programme

Lattices and Boolean Algebra

Home/ 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@aud.ac.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%

 

Reading List:

  • B A Davey and H A Priestley, Introduction to Lattices and Order (2nd Edition) Cambridge University Press, Cambridge, 2008.
  • Birkohoff G and Maclane S, A Survey of Modern Algebra, Universities Press (India) Pvt Ltd, 2003.
  • John R Gregg, Ones and zeros: Understanding Boolean Algebra, Digital Circuits and the logic of sets, Wiley-Interscience, John Wiley and Sons, 1998.
  • Rudolf Lidl and Günter Pilz, Applied Abstract Algebra (2nd Edition), Undergraduate Texts in Mathematics, Springer (SIE), Indian reprint, 2004.
  • C L Liu and D Mohapatra, Elements of Discrete Mathematics (3rd Edition), Tata McGraw Hill, 2008.
  • J Eldon Whitesitt, Boolean Algebra and its Applications, Dover Publications, 2010