Syllabus Discrete Mathematics - (MA3354) UNIT I LOGIC AND PROOFS Propositional logic - Propositional equivalences - Predicates and quantifiers - Nested quantifiers - Rules of inference - Introduction to proofs - Proof methods and strategy. (Chapter - 1) 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. (Chapter - 2) 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. (Chapter - 3) 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. (Chapter - 4) 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 - Sub Boolean Algebra - Boolean Homomorphism. (Chapter - 5)
