# MA8351 – Discrete Mathematics – Regulation 2017 Syllabus

## MA8351 – SYLLABUS

### UNIT I LOGIC AND PROOFS

Propositional logic — Propositional equivalences — Predicates and quantifiers — Nested quantifiers — Rules of inference — Introduction to proofs — Proof methods and strategy.

### UNIT II COMBINATORICS

Mathematical induction — Strong induction and well ordering — The basics of counting — The pigeonhole principle — Permutations and combinations — Recurrence relations — Solving linear recurrence relations — Generating functions — Inclusion and exclusion principle and its applications

### UNIT III GRAPHS

Graphs and graph models — Graph terminology and special types of graphs — Matrix representation of graphs and graph isomorphism — Connectivity — Euler and Hamilton paths.

### UNIT IV ALGEBRAIC STRUCTURES

Algebraic systems — Semi groups and monoids — Groups — Subgroups — Homomorphism?s — Normal subgroup and cosets — Lagrange?s theorem — Definitions and examples of Rings and Fields.

### UNIT V LATTICES AND BOOLEAN ALGEBRA

Partial ordering — Posets — Lattices as posets — Properties of lattices — Lattices as algebraic systems — Sub lattices — Direct product and homomorphism — Some special lattices — Boolean algebra.