TEW - Algebra & Discrete Mathematics (2020)

Speakers and Syllabus

Speaker Affiliation Topic(s) Number of
lecture hours		 Number of
tutorial hours
Anirban Mukhopadhyay IMSc, Chennai

Finite fields
Basics such as why does a finite field have prime power order, existence and uniqueness (upto isomorphism) of a finite field of a given prime power order, counting the number of monic irreducibles ofa given degree, counting the number of points on various geometric objects constructed over finite fields, etc.

 6 2 (conduct) + 2 (assist)
K.N. Raghavan IMSc, Chennai Group actions
Basics of group actions will be covered with a view towards solving counting problems.The Cauchy-Frobenius-Burnside formula for the number of orbits and its applications will form the main showpiece. The class equation along with some of its applications and proofs of Sylow’s theorems will also be covered from the point of view of group actions.		 6 2 (conduct) + 2 (assist)
Sankaran Viswanath IMSc, Chennai Discrete Mathematics
Permutations and combinations, combinations with repetition, principle of inclusion- exclusion, partition of a set, equivalence relations, distributions and multinomial numbers, principle of induction, recurrence relations, generating functions, exponential generating function, Graphs and graph models, Representation of graphs and Graph isomorphism.		 6 2 (conduct) + 2 (assist)

Reference Material:

  1. Norman L. Biggs, Discrete Mathematics, (2nd Edition), Oxford University Press, 2012.
  2. Kenneth H Rosen, Discrete Mathematics and its applications with combinatorics and Graph Theory, (7th Edition reprint), McGraw Hill Education(India), pvt, 2018.
  3. David S. Dummit and Richard M. Foote, Abstract Algebra, (3rd Edition reprint), John Wiley and Sons, 2013
  4. Notes for group actions:  https://www.imsc.res.in/~knr/past/ignou.pdf

Time Table

Date, Days

Lecture
5.30pm - 7.00pm

Tutorial
1.00pm - 2.00pm

Tutorial
5.00pm - 6.00pm

19.11.2020-Thursday

KNR

-

-

21.11.2020-Saturday

SV

-

-

29.11.2020 - Sunday

-

 SV

KNR

03.12.2020-Thursday

AM

-

-

05.12.2020-Saturday

SV

-

-

06.12.2020 - Sunday

-

AM

SV

10.12.2020-Thursday

KNR

-

-

12.12.2020-Saturday

AM

-

-

13.12.2020 - Sunday

-

 KNR

AM

17.12.2020-Thursday

KNR

-

-

19.12.2020-Saturday

SV

-

-

20.12.2020 - Sunday

-

 SV

KNR

24.12.2020-Thursday

AM

-

-

26.12.2020-Saturday

SV

-

-

27.12.2020 - Sunday

-

AM

SV

31.12.2020-Thursday

KNR

-

-

02.01.2021-Saturday

AM

-

-

03.01.2021 - Sunday

-

KNR

AM

KNR = K.N.Raghavan,
AM = Anirban Mukhopadhyay,
SV = Sankaran Viswanath
KNR – 6 lecture hours + 4 tutorial hours;
AM – 6 lecture hours + 4 tutorial hours;
SV– 6 lecture hours + 4 tutorial hours

 

 

File Attachments: