Transition to Advanced Mathematics

ISBN-10: 0495562025
ISBN-13: 9780495562023
Edition: 7th 2011
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Book details

List price: $278.95
Edition: 7th
Copyright year: 2011
Publisher: Brooks/Cole
Publication date: 6/1/2010
Binding: Hardcover
Pages: 416
Size: 7.50" wide x 9.75" long x 1.00" tall
Weight: 2.002
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
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
Relations And Partitions
Relations
Equivalence Relations
Partitions
Ordering Relations
Graphs
Functions
Functions as Relations
Constructions of Functions
Functions That Are Onto
One-to-One Functions
One-to-One Correspondences and Inverse Functions
Images of Sets.
Sequences
Cardinality
Equivalent Sets
Finite Sets
Infinite Sets
Countable Sets
The Ordering of Cardinal Numbers
Comparability of Cardinal Numbers and the Axiom of Choice
Concepts Of Algebra: Groups
Algebraic Structures
Groups
Subgroups
Operation Preserving Maps
Rings and Fields
Concepts Of Analysis: Completeness Of The Real Numbers
Ordered Field Properties of the Real Numbers
The Heine-Borel Theorem
The Bolzano-Weierstrass Theorem
The Bounded Monotone Sequence Theorem
Comparability of Cardinals and the Axiom of Choice

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