TEW - Complex Analysis & Number Theory (2021)
Speakers and Syllabus
Syllabus:
| Name of the Speaker with affiliation | No. of Lectures | Detailed Syllabus |
| Srinivas Kotyada, Professor, The Institute of Mathematical Sciences, Chennai |
10 lectures (90 minutes each) | Division algorithm, GCD, Euclid’s algorithm, solution 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. |
| Tarakanta Nayak Associate Professor, Indian Institute of Technology, Bhubaneswar |
10 lectures (90 minutes each) | Mobius and other elementary maps, Local properties of analytic functions, Behaviour of analytic functions near singularities- removable, pole and essential, Asymptotic values, Cauchy integral formula and its consequences, Evaluation of certain real integrals, Analytic continuation |
References:
(1) Complex Analysis by L. Ahlfors
(2) Complex Analysis by Stein and Shakarchi
(3) The theory of numbers by Niven, Zuckerman and Montgomery
(4) Introduction to Analytic number theory by Apostol
Time Table
Time-table (with names of speakers and tutors):
Week-1 of the TEW (18 - 24 December, 2021)
| Lecture- 1&2 |
Lecture- 3&4 |
Lecture- 5&6 |
Lecture- 7&8 |
Lecture- 9&10 |
Tutorial- 1&2 |
Tutorial- 3&4 |
|
| Day | Saturday | Sunday | Monday | Tues | Wednesday | Thursday | Friday |
| Date | 18 Dec | 19 Dec | 20 Dec | 21 Dec | 22 Dec | 23 Dec | 24 Dec |
| Time (PM) | 5:00-6:30 KS |
5:00-6:30 KS |
5:00-6:30 KS |
5:00-6:30 KS |
5:00-6:30 KS |
5:00-6:30 KS+SP+US |
5:00-6:30 TN+PG+SG |
| Speaker |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
Week-2 of the TEW (25 - 31 December, 2021)
| Lecture- 11&12 |
Lecture- 13&14 |
Lecture- 15&16 |
Lecture- 17&18 |
Lecture- 19&20 |
Tutorial- 5&6 |
Tutorial- 7&8 |
|
| Day | Saturday | Sunday | Monday | Tues | Wednesday | Thursday | Friday |
| Date | 25 Dec | 26 Dec | 27 Dec | 28 Dec | 29 Dec | 30 Dec | 31 Dec |
| Time (PM) | 5:00-6:30 KS |
5:00-6:30 KS |
5:00-6:30 KS |
5:00-6:30 KS |
5:00-6:30 KS |
5:00-6:30 KS+SP+US |
5:00-6:30 TN+PG+SG |
| Speaker |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
7:00-8:30 |
- TN: Tarakanta Nayak
- SK: Srinivas Kotyada
- SG: Subhasis Ghora
- SP: Sudhir Pujahari
- PG: Priyabrat Gochhayat
- US: Usha K Sangale
Speakers:
| S. No. | Name | Affiliation |
| 1 | Srinivas Kotyada | Professor, IMSc, Chennai |
| 2 | Tarakanta Nayak | Associate Prof., IIT Bhubaneswar |
Tutors:
| S. No. | Name | Affiliation |
| 1 | PriyabratGochhayat | Asst. Prof. School of Mathematics, Sambalpur University, Sambalpur, Odisha |
| 2 | Sudhir Pujahari |
PDF, University of Warsaw, Poland.
|
| 3 | Subhasis Ghora | SRF, IIT Bhubaneswar |
| 4 | Usha K Sangale | Asst Prof. SRTM University, Nanded, Maharashtra |
Note: All the speakers and tutors will provide lecture notes and videos of their lectures.