Mathematical logic Books

Book SynopsisAre you smarter than a Singaporean ten-year-old?Can you beat Sherlock Holmes?If you think the answer is yes - I challenge you to solve my problems. Here are 125 of the world's best brainteasers from the last two millennia, taking us from ancient China to medieval Europe, Victorian England to modern-day Japan, with stories of espionage, mathematical breakthroughs and puzzling rivalries along the way.Pit your wits against logic puzzles and kinship riddles, pangrams and river-crossing conundrums. Some solutions rely on a touch of cunning, others call for creativity, others need mercilessly logical thought. Some can only be solved be 2 per cent of the population. All are guaranteed to sharpen your mind. Let's get puzzling!

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Book SynopsisFor thousands of years, mathematicians have used the timeless art of logic to see the world more clearly. In The Art of Logic, Royal Society Science Book Prize nominee Eugenia Cheng shows how anyone can think like a mathematician - and see, argue and think better. Learn how to simplify complex decisions without over-simplifying them. Discover the power of analogies and the dangers of false equivalences. Find out how people construct misleading arguments, and how we can argue back. Eugenia Cheng teaches us how to find clarity without losing nuance, taking a careful scalpel to the complexities of politics, privilege, sexism and dozens of other real-world situations. Her Art of Logic is a practical and inspiring guide to decoding the modern world.Trade ReviewMind-expanding ... a meaningful contribution to creating a better society as well as happier conversations and relationships * Guardian *A mathematician's thought-provoking attempt to lay out the tools of rational argument -- Michael Brooks * New Statesman Books of the Year *With humour, grace, and a natural gift for making explanations seem fun, Eugenia Cheng has done it again. This is a book to savour, to consult, and to buy for all your friends. You'll think more clearly after reading this book, something that is unfortunately in short supply these days. I am buying several copies to send to heads of state. -- Daniel Levitin, bestselling author of The Organised Mind & A Field Guide to Lies and StatisticsIn an era awash with conflict, exploitation, tribalism and fake news, the "illuminating precision" offered by logic is important. Cheng harnesses the power of abstraction to explore real-life phenomena such as sexism and white privilege. She walks us through the grand terrain of logic, from axioms to proofs. And she reveals how to build arguments as long chains of logical implications - a "virtuosic and masterful" skill that, combined with intelligent emotional engagement, can cut through pervasive irrationality * Nature *A perceptive analysis of logic and its limitations ... Cheng is successful not only in helping readers think more clearly, but in helping them understand why others sometimes appear to be illogical. This book has the potential to help understanding and avoid confrontational arguments that serve only to entrench opposing views * Times Higher Education *Radical and liberating * Emerald Street *We're thankful that someone like Eugenia Cheng is here; someone to eloquently and efficiently expound on concepts like logic and truth at a time when their very basis seems to come under attack ... We're forever on the lookout for someone to make mathematics both fun and accessible, and it looks like we've found that person in Eugenia Cheng * How it Works Magazine *A concert pianist, mathematician, polyglot and YouTube star, Cheng has carved out quite a niche for herself ... she brings an ebullient enthusiasm that's infectious * Guardian *Witty, charming, and crystal clear. Eugenia Cheng's enthusiasm and carefully chosen metaphors and analogies carry us effortlessly through the mathematical landscape -- Ian StewartClear, clever and friendly -- Alex Bellos

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Book Synopsis''An invaluable companion for anyone who wants a deep understanding of what's under the hood of often inscrutable machines'' Melanie Mitchell A rich, narrative explanation of the mathematics that has brought us machine learning and the ongoing explosion of artificial intelligenceMachine-learning systems are making life-altering decisions for us: approving mortgage loans, determining whether a tumour is cancerous, or deciding whether someone gets bail. They now influence discoveries in chemistry, biology and physics - the study of genomes, extra-solar planets, even the intricacies of quantum systems.We are living through a revolution in artificial intelligence that is not slowing down. This major shift is based on simple mathematics, some of which goes back centuries: linear algebra and calculus, the stuff of eighteenth-century mathematics. Indeed by the mid-1850s, a lot of the groundwork was all done. It took the development of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see all around us today. In this enlightening book, Anil Ananthaswamy explains the fundamental maths behind AI, which suggests that the basics of natural and artificial intelligence might follow the same mathematical rules.As Ananthaswamy resonantly concludes, to make the most of our most wondrous technologies we need to understand their profound limitations - the clues lie in the maths that makes AI possible.

