Textbook in PDF format

Susanna Epp's "Discrete Mathematics with Applications" provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.

Speaking Mathematically Variables The Language of Sets The Language of Relations and Functions The Language of Graphs The Logic of Compound Statements Logical Form and Logical Equivalence Conditional Statements Valid and Invalid Arguments Application: Digital Logic Circuits Application: Number Systems and Circuits for Addition 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: Writing Advice Direct Proof and Counterexample III: Rational Numbers Direct Proof and Counterexample IV: Divisibility Direct Proof and Counterexample V: Division into Cases and the Quotient-Remainder Theorem Direct Proof and Counterexample VI: Floor and Ceiling Indirect Argument: Contradiction and Contraposition Indirect Argument: Two Famous Theorems Application: The Handshake Theorem Application: Algorithms Sequences, Mathematical Induction, and Recursion Sequences Mathematical Induction I: Proving Formulas Mathematical Induction II: Applications Strong Mathematical Induction and the Well-Ordering Principle for the Integers Application: Correctness of Algorithms Defining Sequences Recursively Solving Recurrence Relations by Iteration Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients General Recursive Definitions and Structural Induction Set Theory Set Theory: Definitions and the Element Method of Proof Properties of Sets Disproofs and Algebraic Proofs Boolean Algebras, Russell’s Paradox, and the Halting Problem Properties of Functions Functions Defined on General Sets One-to-One, Onto, and Inverse Functions Composition of Functions Cardinality with Applications to Computability Properties of Relations Relations on Sets Reflexivity, Symmetry, and Transitivity Equivalence Relations Modular Arithmetic with Applications to Cryptography Partial Order Relations Counting and Probability Introduction to Probability Possibility Trees and the Multiplication Rule Counting Elements of Disjoint Sets: The Addition Rule The Pigeonhole Principle Counting Subsets of a Set: Combinations r-Combinations with Repetition Allowed Pascal’s Formula and the Binomial Theorem Probability Axioms and Expected Value Conditional Probability, Bayes’ Formula, and Independent Events Theory of graphs and Trees 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 Analysis of Algorithm Efficiency Real-Valued Functions of a Real Variable and Their Graphs Big-O, Big-Omega, and Big-Theta Notations Application: Analysis of Algorithm Efficiency I Exponential and Logarithmic Functions: Graphs and Orders Application: Analysis of Algorithm Efficiency II Regular Expressions and Finite-State Automata Formal Languages and Regular Expressions Finite-State Automata Simplifying Finite-State Automata Appendix A: Properties of the real Numbersp Appendix B: Solutions and Hints to Selected Exercises