Conjecture and Proof
Conjecture and Proof
NZD$74.95
inc GSTThe Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on 'Conjecture and Proof'. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of e, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.
- Class tested material
- Proves exciting and deep mathematical results
- Minimum prerequisites and exercises to broaden appeal
Product details
September 2002Paperback
9780883857229
127 pages
229 × 153 × 10 mm
0.181kg
This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
Table of Contents
- Part I. Proofs of Impossibility, Proofs of Nonexistence:
- 1. Proofs of irrationality
- 2. The elements of the theory of geometric constructions
- 3. Constructible regular polygons
- 4. Some basic facts on linear spaces and fields
- 5. Algebraic and transcendental numbers
- 6. Cauchy's functional equation
- 7. Geometric decompositions
- Part II. Constructions, Proofs of Existence:
- 8. The pigeonhole principle
- 9. Liouville numbers
- 10. Countable and uncountable sets
- 11. Isometries of Rn
- 12. The problem of invariant measures
- 13. The Banach-Tarski paradox
- 14. Open and closed sets in R. The Cantor set
- 15. The Peano curve
- 16. Borel sets
- 17. The diagonal method.
