Transition to Advanced Mathematics

ISBN-10: 0534382142
ISBN-13: 9780534382148
Edition: 5th 2001
List price: $113.95
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Description: 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  More...

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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: 1.826
Language: English

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 their spirit and characteristics.

Logic and Proofsp. 1
Propositions and Connectivesp. 1
Conditionals and Biconditionalsp. 9
Quantifiersp. 18
Basic Proof Methods Ip. 26
Basic Proof Methods IIp. 37
Proofs Involving Quantifiersp. 44
Additional Examples of Proofsp. 53
Set Theoryp. 65
Basic Notions of Set Theoryp. 65
Set Operationsp. 73
Extended Set Operations and Indexed Families of Setsp. 80
Inductionp. 91
Equivalent Forms of Inductionp. 103
Principles of Countingp. 111
Relationsp. 123
Cartesian Products and Relationsp. 123
Equivalence Relationsp. 138
Partitionsp. 146
Ordering Relationsp. 151
Graphs of Relationsp. 161
Functionsp. 171
Functions as Relationsp. 171
Constructions of Functionsp. 181
Functions That Are Onto; One-to-One Functionsp. 190
Induced Set Functionsp. 200
Cardinalityp. 207
Equivalent Sets; Finite Setsp. 207
Infinite Setsp. 215
Countable Setsp. 221
The Ordering of Cardinal Numbersp. 230
Comparability of Cardinal Numbers and the Axiom of Choicep. 238
Concepts of Algebra: Groupsp. 245
Algebraic Structuresp. 245
Groupsp. 253
Examples of Groupsp. 258
Subgroupsp. 263
Cosets and Lagrange's Theoremp. 270
Quotient Groupsp. 274
Isomorphism; The Fundamental Theorem of Group Homomorphismsp. 278
Concepts of Analysis: Completeness of the Real Numbersp. 285
Ordered Field Properties of the Real Numbersp. 286
The Heine-Borel Theoremp. 293
The Bolzano-Weierstrass Theoremp. 303
The Bounded Monotone Sequence Theoremp. 307
Equivalents of Completenessp. 316
Answers to Selected Exercisesp. 321
Indexp. 353
List of Symbolsp. 361
Table of Contents provided by Syndetics. All Rights Reserved.

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