TEW - Algebra, Complex Analysis and Number Theory (2025)

Speakers and Syllabus

Speaker and
Affiliation		 Topic(s) Number of
lecture hours		 Number of
tutorial hours
Dr. R. Balasubramanian
IMSc, Chennai		 Number Theory:
Division algorithm, Greatest common divisors, Euclid’s algorithm and continued fractions, Solutions of linear diophantine equations, Fundamental theorem of arithmetic, infinitude of primes, finding primes with a given number of digits, arithmetic modulo m, solution of congruences modulo m, Fermat’s theorem, Euler’s theorem and their applications.		 9 2 (conduct) +
2 (assist)
Dr. K. N. Raghavan
KREA University,
Andhra Pradesh		 Algebra:
Groups, Subgroups, Quotient groups, Group action on a set, Class equations, Sylow’s theorem, Solvable groups, Characterization of small order groups, Some applications of group theory.		 9 2 (conduct) +
2 (assist)

Dr. G. P. Youvaraj
RIASM, Chennai

 Complex Analysis:
Holomorphic functions, Cauchy-Riemann equations, Power series, Singularities, Laurent series expansion, discussion of zeros and singularities of analytic functions, Complex integration, Cauchy’s Theorem, Residue Theorem, with an emphasis on computing/ estimating improper Riemann integrals via contour integration. Linear transformations, linear fractional transformations, Conformal mappings and applications.		 9 2 (conduct) +
2 (assist)

References:

  1. James Ward Brown and Ruel V. Churchill, “Complex Variables and Applications”, McGraw-Hill Education, 9th Edition, 2014.
  2. S.Ponnusamy, “Foundation of Complex Analysis”, Narosa Publishing House, 2011.
  3. Tom M. Apostol, “Introduction to Analytic Number Theory”, Springer, 2010.
  4. David M. Burton, "Elementary Number Theory", Mc Graw Hill Education, 7th Edition, 2017.
  5. David S. Dummit and Richard M. Foote, Abstract Algebra, (3rd Edition reprint), John Wiley and Sons, 2013
  6. Gallian, J.A. Contemporary Abstract Algebra,Ninth Edition (Cengage Learning, 2017).

Time Table

 

Time

09.30
to
11.00

Lecture

 

11.15
to
12.45

Lecture

 

14.00
to
15.30

Lecture

 

15.45
to
16.45

Tutorial

 

Mon
May 26th

RB

 

KNR

L

GPY

 

RB & KNR

S

Tue
May 27th

KNR

T

GPY

U

RB

T

KNR & GPY

N

Wed
May 28th

GPY

E

RB

N

KNR

E

GPY & RB

A

Thu
May 29th

GPY

A

RB

C

KNR

A

RB & KNR

C

Fri
May 30th

RB

 

KNR

H

GPY

 

KNR & GPY

K

Sat
May 31th

KNR

 

GPY

 

RB

 

GPY & RB

S

 RB -  R. Balasubramanian  - 9 lecture hours + 4 tutorial hours
KNR -  K. N. Raghavan       - 9 lecture hours + 4 tutorial hours
GPY - G. P. Youvaraj           - 9 lecture hours + 4 tutorial hours

 

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