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Books > Science & Mathematics > Mathematics > Mathematical foundations > Mathematical logic

Maths on the Back of an Envelope - Clever Ways to Overcome Colossal Calculations (Hardcover): Rob Eastaway Maths on the Back of an Envelope - Clever Ways to Overcome Colossal Calculations (Hardcover)
Rob Eastaway 1
R235 R165 Discovery Miles 1 650 Save R70 (30%) Shipped within 7 - 12 working days

Does that statistic make sense? How much will this round of drinks come to? And what are the chances of winning the lottery? Twice? Learn how to do complex maths with nothing but the back of an envelope, a pencil and some good old-fashioned brain power. Doing mathematics without a calculator seems like an unnecessary feat in the twenty-first century. These clever little electronic devices have helped to take away the drudgery of arithmetic, and given all of us the power to perform in a few seconds what might previously have taken hours to work out. But much of the time, we don't need the exact answer with its endless decimal points - we just need to know whether something is in the right ballpark. Rob Eastaway's clever mathematical techniques do exactly that, as he takes an entertaining look at how to figure without a calculator. From spotting misleading statistics in the news and bad deals, to estimating how long you'll be standing in that slowly crawling queue, this book is packed with amusing anecdotes and handy back-of-the-envelope calculations for every situation. Most importantly, this book is a timely and welcome reminder that sometimes our own brain is the best tool we have to deal with numbers.

Limitless Mind - Learn, Lead and Live without Barriers (Paperback): Jo Boaler Limitless Mind - Learn, Lead and Live without Barriers (Paperback)
Jo Boaler 1
R347 R241 Discovery Miles 2 410 Save R106 (31%) Shipped within 7 - 12 working days

When 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 UNLOCK, Boaler presents original groundbreaking research that proves that limiting beliefs really do hold us back from fulfilling our potential and that with a few careful life hacks we can transform our potential for good.

The GCHQ Puzzle Book II (Paperback): Gchq The GCHQ Puzzle Book II (Paperback)
Gchq 1
R321 R227 Discovery Miles 2 270 Save R94 (29%) Shipped within 7 - 12 working days

Challenge yourself with the GCHQ team's long-awaited second puzzle book - full of both harder and easier brain teasers. 'This is the perfect gift to fuel his ludicrous presumption that he could have definitely been a spy - even better if he's already dog-eared the first version' - Huffington Post, (10 Christmas Gifts for him under GBP15) 'Fiendishly tricky' - Daily Mail With their first bestselling book, The GCHQ Puzzle Book, the UK's intelligence and security experts tested us with puzzles, codes and real-life entrance tests from their archives. Now, they are back with a NEW collection of head-scratching, mind-boggling and brain-bending puzzles that will leave you pondering for hours. For those who often found themselves stumped with the first book, there will be even more starter puzzles to get those brains warmed up. Puzzle aficionados needn't worry though, as there will also be an 'Even Harder' section to test everyone to their limits. Not only that, but in celebration of GCHQ's centenary, the puzzles in this new book will sit alongside stories, facts and photos from the organisation's first 100 years at the heart of the nation's security. From the Government Code & Cipher School, to Bletchley Park, through to protecting against cyberattacks, the security of our country is in the hands of GCHQ. With this book, you'll get exclusive snapshots into the organisation that keeps us all safe. if you haven't yet tested yourself with the first instalment of The GCHQ Puzzle Book, check it out now!

Best Books gegradeerde leesreeks: Vlak 1 Boek 2: Gr 2: Leesboek - Huistaal (Afrikaans, Paperback): Best Books Paneel Best Books gegradeerde leesreeks: Vlak 1 Boek 2: Gr 2: Leesboek - Huistaal (Afrikaans, Paperback)
Best Books Paneel
R70 R61 Discovery Miles 610 Save R9 (13%) Shipped within 4 - 8 working days
The Art of Logic - How to Make Sense in a World that Doesn't (Paperback): Eugenia Cheng The Art of Logic - How to Make Sense in a World that Doesn't (Paperback)
Eugenia Cheng 1
R261 R177 Discovery Miles 1 770 Save R84 (32%) Shipped within 7 - 12 working days

For 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.

How to Prove It - A Structured Approach (Paperback, 3rd Revised edition): Daniel J. Velleman How to Prove It - A Structured Approach (Paperback, 3rd Revised edition)
Daniel J. Velleman
R791 R683 Discovery Miles 6 830 Save R108 (14%) Shipped within 7 - 12 working days

Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed "scratch work" sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians.

