# GITAM University CS Mathematical Structures Syllabus

UNIT – I

Mathematical Logic & Predicates: Statements and notations, Connectives, Well formed formulas, Truth Tables, tautology, equivalence implication, Normal forms. Predicate logic, Free & Bound variables, Rules of inference, Consistency, proof of contradiction, Automatic Theorem Proving.

UNIT – II

Set Theory: Properties of binary Relations, equivalence, compatibility and partial ordering relations, Hasse diagram. Functions: Inverse Function, Composition of functions, recursive Functions, Lattice and its Properties, Pigeon hole principles and its application

UNIT – III

Algebraic structures: Algebraic systems Examples and general properties, Semi groups and monoids, groups, sub groups, homomorphism, Isomorphism.

UNIT – IV

Recurrence Relation: Generating Functions, Function of Sequences Calculating Coefficient of generating function, Recurrence relations, Solving recurrence relation by substitution and Generating functions. Characteristics roots solution of homogeneous Recurrence Relation.

UNIT – V

Graph Theory and Applications: Basic Concepts Isomorphism and Sub graphs, Multi graphs and Euler circuits, Hamiltonian graphs, Chromatic Numbers Representation of Graph, DFS, BFS, Spanning Trees, planar Graphs.

Text Books:

1.Discrete Mathematical Structures with applications to computer science Trembly J.P. & Manohar .P, TMH

2. Discrete and Combinational Mathematics- An Applied Introduction-5th Edition – Ralph. P.Grimaldi. and B.V.Ramana Pearson Education

3. Discrete Mathematics and its Applications, Kenneth H. Rosen, Fifth Edition.TMH.

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.

5. Discrete Mathematics for Computer Scientists & Mathematicians, J.L. Mott, A. Kandel, T.P.

Baker Prentice Hall.

6. Logic and Discrete Mathematics, Grass Man & Trembley, Person Education.