Numbers, Sets and Axioms

Numbers, Sets and Axioms
Author :
Publisher : Cambridge University Press
Total Pages : 272
Release :
ISBN-10 : 0521287618
ISBN-13 : 9780521287616
Rating : 4/5 (18 Downloads)

Synopsis Numbers, Sets and Axioms by : A. G. Hamilton

Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.

Axiomatic Set Theory

Axiomatic Set Theory
Author :
Publisher : Courier Corporation
Total Pages : 290
Release :
ISBN-10 : 9780486136875
ISBN-13 : 0486136876
Rating : 4/5 (75 Downloads)

Synopsis Axiomatic Set Theory by : Patrick Suppes

Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.

A Book of Set Theory

A Book of Set Theory
Author :
Publisher : Courier Corporation
Total Pages : 259
Release :
ISBN-10 : 9780486497082
ISBN-13 : 0486497089
Rating : 4/5 (82 Downloads)

Synopsis A Book of Set Theory by : Charles C Pinter

"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Set Theory for the Working Mathematician

Set Theory for the Working Mathematician
Author :
Publisher : Cambridge University Press
Total Pages : 256
Release :
ISBN-10 : 0521594650
ISBN-13 : 9780521594653
Rating : 4/5 (50 Downloads)

Synopsis Set Theory for the Working Mathematician by : Krzysztof Ciesielski

Presents those methods of modern set theory most applicable to other areas of pure mathematics.

Elements of Set Theory

Elements of Set Theory
Author :
Publisher : Academic Press
Total Pages : 294
Release :
ISBN-10 : 9780080570426
ISBN-13 : 0080570429
Rating : 4/5 (26 Downloads)

Synopsis Elements of Set Theory by : Herbert B. Enderton

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.

Principia Mathematica

Principia Mathematica
Author :
Publisher :
Total Pages : 688
Release :
ISBN-10 : UOM:39015002922881
ISBN-13 :
Rating : 4/5 (81 Downloads)

Synopsis Principia Mathematica by : Alfred North Whitehead

Logic for Mathematicians

Logic for Mathematicians
Author :
Publisher : Cambridge University Press
Total Pages : 240
Release :
ISBN-10 : 0521368650
ISBN-13 : 9780521368650
Rating : 4/5 (50 Downloads)

Synopsis Logic for Mathematicians by : A. G. Hamilton

In Logic for Mathematicians, author Hamilton introduces the reader to the techniques and principle results of mathematical logic.

The Axiom of Choice

The Axiom of Choice
Author :
Publisher : Courier Corporation
Total Pages : 226
Release :
ISBN-10 : 9780486466248
ISBN-13 : 0486466248
Rating : 4/5 (48 Downloads)

Synopsis The Axiom of Choice by : Thomas J. Jech

Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.

Notes on Set Theory

Notes on Set Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 280
Release :
ISBN-10 : 9781475741537
ISBN-13 : 1475741537
Rating : 4/5 (37 Downloads)

Synopsis Notes on Set Theory by : Yiannis Moschovakis

What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.

Naive Set Theory

Naive Set Theory
Author :
Publisher :
Total Pages : 98
Release :
ISBN-10 : 1950217019
ISBN-13 : 9781950217014
Rating : 4/5 (19 Downloads)

Synopsis Naive Set Theory by : Paul Halmos

Written by a prominent analyst Paul. R. Halmos, this book is the most famous, popular, and widely used textbook in the subject. The book is readable for its conciseness and clear explanation. This emended edition is with completely new typesetting and corrections. Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image. The free PDF file available on the publisher's website www.bowwowpress.org