ANDHRA UNIVERSITY, WALTAIR
M.Sc. APPLIED MATHEMATICS, SECOND SEMSTER
AM-204 : DISCRETE MATHEMATICAL STRUCTURES-II
[ A total of seven questions are to be set. All questions carry equal marks. The first question which is compulsory carries 20 marks. It consists of 4 short answer sub questions each of five marks covering the entire syllabus. The remaining six questions each carrying 20 marks are to be set as suggested in the body of the syllabi.]
Mathematical logic statements , structures and notation, connectives, well formed formulas, tautologies, equivalences, implications, normal forms- disjunctive and conjunctive , principal disjunctive and conjunctive normal forms.
Theory of Inference: Theory of inferences for statement calculus, validity using truth tables, values of inference, predicate calculus, predicates, predicate formulas, quantifiers, free and bound variables, inference theory of predicate calculus ( Scope and treatment as in sections :1.1 to 1.6 of Ref.1)
[Three questions are to be set]
Theory of recursion: Recursive functions, primitive recursive functions, partial recursive functions and Ackerman’s functions (scope and treatment as in section 2-6.1 of Ref.1)
Graph Theory: Graphs and multigraphs, sub graphs, isomorphism and homeomorphism, paths, connectivity, traversable multigraph, labeled and weighted graphs, complete , regular and bipartite graphs, tree graphs, planar graphs.
Directed graphs: sequential representation of directed graphs, shortes path, Binary trees, complete and extended binary trees, representation of binary trees : traversing binary trees and binary search tree (scope as in sections 8.2 to 8.9 of chapter 8 , 9.2 to 9.7 of chapter 9 and 10.1 to 10.6 of chapter 10 of the Ref.2).
[Three questions are to be set]
References:
- Discrete Mathematical structures with applications to computer science by J.P. Tremblay and R.Manohar , Tata McGraw – Hill edition.
- Discrete Mathematical , Schaum’s outlines, second edition, by Seymour Lipschutz and Marc Lipson Tata McGraw Hill.
