Second edition of the book “Discrete Mathematics and lts Applications” incorporates a variety of new and improved features. It is designed in a simple, comprehensive and students friendly way to meet the syllabus of B.E., M.E. (Computer SCience). BCA, MCA, M.Sc (Software Engineering, Computer Science) courses of various universities abd Engineering Colleges over India. Also it serves as a reference book for MCA course of Anna University.
Chapter I deals with the concepts of Sets, Counting principles like Pigeonhole principle Permutation, Combination, Mathematical Induction, Inclusion, Exclusion, Partitions and Minsets.
Chapter II discusses Relations, Closure Operations of Relations, Matrices and Graphs of Relations, Functions and its properties. In Chapter III the notion of Recursion and Recurrence Relations, Generating functions are introduced.
Chapter IV is devoted to logic. Mainly it deals with Inference Theory of both Propositional and Predicate Calculus.
Chapter V includes Algebraic Structures. The emphasis is on Semigroup, GroupP, Ring, Field theory which has application in Programming languages and Coding theory.
Chapter VI is concerned with Matrices, Algorithms and Integers. Chapter VII deals with Lattices and Boolean Algebra. Various methods like Karnaugh Map, Quine-McCluskel Algorithm are given to minimize the Boolean function. Applications to Switching Circuits, Fault Detection in Switching Circuits are also discussed.
Chapter VIII gives a detailed description of graphs and trees. Planarity, Coloring, Connectivity are presented with numerous examples. The problems like Network Optimization, Minimal Spanning Tree, Shortest Distance Problems are studied with algorithms.
In Chapter IX topics like Regular Expression, Regular Language, Context Free Language, Deterministic and non-deterministic Finite State Automata are discussed thoroughly.
Chapter X deals with Pushdown Automata and its related language. Turing machines both deterministic and non-deterministic, Multi tape and Multi-dimensional Turing machine, Recursive and Computable functions, Recursively Enumerable Languages, Primitive Recursive Predicates, Godel Number, Church Thesis, Halting Problem.
Chapter XI gives some basic ideas about Fuzzy Sets and Fuzzy Logic. Finally it also includes programming implementation of graph theory algorithms like Bubble Sort, Merge Sort, Heap Sort, BFs, DFS, Prim’s Algorithm. The content matter is presented in a very lucid and simple format. The concepts are exaplained in detail with illustrations, definitions, proofs, important theorems, examples and a variety of solved and unsolved problems. Many of the problems and examples have been selected from recent question papers of various engineering colleges and universities so as to make the reader familiar with the type of questions set therein.
The authors are indebted to many readers and the faculty members for their advice/ suggestions which had helped in preparing the book. Suggestions for the improvement of the text as well as intimation of misprints will be most greatfully received.
