Set Theory and the Continuum Hypothesis

Author: Paul J. Cohen
Publisher: Courier Corporation
ISBN: 9780486469218
Release Date: 2008-12-09
Genre: Mathematics

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Set Theory and the Continuum Problem

Author: Raymond M. Smullyan
Publisher:
ISBN: 0486474844
Release Date: 2010
Genre: Mathematics

A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.

The Philosophy of Set Theory

Author: Mary Tiles
Publisher: Courier Corporation
ISBN: 9780486138558
Release Date: 2012-03-08
Genre: Mathematics

DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

Naive Mengenlehre

Author: Paul R. Halmos
Publisher: Vandenhoeck & Ruprecht
ISBN: 3525405278
Release Date: 1976
Genre: Arithmetic


First order Logic

Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 0486683702
Release Date: 1995
Genre: Mathematics

Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations.

A Book of Set Theory

Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 9780486497082
Release Date: 2014-07-23
Genre: Mathematics

"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"--

Philosophical Introduction to Set Theory

Author: Stephen Pollard
Publisher: Courier Dover Publications
ISBN: 9780486797144
Release Date: 2015-07-15
Genre: Mathematics

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.

What Is Mathematical Logic

Author: J. N. Crossley
Publisher: Courier Corporation
ISBN: 9780486151526
Release Date: 2012-08-29
Genre: Mathematics

A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.

Das BUCH der Beweise

Author: Martin Aigner
Publisher: Springer-Verlag
ISBN: 9783662577677
Release Date: 2018-09-17
Genre: Mathematics

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

Satan Cantor Infinity

Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 9780486470368
Release Date: 2009
Genre: Games

Honorable knights, lying knaves, and other fanciful characters populate this unusual survey of the principles underlying the works of Georg Cantor. Created by a renowned mathematician, these engaging puzzles apply logical precepts to issues of infinity, probability, time, and change. They require a strong mathematics background and feature complete solutions.

The Lady Or the Tiger

Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 9780486470276
Release Date: 2009-04
Genre: Science

"Another scintillating collection of brilliant problems and paradoxes by the most entertaining logician and set theorist who ever lived." — Martin Gardner. Inspired by the classic tale of a prisoner's dilemma, these whimsically themed challenges involve paradoxes about probability, time, and change; metapuzzles; and self-referentiality. Nineteen chapters advance in difficulty from relatively simple to highly complex.

The Surprise Attack in Mathematical Problems

Author: Louis A. Graham
Publisher: Courier Dover Publications
ISBN: 9780486820767
Release Date: 2017-03-17
Genre: Mathematics

An unusual problem book that focuses on the method of solution, this collection spotlights 52 problems, each with several approaches to situations involving measurement of geometrical spaces, probabilities, distances, relative motion, more.