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Godel, Escher, Bach: An Eternal Golden Braid
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by
Douglas R Hofstadter
First published in 1979, this is a genuine interdisciplinary work of nonfiction, with dozens of historical references and subtexts. Critics and reviewers have summed up its meaning in varying ways, yet consistently with praise. A mixture of art, philosophy, music, math, technology, and cognitive science, the book's title only reflects one aspect ...
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Discrete Mathematics and Its Applications
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by
Kenneth H Rosen
"Discrete Mathematics and its Applications, Sixth Edition", is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 600 institutions around the world, gives a ...
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Introduction to the Theory of Computation
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by
Michael Sipser
This market leading text on computational theory provides a mathematical treatment of computer science theory designed around theorems and proofs.
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Is God a Mathematician?
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by
Mario Livio
This fascinating exploration of the great discoveries of history's most important mathematicians seeks an answer to the eternal question: Does mathematics hold the key to understanding the mysteries of the physical world? Illustrations throughout.
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The Art of Reasoning
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by
David Kelley
An inviting alternative to traditional texts in introductory logic, The Art of Reasoning is widely acclaimed for its conversational tone and accessible exposition of rigorous logical concepts.
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How to Prove It: A Structured Approach
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by
Daniel J Velleman
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic ...
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Incompleteness: The Proof and Paradox of Kurt Godel
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by
Rebecca Goldstein, Ph.D.
Considered the 20th century's greatest mathematician, Kurt Godel is the subject of this lucid and accessible study, which explains the significance of his theorems and the remarkable vision behind them, while bringing this eccentric, tortured genius and his world to life.
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The Foundations of Mathematics
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by
Thomas Q Sibley
Finally there's an easy to follow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Key definitions are introduced while readers are encouraged to develop an intuition about these concepts and practice using them in problems. With ...
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Introduction to Automata Theory, Languages, and Computation
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by
John E Hopcroft
It has been more than 20 years since this classic book on formal languages, automata theory, and computational complexity was first published. With this long-awaited revision, the authors continue to present the theory in a concise and straightforward manner, now with an eye out for the practical applications. They have revised this book to make ...
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Gödel's proof
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by
Ernest Nagel, James R Newman
Originally written in 1958, this text clearly explains the tenets and importance of Godel's classic proof, and its influence on mathematics and philosophy.
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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes
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by
Daniel Solow
When engineers, computer scientists, and economists need to learn how to read, think about, and create proofs, they turn to Solow. In order to make the material more relevant, the exercises in each chapter have been revised and expanded. New and more complete discussions are included on how to use a previously-proved proposition in both the ...
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Discrete Mathematics
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by
Richard Johnsonbaugh
For a one- or two-term introductory course in discrete mathematics. Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition ...
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An Introduction to Godel's Theorems
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by
Peter Smith
In 1931, the young Kurt Godel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Godel also outlined an equally significant Second ...
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Introduction to mathematical philosophy
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by
Bertrand Russell, Earl
This seminal work focuses on concepts of number, order, relations, limits and continuity, propositional functions, and more. It is an accesible excursion into the realm where mathematics and philosophy meet.
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Introduction to Logic
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by
Alfred Tarski, Olaf Helmer (Translator)
This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.
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Introduction to Languages and the Theory of Computation
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by
John C Martin
"Introduction to Languages and the Theory of Computation" is an introduction to the theory of computation that emphasizes formal languages, automata and abstract models of computation, and computability; it also includes an introduction to computational complexity and NP-completeness. Through the study of these topics, students encounter profound ...
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Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games
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by
Douglas E Ensley, J Winston Crawley
Did you know that games and puzzles have given birth to many of today's deepest mathematical subjects? Now, with Douglas Ensley and Winston Crawley's "Introduction to Discrete Mathematics", you can explore mathematical writing, abstract structures, counting, discrete probability, and graph theory, through games, puzzles, patterns, magic tricks, ...
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Axiomatic Set Theory
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by
Patrick Suppes
By means of the Zermelo-Fraenkel system, Suppes provides best treatment of axiomatic set theory on upper undergraduate and graduate levels. Topics include relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, more
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Symbolic logic
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by
Irving M. Copi
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Logic: Techniques of Formal Reasoning
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by
Donald Kalish, Richard Montague, Gary Mar
Logic: Techniques of Formal Reasoning, 2/e is an introductory volume that teaches students to recognize and construct correct deductions. It takes students through all logical steps--from premise to conclusion--and presents appropriate symbols and terms, while giving examples to clarify principles. Logic, 2/e uses models to establish the ...
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Introduction to Mathematical Structures and Proofs
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by
Larry J Gerstein
Gerstein wants-very gently-to teach his students to think. He wants to show them how to wrestle with a problem.
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Computability and Logic
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by
George Boolos
This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book has become a classic because of its accessibility to students without a ...
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Languages and machines an introduction to the theory of computer science
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by
Sudkamp
Languages and Machines, which is intended for computer scientists in the theoretical foundations of their subject, gives a mathematically sound presentation of the theory of computing at the junior and senior level. Topics covered include the theory of formal languages and automata, computability, computational complexity, and deterministic ...
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The Nuts and Bolts of Proofs
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by
Antonella Cupillari
This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it ...
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Schaum's Outlines of Discrete Mathematics
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by
Seymour Lipschutz, Ph.D., Marc Lipson
Discrete mathematics becomes more and more important as the digital age goes forward. This newly revised third edition updates all areas of the subject.
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