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Discrete Mathematics with Combinatorics

ISBN-10: 0130869988
ISBN-13: 9780130869982
Edition: 2001
List price: $112.00
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Description: For freshman-level, one- or two-semester 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  More...

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Book details

List price: $112.00
Copyright year: 2001
Publisher: Prentice Hall PTR
Publication date: 7/20/2000
Binding: Hardcover
Pages: 799
Size: 8.31" wide x 9.53" long x 1.42" tall
Weight: 3.674
Language: English

For freshman-level, one- or two-semester 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.

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
Partially Ordered Sets
Equivalence Relations
Logic, Integers, and Proofs
Predicate Calculus
Basic Concepts of Proofs and the Structure of Integers
Mathematical Induction
Prime Integers
Congruence Relations
Functions and Matrices
Special Functions
Cardinals Continued
Algorithms and Recursion
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, and Trees
Directed Graphs
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
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
Groups and Homomorphisms
Number Theory Revisited
Integral Solutions of Linear Equations
Solutions of Congruence Equations
Chinese Remainder Theorem
Properties of the Function
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
Defining the Generating Function (optional)
Generating Functions and Recurrence Relations
Generating Functions and Counting
Exponential Generating Functions
Graphs Revisited
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
Petri Nets
Theory of Computation
Regular Languages
Theory of Codes
Generator Matrices
Hamming Codes
Enumeration of Colors
Burnside's Theorem
Polya's Theorem
Rings, Integral Domains, and Fields
Rings and Integral Domains
Integral Domains
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

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