Transition to Advanced Mathematics

Name: Transition to Advanced Mathematics
Price: 6.75 USD
Availability: InStock
ISBN: 9780534382148

ISBN-10: 0534382142

ISBN-13: 9780534382148

Edition: 5th 2001

Authors: Douglas Smith, Maurice Eggen, Richard St. Andre

List price: $113.95

30 day, 100% satisfaction guarantee!

Marketplace

3 new & used from $6.75

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

Successfully addressing the frustration many students feel as they make the transition from beginning calculus to a more rigorous level of mathematics, A Transition to Advanced Mathematics provides a firm foundation in the major ideas needed for continued work in the discipline. The authors guide students to think and to express themselves mathematically--to analyze a situation, extract pertinent facts, and draw appropriate conclusions. With their proven approach, Smith, Eggen, and St. Andre introduce students to rigorous thinking about sets, relations, functions and cardinality. The text also includes introductions to modern algebra and analysis with sufficient depth to capture some of…

Book details

List price: $113.95
Edition: 5th
Copyright year: 2001
Publisher: Brooks/Cole
Publication date: 1/12/2001
Binding: Hardcover
Pages: 368
Size: 7.75" wide x 9.75" long x 0.75" tall
Weight: 1.892
Language: English

Logic and Proofs	p. 1
Propositions and Connectives	p. 1
Conditionals and Biconditionals	p. 9
Quantifiers	p. 18
Basic Proof Methods I	p. 26
Basic Proof Methods II	p. 37
Proofs Involving Quantifiers	p. 44
Additional Examples of Proofs	p. 53
Set Theory	p. 65
Basic Notions of Set Theory	p. 65
Set Operations	p. 73
Extended Set Operations and Indexed Families of Sets	p. 80
Induction	p. 91
Equivalent Forms of Induction	p. 103
Principles of Counting	p. 111
Relations	p. 123
Cartesian Products and Relations	p. 123
Equivalence Relations	p. 138
Partitions	p. 146
Ordering Relations	p. 151
Graphs of Relations	p. 161
Functions	p. 171
Functions as Relations	p. 171
Constructions of Functions	p. 181
Functions That Are Onto; One-to-One Functions	p. 190
Induced Set Functions	p. 200
Cardinality	p. 207
Equivalent Sets; Finite Sets	p. 207
Infinite Sets	p. 215
Countable Sets	p. 221
The Ordering of Cardinal Numbers	p. 230
Comparability of Cardinal Numbers and the Axiom of Choice	p. 238
Concepts of Algebra: Groups	p. 245
Algebraic Structures	p. 245
Groups	p. 253
Examples of Groups	p. 258
Subgroups	p. 263
Cosets and Lagrange's Theorem	p. 270
Quotient Groups	p. 274
Isomorphism; The Fundamental Theorem of Group Homomorphisms	p. 278
Concepts of Analysis: Completeness of the Real Numbers	p. 285
Ordered Field Properties of the Real Numbers	p. 286
The Heine-Borel Theorem	p. 293
The Bolzano-Weierstrass Theorem	p. 303
The Bounded Monotone Sequence Theorem	p. 307
Equivalents of Completeness	p. 316
Answers to Selected Exercises	p. 321
Index	p. 353
List of Symbols	p. 361
Table of Contents provided by Syndetics. All Rights Reserved.