
Discrete Mathematics with Combinatorics, 1/e
James Anderson, University of South Carolina, Spartanburg Coming March, 2000 by Prentice Hall Engineering/Science/Mathematics
 
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Earlier introduction of matrices and relations, Boolean algebras and circuits than most texts. Includes algorithms for many constructive tasks that occur in discrete systems.
Statements and Connectives. Conditional Statements. Equivalent Statements. Introduction to Axiomatic Systems; Arguments. Completeness in Propositional Logic. Karnaugh Maps. Circuit Diagrams. 2. Set Theory. Introduction to Sets. Set Operations. Venn Diagrams. Boolean Algebras. Relations. Graphs. Directed Graphs. Trees. Partially Ordered Sets. Equivalence Relations. Congruence. Functions. Special Functions. Matrices. Cardinality. 3. Logic, Number Theory, and Proofs. Predicate Calculus. Basic Concepts of Number Theory and Proofs. Mathematical Induction. Divisibility. Prime Integers. Cardinals Revisited. 4. Algorithms and Recursion. The “for” Procedure and Algorithms for Matrix Operations. Prefix and Postfix Notation. Recursive Functions and Algorithms. Complexity of Algorithms. Binary and Hexadecimal Numbers. Signed Numbers. 5. Algorithms in Number Theory. Sieve of Eratosthemes. Fermat's Factorization Method. The Division and Euclidean Algorithms. Integral Solutions of Linear Wquations. Solutions of Congruence Equations. Chinese Remainder Theorem. 6. Counting and Probability. Basic Counting Principles. Permutations, Words, and Arrangements. Combinations and Partitions. Probability. Conditional Probability. Discrete Probability. 7. Graphs Revisited. Special Problems and Graphs. Euler paths and Cycles. Incidence and Adjacency Matrices. Algebraic Properties of Graphs. Planar Graphs. Coloring Graphs. Hamiltonian Graphs. Weighted Graphs and Shortest Path Algorithms. 8. Trees Revisited. Properties of Trees. Binary Search Trees. Weighted Trees. Traversing Binary Trees. Spanning Trees. Minimal Spanning Trees. 9. Algebraic Structures. Partially Ordered Sets Revisited. Semigroups and Semilattices. Lattices. Boolean Algebras. Groups. Rings. Integral Domains. Fields. 10. Theory of Computations. Regular Languages. Automata. Minimal Deterministic Automata and Syntactic Monoids. Kleene's Theorem. Grammars. Pushdown Automata and Contextfree Languages. Turing machines. The Halting Problem for Turing Machines. 11. Recursion Revisited. Difference Equations. Homogeneous Linear Recurrence Relations. Nonhomogeneous Linear Recurrence Relations. Generating Functions and Recurrence Relations.
