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Conjecture and Proof (Classroom Resource Materials)

Laczkovich, Miklós

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ISBN 10: 0883857227 / ISBN 13: 9780883857229
Verlag: The Mathematical Association of America, 2001
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Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: 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. Buchnummer des Verkäufers ABE_book_new_0883857227

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Inhaltsangabe:

The 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.

Inhaltsangabe: 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.

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Bibliografische Details

Titel: Conjecture and Proof (Classroom Resource ...

Verlag: The Mathematical Association of America

Erscheinungsdatum: 2001

Einband: Soft cover

Zustand: New

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