The Foundations of Mathematics

by Ian Stewart, David Tall

Overview

The transition from school to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. This book bridges the divide.

Product Details

ISBN-13:	9780198706434
Publisher:	Oxford University Press
Publication date:	05/01/2015
Edition description:	2nd Revised ed.
Pages:	416
Product dimensions:	5.40(w) x 8.40(h) x 1.00(d)

About the Author

Ian Stewart, Emeritus Professor, University of Warwick,David Tall, Emeritus Professor, University of Warwick

Ian Stewart is Emeritus Professor of Mathematics at the University of Warwick. He remains an active research mathematician and is a Fellow of the Royal Society. Famed for his popular science writing and broadcasting, for which he is the recipient of numerous awards, his bestselling books include: Does God Play Dice?, Nature's Numbers, and Professor Stewart's Cabinet of Mathematical Curiosities. He also co-authored The Science of Discworld series with Terry Pratchett and Jack Cohen

David Tall is Emeritus Professor of Mathematical Thinking at the University of Warwick. Internationally known for his contributions to mathematics education, his most recent book is How Humans Learn to Think Mathematically (2013).

Table of Contents

I: The Intuitive Background1. Mathematical Thinking2. Number SystemsII: The Beginnings of Formalisation3. Sets4. Relations5. FunctionsIII: The Development of Axiomatic Systems8. Natural Numbers and Proof by Induction9. Real Numbers10. Real Numbers as a Complete Ordered Field11. Complex Numbers and BeyondIV: Using Axiomatic Systems12. Axiomatic Structures and Structure Theorems13. Permutations and Groups14. Infinite Cardinal Numbers15. InfinitesimalsV: Strengthening the Foundations16. Axioms for Set Theory

Editorial Reviews

"In their writing of Foundations of Mathematics, the authors motivate, encourage and teach their readers. If I were to offer a future course in foundations, I would certainly use this book and highly recommend it to others, both as a reference and as a text." —Frank Swetz, MAA Reviews

"The writing is both rigorous and thorough, and the authors use compact presentations to support their explanations and proofs. Highly recommended." —CHOICE

From the Publisher