Douglas Hofstadter's book is concerned directly with the nature of maps" or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow…
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can…
Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the…
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 scie…
This textbook offers an extensive list of completely solved problems in mathematical analysis. This first of three volumes covers sets, functions, limits, derivatives, integrals, sequences and series, to name a few. The series contains the material…
An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs.This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents…
An Introduction to Formal Languages and Automata, Sixth Edition provides an accessible, student-friendly presentation of all material essential to an introductory Theory of Computation course. Written to address the fundamentals of formal languages,…
Kurt Gödel var det plågade geniet vars visioner skakade det matematiska resonemangets stabilitet. Priset för att förändra matematiken i grunden var en balansgång på galenskapens rand.Rebecca Goldstein, prisbelönt författare och filosof, ger läsaren…
Written in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classic…
From imaginary numbers to the fourth dimension and beyond, mathematics has always been about imagining impossible things. In x+y, Eugenia Cheng draws on the insights of higher-dimensional mathematics to reveal a transformative new way of talking abo…
Winner of the National Business Book Award From the New York Times bestselling author of The Organized Mind and This Is Your Brain on Music, a primer to the critical thinking that is more necessary now than ever We are bombarded with more informati…
Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context…
"If I have learned anything in ten years of formal debating, it is that arguments are no different: without a good understanding of the rules and tactics, you are likely to do poorly and be beaten."-HENRY ZHANG, President of the Yale Debate Associat…
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…
"Among the many expositions of Goedel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzen gives careful, non-technical explanations both of what those theorems say and, more importantly, w…
The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience,…
The Banach-Tarski Paradox is a most striking mathematical construction: it asserts that a solid ball can be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large. This volume explores the cons…
A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that…
Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting…
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/ind…
Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic…
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 transitio…
The 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,…
From the Introduction. In 1931 there appeared in a German scientific periodical a relatively short paper with the forbidding title ""Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme"" (""On Formally Undecidable prop…
In 1931 Kurt Goedel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic…
This book chronicles the work of mathematician Ernst Zermelo (1871-1953) and his development of set theory's crucial principle, the axiom of choice. It covers the axiom's formulation during the early 20th century, the controversy it engendered, and…
This textbook offers an introduction to the philosophy of science. It helps undergraduate students from the natural, the human and social sciences to gain an understanding of what science is, how it has developed, what its core traits are, how to di…
-Have you been asked to sit a numerical or logical reasoning test?-Do you need some help preparing for the questions you'll be asked?-Do you want to make sure you perform to the best of your abilities?Perfect Numerical and Logical Test Results is an…
Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be forma…
A portrait of the eminent twentieth-century mathematician discusses his groundbreaking theorem of incompleteness, contributions within the famous Vienna circle, relationships with such contemporaries as Albert Einstein, and untimely death as a resul…
Winner of an Outstanding Academic Title Award from CHOICE MagazineMost available cryptology books primarily focus on either mathematics or history. Breaking this mold, Secret History: The Story of Cryptology gives a thorough yet accessible treatment…
Mathematical induction -- along with its equivalents, complete induction and well-ordering, and its immediate consequence, the pigeonhole principle -- constitute essential proof techniques. Every mathematician is familiar with mathematical induction…
This book provides a systematic and comprehensive description of Non-Axiomatic Logic, which is the result of the author's research for about three decades.Non-Axiomatic Logic is designed to provide a uniform logical foundation for Artificial Intelli…
From the exciting history of its development in ancient times to the present day, Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than pr…
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 Introdu…
This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study fo…
This is an introductory 2001 textbook on probability and induction written by one of the world's foremost philosophers of science. The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in…
In this unique fusion of logical thought and inimitable whimsy, Over 350 ingenious problems involve classical logic: logic is expressed in terms of symbols; syllogisms and the sorites are diagrammed; logic becomes a game played with 2 diagrams and a…
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series…
Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, r…
'Another terrific book by Rob Eastaway' SIMON SINGH'A delightfully accessible guide to how to play with numbers' HANNAH FRYHow many cats are there in the world?What's the chance of winning the lottery twice?And just how long does it take to count to…
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart.Potter offers a thorough account of cardinal a…
A comprehensive philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and…
Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so reader…
Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations o…
Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this very accessible bo…
A collection of anecdotal histories defines the relationship between language and logic, sharing visual examples and puzzles that can be used by readers to raise test scores and recognize the illogical in everyday things. By the author of Randomness…
From atom bombs to rebounding slinkies, open your eyes to the mathematical magic in the everyday. Mathematics isn't just for academics and scientists, a fact meteorologist and blogger Peter Lynch has spent the past several years proving through his…
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a…