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Book SynopsisLogic 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.Table of ContentsPREFACE TO SECOND EDITION; PREFACE TO FIRST EDITION; GLOSSARY; PROBLEMS; PROBLEM SOLUTIONS; BIBLIOGRAPHY; GENERAL INDEX

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Book SynopsisThought you had it bad? In this book, you will be:Imprisoned by a sadistic logician.Challenged to raise dogs from the dead. Trapped on a burning island.And much more besides . . .Everything is at stake in this compendium of more than 150 ingenious puzzles, selected to reveal the wonderful diversity of brainteasers that have confounded and intrigued solvers for the last thousand years. You'll need to pit your wits against probability problems, wrestle with wordplay, grapple with geometry and scrabble for survival. Along the way you will discover stories of whip-smart thinkers, eccentric novelists and a poodle with allegedly supernatural powers. You will absorb fascinating and important mathematical ideas. Some solutions will rely on ingenuity, some will challenge you to spot hidden patterns, others call for extreme rationality. All will surprise, entertain and stretch your brain. Will you make it out with your puzzling pride intact?

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Book SynopsisIn this entertaining and challenging collection of logic puzzles, Raymond Smullyan-author of Forever Undecided-continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time.Table of ContentsPART I - LOGIC PUZZLES; PART II - KNIGHTS, KNAVES, AND THE FOUNTAIN OF YOUTH; PART III - TO MOCK A MOCKINGBIRD; PART IV - SINGING BIRDS; PART V - THE MASTER FOREST; PART VI - THE GRAND QUESTION

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Book SynopsisChallenge 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.

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Book Synopsis500 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.

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Book SynopsisThere's so much talk about the threat posed by intelligent machines that it sometimes seems as though we should surrender to our robot overlords. But Junaid Mubeen isn't ready to throw in the towel just yet. As far as he is concerned, we have the creative edge over machines, because of a remarkable system of thought that humans have developed over the millennia. It's familiar to us all, but often badly taught in schools and misrepresented in popular discourse - maths. Computers are, of course, brilliant at totting up sums, pattern-seeking and performing mindless tasks of, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical superpowers.

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Book SynopsisUncover the language of our universe - numbers - in this wide-ranging whistle-stop tour of the history and majesty of mathematics.Our world simply wouldn't function if we didn't have numbers. But where do they come from? Why do we cut cake the wrong way? How can there be different sizes of infinity?All these questions and more are answered in this engaging romp through the history of numbers by acclaimed science writer, Colin Stuart. From the mathematicians who have (and haven't) shouted 'Eureka!' to the theories that affect and inform our everyday lives; Numbers shows us that maths was never boring - we were just being taught it in the wrong way.Consisting of ten bite-sized essays, there's no better guide to this fundamental science.

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Book SynopsisAn introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory.Computer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science. Topics covered include predicate logic, equation-based software, automated testing and theorem proving, and large-scale computation. Formalism is emphasized, and the book employs three formal notations: traditional algebraic formulas of propositional and predicate logic; digital circuit diagrams; and the widely used partially automated theorem prover, ACL2, which provides an accessible introduction to mechanized formalism

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Book SynopsisThe Payment Card Industry Data Security Standard (PCI DSS) is now in its 18th year, and it is continuing to dominate corporate security budgets and resources. If you accept, process, transmit, or store payment card data branded by Visa, MasterCard, American Express, Discover, or JCB (or their affiliates and partners), you must comply with this lengthy standard.Personal data theft is at the top of the list of likely cybercrimes that modern-day corporations must defend against. In particular, credit or debit card data is preferred by cybercriminals as they can find ways to monetize it quickly from anywhere in the world. Is your payment processing secure and compliant? The new Fifth Edition of PCI Compliance has been revised to follow the new PCI DSS version 4.0, which is a complete overhaul to the standard. Also new to the Fifth Edition are: additional case studies and clear guidelines and instructions for maintaining PCI compliance globally, including coverage of technoTable of ContentsForeword. Acknowledgments. Authors. Chapter 1 About PCI DSS and This Book. Chapter 2 Introduction to Fraud, Identity Theft, and Related Regulatory Mandates. Chapter 3 Why Is PCI Here? Chapter 4 Determining and Reducing Your PCI Scope. Chapter 5 Building and Maintaining a Secure Network. Chapter 6 Strong Access Controls. Chapter 7 Protecting Cardholder Data. Chapter 8 Using Wireless Networking. Chapter 9 Vulnerability Management. Chapter 10 Logging Events and Monitoring the Cardholder Data Environment. Chapter 11 Cloud and Virtualization. Chapter 12 Mobile. Chapter 13 PCI for the Small Business. Chapter 14 PCI DSS for the Service Provider. Chapter 15 Managing a PCI DSS Project to Achieve Compliance. Chapter 16 Don’t Fear the Assessor. Chapter 17 The Art of Compensating Control. Chapter 18 You’re Compliant, Now What? Chapter 19 Emerging Technology and Alternative Payment Schemes. Chapter 20 PCI DSS Myths and Misconceptions. Chapter 21 Final Thoughts. Index by Requirement. Alphabetical Index.

