Joy of Sets\u003cbr\u003e'Eugenia Cheng loves mathematics—not the ordinary sort that most people encounter, but the most abstract sort that she calls 'the mathematics of mathematics.' And in this lovely excursion through her abstract world of Category Theory, she aims to give those who are willing to join her a glimpse of that world. The journey will change how they view mathematics. Cheng is a brilliant writer, with prose that feels like poetry. Her contagious enthusiasm makes her the perfect guide.' John Ewing, President, Math for America\u003cbr\u003e'Eugenia Cheng's singular contribution is in making abstract mathematics relevant to all through her great ingenuity in developing novel connections between logic and life. Her latest book, The Joy of Abstraction, provides a long awaited fully rigorous yet gentle introduction to the 'mathematics of mathematics,' allowing anyone to experience the joy of learning to think categorically.' Emily Riehl, Johns Hopkins University, author of Category Theory in Context\u003cbr\u003e'Archimedes is quoted as having said once: 'Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.' In this fascinating book, Eugenia Cheng approaches the abstract mathematical area of Category Theory with pure love, to reveal its beauty to anybody interested in learning something about contemporary mathematics.' Mario Livio, astrophysicist, author of The Golden Ratio and Brilliant Blunders\u003cbr\u003e'Eugenia Cheng's latest book will appeal to a remarkably broad and diverse audience, from non-mathematicians who would like to get a sense of what mathematics is really about, to experienced mathematicians who are not category theorists but would like a basic understanding of category theory. Speaking as one of the latter, I found it a real pleasure to be able to read the book without constantly having to stop and puzzle over the details. I have learnt a lot from it already, including what the famous Yoneda lemma is all about, and I look forward to learning more from it in the future.' Sir Timothy Gowers, Collège de France, Fields Medalist, main editor of The Princeton Companion to Mathematics\u003cbr\u003e'At last: a book that makes category theory as simple as it really is. Cheng explains the subject in a clear and friendly way, in detail, not relying on material that only mathematics majors learn. Category theory – indeed, mathematics as a whole – has been waiting for a book like this.' John Baez, University of California, Riverside\u003cbr\u003e'Many people speak derisively of category theory as the most abstract area of mathematics, but Eugenia Cheng succeeds in redeeming the word 'abstract'. This book is loquacious, conversational, and inviting. Reading this book convinced me I could teach category theory as an introductory course, and that is a real marvel, since it is a subject most people leave for experts.' Francis Su, Harvey Mudd College, author of Mathematics for Human Flourishing\u003cbr\u003e'Finally, a book about category theory that doesn't assume you already know category theory! In this inviting but rigorous introduction to what she calls 'the mathematics of mathematics', Eugenia Cheng brings the subject to us with insight, wit, and a point of view. Her story of finding joy-and advantage-in abstraction will inspire you to find it, too.' Patrick Honner, award-winning high school math teacher, columnist for Quanta Magazine, author of Painless Statistics\u003cbr\u003e'This higher category theory is the mathematics of the twenty-first century (at least my corner of it). If you'd like a taste of it, I recommend Dr. Cheng's book. The first half is an accessible and thought-provoking insight into categorical thinking. The second half climbs into the rarified air of theoretic math, but it is worth a read to get a feel for what some parts of modern mathematics look like.' Jonathan Kujawa, 3 Quarks Daily\u003cbr\u003e'… a successful addition to the literature that I am sure students will use in the future and I would be happy to recommend.' Constanze Roitzheim, Mathematische Semesterberichte\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePrologue; Part I. Building Up to Categories: 1. Categories: the idea; 2. Abstraction; 3. Patterns; 4. Context; 5. Relationships; 6. Formalism; 7. Equivalence relations; 8. Categories: the definition; Interlude: A Tour of Math: 9. Examples we've already seen, secretly; 10. Ordered sets; 11. Small mathematical structures; 12. Sets and functions; 13. Large worlds of mathematical structures; Part II. Doing Category Theory: 14. Isomorphisms; 15. Monics and epics; 16. Universal properties; 17. Duality; 18. Products and coproducts; 19. Pullbacks and pushouts; 20. Functors; 21. Categories of categories; 22. Natural transformations; 23. Yoneda; 24. Higher dimensions; 25. Epilogue: thinking categorically; Appendices: A. Background on alphabets; B. Background on basic logic; C. Background on set theory; D. Background on topological spaces; Glossary; Further reading; Acknowledgements; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738304360791,"sku":"9781108477222","price":23.52,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108477222.jpg?v=1723811906"},{"product_id":"mathematical-logic-through-python-9781108949477","title":"Mathematical Logic through Python","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eUsing a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel''s completeness theorem. A sneak peek to Gödel''s incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'The authors transformed the first course in Mathematical Logic – an experience that many students view as daunting and technical – into an inspiring journey that sails playfully yet rigorously from logic's first principles to Gödel's Completeness Theorem. The secret sauce is making progress by writing many little Python programs instead of proving theorems, a hands-on approach that suits computer science students perfectly.' Shimon Schocken, Reichman University\u003cbr\u003e'Mathematical logic is all about expressions and syntactic operations, and many of its best ideas find a natural home in computer science. Gonczarowski and Nisan make the subject come alive by opening it up to computational implementation and exploration.' Jeremy Avigad, Carnegie Mellon University\u003cbr\u003e'Mathematical Logic through Python offers a refreshingly innovative approach that makes it stand out among several excellent books on mathematical logic. By building on readers' experience and intuition through programming, it naturally provides them with a deep understanding of the fundamental concepts of mathematical logic that underly computer science.' Yoram Moses, Technion - Israel Institute of Technology\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; Introduction and Overview; Part I. Propositional Logic: 1. Propositional Logic Syntax; 2. Propositional Logic Semantics; 3. Logical Operators; 4. Proof by Deduction; 5. Working with Proofs; 6. The Tautology Theorem and the Completeness of Propositional Logic; Part II. Predicate Logic: 7. Predicate Logic Syntax and Semantics; 8. Getting Rid of Functions and Equality; 9. Deductive Proofs of Predicate Logic Formulas; 10. Working with Predicate Logic Proofs; 11. The Deduction Theorem and Prenex Normal Form; 12. The Completeness Theorem; 13. Sneak Peek at Mathematical Logic II: Godel's Incompleteness Theorem; Cheatsheet Axioms and Axiomatic Inference Rules Used in this Book; Notes; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738346893655,"sku":"9781108949477","price":22.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108949477.jpg?v=1723811956"},{"product_id":"an-invitation-to-model-theory-9781316615553","title":"An Invitation to Model Theory","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eModel theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; Part I. Languages and Structures: 1. Structures; 2. Terms; 3. Formulas; 4. Definable sets; 5. Substructures and quantifiers; Part II. Theories and Compactness: 6. Theories and axioms; 7. The complex and real fields; 8. Compactness and new constants; 9. Axiomatisable classes; 10. Cardinality considerations; 11. Constructing models from syntax; Part III. Changing Models: 12. Elementary substructures; 13. Elementary extensions; 14. Vector spaces and categoricity; 15. Linear orders; 16. The successor structure; Part IV. Characterising Definable Sets: 17. Quantifier elimination for DLO; 18. Substructure completeness; 19. Power sets and Boolean algebras; 20. The algebras of definable sets; 21. Real vector spaces and parameters; 22. Semi-algebraic sets; Part V. Types: 23. Realising types; 24. Omitting types; 25. Countable categoricity; 26. Large and small countable models; 27. Saturated models; Part VI. Algebraically Closed Fields: 28. Fields and their extensions; 29. Algebraic closures of fields; 30. Categoricity and completeness; 31. Definable sets and varieties; 32. Hilbert's Nullstellensatz; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738565194071,"sku":"9781316615553","price":30.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781316615553.jpg?v=1791470335"},{"product_id":"quaternions-for-computer-graphics-9781447175087","title":"Quaternions for Computer Graphics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eIf you have ever wondered what quaternions are - then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of the text and equations, all figures are in colour, extra worked examples, an expanded index, and a bibliography arranged for each chapter. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eQuaternions for Computer Graphics\u003c\/i\u003e includes chapters on number sets and algebra, imaginary and complex numbers, the complex plane, rotation transforms, and a comprehensive description of quaternions in the context of rotation. 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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?).