Unit 1 Set Theory and Logic Introduction and si nificance of Discrete Mathematics. Sets - Naϊve Set Theory (Cantorian Set Theory), Axiomatic Set Theory, Set Operations. Cardinality of set. Principle of inclusion and exclusion, Types of Sets - Bounded and Unbounded Sets, Dia onalization Ar ument. Countable and Uncountable Sets. finite and Infinite Sets. Countably Infinite and Uncountably Infinite Sets. Power set. Propositional Logic - Ιοφc, Propositional Equivalences, Application of Propositional Loφc - Translatin En lish Sentences, Proof by Mathematical Induction and Stron Mathematical Induction. (Chapters - ι, 2. 3) Unit II Relations and Functions Relations and their Properties. n-ary relations and their applications. Representin relations. Closures of relations, Equivalence relations. Partial orderin s. Partitions, Hasse dia ram, Lattices, Chains and Anti-Chains, Transitive closure and Warshall's al orithm. Functions - Surjective, lnjective and Bijective functions, Identity function, Partial function. Invertible function. Constant function. Inverse functions and Compositions of functions. The Pi eonhole Principle. (Chapters - 4, 5) (ίν), Unit III Counting Principles The Basics of Counting, rule of Sum and Product, Permutations and Combinations, Binomia l Coefficients and Identities, Generalized Permutations and Combinations, A lgorithms for generating Permutations and Combinations. (Chapter-6) Unit IV Graph Theory Graph Terminology and Special Types of Graphs, Represent ing Graphs nd Graph Isomorphism, Connectivity, Euler and Hamilton Paths, the handshaking lemma, Single source shortest path- Dijkstra's Algorithm, Planar Graphs, Graph Colouring. (Chapter-7) Unit V Trees Introduction, propert ies of trees, Binary search tree, tree traversal, decisicon tree, prefix codes and Huffman coding, cut sets, Spanning Trees and Minimum Spanning Tree, Kruskal's and Prim's algorithms, The Max flow-Min Cut Theorem (Transport network). (Chapter-8) Unit VI Algebraic Structures and Coding Theory The structure of algebra, Algebraic Systems, Semi Groups, Monoids, Groups, Homomorphism and Normal Subgroups, and Congruence relations, Rings, Integral Domains and Fields, Coding theory, Polynomial Rings and polynomial Codes, Galois Theory -Field Theory and Group Theory. (Chapter-9)
