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Transition to Advanced Mathematics

ISBN-10: 0534399002
ISBN-13: 9780534399009
Edition: 6th 2006
List price: $215.95
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Description: TRANSITION TO ADVANCED MATHEMATICS bridges the gap between calculus and advanced math in at least three ways. First, it guides students to think precisely and to express themselves mathematically?to analyze a situation, extract pertinent facts, and  More...

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Book details

List price: $215.95
Edition: 6th
Copyright year: 2006
Publisher: Brooks/Cole
Publication date: 6/14/2005
Binding: Hardcover
Pages: 384
Size: 7.50" wide x 9.25" long x 1.00" tall
Weight: 1.584
Language: English

TRANSITION TO ADVANCED MATHEMATICS bridges the gap between calculus and advanced math in at least three ways. First, it guides students to think precisely and to express themselves mathematically?to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Second, it provides a firm foundation of the basic concepts and methods needed for continued work. Finally, it provides introductions to concepts of modern algebra and analysis in sufficient depth to capture some of their spirit and characteristics. The text will improve the student's ability to think and write in a mature mathematical fashion and provide a solid understanding of the material most useful for advanced courses.

Logic And Proofs
Propositions and Connectives
Conditionals and Biconditionals
Quantifiers
Basic Proof Methods I
Basic Proof Methods II
Proofs Involving Quantifiers
Additional Examples of Proofs (optional)
Set Theory
Basic Notions of Set Theory
Set Operations
Extended Set Operations and Indexed Families of Sets
Induction
Equivalent Forms of Induction
Principles of Counting (optional)
Relations
Cartesian Products and Relations
Equivalence Relations
Partitions
Ordering Relations (optional)
Graphs of Relations (optional)
Functions
Functions as Relations
Constructions of Functions
Functions That Are Onto; One-to-One Functions
Induced Set Functions
Sequences as Functions (optional)
Cardinality
Equivalent Sets; Finite Sets
Infinite Sets
Countable Sets
The Ordering of Cardinal Numbers
Comparability of Cardinal Numbers and the Axiom of Choice (optional)
Concepts Of Algebra: Groups (Optional)
Algebraic Structures
Groups
Examples of Groups
Subgroups
Concepts Of Analysis: Completeness Of The Real Numbers (optional)
Ordered Field Properties of the Real Numbers
The Heine-Borel Theorem
The Bolzano-Weierstrass Theorem
The Bounded Monotone Sequence Theorem
Equivalents of Completeness
Answers to Exercises
Index
List of Symbols

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