\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003e\u003ci\u003eHow to Expect the Unexpected\u003c\/i\u003e\u003c\/b\u003e 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.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eA 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 *\u003cbr\u003eKit 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 *\u003cbr\u003eFascinating 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 *\u003cbr\u003eYates' 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 *\u003cbr\u003eI'm a Yates fan. His style is all-clarity-no-bullshit * Aperiodical *\u003cbr\u003eSeriously good * Caroline Lucas MP *\u003cbr\u003eAbsolutely fascinating * James O'Brien *\u003cbr\u003eAn exceptional book - readable, funny and more needed than ever * Dr Chris van Tulleken, bestselling author of Ultra-Processed People *\u003cbr\u003eYates' writing style imbues the subjects covered with an infectious enthusiasm, artfully dispelling the dry, stuffy perceptions many people have of maths * Physics World *\u003cbr\u003eHOW 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 *","brand":"Quercus Publishing","offers":[{"title":"Default Title","offer_id":48740273619287,"sku":"9781529408676","price":18.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781529408676.jpg?v=1720054281"},{"product_id":"new-frontiers-in-fuzzy-controllers-9781632403780","title":"New Frontiers in Fuzzy Controllers","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eAdvances in the sphere of fuzzy controllers have been rapid, giving rise to the need for literature that documents all the recent advances both in theory and in applications. This book has been published with an aim of serving the same purpose. It is a compilation of various research outcomes on diverse applications of fuzzy control systems. At the center of numerous engineering challenges is the question of controlling different systems. The wide spectrum of these structures includes a variety of systems varying from the inverted pendulum to auto-focusing system of a digital camera. Fuzzy control systems have displayed their improved output in all these areas. This book examines new areas of fuzzy applications such as a two-layered control system, cycle-to-cycle fuzzy logic control etc. It will be a good source of reference for researchers, engineers, and postgraduate students specializing in associated fields of fuzzy control systems.","brand":"Clanrye International","offers":[{"title":"Default Title","offer_id":48740716773719,"sku":"9781632403780","price":66.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"numbers-10-things-you-should-know-9781841885636","title":"Numbers: 10 Things You Should Know","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003cb\u003eUncover the language of our universe - numbers - in this wide-ranging whistle-stop tour of the history and majesty of mathematics.\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eOur 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?\u003cbr\u003e\u003cbr\u003eAll 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; \u003ci\u003eNumbers\u003c\/i\u003e shows us that maths was never boring - we were just being taught it in the wrong way.\u003cbr\u003e\u003cbr\u003eConsisting of ten bite-sized essays, there's no better guide to this fundamental science.\u003c\/p\u003e","brand":"Orion Publishing Co","offers":[{"title":"Default Title","offer_id":48742074909015,"sku":"9781841885636","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781841885636.jpg?v=1720059926"},{"product_id":"metamaths-9781843545255","title":"Metamaths","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003cb\u003eOne of the world's greatest mathematicians explains his revolutionary hypothesis about the enigma at the heart of maths: omega. \u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003e'Chaitin comes across as a kind of mathematical Richard Feynman, intuitive and high-spirited, irreverent and plain-spoken.' -- Peter Pesic, \u003ci\u003eTLS\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003ci\u003eMeta Maths\u003c\/i\u003e 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. \u003ci\u003eMeta Maths\u003c\/i\u003e 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.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003ci\u003eMeta Maths\u003c\/i\u003e is truly idiosyncratic. Informal, chatty and cerebral... it mixes mathematics with Chaitin's outlook on life and philosophy... Great fun. -- Alan Cane * Financial Times *","brand":"Atlantic Books","offers":[{"title":"Default Title","offer_id":48742085460311,"sku":"9781843545255","price":16.19,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781843545255.jpg?v=1791478518"},{"product_id":"logic-and-computation-essays-in-honour-of-amilcar-sernadas-9781848902480","title":"Logic and Computation: Essays in Honour of","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003cem\u003eThis  volume celebrates Amílcar Sernadas' (1952--2017) highly significant and original scientific contributions, as well as his outstanding academic career. This compilation of articles by colleagues, former students and friends was prepared in the months that followed the Conference in Honour of Amílcar, which was held at the Instituto Superior Técnico in April 2016, to celebrate his 64th birthday.\u003c\/em\u003e \u003c\/p\u003e","brand":"College Publications","offers":[{"title":"Default Title","offer_id":48742267486551,"sku":"9781848902480","price":13.5,"currency_code":"GBP","in_stock":false}]},{"product_id":"understanding-proof-explanation-examples-and-solutions-for-a-level-mathematics-and-a-level-further-mathematics-9781911093787","title":"Understanding Proof: Explanation, Examples and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Tarquin Publications","offers":[{"title":"Default Title","offer_id":48742597951831,"sku":"9781911093787","price":22.94,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781911093787.jpg?v=1791379103"},{"product_id":"ludwig-wittgenstein-dictating-philosophy-to-francis-skinner-the-wittgenstein-skinner-manuscripts-9783030360863","title":"Ludwig Wittgenstein: Dictating Philosophy: To","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eIn this volume we witness Wittgenstein in the act of composing and experimenting with his new visions in philosophy. The book includes key explanations of the origin and background of these previously unknown manuscripts. It investigates how Wittgenstein’s philosophical thought-processes are revealed in his dictation to, as well as his editing and revision with Francis Skinner, in the latter’s role of amanuensis. The book displays a considerable wealth and variety of Wittgenstein’s fundamental experiments in philosophy across a wide array of subjects that include the mind, pure and applied mathematics, metaphysics, the identities of ordinary and creative language, as well as intractable problems in logic and life. He also periodically engages with the work of Newton, Fermat, Russell and others. The book shows Wittgenstein strongly battling against the limits of understanding and the bewitchment of institutional and linguistic customs. The reader is drawn in by Wittgenstein as he urges us to join him in his struggles to equip us with skills, so that we can embark on devising new pathways beyond confusion. \u003c\/p\u003e\u003cp\u003eThis collection of manuscripts was posted off by Wittgenstein to be considered for publication during World War 2, in October 1941. None of it was published and it remained hidden for over two generations. Upon its rediscovery, Professor Gibson was invited to research, prepare and edit the Archive to appear as this book, encouraged by Trinity College Cambridge and The Mathematical Association. Niamh O’Mahony joined him in co-editing and bringing this book to publication.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e            \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e                     \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“Gibson and O’Mahony have done a remarkable job and Dictating Philosophy will prove to be of tremendous importance to the field of Wittgenstein scholarship. … the new angles of approach and skillfully crafted examples from these dictations unquestionably provide real food for thought.” (Nuno Venturinha, PHILOSOPHY, The Journal of the Royal Institute of Philosophy, June 16, 2021)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003ePart 1. The Emergence of the Archive.- Chapter 1. Introduction.- Chapter 2. The Amanuensis Matters.- Part 2. The Transcriptions of the Wittgenstien Skinner Manuscripts.- Chapter 3. The Pink Book.- Chapter 4. Communication of Personal Experience.- Chapter 5. Philosophy.- Chapter 6. Visual Image in his Brain.- Chapter 7. Norwegian Notebook.- Chapter 8. Self Evidence and Logic.- Part 3. Calculations in the Hand of Francis Skinner.- Chapter 9. Mathematical Calculations in Skinner’s Hand.\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743033864535,"sku":"9783030360863","price":35.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030360863.jpg?v=1791480476"},{"product_id":"sequents-and-trees-an-introduction-to-the-theory-and-applications-of-propositional-sequent-calculi-9783030571443","title":"Sequents and Trees: An Introduction to the Theory","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results.  The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained.  Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation.  Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus.\u003cbr\u003eAfter a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications.  The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics.\u003cbr\u003e\u003ci\u003eSequents and Trees\u003c\/i\u003e is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics.  It will also be of interest to researchers in computer science and philosophers.