Discrete Mathematics with Combinatorics, 1/e
James Anderson, University of South Carolina, Spartanburg
Coming March, 2000 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 864 pp.
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Discrete Mathematics-Computer Science
For freshman-level, one- or two-semester courses in Discrete
This carefully organized, very readable text covers every
essential topic in discrete mathematics in a logical fashion. Placing
each topic in context, it covers concepts associated with discrete
mathematical systems that have applications in computer science, engineering,
and mathematics. The author introduces more basic concepts at the
freshman level than are found in other texts, in a simple, accessible
form. Introductory material is balanced with extensive coverage of
graphs, trees, recursion, algebra, theory of computing, and combinatorics.
Extensive examples throughout the text reinforce concepts.
More combinatorics/algebraic structures than in
Detailed discussion of and strong emphasis on proofs.
- Removes the necessity of having to go on to take a
separate combinatorics course.
Extensive, in-depth presentation of topics.
- Helps students understand this essential topic, encouraging
them to develop mathematical maturity.
All key ideas grouped together in the first six chapters
(unique to this market).
- Enables instructors to select the topics that best
meet their goals for the course with plenty of material available.
Large selection of applied and computational problemsRanging
from the elementary to the more advanced. More topics in probability
and more statistical interpretations than other texts.
- Introduces students to important concepts early; also
facilitates a one semester course.
Comprehensive discussion of topics such as finite
state machines, automata, and languagesAlso addresses groups,
monoids, lattices, Polish notation, and Karnaugh maps.
- Helps students with other topics they will encounter
in computer science.
Earlier introduction of matrices and relations, Boolean
algebras and circuits than most texts.
Includes algorithms for many constructive tasks that
occur in discrete systems.
- Helps facilitate the use of the computer if so desired
by the professor.
1. Truth Tables, Propositional Logic, and Circuit Diagrams.
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.
3. Logic, Number Theory, and Proofs.
Predicate Calculus. Basic Concepts of Number Theory and
Proofs. Mathematical Induction. Divisibility. Prime Integers. Cardinals
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.
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
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 Context-free Languages. Turing machines. The Halting Problem for
11. Recursion Revisited.
Difference Equations. Homogeneous Linear Recurrence Relations.
Nonhomogeneous Linear Recurrence Relations. Generating Functions and