KSM1C01 : Algebra I - Aug-Dec 2025  at Kerala School of Mathematics (Int M. Sc.-Ph. D. course)

Course plan: We will be learning Linear algebra and basics of Group theory covering material in chapters 3 to 8 of Artin, Algebra, second edition.

Assignments, additional related material will be posted on this page. 

Course grading policy details and dates: see here

Applications of Linear algebra: PageRank algorithm for Google search engine, Original paper of Sergey Brin and Lawrence Page, Further applications

11th August : Lecture 1 Introduction, Subspaces of R^n

12th August : Lecture 2 fields, Vector spaces, span, linear independence (Assignment 1 based on material in Lectures 1 to 2)

solutions of selected problems from Assignment 1 

15th August : Independence Day 

Assignment 1 submission due on 18th Aug (Monday) 10:00 AM 📜 

18th August : Tutorial 1 Problem set 

19th August :  Lecture 3 independence, basis, dimension, covered till section 3.4 in Chapter 3 of Artin's book  (Assignment 2 based on material in Lectures 3 to 4)

22th August : Lecture 4 change of basis, direct sum, infinite dimensional vector spaces

Assignment 2 submission due on 25th Aug (Monday) 10:00 AM AM📜 

25th August : Tutorial 2

26th August : Lecture 5 

29th August : Lecture 6

1st September : Quiz 1 Tutorial 3 session

2nd September : Lecture 7 (assignment 3 will be given based on material in Lectures 5 to 7)

ONAM Festival break 🎉

Assignment 3 submission deadline: 8th Sept (Monday) 10:00 AM📜 

8th September : Tutorial 4 

9th September : Lecture 8  (assignment 4 will be given based on material in Lectures 8 to 9)

12th September : Lecture 9

Assignment 4 submission deadline: 15th Sept (Monday) 10:00 AM 📜 

15th September : Tutorial 5 

16th September :  Lecture 10 (assignment 5 will be given based on material in Lectures 10 to 11)

19th September :  Lecture 11 

Assignment 5 submission deadline: 22nd Sept (Monday) 10:00 AM 📜 

22nd September :  Tutorial 6 

23rd September : Lecture 12 (assignment 6 will be given based on material in Lectures 13 to 14)

26th September : Lecture 13

Assignment 6 submission deadline: 27th Sept (Monday) 10:00 AM📜 

29th September : Tutorial 7 

30th September : Lecture 14 (a problem set will be given based on material but no assignment submission this week)

3rd October : Lecture 15

Mid - semester 6 to 10 October

13th October : Lecture 16/Tutorial session 

14th October : Lecture 17  (assignment 7 will be given based on material in Lectures 17 to 18)

17th October : Lecture 18

20th October-Deepawali-Holiday 🎉

Assignment 7 submission deadline: 21st Oct (Monday) 10:00 AM📜 

21st October : first half Tutorial  and 2nd half Lecture 19

24th October : Lecture 20

27th October : Quiz 2

28th October : Lecture 21

31st October : Lecture 22 

Assignment 8 submission deadline: 3rd Nov (Monday) 10:00 AM📜 

3rd November : Tutorial 

4th November : Lecture 23

7th November : Lecture 24

Assignment 9 submission deadline: 10th Nov (Monday) 10:00 AM 📜 

10th November : Tutorial

11th November : Lecture 25

14th November : Lecture 26

Assignment 10 submission deadline: 17th Nov (Monday) 10:00 AM 📜 

17th November : Quiz 3

18th November : Lecture 27

21st November : Lecture 28/ Tutorial

Final exam in December 1- 5