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Book SynopsisKeeping 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. This 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. 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. This 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. Trade Review“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)Table of ContentsPreface.- 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

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Book SynopsisChallenge 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.

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Book SynopsisTable of Contents1. Getting Started 2. Basic Techniques to Prove If/Then Statements 3. Special Kinds of Theorems 4. Some Mathematical Topics on Which to Practice Proof Techniques 5. Review Exercises

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Book SynopsisThis revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.Trade Review'Priest's Introduction to Non-Classical Logic is my textbook of choice for introducing non-classical logic to undergraduates. It is unique in meeting two almost inconsistent aims. It gives the reader an introduction to a vast range of non-classical logics. No comparable textbook manages to cover modal logics, conditional logics, intuitionistic logic, relevant and paraconsistent logics and fuzzy logic with such clarity and accessibility. Amazingly, it is not merely a catalogue of different logical systems. The distinctive value of this Introduction is that it also tells a coherent story: Priest weaves together these different logics in the one narrative - the search for a logic of conditionals. With the publication of the second volume, this unique combination of breadth and coherence now covers much more ground, and the reader now has an expert guide to much more of the vast field of research in non-classical logics.' Greg Restall, The University of Melbourne'I've used your book (first edition, that is) for years now in my upper level philosophy of logic courses. It is easily the best introduction to non-classical logics. I especially like its coverage of conditionals, and the introduction to relevant logic. Over the years, your book has made my students come to appreciate the variety and scope that exists within in formal logic, I intend to use the new edition so as to carry similar investigations into first order theory.' Jeffry Pelletier, Simon Fraser University'Graham Priest's Introduction to Non-Classical Logic made this fascinating material on alternative logics accessible to my students for the very first time. The very welcome new edition extends the range of what is addressed to include important questions about quantification for modal logic, and the other systems as well.' Tony Roy, California State University, San Bernardino'The first edition of Graham Priest's Introduction to Non-Classical Logic turned out to be an extremely useful and well-written introductory guide to the vast and difficult to survey area of non-classical and philosophical logic. The substantially expanded second edition in two volumes is bound to become a standard reference.' Heinrich Wansing, Dresden University of Technology'Clear, self-contained, generously complete: this is bound to be the classic on non-classical logics for many years to come.' Achille Varzi, Columbia University'This is an excellent introductory book to modern non-classical logics, fully accessible to non-professionals, and useful to professionals too. I have used part of its content in teaching Non-Classical Logic in the past years, and the response from my students shows the great success of the author's intention. The proof system it employs and the meta-proofs it provides are extremely easy to follow, while those followed-up philosophical discussions it summarizes for each logic system are both concise and lucid. It is not only a work introducing modern non-classical logic systems, but also a work full of interesting philosophical discussions on the motivations, advantages and disadvantages of these systems. With one penetrating theme - what a logic of conditionals should be like - in mind, the author has effectively organized a variety of topics into one integrated work. I would recommend it both to logicians and to philosophers, to professionals and to non-professionals.' Wen-fang Wang, National Chung Chen University'The second edition of Graham Priest's book is, like the first, clearly expressed, well thought out for the student and an essential work for all those studying philosophy who want an adequate grounding in non-classical logic. I have used the first edition successfully in my intermediate class for the last five years, and will certainly be adding the second edition to the reading list when it is available.' Steve Read, University of St Andrews'Priest succeeds in offering a marvellously unified treatment of 11 varieties of logic: classical, basic modal, normal modal, non-normal, conditional, intuitionist, many-valued, first-degree entailment, basic relevant, mainstream relevant, and fussy … Excellent references support this concise but clear treatment.' Choice'This book is just what the title says it is … And it is a very good one …' Stewart Shapiro, University of Ohio' … for anyone who wants to explore the non-classical systems, it is the only book of its kind and could not be more highly recommended.' The Times Higher Education Supplement'I've just picked up a copy of the second edition of Graham Preist's An Introduction to Non-Classical Logic from the CUP bookshop. It looks terrific. More than twice the length of the first edition which just covered propositional logics, this covers their extensions with quantifiers and identity too. I thought the fist edition was terrific: so this is a hugely welcome expansion and I'm delighted to report that CUP has published this as a paperback in their Cambridge Introductions to Philosophy Series at just £18.99, which is surely an amazing bargain for a well produced 613 page book. So a must-buy and a must-read!' Logic MattersTable of ContentsPreface to the first edition; Preface to the second edition; Mathematical prolegomenon; Part I. Propositional Logic: 1. Classical logic and the material conditional; 2. Basic modal logic; 3. Normal modal logics; 4. Non-normal modal logics; strict conditionals; 5. Conditional logics; 6. Intuitionist logic; 7. Many-valued logics; 8. First degree entailment; 9. Logics with gaps, gluts, and worlds; 10. Relevant logics; 11. Fuzzy logics; 11a. Appendix: many valued modal logics; Postscript: an historical perspective on conditionals; Part II. Qualification and Identity: 12. Classical logic; 13. Free logic; 14. Constant domain modal logics; 15. Variable domain modal logics; 16. Necessary identity in modal logic; 17. Contingent identity in modal logic; 18. Non-normal modal logics; 19. Conditional logics; 20. Intuitionist logic; 21. Many-valued logics; 22. First degree entailment; 23. Logics with gaps, gluts, and worlds; 24. Relevant logics; 25. Fuzzy logics; Postscript: a methodological coda.

