by James A Anderson (University of South Carolina Spartanburg)

In Stock

£33.99

Placing each topic in context, this text covers concepts associated with discrete mathematical systems that have applications in computer science, engineering, and mathematics. It introduces basic concepts and also covers graphs, trees, recursion, algebra, theory of computing, and combinatorics. It contains many examples to reinforce the concepts.

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**For one-/two- semester, freshman courses in Discrete Mathematics.**

**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.**

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Statements and Connectives. Conditional Statements. Equivalent Statements. Axiomatic Systems: Arguments and Proofs. Completeness in Propositional Logic. Karnaugh Maps. Circuit Diagrams.

Introduction to Sets. Set Operations. Venn Diagrams. Boolean Algebras. Relations. Partially Ordered Sets. Equivalence Relations. Functions.

Predicate Calculus. Basic Concepts of Proofs and the Structure of Integers. Mathematical Induction. Divisibility. Prime Integers. Congruence Relations.

Functions. Special Functions. Matrices. Cardinality. Cardinals Revisited.

The "for" Procedure and Algorithms for Matrices. Recursive Functions and Algorithms. Complexity of Algorithms. Sorting Algorithms. Prefix and Suffix Notation. Binary and Hexadecimal Numbers. Signed Numbers. Matrices Continued.

Graphs. Directed Graphs. Trees. Instant Insanity. Euler Paths and Cycles. Incidence and Adjacency Matrices. Hypercubes and Gray Code.

Sieve of Eratosthenes. Fermat's Factorization Method. The Division and Euclidean Algorithms. Continued Fractions. Convergents.

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.

Partially Ordered Sets Revisited. Semigroups and Semilattices. Lattices. Groups. Groups and Homomorphisms. Linear Algebra.

Integral Solutions of Linear Equations. Solutions of Congruence Equations. Chinese Remainder Theorem. Order of an Integer.

Homogeneous Linear Recurrence Relations. Nonhomogeneous Linear Recurrence Relations. Finite Differences. Factorial Polynomials. Sums of Differences.

Occupancy Problems. Catalan Numbers. General Inclusion-Exclusion and Derangements. Rook Polynomials and Forbidden Positions.

Defining the Generating Function (optional). Generating Functions and Recurrence Relations. Generating Functions and Counting. Partitions. Exponential Generating Functions.

Algebraic Properties of Graphs. Planar Graphs. Coloring Graphs. Hamiltonian Paths and Cycles. Weighted Graphs and Shortest Path Algorithms.

Properties of Trees. Binary Search Trees. Weighted Trees. Traversing Binary Trees. Spanning Trees. Minimal Spanning Trees.

Networks and Flows. Matching. Petri Nets.

Regular Languages. Automata. Finite State Machines with Output. Grammars. Turing Machines.

Introduction. Generator Matrices. Hamming Codes.

Burnside's Theorem. Polya's Theorem.

Rings and Integral Domains. Integral Domains. Polynomials. Algebra and Polynomials.

Complex Numbers. Group Characters. Semigroup Characters.

Application: Pattern Matching. Application: Hashing Functions. Application: Cryptography.

GOR002789519

Discrete Mathematics with Combinatorics by James A Anderson (University of South Carolina Spartanburg)

James A Anderson (University of South Carolina Spartanburg)

Used - Good

Paperback

Pearson Education (US)

2003-08-19

928

0130457914

9780130457912

N/A

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

The book has been read but remains in clean condition. All pages are intact and the cover is intact. Some minor wear to the spine.