Find all the resources you need for CS-302 - Discrete Structure of your B.Tech journey.
UNIT 1: Set Theory: Definition of sets, countable and uncountable sets, Venn Diagrams, proofs of general identities on sets. Relation: Definition, types of relation, composition, Pictorial representation, Equivalence relation, Partial ordering, Job-Scheduling. Function: Definition, types of functions, inverse and composition, pigeonhole principle. Theorem Proving: Mathematical induction, Proof by contradiction.
UNIT 2: Algebraic Structures: Semi Groups, Monoid, Groups, Abelian groups, Subgroups, cyclic groups, Cosets, factor group, Permutation groups, Normal subgroup, Homomorphism and isomorphism of Groups. Rings and Fields: definition and standard results.
UNIT 3: Propositional Logic: Proposition, First order logic, logical operations, truth tables, tautologies, Contradictions, Algebra of Proposition, logical implications, equivalence, predicates, Normal Forms, quantifiers. Finite State Machines: models of physical systems, language recognition.
UNIT 4: Graph Theory: Basic terminology, Planar graphs, Multigraphs, weighted graphs, Isomorphic graphs, Paths, Cycles, connectivity, Shortest path in weighted graphs. Eulerian paths, Hamiltonian circuits, Graph coloring, chromatic number, Isomorphism, and Homomorphism.
UNIT 5: Posets and Lattices: Ordered sets, Hasse diagrams, properties of Lattices, bounded and complemented lattices. Combinatorics: Permutations, combinations, Binomial Theorem, Recurrence Relations: Linear recurrence relations, Recursive algorithms, Generating functions.