Theorems and Counterexamples in Mathematics / Edition 1

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This text is intended to provide graduate and advanced undergraduate students as well as the general mathematical public with a modern treatment of various theorems and examples in mathematics. A carefully arranged mixture of theorems, examples, exercises, hints and discussions sharpens and highlights many of the fundamental aspects of the subject matter, and constitutes a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. Essentially self-contained, the book presents this material with a treatment sensitive to the progress mathematics has made in the last 25 years.

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Editorial Reviews

Successor to the authors' Counterexamples in analysis, this is a nicely produced volume of uncommon design and intent. Addressed to mathematicians of some maturity (professionals, graduate students, exceptional advanced undergraduates), it, under five topical heads (algebra, analysis, complex variable theory, geometry/topology, probability theory, foundations), and numerous subheads presents a large collection of fundamental theorems in association with a collection of counterexamples which serve to sharpen the reader's comprehension of what those theorems precisely entail and mean. The very helpful introductory "Guide" lists 386 primary entries. Theorems, examples and exercises are engagingly mixed, and key references are abundant. (NW) Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780387973425
  • Publisher: Springer New York
  • Publication date: 8/6/1990
  • Series: Problem Books in Mathematics Series
  • Edition description: 1st ed. 1990. 2nd corr. printing 1993
  • Edition number: 1
  • Pages: 348
  • Product dimensions: 0.88 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Contents: Algebra.- Analysis.- Geometry/Topology.- Probability Theory.- Foundations.- Bibliography.- Supplemental Bibliography.- Symbol List.- Glossary/Index.
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