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“Each chapter of the book is structured in a similar way and contains the basic definitions, facts and necessary discussion regarding the key notions, accompanied with new ideas and a wide reference list, followed by the author's clear and approachable style. This book is self-contained, presenting an extensive survey of the applications and usefulness of cut elimination, and seems to be an extremely interesting source not only for logicians and philosophers, but also for researchers in computer science.” (Branislav Boričić, Mathematical Reviews, May, 2022)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction.- Analytic Sequent Calculus for CPL.- Gentzen's Sequent Calculus LK.- Purely Logical Sequent Calculus.- Sequent Calculi for Modal Logics.- Alternatives to CPL.- Appendix.\u003cbr\u003e\u003cbr\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743040811351,"sku":"9783030571443","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030571443.jpg?v=1720063851"},{"product_id":"modelling-puzzles-in-first-order-logic-9783030625467","title":"Modelling Puzzles in First Order Logic","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eKeeping students involved and actively learning is challenging. Instructors in computer science are aware of the cognitive value of modelling puzzles and often use logical puzzles as an efficient pedagogical instrument to engage students and develop problem-solving skills. \u003c\/p\u003e  \u003cp\u003eThis unique book is a comprehensive resource that offers teachers and students fun activities to teach and learn logic. It provides new, complete, and running formalisation in Propositional and First Order Logic for over 130 logical puzzles, including Sudoku-like puzzles, zebra-like puzzles, island of truth, lady and tigers, grid puzzles, strange numbers, or self-reference puzzles.\u003c\/p\u003e  Solving puzzles with theorem provers can be an effective cognitive incentive to motivate students to learn logic. They will find a ready-to-use format which illustrates how to model each puzzle, provides running implementations, and explains each solution.\u003cp\u003e\u003c\/p\u003e  \u003cp\u003eThis concise and easy-to-follow textbook is a much-needed support tool for students willing to explore beyond the introductory level of learning logic and lecturers looking for examples to heighten student engagement in their computer science courses.  \u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“The purpose of this book is to introduce first-order logic (FOL) to newcomers. … The book is a treasure trove of puzzles like this. … All of these are motivated in an approachable, fun way. … the book is a hands-on guide to Prover9 and Mace4 … . It is quite valuable to have so many puzzles in a single book.” (Jesse Adam Alama, Mathematical Reviews, October, 2022)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface.- Getting Started with Prover9 and Mace4.- Micro Arithmetic Puzzles.- Strange Numbers.- Practical Puzzles.- Lady and Tigers.- Einstein Puzzles.- Island of Truth.- Love and Marriage.- Grid Puzzles.- Japanese Puzzles.- Russian Puzzles.- Polyomino Puzzles.- Self-reference and Other Puzzles.- Epigraph in Natural Language","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743042646359,"sku":"9783030625467","price":33.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030625467.jpg?v=1720063860"},{"product_id":"mathematical-logic-9783030738389","title":"Mathematical Logic","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“This newest edition has been reclassified, fittingly, as a graduate text, and it is admirably suited to that role. … Those who are already well-versed in logic will find this text to be a valuable reference and a strong resource for teaching at the graduate level, while those who are new to the field will come to know not only how mathematical logic is studied but also, perhaps more importantly, why.” (Stephen Walk, MAA Reviews, January 6, 2023)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eA.- I Introduction.- II Syntax of First-Order Languages.- III Semantics of First-Order Languages.- IV A Sequent Calculus.- V The Completeness Theorem.- VI The Löwenheim–Skolem and the Compactness Theorem.- VII The Scope of First-Order Logic.- VIII Syntactic Interpretations and Normal Forms.- B.- IX Extensions of First-Order Logic.- X Computability and Its Limitations.- XI Free Models and Logic Programming.- XII An Algebraic Characterization of Elementary Equivalence.- XIII Lindström’s Theorems.- References.- List of Symbols.- Subject Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743047823703,"sku":"9783030738389","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030738389.jpg?v=1791480527"},{"product_id":"computability-9783030832018","title":"Computability","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of “mechanical process” using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. \u003c\/p\u003e\u003cp\u003eAdvanced chapters cover the Ackerman function, Tarski’s theorem on the non-representability of truth, Goedel’s incompleteness and Rosser’s incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church’s thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum’s complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“This textbook is suited for self-study … . As a second reading however a reader interested in rigorous proofs and\/or different approaches to known concepts will benefit from this wealth of material.” (Dieter Riebesehl, zbMATH 1507.03002, 2023)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eMathematical Background; a Review.- A Theory of Computability.- Primitive Recursive Functions.- Loop Programs.-The Ackermann Function.- (Un)Computability via Church's Thesis.- Semi-Recursiveness.- Yet another number-theoretic characterisation of P.- Godel's Incompleteness Theorem via the Halting Problem.- The Recursion Theorem.- A Universal (non-PR) Function for PR.- Enumerations of Recursive and Semi-Recursive Sets.- Creative and Productive Sets Completeness.- Relativised Computability.- POSSIBILITY: Complexity of P Functions.- Complexity of PR Functions.- Turing Machines and NP-Completeness.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743052575063,"sku":"9783030832018","price":71.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030832018.jpg?v=1720063903"},{"product_id":"computability-9783030832049","title":"Computability","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of “mechanical process” using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. \u003c\/p\u003e\u003cp\u003eAdvanced chapters cover the Ackerman function, Tarski’s theorem on the non-representability of truth, Goedel’s incompleteness and Rosser’s incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church’s thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum’s complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“This textbook is suited for self-study … . As a second reading however a reader interested in rigorous proofs and\/or different approaches to known concepts will benefit from this wealth of material.” (Dieter Riebesehl, zbMATH 1507.03002, 2023)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eMathematical Background; a Review.- A Theory of Computability.- Primitive Recursive Functions.- Loop Programs.-The Ackermann Function.- (Un)Computability via Church's Thesis.- Semi-Recursiveness.- Yet another number-theoretic characterisation of P.- Godel's Incompleteness Theorem via the Halting Problem.- The Recursion Theorem.- A Universal (non-PR) Function for PR.- Enumerations of Recursive and Semi-Recursive Sets.- Creative and Productive Sets Completeness.- Relativised Computability.- POSSIBILITY: Complexity of P Functions.- Complexity of PR Functions.- Turing Machines and NP-Completeness.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743052673367,"sku":"9783030832049","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030832049.jpg?v=1720063903"},{"product_id":"the-logical-writings-of-karl-popper-9783030949259","title":"The Logical Writings of Karl Popper","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis open access book is the first ever collection of Karl Popper's writings on deductive logic.\u003cbr\u003eKarl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science (\"falsificationism\") and his social and political philosophy (\"open society\") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics.\u003cbr\u003eThis collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e Part I: Articles.- Chapter 1. Introduction to Popper’s Articles on Logic (David Binder, Thomas Piecha, and Peter Schroeder-Heister).- Chapter 2. Are Contradictions Embracing? (1943) (Karl R. Popper).- Chapter 3. Logic without Assumptions (1947) (Karl R. Popper).- Chapter 4. New Foundations for Logic (1947) (Karl R. Popper).- Chapter 5. Functional Logic without Axioms or Primitive Rules of Inference (1947)(Karl R. Popper).- Chapter 6. On the Theory of Deduction, Part I. Derivation and its Generalizations (1948) (Karl R. Popper).- Chapter 7. On the Theory of Deduction, Part II. The Definitions of Classical and Intuitionist Negation (1948) (Karl R. Popper).- Chapter 8. The Trivialization of Mathematical Logic (1949) (Karl R. Popper).- Chapter 9. A Note on Tarski’s Definition of Truth (1955) (Karl R. Popper).-Chapter 10. On a Proposed Solution of the Paradox of the Liar (1955) (Karl R. Popper).- Chapter 11. On Subjunctive Conditionals with Impossible Antecedents (1959) (Karl R. Popper).- Chapter 12. Lejewski’s Axiomatization of My Theory of Deducibility (1974) (Karl R. Popper).- Chapter 13. Reviews of Popper’s Articles on Logic (Wilhelm Ackermann et.al).- Part II: Manuscripts.- Chapter 14. Introduction to Popper’s Manuscripts on Logic (David Binder, Thomas Piecha, and Peter Schroeder-Heister).- Chapter 15. On Systems of Rules of Inference (Karl R. Popper and Paul Bernays).