Model Theory - Third Edition (Paperback, 3rd Revised edition): Chen Chung Chang, H. Jerome Keisler, C.C. Chang Model Theory - Third Edition (Paperback, 3rd Revised edition)
Chen Chung Chang, H. Jerome Keisler, C.C. Chang
R692 R543 Discovery Miles 5 430 Save R149 (22%) Shipped within 7 - 11 working days

Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods -- including classification theory and nonstandard analysis -- the third edition added entirely new sections, exercises, and references.
Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Skolem functions, indiscernibles, ultraproducts, and special models. The final chapters present more advanced topics that feature a combination of several methods. This classic treatment covers most aspects of first-order model theory and many of its applications to algebra and set theory.

First-Order Logic (Paperback): Raymond M Smullyan First-Order Logic (Paperback)
Raymond M Smullyan
R210 R171 Discovery Miles 1 710 Save R39 (19%) Shipped within 7 - 11 working days

An introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods.

Cambridge Mathematical Textbooks - Exploring Mathematics: An Engaging Introduction to Proof (Hardcover): John Meier, Derek Smith Cambridge Mathematical Textbooks - Exploring Mathematics: An Engaging Introduction to Proof (Hardcover)
John Meier, Derek Smith 2
R895 Discovery Miles 8 950 Shipped within 7 - 12 working days

Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.

An Invitation to Applied Category Theory - Seven Sketches in Compositionality (Paperback): Brendan Fong, David I. Spivak An Invitation to Applied Category Theory - Seven Sketches in Compositionality (Paperback)
Brendan Fong, David I. Spivak
R830 Discovery Miles 8 300 Shipped within 7 - 12 working days

Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.

Alan Turing - The Life of a Genius (Paperback): Dermot Turing Alan Turing - The Life of a Genius (Paperback)
Dermot Turing
R139 R96 Discovery Miles 960 Save R43 (31%) Shipped within 7 - 12 working days

Alan Turing was an extraordinary man who crammed into a life of only 42 years the careers of mathematician, codebreaker, computer scientist and biologist. His codebreaking work at Bletchley Park was so significant it helped to shorten the Second World War, and with Tommy Flowers he built the first computer. A man ahead of his time, many of his theories and calculations are still relevant today. Often believed to be an eccentric loner, recent research by his nephew, Dermot Turing, has unearthed a fresh perspective, and here his story is condensed into a short, accessible Pitkin guide.

Prof: Alan Turing Decoded (Paperback): Dermot Turing Prof: Alan Turing Decoded (Paperback)
Dermot Turing
R241 R172 Discovery Miles 1 720 Save R69 (29%) Shipped within 7 - 12 working days

Alan Turing was an extraordinary man who crammed into a life of only 42 years the careers of mathematician, codebreaker, computer scientist and biologist. He is widely regarded as a war hero grossly mistreated by his unappreciative country and it has become hard to disentangle the real man from the story. It is easy to cast him as a misfit, the stereotypical professor. But actually Alan Turing was never a professor, and his nickname `Prof' was given by his codebreaking friends at Bletchley Park. Now, Alan Turing's nephew, Dermot Turing, has taken a fresh look at the influences on Alan Turing's life and creativity, and the later creation of a legend. For the first time it is possible to disclose the real character behind the cipher-text: how did Alan's childhood experiences influence the man? Who were the influential figures in Alan's formative years? How did his creative ideas evolve? Was he really a solitary, asocial genius? What was his wartime work after 1942, and why was it kept even more secret than the Enigma story? What is the truth about Alan Turing's conviction for gross indecency, and did he commit suicide? What is the significance of the Royal Pardon granted in 2013? In Dermot's own style he takes a vibrant and entertaining approach to the life and work of a true genius.

How to Prove It - A Structured Approach (Hardcover, 3rd Revised edition): Daniel J. Velleman How to Prove It - A Structured Approach (Hardcover, 3rd Revised edition)
Daniel J. Velleman
R1,711 Discovery Miles 17 110 Shipped within 7 - 12 working days

Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed "scratch work" sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians.

