M.Tech.(CS)
ISI Kolkata, 2023-2024 Session
Semester: Second
Instructor: Sujata Ghosh
Meeting Times: Tuesdays, Fridays, 9:30 AM - 11:15 AM
First Class: Tuesday, January 09, 2024
Location: Online
Instructor: Sujata Ghosh
Meeting Times: Tuesdays, Fridays, 9:30 AM - 11:15 AM
First Class: Tuesday, January 09, 2024
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)
Office Hours: By Arrangement (please send an e-mail)
TA
Soham Banerjee
Email: sohamsbanerjee AT gmail DOT com
Office Hours: By Arrangement (please send an e-mail)
Office Hours: By Arrangement (please send an e-mail)
Smiha Samanta
Email: smi1995ha AT gmail DOT com
Office Hours: By Arrangement (please send an e-mail)
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.
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.
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.
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.
Grading
Grades will be based on assignments (20%), mid-semester examination (20%), project (10%),
and end-semester examination (50%).
The latex template for the scribe can be found here.
The latex template for the scribe can be found here.
Lecture schedule
| 09.01.2024 | Sets, relations, functions:
Class notes Aranya and Sandeep: Class scribe |
| 12.01.2024 | Induction and well-ordering:
Class notes Aranya and Sandeep: Class scribe |
| 16.01.2024 | Size of sets:
Class notes Basudeb and Shramana: Class scribe |
| 19.01.2024 | Uncountable sets:
Class notes Basudeb and Shramana: Class scribe |
| 23.01.2024 | Groups and subgroups:
Class notes Sai: Class scribe |
| 30.01.2024 | Tutorial |
| 02.02.2024 | Cyclic Groups and isomorphisms:
Class notes Ritam: Class scribe |
| 06.02.2024 | Normal subgroups and permutation groups:
Class notes Rajdeep and Soumik: Class scribe |
| 09.02.2024 | On cosets:
Class notes Rajdeep and Soumik: Class scribe |
| 13.02.2024 | Cosets and quotient groups:
Class notes Priyanka and Roshni: Class scribe |
| 17.02.2024 | Product of groups:
Class notes Priyanka and Roshni: Class scribe |
| 20.02.2024 | Tutorial |
| 01.03.2024 | MID-SEM EXAM |
| 05.03.2024 | Introduction to rings:
Class notes Aranya and Sandeep: Class scribe |
| 08.03.2024 | Ideals, Quotient rings:
Class notes Aranya and Sandeep: Class scribe |
| 12.03.2024 | Polynomial rings:
Class notes Sandeep: Class scribe |
| 15.03.2024 | On fields:
Class notes Shramana: Class scribe |
| 19.03.2024 | On integral domains:
Class notes Basudeb and Ritam: Class scribe |
| 22.03.2024 | More on Quotient rings:
Class notes Basudeb and Ritam: Class scribe |
| 26.03.2024 | More on fields:
Class notes Sai: Class scribe |
| 02.04.2024 | Field extensions:
Class notes Rajdeep: Class scribe |
| 05.04.2024 | Special Lecture
by Pascal Weil:
Algorithmic problems in free groups: Class slides, Class notes |
| 06.04.2024 | Tutorial |
| 09.04.2024 | More on Field extensions:
Class notes Soumik: Class scribe |
| 12.04.2024 | Splitting fields:
Class notes Roshni: Class scribe |
| 16.04.2024 | Finite fields:
Class notes Priyanka: Class scribe |
| 19/20.04.2024 | Project Presentations |
|
Aranya: Write-up Slides Basudeb: Write-up Slides Priyanka: Write-up Slides Rajdeep: Write-up Tool Ritam: Write-up Slides Roshni: Write-up Slides Sandeep: Write-up Slides Shramana: Write-up Slides Soumik: Write-up Slides Soumya: Write-up Slides |
Homeworks/Handouts
Homework 1
Deadline for submission: February 04, 2024.Homework 2
Deadline for submission: March 10, 2024.Homework 3
Deadline for submission: March 24, 2024.Homework 4
Deadline for submission: April 7, 2024.Homework 5
Deadline for submission: April 30, 2024.