- Chapter 16. A General Theory of Inference (Karl R. Popper).- Chapter 17. On the Logic of Negation (Karl R. Popper).- Chapter 18. A Note on the Classical Conditional (Karl R. Popper).- Part III: Correspondence.- Chapter 19. Introduction to Popper’s Correspondence on Logic (David Binder, Thomas Piecha, and Peter Schroeder-Heister).- Chapter 20. Popper’s Correspondence with Paul Bernays (Karl R. Popper and Paul Bernays).- Chapter 21. Popper’s Correspondence with Luitzen Egbertus Jan Brouwer (Karl R. Popper and Luitzen E. J. Brouwer).- Chapter 22. Popper’s Correspondence with Rudolf Carnap (Karl R. Popper and Rudolf Carnap).- Chapter 23. Popper’s Correspondence with Alonzo Church (Karl R. Popper and Alonzo Church).- Chapter 24. Popper’s Correspondence with Kalman Joseph Cohen (Karl R. Popper and Kalman J. Cohen).- Chapter 25. Popper’s Correspondence with Henry George Forder (Karl R. Popper and Henry George Forder).- Chapter 26. Popper’s Correspondence with Harold Jeffreys (Karl R. Popper and Harold Jeffreys).- Chapter 27. Popper’s Correspondence with Stephen Cole Kleene (Karl R. Popper and Stephen C. Kleene).- Chapter 28. Popper’s Correspondence with William Calvert Kneale (Karl R. Popper and William C. Kneale).- Chapter 29. Popper’s Correspondence with Willard Van Orman Quine (Karl R. Popper and Willard V. O. Quine).- Chapter 30. Popper’s Correspondence with Heinrich Scholz (Karl R. Popper and Heinrich Scholz).- Chapter 31.  Popper’s Correspondence with Peter Schroeder-Heister (Karl R. Popper and Peter Schroeder-Heister).- Concordances.- Bibliography.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743059915095,"sku":"9783030949259","price":40.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030949259.jpg?v=1791480570"},{"product_id":"inquisitive-logic-consequence-and-inference-in-the-realm-of-questions-9783031097058","title":"Inquisitive Logic: Consequence and Inference in","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis open access book makes a case for extending logic beyond its traditional boundaries, to encompass not only statements but also also questions. The motivations for this extension are examined in detail. It is shown that important notions, including logical answerhood and dependency, emerge as facets of the fundamental notion of entailment once logic is extended to questions, and can therefore be treated with the logician’s toolkit, including model-theoretic constructions and proof systems.\u003c\/p\u003e\u003cp\u003eAfter motivating the enterprise, the book describes how classical propositional and predicate logic can be made inquisitive—i.e., extended conservatively with questions—and what the resulting logics look like in terms of meta-theoretic properties and proof systems. Finally, the book discusses the tight connections between inquisitive logic and dependence logic.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1.  Introduction.- 2.  On the role of questions in logic.- 3.  Questions in propositional logic.- 4. Reasoning with questions.- 5.  Questions in first-order logic.- 6.  Questions in modal logic.- 7. Connections with intuitionistic logic.- 8.  Connections with dependence logic.- 9.  Conclusion.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743069122903,"sku":"9783031097058","price":40.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031097058.jpg?v=1791480614"},{"product_id":"the-real-numbers-an-introduction-to-set-theory-and-analysis-9783319015767","title":"The Real Numbers: An Introduction to Set Theory","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eWhile most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself.\u003c\/p\u003e\u003cp\u003eBy focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to \"assume\" the real numbers. Its prerequisites are calculus and basic mathematics.\u003c\/p\u003e\u003cp\u003eMathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets,  countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“This is a book of both analysis and set theory, and the analysis begins at an elementary level with the necessary treatment of completeness of the reals. … the analysis makes it valuable to the serious student, say a senior or first-year graduate student. … Stillwell’s book can work well as a text for the course in foundations, with its good treatment of the cardinals and ordinals. … This enjoyable book makes the connection clear.” (James M. Cargal, The UMAP Journal, Vol. 38 (1), 2017)\u003c\/p\u003e\u003cp\u003e“This book is an interesting introduction to set theory and real analysis embedded in properties of the real numbers. … The 300-plus problems are frequently challenging and will interest both upper-level undergraduate students and readers with a strong mathematical background. … A list of approximately 100 references at the end of the book will help students to further explore the topic. … Summing Up: Recommended. Lower-division undergraduates.” (D. P. Turner, Choice, Vol. 51 (11), August, 2014)\u003c\/p\u003e\u003cp\u003e“This is an informal look at the nature of the real numbers … . There are extensive historical notes about the evolution of real analysis and our understanding of real numbers. … Stillwell has deliberately set out to provide a different sort of construction where you understand what the foundation is supporting and why it is important. I think this is very successful, and his book … is much more informative and enjoyable.” (Allen Stenger, MAA Reviews, February, 2014)\u003c\/p\u003e\u003cp\u003e“This book will be fully appreciated by either professional mathematicians or those students, who already have passed a course in analysis or set theory. … The book contains a quantity of motivation examples, worked examples and exercises, what makes it suitable also for self-study.” (Vladimír Janiš, zbMATH, 2014)\u003c\/p\u003e\u003cp\u003e“The book offers a rigorous foundation of the real number system. It is intended for senior undergraduates who have already studied calculus, but a wide range of readers will find something interesting, new, or instructive in it. … This is an extremely reader-friendly book. It is full of interesting examples, very clear explanations, historical background, applications. Each new idea comes after proper motivation.” (László Imre Szabó, Acta Scientiarum Mathematicarum (Szeged), Vol. 80 (1-2), 2014)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eThe Fundamental Questions.- From Discrete to Continuous.- Infinite Sets.- Functions and Limits.- Open Sets and Continuity.- Ordinals.- The Axiom of Choice.- Borel Sets.- Measure Theory.- Reflections.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743091241303,"sku":"9783319015767","price":32.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319015767.jpg?v=1720064071"},{"product_id":"philosophy-of-science-for-scientists-9783319265490","title":"Philosophy of Science for Scientists","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis textbook offers an introduction to the philosophy of science. It helps undergraduate students from the natural, the human and social sciences to gain an understanding of what science is, how it has developed, what its core traits are, how to distinguish between science and pseudo-science and to discover what a scientific attitude is. It argues against the common assumption that there is fundamental difference between natural and human science, with natural science being concerned with testing hypotheses and discovering natural laws, and the aim of human and some social sciences being to understand the meanings of individual and social group actions. Instead examines the similarities between the sciences and shows how the testing of hypotheses and doing interpretation\/hermeneutics are similar activities. The book makes clear that lessons from natural scientists are relevant to students and scholars within the social and human sciences, and vice versa. It teaches its readers how to effectively demarcate between science and pseudo-science and sets criteria for true scientific thinking.\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003eDivided into three parts, the book first examines the question  What is Science?  It describes the evolution of science, defines knowledge, and explains the use of and need for hypotheses and hypothesis testing. The second half of part I deals with scientific data and observation, qualitative data and methods, and ends with a discussion of theories on the development \u003c\/p\u003eof science. Part II offers philosophical reflections on four of the most important con\u003cp\u003e\u003c\/p\u003ecepts in science: causes, explanations, laws and models. Part III presents discussions on philosophy of mind, the relation between mind and body, value-free and value-related science, and reflections on actual trends in science.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“Target audience comprises ‘students of engineering, physics, biology, social science, medicine and nursing’ … this book allows readers from a global audience to grasp the ‘flavour’ of the long and rich Germanic and Scandinavian tradition.” (Agustín Adúriz-Bravo, Science and Education, Vol. 28, 2019)\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“The aim of Lars-Göran Johansson’s textbook Philosophy of Science for Scientists is … to provide an introduction to the philosophy of science for students in all fields of science. … the book is supposed to be suitable for an undergraduate level course in the philosophy of science for philosophy students.” (Amanda Thorell, Theoria, Vol. 83, 2017)\u003c\/p\u003e\u003cp\u003e“Lars-Göran Johansson’s recent book Philosophy of science for scientists is the only textbook in the philosophy of science that is addressed specifically to an audience consisting of scientists. … In its breadth of treated topics, the book can serve as a basic text to many different courses in the philosophy of science.” (Maarten Franssen, Metascience, Vol. 26, 2017)\u003c\/p\u003e\u003cp\u003e“Philosophy of Science for Scientists by Lars-Goran Johansson: a lovely textbook for undergraduates. It is a highly readable introduction to how one can view the practice of science. … this is an excellent introduction to understanding science in a general sense. Students and practitioners will find it worthwhile to read and discuss.” (David S. Mazel, MAA Reviews, maa.org, November, 2016)\u003c\/p\u003e\u003cp\u003e“This is an excellent book that can serve as a very appropriate textbook for the first course in Philosophy of Science. … it is a very well written book and is an enjoyable reading. … It is well written by a great authority in the field and I strongly recommend it to you if you are interested in to understand what science is and why science is important for knowledge and our understanding of reality.” (Philosophy, Religion and Science Book Reviews, Bookinspections.wordpress.com, July, 2016)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface and overview of the bookPart 1: What is science?.