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Introduction to Mathematical Proofs A Transition

ISBN-10: 1420069551
ISBN-13: 9781420069556
Edition: 2009
Authors: Charles Roberts
List price: $109.95
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Description: Written for sophomore/junior level students, this textbook begins with formal proof reasoning and writing, providing an understanding of the underlying language of mathematics. The author then describes deductive mathematical systems where theorems  More...

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Book details

List price: $109.95
Copyright year: 2009
Publisher: CRC Press LLC
Publication date: 6/24/2009
Binding: Hardcover
Pages: 433
Size: 6.50" wide x 9.25" long x 1.00" tall
Weight: 1.628
Language: English

Written for sophomore/junior level students, this textbook begins with formal proof reasoning and writing, providing an understanding of the underlying language of mathematics. The author then describes deductive mathematical systems where theorems are proved using different mathematical techniques, allowing students to compare and contrast the methods. He covers the role of conjectures along with their proofs and disproof, followed by rational numbers and their properties. He then covers the method used for developing the system of real numbers from rational numbers. The book includes more than 75 examples and more than 600 problems. A solutions manual is available upon qualifying course adoptions.

Preface
Logic
Statements, Negation, and Compound Statements
Truth Tables and Logical Equivalences
Conditional and Biconditional Statements
Logical Arguments
Open Statements and Quantifiers
Chapter Review
Deductive Mathematical Systems and Proofs
Deductive Mathematical Systems
Mathematical Proofs
Techniques for Proving the Conditional Statement P → Q
Additional Proof Techniques
Conjectures, Proofs, and Disproofs
The System of Rational Numbers and the System of Real Numbers
Chapter Review
Set Theory
Sets and Subsets
Set Operations
Additional Set Operations
Generalized Set Union and Intersection
Chapter Review
Relations
Relations
The Order Relations <, &#8804;, >, &#8805;
Reflexive, Symmetric, Transitive, and Equivalence Relations
Equivalence Relations, Equivalence Classes, and Partitions
Chapter Review
Functions
Functions
Onto Functions, One-to-One Functions, and One-to-One Correspondences
Inverse of a Function
Images and Inverse Images of Sets
Chapter Review
Mathematical Induction
Mathematical Induction
The Well-Ordering Principle and the Fundamental Theorem of Arithmetic
Cardinalities of Sets
Finite Sets
Denumerable and Countable Sets
Uncountable Sets
Proofs from Real Analysis
Sequences
Limit Theorems for Sequences
Monotone Sequences and Subsequences
Cauchy Sequences
Proofs from Group Theory
Binary Operations and Algebraic Structures
Groups
Subgroups and Cyclic Groups
A Reading and Writing Mathematical Proofs
Answers to Selected Exercises
References
Index

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