The Mathematics of Infinity
A Guide to Great Ideas
(Sprache: Englisch)
The Mathematics of Infinity addresses infinite cardinals and is appropriate for readers at any level. Inviting the reader to imagine constructing an infinite chain infinities, which are called cardinals, the author successfully prepares and motivates...
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Klappentext zu „The Mathematics of Infinity “
The Mathematics of Infinity addresses infinite cardinals and is appropriate for readers at any level. Inviting the reader to imagine constructing an infinite chain infinities, which are called cardinals, the author successfully prepares and motivates readers for topics covered within the book. The most unique feature of the book is that set theoretic depth is achieved without losing the target audience. Complementing existing popular books on infinity by actually doing the mathematics involved in addition to talking about the mathematics, the reader is gently led into the world of mathematical proofs.
Inhaltsverzeichnis zu „The Mathematics of Infinity “
Preface.1. Elementary Set Theory.
1.1 Sets.
1.2 Cartesian Products.
1.3 Power Sets.
1.4 Something From Nothing.
1.5 Indexed Families of Sets.
2. Functions.
2.1 Functional Preliminaries.
2.2 Images and Preimages.
2.3 One-to-one and Onto .
2.4 Bijections.
2.5 Inverse Functions.
3. Counting Infinite Sets.
3.1 Finite Sets.
3.2 Hilbert's Infinite Hotel.
3.3 Equivalent Sets and Cardinality.
4. Infinite Cardinals.
4.1 Countable Sets.
4.2 Uncountable Sets.
4.3 Two Infinities.
4.4 Power Sets.
4.5 The Arithmetic of Cardinals.
5. Well Ordered Sets.
5.1 Successors of Elements.
5.2 The Arithmetic of Ordinals.
5.4 Magnitude versus Cardinality.
6. Inductions and Numbers.
6.1 Mathematical Induction.
6.2 Transfinite Induction.
6.3 Mathematical Recursion .
6.4 Number Theory.
6.5 The Fundamental Theorem of Arithmetic.
6.6 Perfect Numbers.
7. Prime Numbers.
7.1 Prime Number Generators.
7.2 The Prime Number Theorem.
7.3 Products of Geometric Series.
7.4 The Riernann Zeta Function.
7.5 Real Numbers.
8. Logic and Meta-Mathematics.
8.1 The Collectionof All Sets.
8.2 Other Than True or False.
Bibliography.
Index.
Autoren-Porträt von Theodore G. Faticoni
Theodore G. Faticoni, PhD, is Professor in the Dept. of Mathematics at Fordham University. He received his PhD in Mathematics from the Univ. of Connecticut in 1981. His professional experience includes 30 research papers in peer reviewed journals and 30 lectures on his research to his colleagues.
Bibliographische Angaben
- Autor: Theodore G. Faticoni
- 2006, 287 Seiten, Maße: 24,5 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 0471794325
- ISBN-13: 9780471794325
Sprache:
Englisch
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