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DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE, , BTCOC302: Discrete Mathematics, , [UNIT 1] Fundamental Structures and Basic Logic [7 Hours], Sets, Venn diagram, Cartesian product, Power sets, Cardinality and countability, Propositional logic, Logical, connectives, Truth tables, Normal forms, Validity, Predicate logic, Limitations of predicate logic, Universal, and existential quantification, First order logic, Principles of Mathematical Induction: The Well-Ordering, Principle, Recursive definition, The Division algorithm: Prime Numbers, The Greatest Common Divisor:, Euclidean Algorithm, The Fundamental Theorem of Arithmetic., , , , [UNIT 2] Functions and Relations [7 Hours], , Subjective, Injective, Bijective and inverse functions, Composition of function, Reflexivity, Symmetry,, ‘Transitivity and equivalence relations., Combinatorics: Counting, Recurrence relations, generating functions., , [UNIT 3] Graph [7 Hours], , Basic terminology, Multi graphs and weighted graphs, Paths and circuits, Shortest path problems, Euler and, Hamiltonian paths, Representation of graph, Isomorphic graphs, Planar graphs, Connectivity, Matching, Colouring., , [UNIT 4] Trees (7 Hours}, , Trees: Rooted trees, Path length in rooted tree, Binary search trees, Spanning trees and cut set, Minimal, spanning trees, Kruskal’s and Prim’s algorithms for minimal spanning tree., , [UNIT 5] Algebraic Structures and Morphism [7 Hours], , Algebraic Structures with one Binary Operation, Semi Groups, Monoids, Groups, Congruence Relation and, Quotient Structures, Free and Cyclic Monoids and Groups, Permutation Groups, Substructures, Normal, Subgroups, Algebraic Structures with two Binary Operation, Rings, Integral Domain and Fields, Boolean, Algebra and Boolean Ring, Identities of Boolean Algebra, Duality, Representation of Boolean Function,, Disjunctive and Conjunctive Normal Form., , Text Bool, , , , 1. C.L. Liu, Elements of Discrete Mathematics, McGraw-Hill Publication, 3rd Edition, 2008., , Reference Books:, , 1. Lipschutz, Discrete Mathematics, McGraw-Hill Publication, 3rd Edition, 2009., V.K. Balakrishnan, Schaum's Outline of Graph Theory, McGraw-Hill Publication, Ist Edition,, 1997., , 3. Eric Gossett, Discrete Mathematics with Proof, Wiley Publication, 2nd Edition, 2009., , 4. Kenneth H. Rosen, Discrete Mathematics and its Applications, McGraw-Hill Publication, 6th, Edition, 2010.Y. N. Singh, Discrete Mathematical Structures, Wiley Publication, Ist Edition,, 2010., , 5. Dr. Sukhendu Dey, Graph Theory with Applications, SPD Publication, Ist Edition, 2012.