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Discrete Mathematics Introduction to Mathematical Reasoningby Epp, Susanna S.
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Table of Contents
|The Language of Sets|
|The Language of Relations and Functions|
|The Logic of Compound Statements|
|Logical Form and Logical Equivalence|
|Valid and Invalid Arguments|
|The Logic of Quantified Statements|
|Predicates and Quantified Statements I|
|Predicates and Quantified Statements II|
|Statements with Multiple Quantifiers|
|Arguments with Quantified Statements|
|Elementary Number Theory and Methods of Proof|
|Direct Proof and Counterexample I: Introduction|
|Direct Proof and Counterexample II: Rational Numbers|
|Direct Proof and Counterexample III: Divisibility|
|Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem|
|Indirect Argument: Contradiction and Contraposition|
|Indirect Argument: Two Classical Theorems|
|Sequences, Mathematical Induction, and Recursion|
|Mathematical Induction I|
|Strong Mathematical Induction and the Well-Ordering Principle|
|Defining Sequences Recursively|
|Solving Recurrence Relations by Iteration|
|Set Theory: Definitions and the Element Method of Proof|
|Disproofs and Algebraic Proofs|
|Boolean Algebras and Russell's Paradox|
|Properties of Functions|
|Functions Defined on General Sets|
|One-to-one, Onto, and Inverse Functions|
|Composition of Functions|
|Cardinality and Sizes of Infinity|
|Properties of Relations|
|Relations on Sets|
|Reflexivity, Symmetry, and Transitivity|
|Modular Arithmetic and Zn|
|The Euclidean Algorithm and Applications|
|Counting and Probability|
|The Multiplication Rule|
|Counting Elements of Disjoint Sets: The Addition Rule|
|The Pigeonhole Principle|
|Counting Subsets of a Set: Combinations|
|Pascal's Formula and the Binomial Theorem|
|Graphs and Trees|
|Graphs: An Introduction|
|Trails, Paths, and Circuits|
|Matrix Representations of Graphs|
|Isomorphisms of Graphs|
|Trees: Examples and Basic Properties|
|Table of Contents provided by Publisher. All Rights Reserved.|