bridge to abstract math - mathematical proof and structures, 1st ed. - r. morash

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bridge to abstract math -  mathematical proof and structures, 1st ed. - r. morash

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  • Bridge to Abstract Mathematics - Mathematical Proof and Structures

    • Dedication

    • Preface

    • Contents

    • Book One - The Foundation: Sets, Logic, and Mathematical Argument

      • Chapter 1 Sets

        • 1.1 Basic Definitions and Notation

        • 1.2 Operations on Sets

        • 1.3 Algebraic Properties of Sets

        • 1.4 Theorems of Set Theory

        • 1.5 Counting Properties of Finite Sets (Optional)

        • Chapter 2 Logic, Part I: The Propositional Calculus

          • 2.1 Basic Concepts of the Propositional Calculus

          • 2.2 Tautology, Equivalence, the Conditional,and Biconditional and Biconditional

          • 2.3 Theorems of the Propositional Calculus

          • 2.4 Analysis of Arguments for Logical Validity, Part I (Optional)

          • Chapter 3 Logic, Part II: The Predicate Calculus

            • 3.1 Basic Concepts of the Predicate Calculus

            • 3.2 Quantification

            • 3.3 Theorems About Predicates in One Variable

            • 3.4 Quantification of Propositional Functions in Several Variables

            • 3.5 Analysis of Arguments for Logical Validity, Part I1 (Optional)

            • Chapter 4 Elementary Applications of Logic

              • 4.1 Applications of Logic to Set Theory-Some Proofs

              • 4.2 Infinite Unions and Intersections

              • 4.3 The Limit Concept (Optional)

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