Sunday, January 11, 2009

Logical And Discrete Mathematical Structures (LDMS) - Detailed Syllabus

Logical And Discrete Mathematical Structures is one of the subjects for Semester 3 of B.Sc.-IT and following is the detailed syllabus of the subject :

Fundamentals - Sets and subsets, Operations on sets, Sequences, Division in the integers, Mathematical structures
Logic - Propositions and Logical operations, Conditional Statements, Methods of proof, mathematical induction
Counting - Permutations, Combinations, The pigeon hole principle, elements of probability, recurrence relations Relations and Digraphs.
Product sets and partitions, relations and digraphs, paths in relations and digraphs, properties of relations, equivalence relations, computer representation of relations and digraphs, manipulation of relations, Transitive closure and Warshalls algorithm Functions.
Functions for computer science, permutation functions, growth of functions Graph theory. Graphs, Euler paths and circuits, Hamiltonian paths and circuits,coloring graphs Order relations and structures.
Partially ordered sets, External elements of partially ordered sets, Lattices, Finite Boolean algebra, Functions on Boolean algebra,Boolean functions as Boolean polynomials.
Trees - labeled trees, tree searching, Undirected trees, Minimal spanning trees Semigroups and groups.
Binary operations, semigroups, products and quotients of semigroups, groups, Products and quotients of groups Languages and finite state machines.
Languages, representation of special languages and grammars, Finite state machines, Semi groups , machines and languages, machines and regular languages Groups and coding.
Coding of binary information and error detection Decoding and error correction


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