MTL 180 : Discrete Mathematical Structures
MTL 180 : Discrete Mathematical Structures
Logic: Propositional logic & Truth Tables; Propositional Equivalences & Applications to Switching Circuits; Predicates and Quantifiers; Nested Quantifiers; Rules of Inference; Methods of Proofs.
Set Theory: Relations on sets; Equivalence relations & partitioning of sets; Posets, Boolean Lattices & Boolean Algebras; Equivalence between infinite sets; Cantor’s diagonalization.
Number Theory: Divisibility; gcd & lcm; Primes; Congruences - basic properties; theorems of Fermat, Euler & Wilson; Linear congruences; Chinese Remainder theorem; RSA cryptosystem.
Algebra: Groups - basic definition & examples; Subgroups; Lagrange’s theorem; Cyclic groups; Normality & Quotient groups; Isomorphism theorem.
Combinatorics: Basic counting principles; Counting selections with and without order and with or without replacement; Principle of Inclusion & Exclusion; Some important rules - Parity Principle, Invariance Principle & Pigeonhole Principle; Recurrences - basic definitions & examples; Methods for solving recurrences; Generating functions.
Graph Theory: Basic definitions & examples, Degree sequences, Trees, Eulerian & Hamiltonian graphs, Connectivity, Planarity, Matchings, Colorings.