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UNIT I LOGIC AND PROOFS

1.1 Propositional Logic

1.2 Propositional equivalences

1.3 Predicates and Quantifiers, Nested Quantifiers

1.4 Rules of inference

1.5 Introduction to proofs, Proof methods and strategy.

UNIT II COMBINATORICS

2.1 Mathematical induction

2.2 Strong induction and well ordering

2.3 The basics of counting

2.4 The pigeonhole principle

2.5 Permutations and combinations

2.6 Recurrence relations

2.7 Solving linear recurrence relations Generating functions

2.8 Inclusion and exclusion principle and its applications.

UNIT III GRAPHS

3.1 Graphs and graph models

3.2 Graph terminology

3.3 Special types of graphs

3.4 Matrix representation of graphs

3.5 Matrix representation of graph isomorphism

3.6 Connectivity

3.7 Euler and Hamilton paths

UNIT IV ALGEBRAIC STRUCTURES

4.1 Algebraic systems

4.2 Semi groups and monoids

4.3 Groups

4.4 Subgroups

4.5 Homomorphism’s

4.6 Normal subgroup and cosets

4.7 Lagrange’s theorem

4.8 Definitions and examples of Rings and Fields.

UNIT V LATTICES AND BOOLEAN ALGEBRA

5.1 Partial ordering

5.2 Posets

5.3 Lattices as posets, Properties of lattices,Lattices as algebraic systems Sub lattices

5.4 Direct product and homomorphism

5.5 Some special lattices

5.6 Boolean algebra.