Objectives
Outcomes
Unit – I
Set Theory And Logic - Sets, Functions, Relations, Equivalence Relation,Poset. Functions Logic: Propositional Logic, Truth Tables, Tautologies, Resolution Proof System, Predicate Logic.
Unit – II
Induction And Combinatorics - Peano's Axioms - Mathematical Induction - Pigeon-Hole Principle - Principle Of Inclusion And Exclusion - Review Of Permutations And Combinations - Distribution Problems - Derangements - Bijection Principle.
Unit – III
Algebraic Structures- Semi-Groups, Monoids, Groups, Subgroups And Their Properties -Cyclic Groups - Cosets - Permutation Groups - Lagrange's Theorem - Cayley's Theorem -Normal Subgroups - Homomorphism Of Groups - Quotient Groups –Introduction To Rings And Fields.
Unit – IV
Linear Algebra And Recurrence Relations- Linear Algebra: Vector Space, Basis, Dimension, Orthogonality.Recurrence Relations :Homogeneous And Inhomogeneous Recurrences And Their Solutions - Solving Recurrences Using Generating Functions.
Unit – V
Graph Theory- Definitions And Basic Results - Representation Of A Graph By A Matrix And Adjacency List - Trees - Cycles - Properties - Paths And Connectedness - Subgraphs - Graph Isomorphism - Operations On Graphs - Vertex And Edge Cuts - Vertex And Edge Connectivity.