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Author: Thomas Forster
Publisher: Cambridge University Press
ISBN: 9780521533614
Category : Mathematics
Languages : en
Pages : 248
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Book Description
This is an introduction to logic and the axiomatization of set theory from a unique standpoint. Philosophical considerations, which are often ignored or treated casually, are here given careful consideration, and furthermore the author places the notion of inductively defined sets (recursive datatypes) at the center of his exposition resulting in a treatment of well established topics that is fresh and insightful. The presentation is engaging, but always great care is taken to illustrate difficult points. Understanding is also aided by the inclusion of many exercises. Little previous knowledge of logic is required of the reader, and only a background of standard undergraduate mathematics is assumed.
Author: Thomas Forster
Publisher: Cambridge University Press
ISBN: 9780521826211
Category : Mathematics
Languages : en
Pages : 244
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Book Description
Philosophical considerations, which are often ignored or treated casually, are given careful consideration in this introduction. Thomas Forster places the notion of inductively defined sets (recursive datatypes) at the center of his exposition resulting in an original analysis of well established topics. The presentation illustrates difficult points and includes many exercises. Little previous knowledge of logic is required and only a knowledge of standard undergraduate mathematics is assumed.
Author: Thomas Forster
Publisher: Cambridge University Press
ISBN: 9780521533614
Category : Mathematics
Languages : en
Pages : 248
Get Book Here
Book Description
This is an introduction to logic and the axiomatization of set theory from a unique standpoint. Philosophical considerations, which are often ignored or treated casually, are here given careful consideration, and furthermore the author places the notion of inductively defined sets (recursive datatypes) at the center of his exposition resulting in a treatment of well established topics that is fresh and insightful. The presentation is engaging, but always great care is taken to illustrate difficult points. Understanding is also aided by the inclusion of many exercises. Little previous knowledge of logic is required of the reader, and only a background of standard undergraduate mathematics is assumed.
Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486139646
Category : Mathematics
Languages : en
Pages : 516
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Book Description
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Author: Robert L. Causey
Publisher: Jones & Bartlett Learning
ISBN: 9780763737849
Category : Computers
Languages : en
Pages : 536
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Book Description
The new Second Edition incorporates a wealth of exercise sets, allowing students to test themselves and review important topics discussed throughout the text."--Jacket.
Author: David Makinson
Publisher: Springer Science & Business Media
ISBN: 1447125002
Category : Computers
Languages : en
Pages : 302
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Book Description
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/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.
Author: Moshe Machover
Publisher: Cambridge University Press
ISBN: 9780521479981
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
Author: Dirk van Dalen
Publisher: Springer Science & Business Media
ISBN: 3662023822
Category : Mathematics
Languages : en
Pages : 218
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Book Description
New corrected printing of a well-established text on logic at the introductory level.
Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3662223430
Category : Mathematics
Languages : en
Pages : 194
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Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author: Frank Blume
Publisher: Createspace Independent Publishing Platform
ISBN: 9781973779360
Category :
Languages : en
Pages : 240
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Book Description
Logic, Sets, and Numbers is a brief introduction to abstract mathematics that is meant to familiarize the reader with the formal and conceptual rigor that higher-level undergraduate and graduate textbooks commonly employ. Beginning with formal logic and a fairly extensive discussion of concise formulations of mathematical statements, the text moves on to cover general patterns of proofs, elementary set theory, mathematical induction, cardinality, as well as, in the final chapter, the creation of the various number systems from the integers up to the complex numbers. On the whole, the book's intent is not only to reveal the nature of mathematical abstraction, but also its inherent beauty and purity.
Author: Douglas Cenzer
Publisher: World Scientific
ISBN: 9811201943
Category : Mathematics
Languages : en
Pages : 222
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Book Description
This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.
