# Conjecture and Proof

Cambridge University Press, 2001 jan. 1 - 118 oldal
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.

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### Tartalomjegyzék

 Proofs of Impossibility Proofs of Nonexistence 1 Proofs of Irrationality 3 The Elements of the Theory of Geometric Constructions 11 Constructible Regular Polygons 17 Some Basic Facts About Linear Spaces and Fields 21 Algebraic and Transcendental Numbers 27 Cauchys Functional Equation 33 Geometric Decompositions 39
 Countable and Uncountable Sets 59 Isometries of R 67 The Problem of Invariant Measures 75 The BanachTarski Paradox 81 Open and Closed Sets in R The Cantor Set 85 The Peano Curve 93 Borel Sets 97 The Diagonal Method 103

 Constructions Proofs of Existence 47 The Pigeonhole Principle 49 Liouville Numbers 55

### Hivatkozások weboldalakról

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This book is an elaborate version of the course on 'Conjecture and Proof'. It gives miniature introductions to various areas of mathematics by presenting ...
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BIBCAT AJI-0260
Search for. Other Libraries. You Found Titles in Categories:. Mathematics. Item Information. Conjecture and proof / Miklós Laczkovich. ...
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BSM Courses
"Conjecture and Proof, the Fundamentals of Mathematical Thinking" by M. Laczkovich I. Proofs of impossibility, proofs of non-existence: ...
www.math.princeton.edu/ ~mcucurin/ bsm.htm

Könyvek
Conjecture and Proof. LACZKOVICH Miklós. Témakör: Original editions in English. ISBN-13 978-963-7546-89-1. 100 oldal, B/5. Ára 3400 HUF ...
www.typotex.hu/ index.php?page=en/ konyvek& book_id=861

Conjecture And Proof - jácotei
Pesquisa e compara precos de livros conjecture and proof.
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Phys. Rev. E 69, 046104 (2004): Häggkvist et al. - Computation of ...
M. Laczkovich, Conjecture and Proof (typotex Kft. Elektronikus Kiadó, Budapest, 1998). de Knuth, The Art of Computer Programming, 2nd ed. ...