Subject Code:53022 L:3 T/P/D:1 Credits:3 Int. Marks:25 Ext. Marks:75 Total Marks:100
UNIT I: I
Mathematical Logic : Statements and notations, Connectives, Well formed formulas, Truth Tables, tautology, equivalence implication, Normal forms.
UNIT II: II
Predicates : Predicative logic, Free & Bound variables, Rules of inference, Consistency, proof of contradiction, Automatic Theorem Proving.
UNIT III: III
Relations: Properties of binary Relations, equivalence, compatibility and partial ordering relations, Hasse diagram. Functions: Inverse Function Comports of functions, recursive Functions, Lattice and its Properties, .
UNIT IV: IV
Algebraic structures : Algebraic systems Examples and general properties, Semi groups and monads, groups sub groups� homomorphism, Isomorphism.
UNIT V: V
Elementary Combinatorics: Basis of counting, Combinations & Permutations, with repetitions, Constrained repetitions, Binomial Coefficients, Binomial Multinomial theorems, the principles of Inclusion � Exclusion. Pigeon hole principles and its application
UNIT VI: VI
Recurrence Relation : Generating Functions, Function of Sequences Calculating Coefficient of generating function, Recurrence relations, Solving recurrence relation by substitution and Generating funds. Characteristics roots solution of In homogeneous Recurrence Relation.
UNIT VII: VII
Graph Theory : Representation of Graph, DFS, BFS, Spanning Trees, planar Graphs
UNIT VIII: VIII
Graph Theory and Applications, Basic Concepts Isomorphism and Sub graphs, Multi graphs and Euler circuits, Hamiltonian graphs, Chromatic Numbers
TEXT BOOKS:
1. Elements of DISCRETE MATHEMATICS-A computer oriented approach CL Liu, d p nohapatra, 3rd ed TMH
2. Discrete mathematics for computer scientists & mathematicians JL Mott, A Kandel, TP Baker PHI.
REFERENCE BOOKS:
1. Discrete Mathematics with Applications, Thomas Koshy, Elsevier
2. Discrete Mathematical Structures, Bernand Kolman, Roberty C. Busby, Sharn Cutter Ross, Pearson Education/PHI.
3. Discrete Mathematical structures Theory and application-Malik & Sen
4. Discrete Mathematics for Computer science, Garry Haggard and others, Thomson.