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.
Mit mondanak mások - Írjon ismertetőt
Proofs of Impossibility Proofs of Nonexistence
Proofs of Irrationality
The Elements of the Theory of Geometric Constructions
Constructible Regular Polygons
Some Basic Facts About Linear Spaces and Fields
Algebraic and Transcendental Numbers
Cauchys Functional Equation
Countable and Uncountable Sets
Isometries of R
The Problem of Invariant Measures
The BanachTarski Paradox
Open and Closed Sets in R The Cantor Set
The Peano Curve
The Diagonal Method
Constructions Proofs of Existence
The Pigeonhole Principle
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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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"Conjecture and Proof, the Fundamentals of Mathematical Thinking" by M. Laczkovich I. Proofs of impossibility, proofs of non-existence: ...
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Conjecture and Proof. LACZKOVICH Miklós. Témakör: Original editions in English. ISBN-13 978-963-7546-89-1. 100 oldal, B/5. Ára 3400 HUF ...
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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. ...
link.aps.org/ doi/ 10.1103/ PhysRevE.69.046104