Elements of Logic via Numbers and Sets

Author: D.L. Johnson
Publisher: Springer Science & Business Media
ISBN: 1447106032
Format: PDF
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In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.

Metric Spaces

Author: Mícheál O'Searcoid
Publisher: Springer Science & Business Media
ISBN: 9781846286278
Format: PDF, Docs
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The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.

Elements of Abstract Analysis

Author: Mícheál O'Searcoid
Publisher: Springer Science & Business Media
ISBN: 1447101790
Format: PDF, ePub, Docs
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While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis.

Groups Rings and Fields

Author: David A.R. Wallace
Publisher: Springer Science & Business Media
ISBN: 1447104250
Format: PDF, ePub
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This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.

Fields and Galois Theory

Author: John M. Howie
Publisher: Springer Science & Business Media
ISBN: 9781852339869
Format: PDF, Docs
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This gentle introduction aimed at advanced undergraduates and beginning graduate students takes a modern, more "natural" approach to its subject, developing the theory at a gentle pace. Topics covered include rings and fields, integral domains and polynomials, field extensions and splitting fields, finite fields, and the Galois group. The book contains plenty of worked examples and exercises complete with full solutions.

Sets Logic and Categories

Author: Peter J. Cameron
Publisher: Springer Science & Business Media
ISBN: 1447105893
Format: PDF, ePub, Docs
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Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.

General Relativity

Author: N.M.J. Woodhouse
Publisher: Springer Science & Business Media
ISBN: 9781846284878
Format: PDF, ePub, Mobi
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Based on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.

Elements of Set Theory

Author: Herbert B. Enderton
Publisher: Academic Press
ISBN: 0080570429
Format: PDF, Kindle
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This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Naive Set Theory

Author: Paul R. Halmos
Publisher: Courier Dover Publications
ISBN: 0486814874
Format: PDF, Docs
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Classic by prominent mathematician offers a concise introduction to set theory using language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, more. 1960 edition.

Mathematical Logic

Author: H.-D. Ebbinghaus
Publisher: Springer Science & Business Media
ISBN: 1475723555
Format: PDF, Docs
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This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.