Discrete Mathematical Structures provide the foundation for computer science, enabling the formulation and analysis of algorithms, data structures, and computational systems
MATHEMATICAL LOGIC Propositional Logic: Connectives- negation, conjunction, disjunction, conditional and bi conditional, well-formed formulae, tautologies, equivalence of formulae, tautological implications, Disjunctive and Conjunctive normal forms, Rules of inference and examples, Consistency of premises. Predicative Logic: Statement Functions, Variables and Quantifiers, Free and Bounded variables, Inference theory for predicative logic.
RECURRENCE RELATIONS [8 Hours] Recurrence relations: Recurrence relations, solving homogeneous linear recurrence relations by characteristic roots method, solving non-homogeneous linear recurrence relations.
SETS AND RELATIONS AND ALGEBRAIC STRUCTURES [10 Hours] Sets: Sets, Operations on Sets, Principles of Inclusion–Exclusion, Pigeonhole Principle and its Application. Relations: Definition, representation, types of relations: equivalence relation, equivalence class, partial order, Hasse iagram and total order relations. Functions: Definition, types of functions: surjective, injective and bijective. Algebraic Structures: Binary operations, Algebraic structures, Group, Abelian Group, Subgroups, Lagrange's theorem on finite groups.
UNIT- IV GRAPH THEORY [10 Hours] Graph theory: Definitions, finite and infinite graphs, incidence and degree, isolated and pendant vertices, isomorphism, sub graphs, connected and disconnected graphs, simple graph, complete graph, bipartite graph, complete bipartite graph, planar graph, Isomorphic Graphs, Euler formula(without proof) and Graph colouring, Walk, path and circuit, Euler graph.
UNIT- V TREES [8 Hours] Trees: Some properties of trees, rooted and binary trees, spanning trees, BFS & DFS Algorithms, Minimal spanning trees, Kruskal's algorithm.