# Lattices and Boolean Algebra

Course TypeCourse CodeNo. Of Credits
Foundation ElectiveSUS1MA5134

Semester and Year Offered: Winter Semester 2018-19

Course Coordinator and Team: Balchand Prajapati, Geetha Venkataraman

Email of course coordinator: balchand[at]aud[dot]ac[dot]in

Pre-requisites: Pre-requisite for this course is Mathematics at the XII grade level.

Aim: This course has mainly been designed with the aim of introducing students to the Lattice Theory and Boolean Algebra. The portion on Lattice Theory discusses Modular, distributive and Boolean Lattices. The module on Boolean Algebras includes design of switching circuits.

Course Outcomes:

After completing this course, students will be able

• to understand lattices as algebraic structures
• homomorphisms between lattices and Boolean Algebra
• polynomials, switching circuits

Brief description of modules/ Main modules:

The following topics will be covered in the course under the four main modules as described below.

Definition, examples and basic properties of ordered sets, maps between ordered sets, duality principle, down-sets, up-sets, maximal and minimal elements, building new ordered sets, lattices as ordered sets, complete lattices, lattices as algebraic structures, sublattices, products and homomorphisms. Definition, examples and properties of modular, distributive and Boolean lattices.

Boolean Algebras, Boolean polynomials, ideals, filters and equations, minimal forms of Boolean polynomials, Quinn-McCluskey method, Karnaugh diagrams, switching circuits and applications of switching circuits.

Assessment Details with weights:

 S.No Assessment Date/period in which Assessment will take place Weightage 1 Class test First week of February 10% 2 Mid Semester Exam As per AUD Academic Calendar 25% 3 Home assignment/Tut Throughout the semester 15% 4 Presentation/ Viva May 15% 5 End Semester Exam As per AUD Academic Calendar 35%