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Book SynopsisThis Element addresses the categoricity arguments that have been more effective in historical cases that reflect philosophically on internal mathematical matters than in recent questions of pre-theoretic metaphysics.Table of Contents1. Introduction; 2. Dedekind in 'Was sind und was sollen die Zahlen?' (1888); 3. Dedekind in 'Was sind und was sollen die Zahlen?' (1888); 4. Kreisel in 'Informal rigor and incompleteness proofs' (1967) and 'Two notes on the foundations of set theory'(1969); 5. Parsons in 'The uniqueness of the natural numbers' (1990) and 'Mathematical induction' (2008); 6. Parsons in 'The uniqueness of the natural numbers' (1990) and 'Mathematical induction' (2008); 7. Conclusion; References.

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Book SynopsisThis is a concise book that introduces students to the basics of logical thinking and important mathematical structures that are critical for a solid understanding of logical formalisms themselves as well as for building the necessary background to tackle other fields that are based on these logical principles. Despite its compact and small size, it includes many solved problems and quite a few end-of-section exercises that will help readers consolidate their understanding of the material.This textbook is essential reading for anyone interested in the logical foundations of Informatics, Computer Science, Data Science, Artificial Intelligence, and other related areas. Written with undergraduate students in these disciplines in mind, this book can very well serve the needs of interested and curious readers who wish to get a grasp of the logical principles upon which these fields are built. This book does not require readers to possess math skills beyond those learned in high school.

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Book SynopsisThird 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.

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Book SynopsisWhen 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

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Book SynopsisCategory 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.Trade ReviewThe 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 *Table of ContentsPreface ; 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

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Book SynopsisSheaves also appear in logic as carriers for models of set theory. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.Trade ReviewFrom the reviews: "A beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. … authors have a rare gift for conveying an insider’s view of the subject from the start. This book is written in the best Mac Lane style, very clear and very well organized. … it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field." (Wordtrade, 2008)Table of ContentsPreface; Prologue; Categorical Preliminaries; 1. Categories of Functors; 2. Sheaves of Sets; 3. Grothendieck Topologies and Sheaves; 4. First Properties of Elementary Topoi; 5. Basic Constructions of Topoi; 6. Topoi and Logic; 7. Geometric Morphisms; 8. Classifying Topoi; 9. Localic Topoi; 10. Geometric Logic and Classifying Topoi; Appendix: Sites for Topoi; Epilogue; Bibliography; Index of Notations; Index

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Book SynopsisComprehensive overview, suitable for advanced undergraduates and graduate students, covers propositional logic; first-order languages and logic; incompleteness, undecidability, and indefinability; recursive functions; computability; and Hilbert's Tenth Problem. 1995 edition.

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Book SynopsisThis is the first self-contained introduction to the use of string diagrams to reason in elementary category theory. Written in an informal expository style, it features hundreds of carefully chosen diagrams to aid understanding. With numerous worked examples and exercises, the text is ideal for graduate students and advanced undergraduates.Trade Review'String diagrams have proven an indispensable tool in modern category theory, enabling intuitive graphical reasoning while doing away with much of the bookkeeping that tends to bog down equational arguments. This textbook introduces category theory by way of string diagrams, making it an excellent choice both for beginners in category theory, as well as for more experienced category theorists seeking to add string diagrammatic reasoning to their repertoire.' Robin Kaarsgaard, University of Edinburgh'Well-chosen notation plays a vital role in constructive calculation because it facilitates the exploitation of algebraic properties. This book's exemplary use of string diagrams in category theory will inspire and invigorate the calculational method. Peruse and ponder its colourful beauty.' Roland Backhouse, University of NottinghamTable of ContentsPrologue; 1. Category theory; 2. String diagrams; 3. Monads; 4. Adjunctions; 5. Putting it all together; Epilogue; Appendix. Notation; References; Index.

