Section A: Set Theory and Propositional Calculus:
Introduction to set theory, Set operations, Algebra of sets, Duality, Finite and Infinite sets,
Classes of sets, Power Sets, Multi sets, Cartesian Product, Representation of relations, Types
of relation, Equivalence relations and partitions , Partial ordering relations and lattices
Function and its types, Composition of function and relations, Cardinality and inverse
relations
Introduction to propositional Calculus: Basic operations: AND(^), OR(v), NOT(~), Truth
value of a compound statement, propositions, tautologies, contradictions.
Section B: Techniques of Counting and Recursion and recurrence Relation:
Permutations with and without repetition, Combination.Polynomials and their evaluation,
Sequences, Introduction to AP, GP and AG series, partial fractions, linear recurrence relation
with constant coefficients, Homogeneous solutions, Particular solutions, Total solution of a
recurrence relation using generating functions.
Section C: Algebric Structures
Definition and examples of a monoid, Semigroup, Groups and rings, Homomorphism,
Isomorphism and Automorphism, Subgroups and Normal subgroups, Cyclic groups, Integral
domain and fields, Cosets, Lagrange’s theorem
Section D: Section Graphs and Trees:
Introduction to graphs, Directed and Undirected graphs, Homomorphic and Isomorphic
graphs, Subgraphs, Cut points and Bridges, Multigraph and Weighted graph, Paths and
circuits, Shortest path in weighted graphs, Eurelian path and circuits, Hamilton paths and
circuits, Planar graphs, Euler’s formula, Trees, Spanning trees, Binary trees and its traversals