Normal view MARC view ISBD view

The foundations of mathematics / Ian Stewart, David Tall

Main Author Stewart, Ian, 1945- Coauthor Tall, David Orme Country Reino Unido. Publication Oxford : Oxford University Press, imp. 1990 Description IX, 263 p. : il. ; 22 cm Series Oxford science publications) ISBN 0-19-853165-6 CDU 510.2
Tags from this library: No tags from this library for this title. Log in to add tags.
    average rating: 0.0 (0 votes)
Item type Current location Call number Status Date due Barcode Item holds Course reserves
Monografia Biblioteca Geral da Universidade do Minho
BGUM 510.2 - S Available 79189

Licenciatura em Ciências da Computação Tópicos de Matemática 1º semestre

Total holds: 0

Enhanced descriptions from Syndetics:

"There are many textbooks available for a so-called transition course from calculus to abstract mathematics. I have taught this course several times and always find it problematic. The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and
there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books

Table of contents provided by Syndetics

  • 1 The intuitive background
  • 1 Mathematical thinking
  • 2 Number systems
  • 2 The beginnings of formalization
  • 3 Sets
  • 4 Relations
  • 5 Functions
  • 6 Mathematical logic
  • 7 Mathematical proof
  • 3 The development of axiomatic systems
  • 8 Natural numbers and proof by induction
  • 9 The real numbers
  • 10 The real numbers as a complete ordered field
  • 11 Complex numbers and beyond
  • 12 Cardinal numbers
  • 4 Strengthening the foundations
  • 13 Axioms for set theory
  • References
  • Index

Reviews provided by Syndetics


As students of mathematics progress through their formal studies, they transition from concentrating on procedure and algorithm to dealing with conceptualization and proof. This evolution often proves to be quite challenging, and Stewart and Tall (both emer., Univ. of Warwick, UK) quite effectively introduce what it means to think like a mathematician. Part 1, entitled "The Intuitive Background," provides a clear exposition which prompts the reader to look carefully at the precise nature of mathematical language and logical connections. It sets the stage for the more demanding ideas of sets and functional relationships, induction, proof by contradiction, and the role of definitions and propositions which follow. The writing is both rigorous and thorough, and the authors use compact presentations to support their explanations and proofs. While the first half of the book stresses higher-level mathematical thinking based on concepts that are generally already familiar to the reader, it clearly offers new insights as well. The second half emphasizes proofs based on formal algorithmic systems, especially stressing concepts generally associated with abstract algebra coursework. Summing Up: Highly recommended. Lower- and upper-division undergraduates. --Ned W. Schillow, emeritus, Lehigh Carbon Community College

Author notes provided by Syndetics

Ian Stewart is Professor of Mathematics at Warwick University, and Director of the Mathematics Awareness Centre at Warwick. An active research mathematician, he is also a well-known popularizer of mathematics and related areas of science.

There are no comments for this item.

Log in to your account to post a comment.