Transition to Advanced Mathematics

Name: Transition to Advanced Mathematics
Price: 72.0 USD
Availability: InStock
ISBN: 9780534399009

ISBN-10: 0534399002

ISBN-13: 9780534399009

Edition: 6th 2006

Authors: Douglas Smith, Maurice Eggen, Richard St Andre

List price: $215.95

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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…

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: 1.892
Language: English




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