MTU Library Catalogue

Syndetics cover image
Image from Syndetics

The foundations of mathematics / Ian Stewart and David Tall.

By: Stewart, Ian, 1945-.
Contributor(s): Tall, David Orme.
Material type: materialTypeLabelBookPublisher: Oxford [Eng.] : New York : Oxford University Press, 1977Description: ix, 263 p. : ill. ; 23 cm. + pbk.ISBN: 0198531648 (v); 0198531656 (m)pbk..Subject(s): Logic, Symbolic and mathematicalDDC classification: 512
Contents:
I: The intuitive background -- II: The beginnings of formalization -- III: The development of axiomatic systems -- IV: Strengthening the foundations.
Holdings
Item type Current library Call number Copy number Status Barcode
General lending MTU Bishopstown Library Lending 512 (Browse shelf(Opens below)) 1 Available 00090552
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

Includes bibliographical references (page 259) and index.

I: The intuitive background -- II: The beginnings of formalization -- III: The development of axiomatic systems -- IV: Strengthening the foundations.

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

CHOICE Review

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