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Book SynopsisThis book, for a first undergraduate course in Discrete Mathematics, systematically exploits the relationship between discrete mathematics and computer programming. Unlike most discrete mathematics texts focusing on one of the other, the book explores the rich and important connection between these two disciplines and shows how each discipline reinforces and enhances the other.The mathematics in the book is self-contained, requiring only a good background in precalculus and some mathematical maturity. New mathematical topics are introduced as needed.The coding language used is VBA Excel. The language is easy to learn, has intuitive commands, and the reader can develop interesting programs from the outset. Additionally, the spreadsheet platform in Excel makes for convenient and transparent data input and output and provides a powerful venue for complex data manipulation. Manipulating data is greatly simpli?ed using spreadsheet features and visualizing the data can make Table of Contents1. Introduction. 2. VBA Operators. 3. Conditional Statements. 4. Loops, 5. Arrays. 6. String Functions. 7. Grids. 8. Recursion. 9. Charts and Graphs, 10. Random Numbers. 11. Linear Equations. 12. Linear Programming. 13. Matrix Algebra. 14. Determinants. 15. Propositional Logic. 16. Switching Circuits. 17. Gates and Logic Circuits. 18. Sets. 19. Counting. 20. Probability. 21. Random Variables. 22. Markov Chains. 23. Divisibility and Prime Numbers. 24. Congruence. 25. The Enigma Machine. 26. Large Numbers.

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Book SynopsisParabola is a mathematics magazine published by UNSW, Sydney. Among other things, each issue of Parabola has contained a collection of puzzles/problems, on various mathematical topics and at a suitable level for younger (but mathematically sophisticated) readers.Parabolic Problems: 60 Years of Mathematical Puzzles in Parabola collects the very best of almost 1800 problems and puzzles into a single volume. Many of the problems have been re-mastered, and new illustrations have been added. Topics covered range across geometry, number theory, combinatorics, logic, and algebra. Solutions are provided to all problems, and a chapter has been included detailing some frequently useful problem-solving techniques, making this a fabulous resource for education and, most importantly, fun!Features Hundreds of diverting and mathematically interesting problems and puzzles. Accessible for anyone with a high school-level mathematics educati

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis book explores the critical intersection of human behaviour, cybersecurity, and the transformative potential of quantum technologies. It delves into the vulnerabilities and resilience of human intelligence in the face of cyber threats, examining how cognitive biases, social dynamics, and mental health can be exploited in the digital age.Cybersecurity 2050: Protecting Humanity in a Hyper-Connected World explores the cutting-edge applications of quantum computing in cybersecurity, discussing the efficiency of quantum security algorithms on Earth and over space communications such as those needed to inhabit Mars. The challenges and opportunities of human life on extraterrestrial worlds, such as Mars, will further shape the evolution of human intelligence. The isolated and confined environment of a Martian habitat, coupled with the reliance on advanced technologies for survival, will demand new forms of adaptability, resilience, and social cooperation. The author addresses the imminent revolution in cybersecurity regulations and transforms the attention of bright minds of businesses and policymakers for the challenges and opportunities of quantum advancements. This book attempts to bridge the gap between social intelligence and cybersecurity, offering a holistic and nuanced understanding of these interconnected domains. Through real-world case studies, the author provides practical insights and strategies for adapting to the evolving technological landscape and building a more secure digital future.This book is intended for futuristic minds, computer engineers, policymakers, or regulatory experts interested in the implications of the revolution of human intelligence on cybersecurity laws and regulations. It will be of interest to cybersecurity professionals and researchers looking for a historic and comprehensive understanding of the evolving landscape, including social intelligence, quantum computing and algorithm design.

