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Pure and Applied Mathematics: A Wiley-Interscience Series of #80: The Mathematics of Infinity: A Guide to Great Ideas

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Pure and Applied Mathematics: A Wiley-Interscience Series of #80: The Mathematics of Infinity: A Guide to Great Ideas Cover

 

Synopses & Reviews

Publisher Comments:

A balanced and clearly explained treatment of infinity in mathematics.

The concept of infinity has fascinated and confused mankind for centuries with concepts and ideas that cause even seasoned mathematicians to wonder. For instance, the idea that a set is infinite if it is not a finite set is an elementary concept that jolts our common sense and imagination. the Mathematics of Infinity: A guide to Great Ideas uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing.

Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the book presents a user-friendly approach to ideas involving the infinite. readers will discover the main ideas of infinite cardinals and ordinal numbers without experiencing in-depth mathematical rigor. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun your intuitive view of the world.

With a thoughtful and balanced treatment of both concepts and theory, The Mathematics of Infinity focuses on the following topics:

  • Sets and Functions
  • Images and Preimages of Functions
  • Hilbert's Infinite Hotel
  • Cardinals and Ordinals
  • The Arithmetic of Cardinals and Ordinals
  • the Continuum Hypothesis
  • Elementary Number Theory
  • The Riemann Hypothesis
  • The Logic of Paradoxes

Recommended as recreational reading for the mathematically inquisitive or as supplemental reading for curious college students, the Mathematics of Infinity: A Guide to Great Ideas gently leads readers into the world of counterintuitive mathematics.

Book News Annotation:

Common sense abhors the very concept of infinity, but curiosity always brings us back. In this accessible treatment written for the mathematically inquisitive general reader or undergraduates, Faticoni (mathematics, Fordham U.) describes the uses of infinity as he explains elementary set theory, functions (including inverse functions), counting infinite sets (including Hilbert's Infinite Hotel), infinite Cardinals (including the two infinities), well-ordered sets (such as the arithmetic of ordinals and cardinals as ordinals), inductions and numbers, including number theory, prime numbers, including the Riemann Zeta function. Faticoni closes by describing logic and meta-mathematics.
Annotation 2006 Book News, Inc., Portland, OR (booknews.com)

Book News Annotation:

Common sense abhors the very concept of infinity, but curiosity always brings us back. In this accessible treatment written for the mathematically inquisitive general reader or undergraduates, Faticoni (mathematics, Fordham U.) describes the uses of infinity as he explains elementary set theory, functions (including inverse functions), counting infinite sets (including Hilbert's Infinite Hotel), infinite Cardinals (including the two infinities), well-ordered sets (such as the arithmetic of ordinals and cardinals as ordinals), inductions and numbers, including number theory, prime numbers, including the Riemann Zeta function. Faticoni closes by describing logic and meta-mathematics. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Recommended as recreational reading for the mathematically inquisitive or as supplemental reading for curious college students, the Mathematics of Infinity: A Guide to Great Ideas gently leads readers into the world of counterintuitive mathematics.

About the Author

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.

Table of Contents

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 Collection of All Sets.

8.2 Other Than True or False.

Bibliography.

Index.

Product Details

ISBN:
9780471794325
Subtitle:
A Guide to Great Ideas
Publisher:
Wiley-Interscience
Author:
Faticoni, Theodore G.
Author:
Cram101 Textbook Reviews
Subject:
Set Theory
Subject:
Infinity
Subject:
Infinite
Subject:
Mathematics - General
Subject:
Popular Interest Mathematics
Subject:
Education-General
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
Series Volume:
80
Publication Date:
20060630
Binding:
Online electronic file accessible through online networks
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Y
Pages:
304
Dimensions:
9.56x7.88x.81 in. 1.20 lbs.

Related Subjects

Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Set Theory

Pure and Applied Mathematics: A Wiley-Interscience Series of #80: The Mathematics of Infinity: A Guide to Great Ideas
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Product details 304 pages Wiley-Interscience - English 9780471794325 Reviews:
"Synopsis" by , Recommended as recreational reading for the mathematically inquisitive or as supplemental reading for curious college students, the Mathematics of Infinity: A Guide to Great Ideas gently leads readers into the world of counterintuitive mathematics.
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