IST - Algebra and Number Theory (2020)

Speakers and Syllabus


Syllabus:

Name of the Speaker
with affiliation
No. of
Lectures
Detailed Syllabus
Prof. S.D.Adhikari
Ramakrishna Mission
Vivekananda Educational
and Research Institute,
Belur
6 Divisibility Theory in Integers; Congruences: Euler-Fermat,
Wilson's Theorem, Chinese Remainder Theorem, quadratic reciprocity
law, Sum of two squares. (first week)
Prof. D.S. Ramana
H.R.I. Allahabad.
6 Arithmetical functions - average order of some functions; Distribution
of Primes: Chebyshev's bound. (first week)
Prof. D. Khurana
Panjab University,
Chandigarh
9 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)
Dr. A.M.Buhphang
NEHU, Shillong.
3 Unique Factorization Domains, Principal Ideal Domains, Euclidean
Domains: Basic properties and interrelations, Number fields and
Number rings. (second week)

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.

Tutorial Assistants:

S. No Name Affiliation
1 Ramdin Mawia I.S.I. Kolkata

Time Table

Day Date

Lecture1
(9.30
to
11.00)

Tea
(11.05
to
11.25)

Lecture 2
(11.30
to
1.00)
Lunch
(1.05
to
2.25)
Tutorial
(2.30–3.30)
Tea
(3.35
to
3.55)
Tutorial
(4.00
to
5.00)
Snacks
5.05
to
5.30
    (name
of the
speaker)
  (name of
the
speaker)
  (name of
the speaker
+ tutors)
  (name of
the speaker
+ tutors)
 
Mon 29.06.20 SDA   DSR   DSR+SDA
+RM
  SDA+DSR
+RM
 
Tue 30.06.20 SDA   DSR   DSR+SDA
+RM
  SDA+DSR
+RM
 
Wed 01.07.20 SDA   DSR   DSR+SDA
+RM
  SDA+DSR
+RM
 
Thu 02.07.20 SDA   DSR   DSR+SDA
+RM
  SDA+DSR
+RM
 
Fri 03.07.20 SDA   DSR   DSR+SDA
+RM
  SDA+DSR
+RM
 
Sat 04.07.20 SDA   DSR   DSR+SDA
+RM
  SDA+DSR
+RM
 
SUNDAY : OFF
Mon 06.07.20 DK   DK   DK+AMB
+RM
  AMB+DK
+RM
 
Tue 07.07.20 DK   AMB   DK+AMB
+RM
  AMB+DK
+RM
 
Wed 08.07.20 DK   DK   DK+AMB
+RM
  AMB+DK
+RM
 
Thu 09.07.20 DK   AMB   DK+AMB
+RM
  AMB+DK
+RM
 
Fri 10.07.20 DK   AMB   DK+AMB
+RM
  AMB+DK
+RM
 
Sat 11.07.20 DK   DK   DK+AMB
+RM
  AMB+DK
+RM
 

DSR – D.S. Ramana.
SDA – S.D. Adhikari.
D.K. – D. Khurana.
AMB – A. M. Buhphang.
RM – Ramdin Mawia.

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