9780534340285

A Transition to Advanced Mathematics

by ; ;
  • ISBN13:

    9780534340285

  • ISBN10:

    0534340288

  • Format: Hardcover
  • Copyright: 8/15/1997
  • Publisher: Brooks Cole
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Table of Contents

Logic and Proofs
1(58)
Propositions and Connectives
1(8)
Conditionals and Biconditionals
9(9)
Quantifiers
18(8)
Mathematical Proofs
26(14)
Proofs Involving Quantifiers
40(9)
Additional Examples of Proofs
49(10)
Set Theory
59(56)
Basic Notions of Set Theory
59(8)
Set Operations
67(7)
Extended Set Operations and Indexed Families of Sets
74(11)
Induction
85(12)
Equivalent Forms of Induction
97(7)
Principles of Counting
104(11)
Relations
115(46)
Cartesian Products and Relations
115(13)
Equivalence Relations
128(8)
Partitions
136(5)
Ordering Relations
141(10)
Graphs of Relations
151(10)
Functions
161(34)
Functions as Relations
161(10)
Constructions of Functions
171(8)
Functions That Are Onto; One-to-One Functions
179(9)
Induced Set Functions
188(7)
Cardinality
195(38)
Equivalent Sets; Finite Sets
195(8)
Infinite Sets
203(6)
Countable Sets
209(9)
The Ordering of Cardinal Numbers
218(8)
Comparability of Cardinal Numbers and the Axiom of Choice
226(7)
Concepts of Algebra: Groups
233(40)
Algebraic Structures
233(8)
Groups
241(5)
Examples of Groups
246(5)
Subgroups
251(7)
Cosets and Lagrange's Theorem
258(4)
Quotient Groups
262(4)
Isomorphism; The Fundamental Theorem of Group Homomorphisms
266(7)
Concepts of Analysis: Completeness of the Real Numbers
273(34)
Ordered Field Properties of the Real Numbers
273(7)
The Heine-Borel Theorem
280(10)
The Bolzano-Weierstrass Theorem
290(4)
The Bounded Monotone Sequence Theorem
294(9)
Equivalents of Completeness
303(4)
Answers to Selected Exercises 307(30)
Index 337(6)
List of Symbols 343

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