Discrete Mathematical Structures-II Syllabus
Periods/week : 3 Periods & 1 Tut /week. Ses. : 30 Exam : 70 Examination (Practical): 3hrs. Credits: 4
- Introduction: Relations-Types of relations-Matrix representation of relations- Representation of relations as graphs-Ordering-Partial Ordering-Functions-Composition of Functions-Binary and n-ary Operations-Characteristic Functions of a set-Hashing functions-Recursion-Primitive recursive functions-Recursive functions.
Algebraic Structures: Algebraic Systems-Semi groups and Monoids-Grammars and Languages-Polish expression and their compilation-Groups-The application of residue arithmetic to Computers- Group Codes
Lattices: Lattices as Partially Ordered Sets-Properties of Lattices- Sublattices-Direct Product 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 of Boolean 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.
Discrete Mathematical Structures with applications to computer science by J. P. Trembley & R. Manohar Tata McGraw-Hill Publishing Company, New Delhi.
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 Publishing
Company, New Delhi.