Arithmetic (Paperback): Paul Lockhart Arithmetic (Paperback)
Paul Lockhart
R284 R230 Discovery Miles 2 300 Save R54 (19%) Shipped within 7 - 11 working days

Because we have ten fingers, grouping by ten seems natural, but it has serious shortcomings. 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 a rote manipulation of numbers-a practical if mundane branch of knowledge best suited for filling out tax forms-but 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. "Inspiring and informative ... deserves to be widely read." -Wall Street Journal "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." -Jonathon Keats, New Scientist "This fun book offers a philosophical take on number systems and revels in the beauty of math." -Science News "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...A wonderful book." -Keith Devlin, author of Finding Fibonacci

Perspectives in Logic, Series Number 5 - Proper and Improper Forcing (Hardcover, 2nd Revised edition): Saharon Shelah Perspectives in Logic, Series Number 5 - Proper and Improper Forcing (Hardcover, 2nd Revised edition)
Saharon Shelah
R3,487 R3,201 Discovery Miles 32 010 Save R286 (8%) Shipped within 7 - 12 working days

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifth publication in the Perspectives in Logic series, studies set-theoretic independence results (independence from the usual set-theoretic ZFC axioms), in particular for problems on the continuum. The author gives a complete presentation of the theory of proper forcing and its relatives, starting from the beginning and avoiding the metamathematical considerations. No prior knowledge of forcing is required. The book will enable a researcher interested in an independence result of the appropriate kind to have much of the work done for them, thereby allowing them to quote general results.

Cambridge Tracts in Theoretical Computer Science, Series Number 60 - Finite-State Techniques: Automata, Transducers and... Cambridge Tracts in Theoretical Computer Science, Series Number 60 - Finite-State Techniques: Automata, Transducers and Bimachines (Hardcover)
Stoyan Mihov, Klaus U. Schulz
R1,345 R1,267 Discovery Miles 12 670 Save R78 (6%) Shipped within 7 - 12 working days

Finite-state methods are the most efficient mechanisms for analysing textual and symbolic data, providing elegant solutions for an immense number of practical problems in computational linguistics and computer science. This book for graduate students and researchers gives a complete coverage of the field, starting from a conceptual introduction and building to advanced topics and applications. The central finite-state technologies are introduced with mathematical rigour, ranging from simple finite-state automata to transducers and bimachines as 'input-output' devices. Special attention is given to the rich possibilities of simplifying, transforming and combining finite-state devices. All algorithms presented are accompanied by full correctness proofs and executable source code in a new programming language, C(M), which focuses on transparency of steps and simplicity of code. Thus, by enabling readers to obtain a deep formal understanding of the subject and to put finite-state methods to real use, this book closes the gap between theory and practice.

Single Digits - In Praise of Small Numbers (Hardcover): Marc Chamberland Single Digits - In Praise of Small Numbers (Hardcover)
Marc Chamberland
R581 R400 Discovery Miles 4 000 Save R181 (31%) Shipped within 7 - 12 working days

In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? And, are there really "six degrees of separation" between all pairs of people? Chamberland explores these questions and covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, the number of guards needed to protect an art gallery, problematic election results and so much more. The book's short sections can be read independently and digested in bite-sized chunks--especially good for learning about the Ham Sandwich Theorem and the Pizza Theorem. Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.

Cambridge Introductions to Philosophy - An Introduction to Non-Classical Logic: From If to Is (Paperback, 2nd Revised edition):... Cambridge Introductions to Philosophy - An Introduction to Non-Classical Logic: From If to Is (Paperback, 2nd Revised edition)
Graham Priest
R822 R714 Discovery Miles 7 140 Save R108 (13%) Shipped within 7 - 12 working days

This 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.

Making Up Your Own Mind - Thinking Effectively through Creative Puzzle-Solving (Hardcover): Edward B. Burger Making Up Your Own Mind - Thinking Effectively through Creative Puzzle-Solving (Hardcover)
Edward B. Burger
R392 R276 Discovery Miles 2 760 Save R116 (30%) Shipped within 7 - 12 working days

How you can become better at solving real-world problems by learning creative puzzle-solving skills We solve countless problems--big and small--every day. With so much practice, why do we often have trouble making simple decisions--much less arriving at optimal solutions to important questions? Are we doomed to this muddle--or is there a practical way to learn to think more effectively and creatively? In this enlightening, entertaining, and inspiring book, Edward Burger shows how we can become far better at solving real-world problems by learning creative puzzle-solving skills using simple, effective thinking techniques. Making Up Your Own Mind teaches these techniques--including how to ask good questions, fail and try again, and change your mind--and then helps you practice them with fun verbal and visual puzzles. The goal is not to quickly solve each challenge but to come up with as many different ways of thinking about it as possible. As you see the puzzles in ever-greater depth, your mind will change, helping you become a more imaginative and creative thinker in daily life. And learning how to be a better thinker pays off in incalculable ways for anyone--including students, businesspeople, professionals, athletes, artists, leaders, and lifelong learners. A book about changing your mind and creating an even better version of yourself through mental play, Making Up Your Own Mind will delight and reward anyone who wants to learn how to find better solutions to life's innumerable puzzles. And the puzzles extend to the thought-provoking format of the book itself because one of the later short chapters is printed upside down while another is printed in mirror image, further challenging the reader to see the world through different perspectives and make new meaning.