- 1. The Evolution of Science.- 2. Knowledge.- 3. Hypotheses and Hypothesis Testing.- 4. On Scientific Data.- 5. Qualitative Data and Methods.- 6. Theories about the Development of Science.- Part 2. Philosophical reflections on four core concepts in science: causes, explanations, laws and models.- 7. On Causes and Correlations.- 8. Explanations.- 9. Explanation in the Humanities and Social Sciences.- 10. Scientific Laws.- 11. Theories, Models and Reality.- Part 3. Some auxiliaries.- 12. The Mind-Body Problem.- 13. Science and Values.- 14. Some trends in science.- Appendix.- Logical Forms.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743093666135,"sku":"9783319265490","price":61.74,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319265490.jpg?v=1791481713"},{"product_id":"number-theory-an-introduction-via-the-density-of-primes-9783319438733","title":"Number Theory: An Introduction via the Density of","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eNow in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of \u003ci\u003ep\u003c\/i\u003e-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing.\u003cbr\u003eKey topics and features include:\u003cul\u003e\n\u003cli\u003eA solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eConcise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals\u003c\/li\u003e\n\u003cli\u003eDiscussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eMany interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers\u003c\/li\u003e\n\u003c\/ul\u003eThe user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make \u003ci\u003eNumber Theory: An Introduction via the Density of Primes\u003c\/i\u003e ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“In this text, Fine (mathematics, Fairfield Univ.) and Rosenberger (Univ. of Hamburg, Germany) successfully present number theory from the inception of primes to recent developments in algebraic and analytic number theory and cryptography. … Numerous exercises and open problems are provided. The breadth and depth of topics covered are impressive, making this an excellent text for those interested in the field of number theory. Summing Up: Recommended. Upper-division undergraduates and graduate students.” (J. T. Zerger, Choice, Vol. 54 (9), May, 2017)\u003c\/p\u003e“The book is chatty and leisurely, with lots of historical notes and lots of worked examples. The exercises at the end of each chapter are good and there are a reasonable number of them. … a good text for an introductory course … .” (Allen Stenger, MAA Reviews, maa.org, November, 2016)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction and Historical Remarks.- Basic Number Theory.- The Infinitude of Primes.- The Density of Primes.- Primality Testing: An Overview.- Primes and Algebraic Number Theory.- The Fields Q_\u003ci\u003ep\u003c\/i\u003e of \u003ci\u003ep\u003c\/i\u003e-adic Numbers: Hensel's Lemma.- References.- Index.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743095566679,"sku":"9783319438733","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319438733.jpg?v=1791481720"},{"product_id":"don-pigozzi-on-abstract-algebraic-logic-universal-algebra-and-computer-science-9783319747712","title":"Don Pigozzi on Abstract Algebraic Logic,","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life.\u003c\/p\u003e  \u003cp\u003eIt reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eA Mathematical Life; Pigozzi, Don.- Assertional logics, truth-equational logics, and the hierarchiesof abstract algebraic logic; Albuquerque, Hugo, Font, Josep Maria, Jansana, Ramon, and Moraschini, Tommaso.- Deduction-Detachment Theorem and Gentzen-Style Deductive Systems; Babenyshev, Sergey.- Introducing Boolean Semilattices; Bergman, Clifford.- The Equationally-Defined Commutator in Quasivarieties Generated by Two-Element Algebras; Czelakowski, Janusz.- A short overview of Hidden Logic; Ferreirim, Isabel and Martins, Manuel A.- Absorption and directed J´onsson terms; Kazda, Alexandr, Kozik, Marcin, McKenzie, Ralph and Moore, Matthew.- Relatively congruence modular quasivarieties of modules; Kearnes, Keith A. - The computational complexity of deciding whether a finite algebra generates a minimal variety; McNulty, George F.- Characterization of protoalgebraic \u003ci\u003ek\u003c\/i\u003e-deductive systems; Palasinska; Katarzyna.- Diagrammatic duality; Romanowska, Anna B. and Smith, Jonathan D.H.- Boolean product representations of algebras via binary polynomials; Salibra, Antonino, Ledda, Antonio, and Paoli, Francesco.- Paraconsistent constructive logic with strong negation as a contraction-free relevant logic; Spinks, Matthew and Veroff, Robert.- Possible classification of finite-dimensional compact Hausdorfftopological algebras; Taylor, Walter.- Categorical Abstract Algebraic Logic: Compatibility Operators and Correspondence Theorems; Voutsadakis; George.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743104282967,"sku":"9783319747712","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319747712.jpg?v=1720064130"},{"product_id":"relations-concrete-abstract-and-applied-an-introduction-9789811220340","title":"Relations: Concrete, Abstract, And Applied - An","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743277166935,"sku":"9789811220340","price":139.5,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811220340.jpg?v=1791483813"},{"product_id":"sparse-estimation-with-math-and-r-100-exercises-for-building-logic-9789811614453","title":"Sparse Estimation with Math and R: 100 Exercises","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of sparse estimation by considering math problems and building R programs.  \u003cp\u003eEach chapter introduces the notion of sparsity and provides procedures followed by mathematical derivations and source programs with examples of execution. To maximize readers’ insights into sparsity, mathematical proofs are presented for almost all propositions, and programs are described without depending on any packages. The book is carefully organized to provide the solutions to the exercises in each chapter so that readers can solve the total of 100 exercises by simply following the contents of each chapter.\u003c\/p\u003e\u003cp\u003eThis textbook is suitable for an undergraduate or graduate course consisting of about 15 lectures (90 mins each). Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning by data scientists, machine learning engineers, and researchers interested in linear regression, generalized linear lasso, group lasso, fused lasso, graphical models, matrix decomposition, and multivariate analysis.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book is one of a series of textbooks in machine learning by the same author. Other titles are: \u003c\/p\u003e\u003cp\u003e- Statistical Learning with Math and R (https:\/\/www.springer.com\/gp\/book\/9789811575679)\u003c\/p\u003e  \u003cp\u003e- Statistical Learning with Math and Python (https:\/\/www.springer.com\/gp\/book\/9789811578762)\u003c\/p\u003e  \u003cp\u003e- Sparse Estimation with Math and Python\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eChapter 1: Linear Regression.- Chapter 2: Generalized Linear Regression.- Chapter 3: Group Lasso.- Chapter 4: Fused Lasso.- Chapter 5: Graphical Model.- Chapter 6: Matrix Decomposition.- Chapter 7: Multivariate Analysis.\u003cbr\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743289323863,"sku":"9789811614453","price":26.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811614453.jpg?v=1791483971"},{"product_id":"statistical-learning-with-math-and-python-100-exercises-for-building-logic-9789811578762","title":"Statistical Learning with Math and Python: 100","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of machine learning and data science by considering math problems and building Python programs.\u003cp\u003e\u003c\/p\u003e  \u003cp\u003eAs the preliminary part, Chapter 1 provides a concise introduction to linear algebra, which will help novices read further to the following main chapters. Those succeeding chapters present essential topics in statistical learning: linear regression, classification, resampling, information criteria, regularization, nonlinear regression, decision trees, support vector machines, and unsupervised learning. \u003c\/p\u003e  Each chapter mathematically formulates and solves machine learning problems and builds the programs. The body of a chapter is accompanied by proofs and programs in an appendix, with exercises at the end of the chapter. Because the book is carefully organized to provide the solutions to the exercises in each chapter, readers can solve the total of 100 exercises by simply following the contents of each chapter.\u003cp\u003e\u003c\/p\u003e  \u003cp\u003eThis textbook is suitable for an undergraduate or graduate course consisting of about 12 lectures. Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eChapter 1: Linear Algebra.