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Application: Number Systems and Circuits for Addition. Predicates and Quantified Statements I. Predicates and Quantified Statements II. Statements with Multiple Quantifiers. Arguments with Quantified Statements. Direct Proof and Counterexample I: Introduction. Indirect Argument: Contradiction and Contraposition.
Indirect Argument: Two Famous Theorems. Application: Algorithms. Mathematical Induction I: Proving Formulas. Mathematical Induction II: Applications.
Application: Correctness of Algorithms. Defining Sequences Recursively. Solving Recurrence Relations by Iteration. General Recursive Definitions and Structural Induction. Properties of Sets. Disproofs and Algebraic Proofs. Functions Defined on General Sets. One-to-one, Onto, and Inverse Functions. Composition of Functions. Cardinality with Applications to Computability.
Relations on Sets. Reflexivity, Symmetry, and Transitivity. Equivalence Relations. Modular Arithmetic with Applications to Cryptography. Partial Order Relations. Possibility Trees and the Multiplication Rule. The Pigeonhole Principle. Counting Subsets of a Set: Combinations. Probability Axioms and Expected Value. Trails, Paths, and Circuits. Matrix Representations of Graphs. Isomorphisms of Graphs. Trees: Examples and Basic Properties.
Rooted Trees. Spanning Trees and a Shortest Path Algorithm. Application: Analysis of Algorithm Efficiency I. Exponential and Logarithmic Functions: Graphs and Orders. Formal Languages and Regular Expressions. Finite-State Automata. Simplifying Finite-State Automata.
Epp received her Ph. After initial research in commutative algebra, she became interested in cognitive issues associated with teaching analytical thinking and proof and published a number of articles related to this topic, one of which was chosen for inclusion in The Best Writing on Mathematics She has spoken widely on discrete mathematics and organized sessions at national meetings on discrete mathematics instruction.
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DISCRETE MATHEMATICS WITH APPLICATIONS, 3rd Edition by
Application: Number Systems and Circuits for Addition. Predicates and Quantified Statements I. Predicates and Quantified Statements II. Statements with Multiple Quantifiers. Arguments with Quantified Statements.
Discrete Mathematics with Applications by Susanna S. Epp - PDF free download eBook
Discrete Mathematics with Applications