Unit-I
Set Theory: Introduction, Combination of sets, Multisets, Ordered pairs, Set Identities.
Relations: Definition, Operations on relations, Properties of relations, Composite Relations,
Equality of relations, Order of relations.
Functions: Definition, Classification of functions, Operations on functions, Recursively defined
functions.
Natural Numbers: Introduction, Mathematical Induction, Variants of Induction, Induction with
Nonzero Base cases.
Unit-II
Algebraic Structures: Definition, Groups, Subgroups and order, Cyclic Groups, Cosets, Lagrange's theorem,
Normal Subgroups, Permutation and Symmetric groups, Group Homomorphisms , Definition and elementary
properties of Rings and Fields, Integers Modulo n.
Unit-III
Partial order sets: Definition, Partial order sets, Combination of partial order sets, Hasse diagram.
Lattices: Definition, Properties of lattices – Bounded, Complemented, Modular and Complete
Lattice,Morphisms of lattices.
Boolean Algebra: Introduction, Axioms and Theorems of Boolean algebra, Algebraic manipulation of Boolean
expressions. Simplification of Boolean Functions, Karnaugh maps, Logic gates, Digital circuits and Boolean
algebra. Combinational and sequential Circuits
Unit-IV
Propositional Logic: Proposition, well formed formula, Truth tables, Tautology, Satisfiability,
Contradiction, Algebra of proposition, Theory of Inference ,Natural Deduction.
Predicate Logic: First order predicate, well formed formula of predicate, quantifiers, Inference
theory of predicate logic.
Unit-V
Trees : Definition, Binary tree, Binary tree traversal, Binary search tree.
Graphs: Definition and terminology, Representation of graphs, Multigraphs, Bipartite graphs,
Planar graphs, Isomorphism and Homeomorphism of graphs, Euler and Hamiltonian paths, Graph coloring .
Recurrence Relation & Generating function: Recursive definition of functions, Recursive
algorithms, Method of solving recurrences.
Combinatorics: Introduction, Counting Techniques, Pigeonhole Principle