An Invitation to Model Theory (Paperback): Jonathan Kirby An Invitation to Model Theory (Paperback)
Jonathan Kirby
R682 R595 Discovery Miles 5 950 Save R87 (13%) Shipped within 7 - 12 working days

Model 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.

Prof: Alan Turing Decoded (Hardcover): Dermot Turing Prof: Alan Turing Decoded (Hardcover)
Dermot Turing 1
R489 R344 Discovery Miles 3 440 Save R145 (30%) Shipped within 7 - 12 working days

Alan Turing was an extraordinary man who crammed into a life of only 42 years the careers of mathematician, codebreaker, computer scientist and biologist. He is widely regarded as a war hero grossly mistreated by his unappreciative country and it has become hard to disentangle the real man from the story. It is easy to cast him as a misfit, the stereotypical professor. But actually Alan Turing was never a professor, and his nickname `Prof' was given by his codebreaking friends at Bletchley Park. Now, Alan Turing's nephew, Dermot Turing, has taken a fresh look at the influences on Alan Turing's life and creativity, and the later creation of a legend. For the first time it is possible to disclose the real character behind the cipher-text: how did Alan's childhood experiences influence the man? Who were the influential figures in Alan's formative years? How did his creative ideas evolve? Was he really a solitary, asocial genius? What was his wartime work after 1942, and why was it kept even more secret than the Enigma story? What is the truth about Alan Turing's conviction for gross indecency, and did he commit suicide? What is the significance of the Royal Pardon granted in 2013? In Dermot's own style he takes a vibrant and entertaining approach to the life and work of a true genius.

Logic: A Very Short Introduction (Paperback, 2nd Revised edition): Graham Priest Logic: A Very Short Introduction (Paperback, 2nd Revised edition)
Graham Priest
R233 R156 Discovery Miles 1 560 Save R77 (33%) Shipped within 7 - 12 working days

Logic 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.

Conceptual Mathematics - A First Introduction to Categories (Paperback, 2nd Revised edition): F. William Lawvere, Stephen H.... Conceptual Mathematics - A First Introduction to Categories (Paperback, 2nd Revised edition)
F. William Lawvere, Stephen H. Schanuel
R1,108 R950 Discovery Miles 9 500 Save R158 (14%) Shipped within 7 - 12 working days

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.

Natural Language Semantics - Formation and Valuation (Hardcover): Brendan S. Gillon Natural Language Semantics - Formation and Valuation (Hardcover)
Brendan S. Gillon
R1,489 R1,236 Discovery Miles 12 360 Save R253 (17%) Shipped within 7 - 13 working days

An introduction to natural language semantics that offers an overview of the empirical domain and an explanation of the mathematical concepts that underpin the discipline. This textbook offers a comprehensive introduction to the fundamentals of those approaches to natural language semantics that use the insights of logic. Many other texts on the subject focus on presenting a particular theory of natural language semantics. This text instead offers an overview of the empirical domain (drawn largely from standard descriptive grammars of English) as well as the mathematical tools that are applied to it. Readers are shown where the concepts of logic apply, where they fail to apply, and where they might apply, if suitably adjusted. The presentation of logic is completely self-contained, with concepts of logic used in the book presented in all the necessary detail. This includes propositional logic, first order predicate logic, generalized quantifier theory, and the Lambek and Lambda calculi. The chapters on logic are paired with chapters on English grammar. For example, the chapter on propositional logic is paired with a chapter on the grammar of coordination and subordination of English clauses; the chapter on predicate logic is paired with a chapter on the grammar of simple, independent English clauses; and so on. The book includes more than five hundred exercises, not only for the mathematical concepts introduced, but also for their application to the analysis of natural language. The latter exercises include some aimed at helping the reader to understand how to formulate and test hypotheses.

Alan Turing's Systems of Logic - The Princeton Thesis (Paperback): Andrew W. Appel Alan Turing's Systems of Logic - The Princeton Thesis (Paperback)
Andrew W. Appel
R298 R240 Discovery Miles 2 400 Save R58 (19%) Shipped within 7 - 12 working days

Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912-1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt Godel, John von Neumann, and Stephen Kleene--were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton.

A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal--a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine.

Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science."

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