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ISBN: 052141413X 9780521414135 Year: 1992 Publisher: Cambridge : Cambridge university press,
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ISBN: 0415223873 Year: 2001 Publisher: London Routledge
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ISBN: 0521779111 9780521779111 Year: 2000 Volume: 43 Publisher: Cambridge : Cambridge university press,
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ISBN: 9798595265973 Year: 2021 Publisher: [Sacramento, CA]: [LongFormMath.com],
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This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own. This book covers intuitive proofs, direct proofs, sets, induction, logic, the contrapositive, contradiction, functions and relations. The text aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and conversational, and includes periodic attempts at humor. This text is also an introduction to higher mathematics. This is done in-part through the chosen examples and theorems. Furthermore, following every chapter is an introduction to an area of math. These include Ramsey theory, number theory, topology, sequences, real analysis, big data, game theory, cardinality and group theory. After every chapter are "pro-tips," which are short thoughts on things I wish I had known when I took my intro-to-proofs class. They include finer comments on the material, study tips, historical notes, comments on mathematical culture, and more. Also, after each chapter's exercises is an introduction to an unsolved problem in mathematics. In the first appendix we discuss some further proof methods, the second appendix is a collection of particularly beautiful proofs, and the third is some writing advice.
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Year: 2020 Publisher: [Place of publication not identified] : MDPI - Multidisciplinary Digital Publishing Institute,
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The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the state-of-the-art of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.
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ISBN: 0511896263 Year: 1993 Publisher: Cambridge : Cambridge University Press,
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The lecture courses in this work are derived from the SERC 'Logic for IT' Summer School and Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles; put together in this book they form an invaluable introduction to proof theory that is aimed at both mathematicians and computer scientists.
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ISBN: 131604453X 1139168711 Year: 2000 Publisher: Cambridge : Cambridge University Press,
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This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
ISBN: 0821845764 9780821845769 Year: 1993 Publisher: Providence (R.I.): American mathematical society,
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ISBN: 8870882284 9788870882285 Year: 1992 Publisher: Napoli: Bibliopolis,
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ISBN: 0521572231 9780521572231 Year: 1996 Publisher: Cambridge: Cambridge university press,
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