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.

9 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.
9 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.
9 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

Time 09:30 to 11:00   11:15 to 12:45   14:00 to 15:30   15:45 to 16:45  
Mon 25th KNR TEA SV LUNCH AM TEA Tutorials(KNR & AM) S
Tue 26th KNR SV AM Tutorials(SV & AM) N
Wed 27th KNR AM SV Tutorials(KNR & SV) A
Thur 28th KNR AM SV Tutorials(AM & SV) C
Fri 29th KNR SV AM Tutorials(SV & KNR) K
Sat 30th KNR AM SV Tutorials(AM & KNR) S

KNR = K.N.Raghavan, AM = Anirban Mukhopadhyay, SV = Sankaran Viswanath

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