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Book SynopsisImre Lakatos's influential and enduring work on the nature of mathematic discovery and development continues to be relevant to philosophers of mathematics. Including a specially commissioned preface written by Paolo Mancosu, and presented in a fresh twenty-first-century series livery, it is now available for a new generation of readers.Trade Review'For anyone interested in mathematics who has not encountered the work of the late Imre Lakatos before, this book is a treasure; and those who know well the famous dialogue, first published in 1963–4 in the British Journal for the Philosophy of Science, that forms the greater part of this book, will be eager to read the supplementary material … the book, as it stands, is rich and stimulating, and, unlike most writings on the philosophy of mathematics, succeeds in making excellent use of detailed observations about mathematics as it is actually practised.' Michael Dummett, Nature'The whole book, as well as being a delightful read, is of immense value to anyone concerned with mathematical education at any level.' C. W. Kilmister, The Times Higher Education Supplement'In this book the late Imre Lakatos explores 'the logic of discovery' and 'the logic of justification' as applied to mathematics … The arguments presented are deep … but the author's lucid literary style greatly facilitates their comprehension … The book is destined to become a classic. It should be read by all those who would understand more about the nature of mathematics, of how it is created and how it might best be taught.' Education'How is mathematics really done, and - once done - how should it be presented? Imre Lakatos had some very strong opinions about this. The current book, based on his PhD work under George Polya, is a classic book on the subject. It is often characterized as a work in the philosophy of mathematics, and it is that - and more. The argument, presented in several forms, is that mathematical philosophy should address the way that mathematics is done, not just the way it is often packaged for delivery.' William J. Satzer, MAA ReviewsTable of ContentsPreface to this edition Paolo Mancosu; Editors' preface; Acknowledgments; Author's introduction; Part I: 1. A problem and a conjecture; 2. A proof; 3. Criticism of the proof by counterexamples which are local but not global; 4. Criticism of the conjecture by global counterexamples; 5. Criticism of the proof-analysis by counterexamples which are global but not local. The problem of rigour; 6. Return to criticism of the proof by counterexamples which are local but not global. The problem of content; 7. The problem of content revisited; 8. Concept-formation; 9. How criticism may turn mathematical truth into logical truth; Part II: Editors' introduction; Appendix 1. Another case-study in the method of proofs and refutations; Appendix 2. The deductivist versus the heuristic approach; Bibliography; Index of names; Index of subjects.

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Book SynopsisUsing 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.Trade Review'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'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'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 TechnologyTable of ContentsPreface; 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.

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Book SynopsisMany believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more. In the book you will, among other things, find answers to: What is a proof? What is a counterexample? What does it mean to say that something follows logically from a set of premises? What does it mean to abstract over something? How can knowledge and information be represented and used in calculations? What is the connection between Morse code and Fibonacci numbers? Why could it take billions of years to solve Hanoi's Tower? Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.Trade Review"The definitions are followed by examples to help explain their meaning, along with counterexamples ... . Therefore, very little basic knowledge is required for this introduction to logical methods ... which is written in an accessible style ... . contained in the book are several hundred small figures; arrow, Venn, and Hasse diagrams; and simplifies visual representations ... . The author has also elected to use color to draw the reader's attention ... ." “From personal teaching experience, knowledge of these mathematical areas is necessary for disparate fields of CS and informatics. These foundations are needed for many fields, from database theory to various domains of information systems applications. The book’s presentation of topics and incentives for problem-solving, along with its exercises, is very useful for university-level instructors and students. The compact chapters contain clear explanations, diagrams, and brief descriptions of interesting facts.” (Bálint Molnár, Computing Reviews, July 27, 2021)Table of ContentsPreface.- 0 The Art of Thinking Abstractly and Mathematically.- 1 Basic Set Theory.- 2 Propositional Logic.- 3 Semantics from Propositional Logic.- 4 Concepts in Propositional Logic.- 5 Proofs, Conjectures, and Counterexamples.- 6 Relations.- 7 Functions.- 8 A Little More Set Theory.- 9 Closures and Inductively Defined Sets.- 10 Recursively Defined Functions.- 11 Mathematical Induction.- 12 Structural Induction.- 13 First-Order Languages.- 14 Representation of Quantified Statements.- 15 Interpretation in Models.- 16 Reasoning About Models.- 17 Abstraction with Equivalences and Partitions.- 18 Combinatorics.- 19 A Little More Combinatorics.- 20 A Bit of Abstract Algebra.- 21 Graph Theory.- 22 Walks in Graphs.- 23 Formal Languages and Grammars.- 24 Natural Deduction.- The Road Ahead.- Index. Symbols.

