Conjecture and Proof - Brossura

Laczkovich, Miklós

Brossura

ISBN 10: 0883857227 ISBN 13: 9780883857229

Casa editrice: The Mathematical Association of America, 2002

Riassunto

How to prove interesting and deep mathematical results from first principles, with exercises.

Su questo libro

Descrizione del libro

The Budapest semesters in mathematics aim to convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course 'Conjecture and Proof'. Prerequisites are kept to a minimum and exercises are included. This book should prove fascinating for any mathematically literate reader.

Contenuti

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.

Dettagli dell?edizione

• Editore: The Mathematical Association of America
• Data di pubblicazione: 2002
• ISBN 10: 0883857227
• ISBN 13: 9780883857229
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 127
• Contatto del produttore: non disponibile