A Book of Set Theory

Author: Charles C Pinter

Publisher: Courier Corporation

ISBN: 0486497089

Category: Mathematics

Page: 256

View: 7261

"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"--
Posted in Mathematics

Naive Mengenlehre

Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 3606

Posted in Arithmetic

Axiomatic Set Theory

Author: Patrick Suppes

Publisher: Courier Corporation

ISBN: 0486136876

Category: Mathematics

Page: 265

View: 5806

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.
Posted in Mathematics

Set Theory and Logic

Author: Robert R. Stoll

Publisher: Courier Corporation

ISBN: 0486139646

Category: Mathematics

Page: 512

View: 8006

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.
Posted in Mathematics

Basic Set Theory

Author: Azriel Levy

Publisher: Courier Corporation

ISBN: 0486150739

Category: Mathematics

Page: 416

View: 9301

The first part of this advanced-level text covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). 1979 edition.
Posted in Mathematics

Introduction to the Theory of Sets

Author: Joseph Breuer

Publisher: Courier Corporation

ISBN: 0486154874

Category: Mathematics

Page: 128

View: 3019

This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
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An Outline of Set Theory

Author: James M. Henle

Publisher: Courier Corporation

ISBN: 0486453375

Category: Mathematics

Page: 145

View: 8246

An innovative problem-oriented introduction to set theory, this volume is intended for undergraduate courses in which students work in groups on projects and present their solutions to the class. The three-part treatment consists of problems, hints for their solutions, and complete answers. 1986 edition.
Posted in Mathematics

Theory of Sets

Author: E. Kamke

Publisher: Courier Corporation

ISBN: 048645083X

Category: Mathematics

Page: 144

View: 5128

This introduction to the theory of sets employs the discoveries of Cantor, Russell, Weierstrass, Zermelo, Bernstein, Dedekind, and others. It analyzes concepts and principles, offering numerous examples. Topics include the rudiments of set theory, arbitrary sets and their cardinal numbers, ordered sets and their order types, and well-ordered sets and their ordinal numbers. 1950 edition.
Posted in Mathematics

Naive Set Theory

Author: Paul R. Halmos

Publisher: Courier Dover Publications

ISBN: 0486814874

Category: Mathematics

Page: 112

View: 3474

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.
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Philosophical Introduction to Set Theory

Author: Stephen Pollard

Publisher: Courier Dover Publications

ISBN: 0486805824

Category: Mathematics

Page: 192

View: 925

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
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Introduction to Logic

Author: Patrick Suppes

Publisher: Courier Corporation

ISBN: 0486138054

Category: Mathematics

Page: 336

View: 6299

Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.
Posted in Mathematics

The Philosophy of Set Theory

An Historical Introduction to Cantor's Paradise

Author: Mary Tiles

Publisher: Courier Corporation

ISBN: 9780486435206

Category: Mathematics

Page: 239

View: 8471

A century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics. As Cantor's sometime collaborator, David Hilbert, remarked, "No one will drive us from the paradise that Cantor has created." This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure. Philosophers with only a basic grounding in mathematics, as well as mathematicians who have taken only an introductory course in philosophy, will find an abundance of intriguing topics in this text, which is appropriate for undergraduate-and graduate-level courses.
Posted in Mathematics

An Introduction to Matrices, Sets and Groups for Science Students

Author: G. Stephenson

Publisher: Courier Dover Publications

ISBN: 0486650774

Category: Mathematics

Page: 164

View: 7563

Concise, readable text introduces sets, groups, and, most importantly, matrices to undergraduate students of physics, chemistry, and engineering. Each chapter contains worked examples and many problems with answers. 1974 edition.
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Eine kurze Geschichte der Menschheit

