Rosen K.H., Michaels J.G. et al. Handbook of Discrete and Combinatorial Mathematics



Rosen K.H., Michaels J.G. et al. Handbook of Discrete and Combinatorial Mathematics
31.01.2012 в 00:44 8.11 Мб djvu 20 раз
Crc press, 2000. - 1183 pages.

The Handbook of Discrete and Combinatorial Mathematics is the first book presenting a comprehensive collection of reference material for the essential areas of discrete mathematics as well as for important applications to computer science and engineering. Topics include logic and foundations, counting, number theory, abstract and linear algebra, probability, graph theory, networks and optimization, cryptography and coding, and combinatorial designs.

Foundations.
propositional and Predicate Logic.
Set Theory.
Functions.
Relations.
Proof Techniques.
Axiomatic Program Verification.
Logic-Based Computer Programming Paradigms.
Counting methods.
summary of Counting Problems.
Basic Counting Techniques.
Permutations and Combinations.
Inclusion/Exclusion.
Partitions.
Burnside Counting Formula.
Mobius Inversion Counting.
Young Tableaux.
Sequences.
special Sequences.
Generating Functions.
Recurrence Relations.
Finite Differences.
Finite Sums and Summation.
Asymptotics of Sequences.
Mechanical Summation Procedures.
Number theory.
basic Concepts.
Greatest Common Divisors.
Congruences.
Prime Numbers.
Factorization.
Arithmetic Functions.
Primitive Roots and Quadratic Residues.
Diophantine Equations.
Diophantine Approximation.
Quadratic Fields.
Algebraic structures.
algebraic Models.
Groups.
Permutation Groups.
Rings.
Polynomial Rings.
Fields.
Lattices.
Boolean Algebras.
Linear algebra.
vector Spaces.
Linear Transformations.
Matrix Algebra.
Linear Systems.
Eigenanalysis.
Combinatorial Matrix Theory.
Discrete probability.
fundamental Concepts.
Independence and Dependence.
Random Variables.
Discrete Probability Computations.
Random Walks.
System Reliability.
Discrete-'Rme Markov Chains.
Queueing Theory.
Simulation.
Graph theory.
introduction to Graphs.
Graph Models.
Directed Graphs.
Distance, Connectivity, Traversability.
Graph Invariants and Isomorphism Types.
Graph and Map Coloring.
Planar Drawings.
Topological Graph Theory.
Enumerating Graphs.
Algebraic Graph Theory.
Analytic Graph Theory.
Hypergraphs.
Trees.
characterizations and Types of Trees.
Spanning Trees.
Enumerating Trees.
Networks and flows.
minimum Spanning Trees.
Matchings.
Shortest Paths.
Maximum Flows.
Minimum Cost Flows.
Communication Networks.
Difficult Routing and Assignment Problems.
Network Representations and Data Structures.
Partially ordered sets.
basic Poset Concepts.
Poset Properties.
Combinatorial designs.
block Designs.
Symmetric Designs & Finite Geometries.
Latin Squares and Orthogonal Arrays.
Matroids.
Discrete and computational geometry.
arrangements of Geometric Objects.
Space Filling.
Combinatorial Geometry.
Polyhedra.
Algorithms and Complexity in Computational Geometry.
Geometric Data Structures and Searching.
Computational Techniques.
Applications of Geometry.
Coding theory and cryptology.
communication Systems and Information Theory.
Basics of Coding Theory.
Linear Codes.
Bounds for Codes.
Nonlinear Codes.
Convolutional Codes.
Basics of Cryptography.
Symmetric-Key Systems.
Public-Key Systems.
Discrete optimization.
linear Programming.
Location Theory.
Packing and Covering.
Activity Nets.
Game Theory.
Sperner's Lemma and Fixed Points.
Theoretical computer science.
computational Models.
Computability.
Languages and Grammars.
Algorithmic Complexity.
Complexity Classes.
Randomized Algorithms.
Information structures.
abstract Datatypes.
Concrete Data Structures.
Sorting and Searching.
Hashing.
Dynamic Graph Algorithms.
Biographies.
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