- Chapter 2: Linear Regression.- Chapter 3: Classification.- Chapter 4: Resampling.- Chapter 5: Information Criteria.- Chapter 6: Regularization.- Chapter 7: Nonlinear Regression.- Chapter 8: Decision Trees.- Chapter 9: Support Vector Machine.- Chapter 10: Unsupervised Learning.\u003cp\u003e\u003c\/p\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743289913687,"sku":"9789811578762","price":26.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811578762.jpg?v=1791483967"},{"product_id":"the-times-mindgames-number-logic-puzzles-book-1-9780008190309","title":"The Times Mindgames Number  Logic Puzzles Book 1","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e500 number and logic puzzles to test your mental agility with this collection from the MindGames section of The Times, featuring 7 different types of puzzle challenge.The perfect gift for all number and logic puzzle enthusiasts who are looking for a varied challengeThis collection contains the favourites Suko, Brain Trainer, Cell Blocks, Futoshiki, Kakuro, Set Square and KenKen, all from the Times puzzles section.","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48863899353431,"sku":"9780008190309","price":7.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008190309.jpg?v=1722269528"},{"product_id":"the-times-super-fiendish-su-doku-book-6-9780008285487","title":"The Times Super Fiendish Su Doku Book 6","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eChallenge yourself at home with word and number puzzlesThese are previously unpublished quality Su Doku grids from The Times, and help to develop you to take on Extreme Su Doku.The 200 puzzles in this collection of treacherously difficult puzzles will stretch even the most advanced Su Doku enthusiast. You will need to use all of your best solving techniques to get to the end of this testing challenge.The puzzles in the collection are of the highest quality and are perfect for the advanced solver in need of a constant supply of ultra-difficult puzzles.Guaranteed to provide hours of mind-stretching entertainment.","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48863931531607,"sku":"9780008285487","price":7.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008285487.jpg?v=1722269666"},{"product_id":"limitless-mind-learn-lead-and-live-without-barriers-9780008305666","title":"Limitless Mind Learn Lead and Live Without","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eWhen we learn, we change what we believe and how we interact with the world. This changes who we are as people and what we can achieve.Many people grow up being told they are not a maths person' or perhaps not smart'. They come to believe their potential is limited.Now, however, the latest science has revealed that our identities are constantly in flux; when we learn new things, we can change our identities, increase our potential and broaden our capacity to receive new information.Drawing from the latest research, Professor Boaler followed thousands of school students, studied their learning practices and examined the most effective ways to transform pupils from low to high achievers. Throughout her study, Boaler has collaborated with Stanford University neuroscience experts, harnessing their expertise to reinforce her advanced understanding of learning and educational development.In Limitless Mind, Boaler presents original groundbreaking research that proves that limiting beliefs rea","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48863940575575,"sku":"9780008305666","price":13.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008305666.jpg?v=1722269698"},{"product_id":"the-times-killer-su-doku-book-16-9780008342913","title":"The Times Killer Su Doku Book 16","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eChallenge yourself at home with word and number puzzlesThe latest volume in the hugely popular Killer Su Doku series from The Times, featuring the highest-quality puzzles with an extra element of arithmetic.This addition to the successful Times Killer Su Doku series will test your skills to the limit, adding the challenge of arithmetic and taking Su Doku to a new and even deadlier level of difficulty.The puzzles use the same 9x9 grid as Su Doku but with an added mathematical challenge. The aim is not only to complete every row, column and cube so that it contains the numbers 1-9, it is also necessary to ensure that the outlined cubes add up to the same number as well.With 200 new Moderate, Tricky, Tough and Deadly Killer Su Doku puzzles, there is no chance to ease yourself in with simple puzzles. For those who like to live dangerously and pushbeyond their mental comfort zone, steel yourself for The Times'' next, terribly tough instalment.","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48863954960727,"sku":"9780008342913","price":6.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008342913.jpg?v=1722269756"},{"product_id":"the-times-killer-su-doku-book-17-9780008404338","title":"The Times Killer Su Doku Book 17","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe latest volume in the hugely popular Killer Su Doku series from The Times, featuring the highest-quality puzzles with an extra element of arithmetic.This addition to the successful Times Killer Su Doku series will test your skills to the limit, adding the challenge of arithmetic and taking Su Doku to a new and even deadlier level of difficulty.The puzzles use the same 9x9 grid as Su Doku but with an added mathematical challenge. The aim is not only to complete every row, column and cube so that it contains the numbers 1-9, it is also necessary to ensure that the outlined cubes add up to the same number as well.With 200 new Moderate, Tricky, Tough and Deadly Killer Su Doku puzzles, there is no chance to ease yourself in with simple puzzles. For those who like to live dangerously and push beyond their mental comfort zone, steel yourself for The Times'' next, terribly tough instalment.","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48863971017047,"sku":"9780008404338","price":6.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008404338.jpg?v=1722269823"},{"product_id":"maths-on-the-back-of-an-envelope-9780008444495","title":"Maths on the Back of an Envelope","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eAnother terrific book by Rob Eastaway' SIMON SINGHA delightfully accessible guide to how to play with numbers' HANNAH FRYHow many cats are there in the world?What''s the chance of winning the lottery twice?And just how long does it take to count to a million?Learn how to tackle tricky maths problems with nothing but the back of an envelope, a pencil and some good old-fashioned brain power.Join Rob Eastaway as he takes an entertaining look at how to figure without a calculator. Packed with amusing anecdotes, quizzes, and handy calculation tips for every situation, Maths on the Back of an Envelope is an invaluable introduction to the art of estimation, and a welcome reminder that sometimes our own brain is the best tool we have to deal with numbers.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e‘A delightfully accessible guide to how to play with numbers’ – Dr Hannah Fry, author of \u003cem\u003eHello World\u003c\/em\u003e and \u003cem\u003eThe Mathematics of Love\u003c\/em\u003e\u003c\/p\u003e           \u003cp\u003e‘Put aside those calculators and computers, and find a pen and piece of paper! In a collection of riveting tips and examples, Eastaway shows us amazing short-cuts to get rough answers to important questions. I still find it remarkable that 16% of 25 is exactly the same as 25% of 16!’ – Professor Sir David Spiegelhalter, author of \u003cem\u003eThe Art of Statistics\u003c\/em\u003e\u003c\/p\u003e           \u003cp\u003e‘Another terrific book by Rob Eastaway’ – Simon Singh\u003c\/p\u003e           \u003cp\u003e‘Packed with fun examples and fresh ideas. I thought I was on top of this subject, but I learned a lot’ – Tim Harford\u003c\/p\u003e           \u003cp\u003e‘A joyful primer about the lost art of calculating without a calculator’ – \u003cem\u003eGuardian\u003c\/em\u003e\u003c\/p\u003e","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48863980749143,"sku":"9780008444495","price":9.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008444495.jpg?v=1722269860"},{"product_id":"logic-for-dummies-9780471799412","title":"Logic For Dummies","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eLogic concepts are more mainstream than you may realize. There's logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cb\u003eIntroduction.\u003c\/b\u003e  \u003cp\u003e\u003cb\u003ePart I: Overview of Logic.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 1: What Is This Thing Called Logic?\u003c\/p\u003e \u003cp\u003eChapter 2: Logical Developments from Aristotle to the Computer.\u003c\/p\u003e \u003cp\u003eChapter 3: Just for the Sake of Argument.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II: Formal Sentential Logic (SL).\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 4: Formal Affairs.\u003c\/p\u003e \u003cp\u003eChapter 5: The Value of Evaluation.\u003c\/p\u003e \u003cp\u003eChapter 6: Turning the Tables: Evaluating Statements with Truth Tables.\u003c\/p\u003e \u003cp\u003eChapter 7: Taking the Easy Way Out: Creating Quick Tables.\u003c\/p\u003e \u003cp\u003eChapter 8: Truth Grows on Trees.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III: Proofs, Syntax, and Semantics in SL.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 9: What Have You Got to Prove?\u003c\/p\u003e \u003cp\u003eChapter 10: Equal Opportunities: Putting Equivalence Rules to Work.\u003c\/p\u003e \u003cp\u003eChapter 11: Big Assumptions with Conditional and Indirect Proofs.\u003c\/p\u003e \u003cp\u003eChapter 12: Putting It All Together: Strategic Moves to Polish Off Any Proof.\u003c\/p\u003e \u003cp\u003eChapter 13: One for All and All for One.