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Introduction to Advanced Mathematics : A Guide to Understanding Proofs

Introduction to Advanced Mathematics : A Guide to Understanding Proofs

ISBN 9780547165387
Edition 1
Publication Date
Publisher Cengage
Author(s)
Overview
1. LOGIC. Introduction and Terminology. Statements and Truth Tables. Logical Equivalence and Logical Deductions. The Contrapositive, Negation, and Converse of an Implication Statement. Quantifiers. 2. PROOF WRITING. Terminology and Goals. Existence Proofs and Counterexamples. Direct Proofs ('If, then' or 'For every' Statements). Using Cases in Proofs. Contrapositive Arguments. Contradiction Arguments. Putting it All Together. Regular Induction. Induction with Inequalities. Recursion and Extended Induction. Uniqueness Proofs, the WOP, and a Proof of the Division. Algorithm. 3. SETS, RELATIONS, AND FUNCTIONS. Sets. Set Operations. Set Theory. Indexed Families of Sets. Cartesian Products. Relations. Functions. Composition of Functions. Cardinality.
Overview
1. LOGIC. Introduction and Terminology. Statements and Truth Tables. Logical Equivalence and Logical Deductions. The Contrapositive, Negation, and Converse of an Implication Statement. Quantifiers. 2. PROOF WRITING. Terminology and Goals. Existence Proofs and Counterexamples. Direct Proofs ('If, then' or 'For every' Statements). Using Cases in Proofs. Contrapositive Arguments. Contradiction Arguments. Putting it All Together. Regular Induction. Induction with Inequalities. Recursion and Extended Induction. Uniqueness Proofs, the WOP, and a Proof of the Division. Algorithm. 3. SETS, RELATIONS, AND FUNCTIONS. Sets. Set Operations. Set Theory. Indexed Families of Sets. Cartesian Products. Relations. Functions. Composition of Functions. Cardinality.

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