IST - Algebra and Number Theory (2023)
Speakers and Syllabus
Syllabus:
| Sr. | Name of the speaker and Affiliation |
Topic of lectures | Number of lectures |
| 1 | Prof. S. D. Adhikari Ramakrishna Mission Vivekananda Educational and Research Institute, Belur |
Divisibility Theory in Integers; Congruences: Euler-Fermat, Wilson's Theorem, Chinese Remainder Theorem, quadratic reciprocity law, Sum of two squares. (first week) | 6 lectures |
| 2 | Prof. D. S. Ramana H.R.I. Allahabad. |
Arithmetical functions - average order of some functions; Distribution of Primes: Chebyshev's bound. (first week) | 6 lectures |
| 3 | Prof. D. Khurana Panjab University, Chandigarh. |
Historical importance of Rings in solving problems of Number theory, Fermat's Last Theorem, Elliptic Curves, Classification of primitive Pythagorean triples, Fermat’s Theorem on sum of two squares; Norms and Traces, Number Rings of quadratic and cyclotomic number fields, Discriminant, Number Rings as free abelian groups, Integral Bases, Norms and Classes of Ideals, Class Numbers of Number Fields and their finiteness. (second week) |
9 lectures |
| 4 | Dr. A. M. Buhphang NEHU, Shillong. |
Unique Factorization Domains, Principal Ideal Domains, Euclidean Domains: Basic properties and interrelations, Number fields and Number rings. (second week) | 3 lectures |
References:
1. David M. Burton, Elementary Number theory, Universal Book stall, New Delhi, 2011.
2. G.H. Hardy and E.M. Wright , An Introduction to the Theory of Numbers, The English Language Society and Oxford University Press, 1998.
3. Paolo Ribenboim, Classical Theory of Algebraic Numbers, Springer-Verlag, New York, 2001.
Time Table
Tentative time-table
|
Day |
Date |
Lec 1 |
Tea |
Lec 2 |
Lunch |
Tut |
Tea |
Tut |
Snacks |
||||
|
|
|
name of the |
|
name of the speaker |
|
name of the speaker + tutors |
|
name of the speaker + tutors |
|
||||
|
Mon |
26.06.23 |
SDA |
|
DSR |
|
DSR+SDA +RM |
|
SDA+DSR +RM |
|
||||
|
Tues |
27.06.23 |
SDA |
|
DSR |
|
DSR+SDA +RM |
|
SDA+DSR +RM |
|
||||
|
Wed |
28.06.23 |
SDA |
|
DSR |
|
DSR+SDA +RM |
|
SDA+DSR +RM |
|
||||
|
Thu |
29.06.23 |
SDA |
|
DSR |
|
DSR+SDA +RM |
|
SDA+DSR +RM |
|
||||
|
Fri |
30.06.23 |
SDA |
|
DSR |
|
DSR+SDA +RM |
|
SDA+DSR +RM |
|
||||
|
Sat |
01.07.23 |
SDA |
|
DSR |
|
DSR+SDA +RM |
|
SDA+DSR +RM |
|
||||
|
SUNDAY : OFF |
|||||||||||||
|
Mon |
03.07.23 |
DK |
|
DK |
DK+AMB +SD |
|
AMB+DK +SD |
|
|||||
|
Tues |
04.07.23 |
DK |
|
AMB |
|
DK+AMB +SD |
|
AMB+DK +SD |
|
||||
|
Wed |
05.07.23 |
DK |
|
DK |
|
DK+AMB +SD |
|
AMB+DK +SD |
|
||||
|
Thu |
06.07.23 |
DK |
|
AMB |
|
DK+AMB +SD |
|
AMB+DK +SD |
|
||||
|
Fri |
07.07.23 |
DK |
|
AMB |
|
DK+AMB +SD |
|
AMB+DK +SD |
|
||||
|
Sat |
08.07.23 |
DK |
|
DK |
|
DK+AMB +SD |
|
AMB+DK +SD |
|
||||
TutorialAssistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Dr. Ramdin Mawia |
I.S.I. Bangalore |
|
2 |
Dr. Soumitra Das |
I.I.S.E.R. Berhampur |
- DSR – D.S.Ramana.
- SDA – S.D. Adhikari.
- D.K. – D. Khurana.
- AMB – A. M. Buhphang.
- RM – Ramdin Mawia.
- SD- Soumitra Das