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Lackzovich M. — Conjecture and Proof
Lackzovich M. — Conjecture and Proof

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Название: Conjecture and Proof

Автор: Lackzovich M.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 118

Добавлена в каталог: 13.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\sigma$-additive measure      75
Additive function      33
Algebraic number      17
Axiom of Choice      75
Banach — Tarski paradox      82
Basis of a linear space      21
Borel set      97
Cantor function      88
Cantor set      87
Cantor — Bernstein — Schroeder — Banach theorem      64
Cardinality      62
Cauchy's functional equation      33
Closed set      87
Component of a set      85
Congruent sets      39
Constructible number      12
Countable set      59
Countably infinite set      61
Degree of a field extension      22
Degree of an algebraic number      18
Devil's staircase      88
Dimension of a linear space      22
Doubling the cube      11
Equidecomposable sets      81
Equidecomposable sets in the geometric sense      39
Equivalent sets      62
Euler's constant      1
Fermat numbers      17
Fibonacci sequence      52
Field      12
Field extension      22
Finite field extension      22
Fixed point of an isometry      67
Fundamental Theorem of Arithmetic      4
Generating system      21
Geometric construction      11
Glide reflection      69
Hamel basis      34
Hausdorff Paradox      77
Helical motion      71
Hyperplane      67
Interior of an interval      86
interval      85
Interval contiguous to a closed set      89
Irrational number      3
Isolated point of a set      89
Isometry      67
Isomorphism of fields      35
linear combination      21
Linear space      21
Linearly independent elements      21
Liouville number      57
Measure      75
Open set      86
Peano curve      93
Perfect set      89
Perpendicular bisector      67
Point of condensation      91
Points in general position      67
Rational number      3
Reflection about a hyperplane      67
Russell paradox      104
Sets of the power of the continuum      62
Sets of the same cardinality      62
Sets of the same power      62
Sidon sequence      49
Squaring the circle      11
Transcendental number      29
Trisection of angles      11
Uncountable set      59
Universal set      99
Vector space      21
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