Course: MAT 315 2.0 Boolean Algebra and Switching Circuits (Optional)
Course content: The Algebra of Sets, Relations, POSETS: Definitions and examples, Diagrammatical representation & Isomorphisms of posets. Chains: Maximal and Minimal elements & Product of two posets, Lattices: Definition of a Lattice ( as Posets) and examples, Properties of Lattice, Idempotency, Commutativity, Associativity, Consistency, Absorption, Distributive Inequalities, Modular Inequalities, Defining a Lattice as an Algebra, Equivalence of two definitions, Semi Lattices, Complete Lattices & Sub Lattices. Modular lattices: Definition of a Modular lattice and examples, Homomorphisms and Isomorphisms of Lattices & Basic Theorems. Distributive Lattices: Definition of a Distributive lattice, Basic theorems on Distributive lattices, Definition of a complemented lattice & Basic theorems on complemented lattices. Boolean Algebras: Definition of a Boolean Algebra, Definition of a Boolean function, Definition of a Disjunctive Normal Form & Definition of a Conjunctive Normal Form. Switching Circuits: Representation of circuits, Simplification of circuits, Design of circuits, Don’t care conditions & Non-series-parallel circuits.
Recommended Readings: Lattices and Boolean Algebras [first concepts], Vijay K Khanna, Moddern Printera Delhi