M.Sc- Computer Science 2 Year Program

UNIT 1:

Vedic mathematics :
History and salient features, Vedic mathematics formulas, 16 sutras and 13 sub sutras, terms and operations, Beejank, Vinculum Operations, High speed addition by using the concept of completing the whole and superfast subtraction by Nikhilam Sutram. Multiplication by Nikhilam Sutra, Anatyodarshkeyapi, Urdhavtriyaghbhyamsutram,
The Foundations: Logic, Sets and Functions: Introduction to set theory, mathematical logic , prepositions, prepositional equivalences, predicates and quantifiers. Importance of Quantifiers.
The Foundations: Logic, Sets and Functions: Sets, set operations, fuzzy sets, functions, functions for computer science, sequences and summations. Logic and computation in ancient Indian texts.
Mathematical reasoning: Introduction to Methods of proof, mathematical induction. Use of mathematical induction to solve different problems. Importance of recursions in computer science, scope of recursions, Recursive definitions, recursive algorithms.

UNIT 2:

Combinatorics: The basics of counting, The sum rule, The product rule, The Pigeonhole Principle, Permutations with repetitions, Permutations without repetitions, Circular Permutations.
Applications of combinations: Applications of Combinatorics to solve Committee problems, word problems, puzzle problems etc. Applications of Combinatorics to understand Telephone numbering plan, understanding Internet addresses, Advanced counting techniques, recurrence relations, solving recurrence relations, algorithm design, Basic understanding of complexities, basic problems of complexity of algorithms.

UNIT 3:

Relations: Relation definition, Importance of relations in computer science, Relations and their properties, Unary relations, Binary relations, Ternary relations, n-ary relations and their applications, closures of relations, equivalence relations, partial ordering. Representing relations, relation matrix, relation graph, composite relation.
Operations on relations: union, intersection and join. Concepts of least upper bond, Greatest lower bond, maximal element, minimal element, Greatest element, Least element of a partially ordered set, lattices, sub lattices, chains and antichains.

UNIT 4:

Graphs: Introduction to Graphs, Importance of graph theory in computer science, Graph terminology, representing graphs, graph types, graph models, and graph isomorphism. Connectivity, Euler and Hamiltonian Paths, shortest path problems, planar graphs, graph colouring, chromatic number, Euler’s formula, kuratowski’s theorem. The four colour problem, Applications of Graph Colouring, Introduction to Trees, applications of trees, tree traversal, trees and sorting, Spanning trees, minimum spanning trees.

UNIT 5:

Languages and Grammars: Introduction to Languages and Grammars, solving problems for validity of statements according to the grammar. Importance of Language theory in Computer Science, Importance of Derivation trees, solving problems of Derivation trees, Importance of Parsing, Phrase Structure Grammars, Types of Phrase structure grammars.