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Book SynopsisA Waterstones Best Popular Science Book of 2023'Delightfully clear and vivid to read...A splendid book! Philip Pullman'Absolutely fascinating' James O'Brien'An exceptional book - readable, funny and more needed than ever' Dr Chris van Tulleken, bestselling author of Ultra-Processed PeopleAre you more likely to become a professional footballer if your surname is Ball?· How can you be one hundred per cent sure you will win a bet?· Why did so many Pompeiians stay put while Mount Vesuvius was erupting?· How do you prevent a nuclear war?Ever since the dawn of human civilisation, we have been trying to make predictions about what's in store for us. We do this on a personal level, so that we can get on with our lives efficiently (should I hang my laundry out to dry, or will it rain?). But we also have to predict on a much larger scale, often for the good of our broader society (how can we spot economic downturns or prevent terrorist attacks?). For just as long, we have been getting it wrong. From religious oracles to weather forecasters, and from politicians to economists, we are subjected to poor predictions all the time. Our job is to separate the good from the bad. Unfortunately, the foibles of our own biology - the biases that ultimately make us human - can let us down when it comes to making rational inferences about the world around us. And that can have disastrous consequences.How to Expect the Unexpected will teach you how and why predictions go wrong, help you to spot phony forecasts and give you a better chance of getting your own predictions correct.Trade ReviewA vivid, wide-ranging and delightful guide to the light and the dark side of prediction * Tim Harford, bestselling author of How to Make the World Add Up *Kit Yates presents maths as it should be taught to everyone: accessible, fun, stimulating, and deeply relevant to our lives. Spend some time with this book and you're likely to make better judgements and decisions, to see through the charlatans and snake-oil salespeople - and perhaps even to fool yourself a little less. * Philip Ball, author of the award-winning Critical Mass *Fascinating and fun. From the everyday to global challenges, Kit Yates explores how changing your mind - so often thought to be a weakness - is the best life skill we can all acquire. A brilliant book * Professor Alice Roberts *Yates' writing is a beacon of clarity sorely needed in a complicated and confusing world. How do we overcome our biases, understand coincidences or tackle the unreliability of our intuition? With bountiful familiar examples, he effortlessly overturns so many of our deep-rooted wrong-headed notions gently and persuasively. I'll be quoting from this book * Jim Al-Khalili *I'm a Yates fan. His style is all-clarity-no-bullshit * Aperiodical *Seriously good * Caroline Lucas MP *Absolutely fascinating * James O'Brien *An exceptional book - readable, funny and more needed than ever * Dr Chris van Tulleken, bestselling author of Ultra-Processed People *Yates' writing style imbues the subjects covered with an infectious enthusiasm, artfully dispelling the dry, stuffy perceptions many people have of maths * Physics World *HOW TO EXPECT THE UNEXPECTED is fascinating and (very much to the point) delightfully clear and vivid to read. Like many people, I like reading about maths without actually knowing how to do it, and part of the pleasure of reading this came from its many examples from everyday life. A splendid book! * Philip Pullman *

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Book SynopsisThe 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.

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Book SynopsisTable of ContentsContents Preface List of Symbols Chapter 1 Introduction Baby Set Theory Sets—An Informal View Classes Axiomatic Method Notation Historical Notes Chapter 2 Axioms and Operations Axioms Arbitrary Unions and Intersections Algebra of Sets Epilogue Review Exercises Chapter 3 Relations and Functions Ordered Pairs Relations n-Ary Relations Functions Infinite Cartesian Products Equivalence Relations Ordering Relations Review Exercises Chapter 4 Natural Numbers Inductive Sets Peano's Postulates Recursion on ? Arithmetic Ordering on ? Review Exercises Chapter 5 Construction of the Real Numbers Integers Rational Numbers Real Numbers Summaries Two Chapter 6 Cardinal Numbers and the Axiom of Choice Equinumerosity Finite Sets Cardinal Arithmetic Ordering Cardinal Numbers Axiom of Choice Countable Sets Arithmetic of Infinite Cardinals Continuum Hypothesis Chapter 7 Orderings and Ordinals Partial Orderings Well Orderings Replacement Axioms Epsilon-Images Isomorphisms Ordinal Numbers Debts Paid Rank Chapter 8 Ordinals and Order Types Transfinite Recursion Again Alephs Ordinal Operations Isomorphism Types Arithmetic of Order Types Ordinal Arithmetic Chapter 9 Special Topics Well-Founded Relations Natural Models Cofinality Appendix Notation, Logic, and Proofs Selected References for Further Study List of Axioms Index

