Shivaji University, Maharashtra, Computer Engineering Semester 3, Discrete Mathematics & Structures Syllabus

Discrete Mathematics & Structures (PCC-CS302)

Credits:- 4

1 Mathematical Logic:

Statements & Notations, Connectives, Statement Formulas & truth table, Well formed formulas, Tautologies , Equivalence of formulas, Duality law, Tautological Implications, Functionally complete set of connectives, Other connectives, Normal Forms, Theory of Inference for statement calculus.

2 Set Theory:
Basic concepts of set theory, Operations on Sets, Ordered pairs & n-tuples, Cartesian product

3 Relations & Functions:
Relations. Properties of binary relations. Matrix & Graph Representation of Relation., Partition & covering of Set, Equivalence Relations. , Composition of Binary Relation., POSET & Hasse Diagram, Functions, Types of Functions, Composition of functions..

4 Algebraic Systems:
Algebraic Systems: Examples & general Properties, Semi groups & Monoids, Groups: Definitions & Examples, Subgroup & Homomorphism.

5 Lattice and boolean algebra
Lattice as partially ordered sets, Lattice as Algebraic Systems., Special Lattices., Boolean Algebra: Definitions & examples, Boolean Functions., Representation & Minimization of Boolean Functions.

6 GraphTheory: 
Basic concepts of graph theory., Paths, Reachability & Connectedness, Matrix, Representations of Graphs., Storage Representation & Manipulations of Graphs. PERT & Related technologies.

Text Books:
1. “Discrete Mathematical Structures with Application to Computer Science”by J.P.Tremblay & R. Manohar (MGH International)

Reference Books:
1. Discrete Mathematics –SemyourLipschutz, Marc Lipson (MGH), Schaum’s outlines.
2. Discrete Mathematics and its Applications – Kenneth H. Rosen (AT&T Bell Labs) (mhhe.com/rosen)

3. Discrete Mathematical Structures – Bernard Kolman, Robert Busby, S. C. Ross and Nadeemur- Rehman (PearsonEducation)