Advanced Discrete Mathematics

Advanced Discrete Mathematics
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Advanced Discrete Mathematics

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Publisher: PHI Learning
ISBN: 9788120345898
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About The Book Advanced Discrete Mathematics
Book Summary:

Written in an accessible style, this text provides a complete coverage of discrete mathematics and its applications at an appropriate level of rigour.

The book discusses algebraic structures, mathematical logic, lattices, Boolean algebra, graph theory, automata theory, grammars and recurrence relations. It covers the important topics such as coding theory, Dijkstras shortest path algorithm, reverse polish notation, Warshalls algorithm, Mengers theorem, Turing machine, and LR(k) parsers, which form a part of the fundamental applications of discrete mathematics in computer science. In addition, Pigeonhole principle, ring homomorphism, field and integral domain, trees, network flows, languages, and recurrence relations. The text is supported with a large number of examples, worked-out problems and diagrams that help students understand the theoretical explanations.

The book is intended as a text for postgraduate students of mathematics, computer science, and computer applications. In addition, it will be extremely useful for the undergraduate students of computer science and engineering.


Table of Contents:
Preface
PART A: ALGEBRAIC STRUCTURE
Chapter 1 Preliminaries of Set Theory
Chapter 2 Relations and Functions
Chapter 3 Semigroup
Chapter 4 Monoid
Chapter 5 Group
Chapter 6 Ring Theory
PART B: MATHEMATICAL LOGIC
Chapter 7 Statement Calculus
Chapter 8 Predicate Calculus
PART C: LATTICE AND BOOLEAN STRUCTURE
Chapter 9 Lattice Theory
Chapter 10 Boolean Algebra
Chapter 11 Boolean Function Minimization
Chapter 12 Logic Gates and Circuit Design
PART D: GRAPH THEORY
Chapter 13 Directed and Undirected Graphs
Chapter 14 Planarity and Trees
Chapter 15 Graph Connectivity and Flow Network
PART E: AUTOMATA THEORY AND GRAMMAR
Chapter 16 Finite State Automaton
Chapter 17 Grammars and Languages
PART F: RECURRENCE RELATIONS
Chapter 18 Discrete Numeric Functions and Recurrence Relations
Symbols Bibliography Answers to Exercises Index