Author: Yuval Noah Harari

Publisher: DVA

ISBN: 364110498X

Category: History

Page: 528

View: 8503

Krone der Schöpfung? Vor 100 000 Jahren war der Homo sapiens noch ein unbedeutendes Tier, das unauffällig in einem abgelegenen Winkel des afrikanischen Kontinents lebte. Unsere Vorfahren teilten sich den Planeten mit mindestens fünf weiteren menschlichen Spezies, und die Rolle, die sie im Ökosystem spielten, war nicht größer als die von Gorillas, Libellen oder Quallen. Vor 70 000 Jahren dann vollzog sich ein mysteriöser und rascher Wandel mit dem Homo sapiens, und es war vor allem die Beschaffenheit seines Gehirns, die ihn zum Herren des Planeten und zum Schrecken des Ökosystems werden ließ. Bis heute hat sich diese Vorherrschaft stetig zugespitzt: Der Mensch hat die Fähigkeit zu schöpferischem und zu zerstörerischem Handeln wie kein anderes Lebewesen. Anschaulich, unterhaltsam und stellenweise hochkomisch zeichnet Yuval Harari die Geschichte des Menschen nach und zeigt alle großen, aber auch alle ambivalenten Momente unserer Menschwerdung.
Posted in History

Toposes and Local Set Theories

An Introduction

Author: John L. Bell

Publisher: Courier Corporation

ISBN: 0486462862

Category: Mathematics

Page: 267

View: 7501

This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
Posted in Mathematics

Das BUCH der Beweise

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662577674

Category: Mathematics

Page: 360

View: 3262

Diese fünfte deutsche Auflage enthält ein ganz neues Kapitel über van der Waerdens Permanenten-Vermutung, sowie weitere neue, originelle und elegante Beweise in anderen Kapiteln. Aus den Rezensionen: “... es ist fast unmöglich, ein Mathematikbuch zu schreiben, das von jedermann gelesen und genossen werden kann, aber Aigner und Ziegler gelingt diese Meisterleistung in virtuosem Stil. [...] Dieses Buch erweist der Mathematik einen unschätzbaren Dienst, indem es Nicht-Mathematikern vorführt, was Mathematiker meinen, wenn sie über Schönheit sprechen.” Aus der Laudatio für den “Steele Prize for Mathematical Exposition” 2018 "Was hier vorliegt ist eine Sammlung von Beweisen, die in das von Paul Erdös immer wieder zitierte BUCH gehören, das vom lieben (?) Gott verwahrt wird und das die perfekten Beweise aller mathematischen Sätze enthält. Manchmal lässt der Herrgott auch einige von uns Sterblichen in das BUCH blicken, und die so resultierenden Geistesblitze erhellen den Mathematikeralltag mit eleganten Argumenten, überraschenden Zusammenhängen und unerwarteten Volten." www.mathematik.de, Mai 2002 "Eine einzigartige Sammlung eleganter mathematischer Beweise nach der Idee von Paul Erdös, verständlich geschrieben von exzellenten Mathematikern. Dieses Buch gibt anregende Lösungen mit Aha-Effekt, auch für Nicht-Mathematiker." www.vismath.de "Ein prächtiges, äußerst sorgfältig und liebevoll gestaltetes Buch! Erdös hatte die Idee DES BUCHES, in dem Gott die perfekten Beweise mathematischer Sätze eingeschrieben hat. Das hier gedruckte Buch will eine "very modest approximation" an dieses BUCH sein.... Das Buch von Aigner und Ziegler ist gelungen ..." Mathematische Semesterberichte, November 1999 "Wer (wie ich) bislang vergeblich versucht hat, einen Blick ins BUCH zu werfen, wird begierig in Aigners und Zieglers BUCH der Beweise schmökern." www.mathematik.de, Mai 2002
Posted in Mathematics

First Order Mathematical Logic

Author: Angelo Margaris

Publisher: Courier Corporation

ISBN: 9780486662695

Category: Mathematics

Page: 211

View: 1486

"Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smooth-running technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to first-order theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews
Posted in Mathematics

Elements of Abstract Algebra

Author: Allan Clark

Publisher: Courier Corporation

ISBN: 0486140350

Category: Mathematics

Page: 224

View: 3137

Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.
Posted in Mathematics

The Stanford Mathematics Problem Book

With Hints and Solutions

Author: George Polya,Jeremy Kilpatrick

Publisher: Courier Corporation

ISBN: 048631832X

Category: Mathematics

Page: 80

View: 4516

Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.
Posted in Mathematics