Foundations of Mathematics

ISBN-10: 0470085010
ISBN-13: 9780470085011
Edition: 2009
Authors: Thomas Q. Sibley
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Description: Finally there's an easy-to-follow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Key definitions are introduced while readers  More...

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Book details

List price: $218.95
Copyright year: 2009
Publisher: John Wiley & Sons, Incorporated
Publication date: 4/7/2008
Binding: Hardcover
Pages: 408
Size: 6.50" wide x 9.25" long x 1.00" tall
Weight: 2.156
Language: English

Finally there's an easy-to-follow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Key definitions are introduced while readers are encouraged to develop an intuition about these concepts and practice using them in problems. With this approach, they'll gain a strong understanding of the mathematical language as they discover how to apply it in order to find proofs.

Preface
Part I
Language, Logic, and Sets
Logic and Language
Implication
Quantifiers and Definitions
Introduction to Sets
Introduction to Number Theory
Additional Set Theory
Definitions from Chapter 1
Algebraic and Order Properties of Number Systems
Proofs
Proof Format I: Direct Proofs
Proof Format II: Contrapositive and Contradiction
Proof Format III: Existence, Uniqueness, Or
Proof Format IV: Mathematical Induction
The Fundamental Theorem of Arithmetic
Further Advice and Practice in Proving
Proof Formats
Functions
Definitions, Notation, and Examples
Composition, One-to-One, Onto, and Inverses
Images and Pre-Images of Sets
Definitions from Chapter 3
Relations
Relations
Equivalence Relations
Partitions and Equivalence Relations
Partial Orders
Definitions from Chapter 4
Part II
Infinite Sets
The Sizes of Sets
Countable Sets
Uncountable Sets
The Axiom of Choice and Its Equivalents
Definitions from Chapter 5
Introduction to Discrete Mathematics
Graph Theory
Trees and Algorithms
Counting Principles I
Counting Principles II
Definitions from Chapter 6
Introduction to Abstract Algebra
Operations and Properties
Groups
Groups in Geometry
Rings and Fields
Lattices
Homomorphisms
Definitions from Chapter 7
Introduction to Analysis
Real Numbers, Approximations, and Exact Values
Zeno's Paradoxes
Limits of Functions
Continuous Functions and Counterexamples
Counterexamples in Rational Analysis
Sequences and Series
Discrete Dynamical Systems
The Intermediate Value Theorem
Definitions for Chapter 8
Metamathematics and the Philosophy of Mathematics
Metamathematics
The Philosophy of Mathematics
Definitions for Chapter 9
The Greek Alphabet
Answers: Selected Answers
Index
List of Symbols

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