6 Algebraic Structures

M.Tech.(CS) Year I
ISI Kolkata, 2021-2022 Session

Semester: First
Instructor: Sujata Ghosh
Meeting Times: Mondays, Wednesdays 4:15PM - 6:00PM
First Class: Monday, October 4
Location: Online


[Teaching staff | Course overview | References | Grading | Lecture schedule | Homeworks/Handouts]



Teaching staff

Instructor

Sujata Ghosh
Email: sujata AT isichennai DOT res DOT in
Office Hours: By Arrangement (please send an e-mail)

TA

Avijeet Ghosh
Email: avi DOT ghosh23 AT gmail DOT com
Office Hours: By Arrangement (please send an e-mail)



Course overview


Course Description: This course can be considered as an introductory course on different algebraic structures. The focus will be on groups, rings, fields and vector spaces. We will have a brief recapitulation of the concepts of sets, relations and functions at the beginning of the course. Towards the end, we will look into some applications of algebra in computer science. The complete syllabus of the course can be found here.

This course is also about building up mathematical maturity, e.g., how to read and write mathematics, especially mathematical proofs, and how to communicate mathematics.

Pre-requisites: There are no pre-requisites for this course.


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References


Text book: This main text book for the course is Algebra by Mike Artin.

Some other books which might prove to be helpful are A first course in Abstract Algebra by J.B. Fraleigh, the classic Topics in Algebra by I.N. Herstein, Abstract Algebra by D.S. Dummit and R.M. Foote.


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Grading


Grades will be based on assignments (20%), mid-semester examination (20%), project (10%), and end-semester examination (50%).



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Lecture schedule

04.10.2021 Sets, relations, functions: Class notes
06.10.2021 Sets, relations, functions (contd.): Class notes
20.10.2021 Finite and infinite sets: Class notes
25.10.2021 Countable sets: Class notes
27.10.2021 Uncountable sets: Class notes
27.10.2021 Tutorial 1 (included in the homework set)
01.11.2021 Groups and subgroups: Class notes
03.11.2021 Cyclic groups and isomorphisms: Class notes
10.11.2021 Homomorphisms and isomorphisms: Class notes
15.11.2021 Normal subgroups: Class notes
15.11.2021 Tutorial 2 (included in the homework set)
17.11.2021 Left and right cosets: Class notes
22.11.2021 Cosets and quotient groups: Class notes
24.11.2021 Product of groups: Class notes
06.12.2021 Introduction to rings: Class notes
08.12.2021 Tutorial 3 (included in the homework set)
13.12.2021 Ideals and quotient rings: Class notes
15.12.2021 Polynomial rings: Class notes
20.12.2021 Fields and integral domains: Class notes
22.12.2021 Quotient rings and isomorphisms: Class notes
23.12.2021 Adjoining elements to a ring: Class notes
02.01.2022 Tutorial 4 (included in the homework set)
03.01.2022 Field extensions: Class notes
05.01.2022 Field extensions (contd.): Class notes
14.01.2022 Splitting fields: Class notes
17.01.2022 Finite fields: Class notes


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Homeworks/Handouts


  • Homework 1
    (Firm) deadline for submission: October 31, 2021.

  • Homework 2
    (Firm) deadline for submission: November 21, 2021.

  • Homework 3
    (Firm) deadline for submission: December 12, 2021.

  • Homework 4
    (Firm) deadline for submission: January 9, 2022.

  • Homework 5
    (Firm) deadline for submission: January 28, 2022.


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