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Book Synopsis'Oxford Logic Guide provides comprehensive coverage of a new research area in algebra and model theory. Model theoretical and group theoretical notions are explained in detail, and almost all the known results in the area are included. Aimed at the needs of the graduate student, there are many exercises (with hints) and carefully chosen examples.Table of Contents1. Basic Group Theory ; 2. Definability ; 3. Interpretability ; 4. Ranked Universe ; 5. Basic Properties ; 6. Nilpotent Groups ; 7. Semisimple Groups ; 8. Fields and Rings ; 9. Solvable Groups ; 10. 2-Sylow Theory ; 11. Permutation Groups ; 12. Gepometrics ; 13. bad Groups ; 14. CN and CIT-Groups ; A. Miscellaneous Results ; B. Open Problems ; C. Link with Model Theory ; D. Hints to the Exercises ; Bibliography ; Index

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Book SynopsisThe 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.Trade ReviewThe writing is both rigorous and thorough, and the authors use compact presentations to support their explanations and proofs. Highly recommended. * N. W. Schillow, CHOICE *Table of ContentsI: THE INTUITIVE BACKGROUND; II: THE BEGINNINGS OF FORMALISATION; III: THE DEVELOPMENT OF AXIOMATIC SYSTEMS; IV: USING AXIOMATIC SYSTEMS; V: STRENGTHENING THE FOUNDATIONS

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis book addresses the topics related to artificial intelligence, the Internet of Things, blockchain technology, and machine learning. It brings together researchers, developers, practitioners, and users interested in cybersecurity and forensics. The first objective is to learn and understand the need for and impact of advanced cybersecurity and forensics and its implementation with multiple smart computational technologies. This objective answers why and how cybersecurity and forensics have evolved as one of the most promising and widely-accepted technologies globally and has widely-accepted applications. The second objective is to learn how to use advanced cybersecurity and forensics practices to answer computational problems where confidentiality, integrity, and availability are essential aspects to handle and answer. This book is structured in such a way so that the field of study is relevant to each readerâs major or interests. It aims to help each reader see the relevance of cybersecurity and forensics to their career or interests. This book intends to encourage researchers to develop novel theories to enrich their scholarly knowledge to achieve sustainable development and foster sustainability. Readers will gain valuable knowledge and insights about smart computing technologies using this exciting book.This book:â Includes detailed applications of cybersecurity and forensics for real-life problemsâ Addresses the challenges and solutions related to implementing cybersecurity in multiple domains of smart computational technologies â Includes the latest trends and areas of research in cybersecurity and forensicsâ Offers both quantitative and qualitative assessments of the topics Includes case studies that will be helpful for the researchersProf. Keshav Kaushik is Assistant Professor in the Department of Systemics, School of Computer Science at the University of Petroleum and Energy Studies, Dehradun, India.Dr. Shubham Tayal is Assistant Professor at SR University, Warangal, India.Dr. Akashdeep Bhardwaj is Professor (Cyber Security & Digital Forensics) at the University of Petroleum & Energy Studies (UPES), Dehradun, India.Dr. Manoj Kumar is Assistant Professor (SG) (SoCS) at the University of Petroleum and Energy Studies, Dehradun, India.Table of Contents1. Detection of Cross-Site Scripting and Phishing Website Vulnerabilities Using Machine Learning. 2. A Review: Security and Privacy Defensive Techniques for Cyber Security Using Deep Neural Networks (DNNs). 3. DNA-Based Cryptosystem for Connected Objects and IoT Security. 4. A Role of Digital Evidence: Mobile Forensics Data. 5. Analysis of Kernel Vulnerabilities Using Machine Learning. 6. Cyber Threat Exploitation and Growth during COVID-19 Times. 7. An Overview of the Cybersecurity in Smart Cities in the Modern Digital Age. 8. The Fundamentals and Potential for Cyber Security of Machine Learning in the Modern World. 9. Qualitative and Quantitative Evaluation of Encryption Algorithms. 10. Analysis and Investigation of Advanced Malware Forensics. 11. Network Intrusion Detection System Using Naïve Bayes Classification Technique for Anomaly Detection. 12. Data Security Analysis in Mobile Cloud Computing for Cyber Security. 13. A Comprehensive Review of Investigations of Suspects of Cyber Crimes. 14. Fault Analysis Techniques in Lightweight Ciphers for IoT Devices.

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Book SynopsisA crystal clear introduction to category theory that demystifies functors, natural transformations, limits and colimits, adjunctions and more. Any beginning postgraduate mathematician will find all they need in this excellent text to access the subject. Over 200 exercises are provided with solutions available online.Trade Review"This textbook presents a useful introduction to basic category theory, and would be suitable for a first course at the undergraduate level in computer science or mathematics." Steve Awodey, Mathematical ReviewsTable of ContentsPreface; 1. Categories; 2. Basic gadgetry; 3. Functors and natural transformations; 4. Limits and colimits in general; 5. Adjunctions; 6. Posets and monoid sets; Bibliography; Index.

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