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Mathematical reasoning : writing and proof / Ted Sundstrom

By: Sundstrom, Theodore A.
Publisher: Upper Saddle River, N.J. : Prentice Hall, c2003Description: xiv, 435 p. : ill. ; 24 cm.ISBN: 0130618152.Subject(s): Proof theoryDDC classification: 511.3
Contents:
Preface. - 1. Introduction to writing in mathematics. 1.1. Statements. 1.2. Constructing direct proofs. - 2. Logical reasoning. 2.1. Predicates, sets, and quantifiers. 2.2. Statements and logical operators. 2.3. Logically equivalent statements. 2.4. Quantifiers and negations. - 3. Constructing and writing proofs in mathematics. 3.1. Direct proofs. 3.2. More methods of proof. 3.3. Proof by contradiction. 3.4. Using cases in proofs. 3.5. Constructive proofs. - 4. Set theory. 4.1. Operations on sets. 4.2. Proving set relationships. 4.3. Properties of set operations. 4.4. Cartesian products. - 5. Mathematical induction. 5.1. The principle of mathematical induction. 5.2. Other forms of mathematical induction. 5.3. Induction and recursion. 6. Function. 6.1. Introduction to functions. 6.2. More about functions. 6.3. Types of functions. 6.4. Composition of functions. 6.5. Inverse functions. - 7. Equivalence relations. 7.1. Relations. 7.2. Equivalence relations. 7.3. Equivalence classes. 7.4. Modular arithmetic. - 8. Topics in number theory. 8.1. The greatest common divisor. 8.2. Prime numbers and prime factorizations. 8.3. Linear diophantine equations. - 9. Topics in set theory. 9. 1. Functions acting on sets. 9.2. Finite sets. 9.3. Countable sets. 9.4. Uncountable sets. - A guidelines for writing mathematical proofs. - B. Answers and hints for selected exercises. - C. List of symbols. - Index.
Item type Current location Shelf location Call number Copy number Status Notes Date due Barcode
Main Collection Taylor's Library-TU

Floor 4, Shelf 15 , Side 1, TierNo 4, BayNo 4

 511.3 SUN (Browse shelf) 1 Available SOCIT,15009,03,GR 5000030379

Preface. - 1. Introduction to writing in mathematics. 1.1. Statements. 1.2. Constructing direct proofs. - 2. Logical reasoning. 2.1. Predicates, sets, and quantifiers. 2.2. Statements and logical operators. 2.3. Logically equivalent statements. 2.4. Quantifiers and negations. - 3. Constructing and writing proofs in mathematics. 3.1. Direct proofs. 3.2. More methods of proof. 3.3. Proof by contradiction. 3.4. Using cases in proofs. 3.5. Constructive proofs. - 4. Set theory. 4.1. Operations on sets. 4.2. Proving set relationships. 4.3. Properties of set operations. 4.4. Cartesian products. - 5. Mathematical induction. 5.1. The principle of mathematical induction. 5.2. Other forms of mathematical induction. 5.3. Induction and recursion. 6. Function. 6.1. Introduction to functions. 6.2. More about functions. 6.3. Types of functions. 6.4. Composition of functions. 6.5. Inverse functions. - 7. Equivalence relations. 7.1. Relations. 7.2. Equivalence relations. 7.3. Equivalence classes. 7.4. Modular arithmetic. - 8. Topics in number theory. 8.1. The greatest common divisor. 8.2. Prime numbers and prime factorizations. 8.3. Linear diophantine equations. - 9. Topics in set theory. 9. 1. Functions acting on sets. 9.2. Finite sets. 9.3. Countable sets. 9.4. Uncountable sets. - A guidelines for writing mathematical proofs. - B. Answers and hints for selected exercises. - C. List of symbols. - Index.