MM1231.10: MATHEMATICS II

SYLLABUS

Module I: Proof Methods, Logic: Formal proofs, Propositional reasoning, Proofs by contradiction, False Proofs, Proofs by Induction, Symbolic Logic: Boolean expressions, Logical Equivalence, De-Morgan’s Law, tautologies, Implications, Arguments, Fallacies, Normal forms in prepositional logic, Resolution

Module II: Set Theory, Relations, Functions: Review of Set theory concepts, set operations, characteristic functions, fuzzy set theory basics, Relations: operations on relations, equivalence relations & partitions, partial orders, ordered sets, Warshal’s algorithm, Functions, Recursion,
Module III:Algebraic Structures: Algebra, De-Morgan’s Law, Group, Ring, Polish expressions, Communication Model and error corrections, Hamming Codes

Module IV: Graph Theory: Introductio n, Graph Notation, Topological sort, Graph Propagation algorithm, Depth First, Breadth-first searches, Shortest Path algorithms, Directed acyclic graphs.

BOOK:

V.Ramaswamy, Discrete Mathematical Structures with Applications to Combinatorics