Mathematical Reasoning : Writing and Proof,9780131877184

Mathematical Reasoning : Writing and Proof

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Edition: 2nd
ISBN13: 9780131877184
ISBN10: 0131877186
Format: Paperback
Pub. Date: 2006-03-13
Publisher(s): Pearson
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Summary

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with "Preview Activities" at the start of each section. Includes "Activities" throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom

Table of Contents

Preface ix
Introduction to Writing Proofs in Mathematics
1(28)
Conditional Statements
1(12)
Constructing Direct Proofs
13(13)
Solutions for the Progress Checks
26(1)
Summary
27(2)
Logical Reasoning
29(47)
Statements and Logical Operators
29(8)
Logically Equivalent Statements
37(10)
Predicates, Sets, and Quantifiers
47(11)
Quantifiers and Negations
58(13)
Solutions for the Progress Checks
71(3)
Summary
74(2)
Constructing and Writing Proofs in Mathematics
76(75)
Direct Proofs
76(17)
More Methods of Proof
93(14)
Proof by Contradiction
107(13)
Using Cases in Proofs
120(8)
The Division Algorithm and Congruence
128(14)
Solutions for the Progress Checks
142(4)
Summary
146(5)
Set Theory
151(67)
Operations on Sets
151(17)
Proving Set Relationships
168(12)
Properties of Set Operations
180(10)
Cartesian Products
190(9)
Indexed Families of Sets
199(12)
Solutions for the Progress Checks
211(4)
Summary
215(3)
Mathematical Induction
218(46)
The Principle of Mathematical Induction
218(17)
Other Forms of Mathematical Induction
235(13)
Induction and Recursion
248(11)
Solutions for the Progress Checks
259(2)
Summary
261(3)
Functions
264(85)
Introduction to Functions
264(14)
More about Functions
278(12)
Injections, Surjections, and Bijections
290(16)
Composition of Functions
306(11)
Inverse Functions
317(16)
Functions Acting on Sets
333(10)
Solutions for the Progress Checks
343(3)
Summary
346(3)
Equivalence Relations
349(50)
Relations
349(10)
Equivalence Relations
359(13)
Equivalence Classes
372(12)
Modular Arithmetic
384(11)
Solutions for the Progress Checks
395(2)
Summary
397(2)
Topics in Number Theory
399(38)
The Greatest Common Divisor
399(11)
Prime Numbers and Prime Factorizations
410(12)
Linear Diophantine Equations
422(9)
Solutions for the Progress Checks
431(4)
Summary
435(2)
Finite and Infinite Sets
437(38)
Finite Sets
437(9)
Countable Sets
446(13)
Uncountable Sets
459(11)
solutions for the Progress Checks
470(3)
Summary
473(2)
Guidelines for Writing Mathematical Proofs 475(5)
Answers and Hints for Selected Exercises 480(25)
List of Symbols 505(3)
Index 508

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