\u003c\/p\u003e \u003cp\u003eChapter 14: Syntactical Maneuvers and Semantic Considerations.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV: Quantifier Logic (QL).\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 15: Expressing Quantity with Quality: Introducing Quantifier Logic.\u003c\/p\u003e \u003cp\u003eChapter 16: QL Translations.\u003c\/p\u003e \u003cp\u003eChapter 17: Proving Arguments with QL.\u003c\/p\u003e \u003cp\u003eChapter 18: Good Relations and Positive Identities.\u003c\/p\u003e \u003cp\u003eChapter 19: Planting a Quantity of Trees.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V: Modern Developments in Logic.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 20: Computer Logic.\u003c\/p\u003e \u003cp\u003eChapter 21: Sporting Propositions: Non-Classical Logic.\u003c\/p\u003e \u003cp\u003eChapter 22: Paradox and Axiomatic Systems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VI: The Part of Tens.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 23: Ten Quotes about Logic.\u003c\/p\u003e \u003cp\u003eChapter 24: Ten Big Names in Logic.\u003c\/p\u003e \u003cp\u003eChapter 25: Ten Tips for Passing a Logic Exam.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex.\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864653115735,"sku":"9780471799412","price":17.09,"currency_code":"GBP","in_stock":false}]},{"product_id":"topoi-9780486450261","title":"Topoi","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eA classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Robert Goldblatt is Professor of Pure Mathematics at New Zealand''s Victoria University. 1983 edition.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864733921623,"sku":"9780486450261","price":23.37,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486450261.jpg?v=1722272995"},{"product_id":"stewart-i-game-set-and-math-9780486458847","title":"Stewart I Game Set and Math","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThese pun-studded fables by a popular science writer make complicated mathematical concepts accessible and fun. Twelve essays take a playful approach to mathematics, investigating the topology of a warm blanket, the odds of beating a superior tennis player, and how to distinguish between fact and fallacy. 1991 edition.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864734675287,"sku":"9780486458847","price":9.49,"currency_code":"GBP","in_stock":false}]},{"product_id":"on-formally-undecidable-propositions-of-principia-mathematica-and-related-systems-dover-books-on-mathematics-9780486669809","title":"On Formally Undecidable Propositions of Principia","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eFirst English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864740376919,"sku":"9780486669809","price":9.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"category-theory-in-context-9780486809038","title":"Category Theory in Context","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eDerived from courses the author taught at Harvard and Johns Hopkins, this original book introduces the concepts of category theory ― categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctive, monads ― and other topics, revisiting a broad range of mathematical examples from the categorical perspective. Basic set theory and logic are the only prerequisites.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864743293271,"sku":"9780486809038","price":25.07,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486809038.jpg?v=1722273039"},{"product_id":"lambdacalculus-and-combinators-an-introduction-9780521898850","title":"LambdaCalculus and Combinators An Introduction","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eCombinatory logic and lambda-calculus, originally devised in the 1920s, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this version is thoroughly revised and offers an account of the subject with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eFrom reviews of the first edition: 'The book of R. Hindley and J. Seldin is a very good introduction to fundamental  techniques and results in these fields ... the book is clear, pleasant to read, and it needs no previous knowledge in the domain, but only basic notions of mathematical logic ... Clearly, it was impossible to treat everything in detail; but  even when a subject is only skimmed, the book always provides an incentive for going deeper, and furnishes the means to do it, owing to a substantial bibliography.  Several chapters end with interesting and useful notes with history, comments, and indications for further reading ... In conclusion, this book is very interesting and well written, and is highly recommended to everyone who wants to approach combinatory logic and lambda-calculus (logicians or computer scientists). J. Symbolic Logic\u003cbr\u003e'The best general book on lambda-calculus (typed or untyped) and the theory of combinators.' Gérard Huet, INRIA\u003cbr\u003e'… for teaching and for research or self-study the book is an outstanding source with its own clear merits. I think this second edition of this classical book is a beautiful asset for the literature on λ-calculus and CL.' Theory and Practice of Logic Programming\u003cbr\u003e'… well written and offers a broad coverage backed by an extensive list of references. It could serve as an excellent study material for classes on λ-calculus and CL as well as a reference for logicians and computer scientists interested in the formal background for functional programming and related areas.' EMS Newsletter\u003cbr\u003e'Without doubt this is a valuable treatment of a venerable topic that rewards those who understand it. The authors successfully promulgate their tradition, and that is certainly more important than providing full proofs for every result.' The Journal of JFP\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; 1. The λ-calculus; 2. Combinatory logic; 3. The power of λ and CL; 4. Computable functions; 5. Undecidability; 6. Formal theories; 7. Extensionality in λ-calculus; 8. Extensionality in CL; 9. Correspondence between λ and CL; 10. Simple typing, Church-style; 11. Simple typing, Curry-style in CL; 12. Simple typing, Curry-style in λ; 13. Generalizations of typing; 14. Models of CL; 15. Models of λ ; 16. Scott's D∞ and other models; Appendix 1. α-conversion; Appendix 2. Confluence proofs; Appendix 3. Normalization proofs; Appendix 4. Care of your pet combinator; Appendix 5. Answers to starred exercises; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48864978960727,"sku":"9780521898850","price":64.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"arithmetic-9780674237513","title":"Arithmetic","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eInspiring and informativedeserves to be widely read.Wall Street JournalThis fun book offers a philosophical take on number systems and revels in the beauty of math.Science NewsBecause we have ten fingers, grouping by ten seems natural, but twelve would be better for divisibility, and eight is well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.   Paul Lockhart presents arithmetic not as rote manipulation of numbersa practical if mundane branch of knowledge best suited for filling out tax formsbut as a fascinating, sometimes surprising intellectual craft that arises from our desire to add, divide, and multiply important things. Passionate and entertaining, Arithmetic invites us to experience the beauty of mathematics through the eyes of a beguiling teacher.   A nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by educationLockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting.Jonathon Keats, New ScientistWhat are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind's most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating storyA wonderful book.Keith Devlin, author of Finding Fibonacci\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eToday’s world is more dependent on numbers than at any time in human history, yet with the ready availability of cheap, reliable devices that handle computation, we have never had less need to master arithmetic. Our newfound freedom from the chore of hand computation makes it both possible and, Paul Lockhart argues in this wonderful new book, desirable to step back and reflect on the entire development of arithmetic over several millennia. What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind’s most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story. -- Keith Devlin, mathematician, author of \u003ci\u003eThe Man of Numbers\u003c\/i\u003e and \u003ci\u003eFinding Fibonacci\u003c\/i\u003e\u003cbr\u003eWhat an exuberant, exciting invitation to take joy in the wonderful human activity of counting, and to think deeply about its many origins. Marvelously personal, quite surprising at times, and fun to read. -- Barry Mazur, Gerhard Gade University Professor at Harvard University, coauthor of \u003ci\u003ePrime Numbers and the Riemann Hypothesis\u003c\/i\u003e\u003cbr\u003eOnce I started reading, the text proved mind-blowing. Some of the most ingrained and fundamental assumptions about the way we count and understand numbers are here deconstructed and shown to be arbitrary… For the mathematical layman, this book will be a very pleasant surprise… I am delighted to say that Lockhart is a fabulously entertaining writer, and that his light-hearted approach managed to keep me cheerfully engaged even when his discussions were most abstract… It’s in equal measures entertaining and educational, and a pleasant surprise on more levels than one. -- Andrea Tallarita * PopMatters *\u003cbr\u003e\u003ci\u003eArithmetic\u003c\/i\u003e is inspiring and informative, and deserves to be widely read. -- Jane Gleeson-White * Wall Street Journal *\u003cbr\u003eBeginning with counting and moving through topics such as multiplication and fractions, \u003ci\u003eArithmetic\u003c\/i\u003e provides a nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education…Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting. Manipulating calculi on a tabula, you can see what he means. -- Jonathon Keats * New Scientist *\u003cbr\u003eMore than just an informative survey of the fundamentals of basic arithmetic, this fun book offers a philosophical take on number systems and revels in the beauty of math. * Science News *","brand":"Harvard University Press","offers":[{"title":"Default Title","offer_id":48865482441047,"sku":"9780674237513","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780674237513.jpg?v=1722274180"},{"product_id":"agentzero-9780691158884","title":"AgentZero","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eIntroduces a theoretical entity: Agent_Zero. This title weaves a computational tapestry with threads from Plato, Hume, Darwin, Pavlov, Smith, Tolstoy, Marx, James, and Dostoevsky, among others.