Includes bibliographical references and index.

Truth Tables, Logic, and Proofs -- Statements and Connectives -- Conditional Statements -- Equivalent Statements -- Axiomatic Systems: Arguments and Proofs -- Completeness in Propositional Logic -- Karnaugh Maps -- Circuit Diagrams -- Set Theory -- Introduction to Sets -- Set Operations -- Venn Diagrams -- Boolean Algebras -- Relations -- Partially Ordered Sets -- Equivalence Relations -- Logic, Integers, and Proofs -- Predicate Calculus -- Basic Concepts of Proofs and the Structure of Integers -- Mathematical Induction -- Divisibility -- Prime Integers -- Congruence Relations -- Functions and Matrices -- Functions -- Special Functions -- Matrices -- Cardinality -- Cardinals Continued -- Algorithms and Recursion -- The "for" Procedure and Algorithms for Matrices -- Recursive Functions and Algorithms -- Complexity of Algorithms -- Sorting Algorithms -- Prefix and Suffix Natation -- Binary and Hexadecimal Numbers -- Signed Numbers -- Matrices Continued -- Graphs, Directed Graphs, and Trees -- Graphs -- Directed Graphs -- Trees -- Instant Insanity -- Euler Paths and Cycles -- Incidence and Adjacency Matrices -- Hypercubes and Gray Code -- Number Theory -- Sieve of Eratosthenes -- Fermat's Factorization Method -- The Division and Euclidean Algorithms -- Continued Fractions -- Convergents -- Counting and Probability -- Basic Counting Principles -- Inclusion-Exclusion Introduced -- Permutations and Combinations -- Generating Permutations and Combinations -- Probability Introduced -- Generalized Permutations and Combinations -- Permutations and Combinations with Repetition -- Pigeonhole Principle -- Probability Revisited -- Bayes' Theorem -- Markov Chains -- Algebraic Structures -- Partially Ordered Sets Revisited -- Semigroups and Semilattices -- Lattices -- Groups -- Groups and Homomorphisms -- Number Theory Revisited -- Integral Solutions of Linear Equations -- Solutions of Congruence Equations -- Chinese Remainder Theorem -- Properties of the Function [phis] -- Order of an Integer -- Recursion Revisited -- Homogeneous Linear Recurrence Relations -- Nonhomogeneous Linear Recurrence Relations -- Finite Differences -- Factorial Polynomials -- Sums of Differences -- Counting Continued -- Occupancy Problems -- Catalan Numbers -- General Inclusion-Exclusion and Derangements -- Rook Polynomials and Forbidden Positions -- Generating Functions -- Definining the Generating Function (optional) -- Generating Functions and Recurrence Relations -- Generating Functions and Counting -- Partitions -- Exponential Generating Functions -- Graphs Revisited -- Algebraic Properties of Graphs -- Planar Graphs -- Coloring Graphs -- Hamiltonian Paths and Cycles -- Weighted Graphs and Shortest Path Algorithms -- Trees -- Properties of Trees -- Binary Search Trees -- Weighted Trees -- Traversing Binary Trees -- Spanning Trees -- Minimal Spanning Trees -- Networks -- Networks and Flows -- Matching -- Petri Nets -- Theory of Computation -- Regular Languages -- Automata -- Grammars -- Theory of Codes -- Generator Matrices -- Hamming Codes -- Enumeration of Colors -- Burnside's Theorm -- Polya's Theorem -- Rings, Integral Domains, and Fields -- Rings and Integral Domains -- Integral Domains -- Polynomials -- Algebra and Polynomials -- Group and Semigroup Characters -- Complex Numbers -- Group Characters -- Semigroup Characters -- Applications of Number Theory -- Application: Pattern Matching -- Application: Hashing Functions -- Application: Cryptography.