Discrete Mathematical Structures - II

Instruction: 3 Periods & 1 Tut /week

Univ. Exam : 3 Hours

Sessional Marks: 30

Univ-Exam-Marks:70

Introduction: Relations-Types of relations-Matrix representation of relations-Representation of relations as graphs-Ordering-Partial Ordering-Functions-Compositionof Functions-Binary and n-ary Operations-Characteristic Functions of a set-Hashingfunctions-Recursion-Primitive recursive functions-Recursive functions.

Algebraic Structures: Algebraic Systems-Semi groups and Monoids-Grammars andLanguages-Polish expression and their compilation-Groups-The application of residuearithmetic to Computers- Group Codes

Lattices: Lattices as Partially Ordered Sets-Properties of Lattices- Sublattices-DirectProduct and Homomorphisms-Isomorphisms-Modular Lattices-Distributive lattices-Complimented lattices –Their Properties

Boolean Algebra: Definition- Subalgebra-Direct Product-Homomorphisms-Isomorphisms-Boolean Functions-Representation of Boolean Functions-Minimization ofBoolean Functions-Design examples of Boolean Algebra

Computability: Introduction-Finite State Machines-Introductory Sequential Circuits-Equivalence of Finite State Machines-Finite State Acceptors and Regular Grammars-Turing Machines and Partial Recursive Functions.

Text Book:

Discrete Mathematical Structures with applications to computer science by J. P.Trembley & R. Manohar Tata McGraw-Hill Publishing Company, New Delhi.

Reference Books:

1) Discrete and combinatorial mathematics by Ralph. G. Grimaldi Pearson Education,New Delhi

2) Elements of discrete mathematics by C. L. Liu, Tata McGraw-Hill PublishingCompany, New Delhi