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\"\u003ci\u003eAgent Zero\u003c\/i\u003e offers a solution to some of social science's great puzzles. Its behavioral basis is the interplay of emotion, cognition, and network contagion effects. It elegantly explains why so many human actions are so manifestly dysfunctional, and why some are downright evil.\"\u003cb\u003e—George Akerlof, Nobel Laureate in Economics\u003c\/b\u003e\u003cbr\u003e\"Rarely has a book stimulated me intellectually as much as this one. Particularly exciting is the incorporation of agents who feel (affect) and deliberate, as well as influence one another through social interaction. Epstein is a brilliantly creative scholar and the range of applications showcased here is stunning. In sum, this is a pathbreaking book.\"\u003cb\u003e—Paul Slovic, University of Oregon\u003c\/b\u003e\u003cbr\u003e\"Joshua Epstein proposes a parsimonious but powerful model of individual behavior that can generate an extraordinary range of group behaviors, including mob violence, manias and financial panics, rebellions, network dynamics, and a host of other complex social phenomena. This is a highly original, beautifully conceived, and important book.\"\u003cb\u003e—Peyton Young, University of Oxford\u003c\/b\u003e\u003cbr\u003e\"In social science generally and most notably in economics, the rational actor model has long been the benchmark for policy analysis and institutional design. Epstein now offers a worthy alternative: \u003ci\u003eAgent_Zero\u003c\/i\u003e, a mathematically and computationally tractable agent whose inner workings are grounded in neuroscience. Much like you and me, \u003ci\u003eAgent_Zero\u003c\/i\u003e is influenced by emotion, reason, and social pressures. Epstein demonstrates that collections of Agent Zeros perform amazingly like real groups, teams, and societies and can therefore serve as the fundamental building blocks for what he calls Generative Social Science. The rational actor now has a true competitor. \u003ci\u003eAgent_Zero\u003c\/i\u003e is a major advance.\"\u003cb\u003e—Scott Page, University of Michigan\u003c\/b\u003e\u003cbr\u003e\"This is social science based on how our brains actually work. Epstein's computerized 'agents' can feel passion and fear, and can influence each other emotionally. And when they interact, we see many of the realities of social life, from the dynamics of juries to racist violence to Arab springs. A remarkable and original piece of work.\"\u003cb\u003e—W. Brian Arthur, Santa Fe Institute\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eForeword xi Preface xiii Acknowledgments xv INTRODUCTION 1 MOTIVATION 1 Generate Social Dynamics 2 A Core Target 2 THE MODEL COMPONENTS 5 Model Overview 6 Skeletal Equation 8 Specific Components 9 ORGANIZATION 10 Part I: Mathematical Model 10 Part II: Agent-Based Model 11 Part III: Extensions 13 Replicability and Research Resources on the Princeton University Press Website 16 Part IV: Future Research and Conclusions 17 PART 1. MATHEMATICAL MODEL 19 I.1. THE PASSIONS: FEAR CONDITIONING 19 Fear Circuitry and the Perils of Fitness 20 Nomenclature of Conditioning 29 The Rescorla-Wagner Model 33 Social Examples 37 Fear Extinction 41 I.2. REASON: THE COGNITIVE COMPONENT 46 I.3. THE SOCIAL COMPONENT 51 Simple Version of the Core Target 55 Examples of Fear Contagion 57 Mechanisms of Fear Contagion 59 Conformist Empirical Estimates 63 Generalizing Rescorla-Wagner 67 The Central Case 69 Tolstoy: The First Agent Modeler 71 A Mathematical Aside on Social Norms as Vector Fields 74 Extinction of Majorities 78 I.4. INTERIM CONCLUSIONS 80 PART II. AGENT-BASED COMPUTATIONAL MODEL 81 Affective Component 84 \"Rational\" Component 85 Social Component 88 Action 89 Pseudocode 89 II.1. COMPUTATIONAL PARABLES 90 Parable 1: The Slaughter of Innocents through Dispositional Contagion 90 Parable 2: Agent_Zero Initiates: Leadership as Susceptibility to Dispositional Contagion 94 Run 3. Information Cuts Both Ways 96 Run 4. A Day in the Life of Agent_Zero: How Affect and Probability Can Change on Different Time Scales 98 Run 5. Lesion Studies 102 PART III. EXTENSIONS 107 III.1. ENDOGENOUS DESTRUCTIVE RADIUS 107 III.2. AGE AND IMPULSE CONTROL 109 III.3. FIGHT VS. FLIGHT 110 Case 1: Fight 111 Case 2: Flight 112 Capital Flight 114 III.4. REPLICATING THE Latane-DARLEY EXPERIMENT 114 Threshold Imputation 115 The Dialogue 118 III.5. MEMORY 118 III.6. COUPLINGS: ENTANGLEMENT OF PASSION AND REASON 122 Mathematical Treatment 124 III.7.ENDOGENOUS DYNAMICS OF CONNECTION STRENGTH 128 Affective Homophily 128 General Setup 130 Agent-Based Model: Nonequlibrium Dynamics 135 III.8. GROWING THE 2011 ARAB SPRING 138 III.9. JURY PROCESSES 143 Phase 1. Public Phase 143 Phase 2. Courtroom Trial Phase 145 Phase 3. Jury Phase 147 III.10. EMERGENT DYNAMICS OF NETWORK STRUCTURE 152 Network Structure Dynamics as a Poincare Map 153 Relation to Literature 159 III.11. MULTIPLE SOCIAL LEVELS 160 Agent_Zero as Witness to History 161 III.12. THE 18TH BRUMAIRE OF AGENT_ZERO 165 III.13. INTRODUCTION OF PRICES AND SEASONAL ECONOMIC CYCLES 168 Prices 168 A Christmas Story 173 III.14. SPIRALS OF MUTUAL ESCALATION 176 PART IV. FUTURE RESEARCH AND CONCLUSION 181 IV.1. FUTURE RESEARCH 181 IV.2. CONCLUSION 187 Civil Violence 187 Economics 188 Health Behavior 189 Psychology 190 Jury Dynamics 191 The Formation and Dynamics of Networks 191 Mutual Escalation Dynamics 192 Birth and Intergenerational Transmission 192 IV.3. TOWARD NEW GENERATIVE FOUNDATIONS 192 Appendix I. Threshold Imputation Bounds 195 Appendix II. Mathematica Code 197 Appendix III. Agent_Zero NetLogo Source Code 213 Appendix IV. Parameter Settings for Model Runs 221 References 227 Index 243","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865529135447,"sku":"9780691158884","price":46.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691158884.jpg?v=1722274407"},{"product_id":"an-introduction-to-benfords-law-9780691163062","title":"An Introduction to Benfords Law","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the law'\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\"This is a marvelous and excellent introduction.\"--Adhemar Bultheel, European Mathematical Society Bulletin \"A must-read for novices and experts alike. It can be used for a graduate-level topics course or as a reference text for researchers in the field. The exposition is outstanding, with hundreds of carefully chosen examples, figures and diagrams to illustrate the theory. For those who are up for a challenge, the book contains several open problems as well. An Introduction to Benford's Law will surely be the go-to text on the subject for years to come.\"--Pieter C. Allaart, Mathematical Reviews\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface vii  1 Introduction 1  1.1 History 3  1.2 Empirical evidence 4  1.3 Early explanations 6  1.4 Mathematical framework 7  2 Significant Digits and the Significand 11  2.1 Significant digits 11  2.2 The significand 12  2.3 The significand sigma-algebra 14  3 The Benford Property 22  3.1 Benford sequences 23  3.2 Benford functions 28  3.3 Benford distributions and random variables 29  4 The Uniform Distribution and Benford's Law 43  4.1 Uniform distribution characterization of Benford's law 43  4.2 Uniform distribution of sequences and functions 46  4.3 Uniform distribution of random variables 54  5 Scale-, Base-, and Sum-Invariance 63  5.1 The scale-invariance property 63  5.2 The base-invariance property 74  5.3 The sum-invariance property 80  6 Real-valued Deterministic Processes 90  6.1 Iteration of functions 90  6.2 Sequences with polynomial growth 93  6.3 Sequences with exponential growth 97  6.4 Sequences with super-exponential growth 101  6.5 An application to Newton's method 111  6.6 Time-varying systems 116  6.7 Chaotic systems: Two examples 124  6.8 Differential equations 127  7 Multi-dimensional Linear Processes 135  7.1 Linear processes, observables, and difference equations 135  7.2 Nonnegative matrices 139  7.3 General matrices 145  7.4 An application to Markov chains 162  7.5 Linear difference equations 165  7.6 Linear differential equations 170  8 Real-valued Random Processes 180  8.1 Convergence of random variables to Benford's law 180  8.2 Powers, products, and sums of random variables 182  8.3 Mixtures of distributions 202  8.4 Random maps 213  9 Finitely Additive Probability and Benford's Law 216  9.1 Finitely additive probabilities 217  9.2 Finitely additive Benford probabilities 219  10 Applications of Benford's Law 223  10.1 Fraud detection 224  10.2 Detection of natural phenomena 225  10.3 Diagnostics and design 226  10.4 Computations and Computer Science 228  10.5 Pedagogical tool 230  List of Symbols 231  Bibliography 234  Index 245","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865530839383,"sku":"9780691163062","price":67.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691163062.jpg?v=1722274416"}],"url":"https:\/\/bookcurl.com\/collections\/mathematical-logic.oembed?page=16","provider":"Book Curl","version":"1.0","type":"link"}