Advanced Training School in Mathematics for Lecturers(ATML)

in Algebra and Number Theory

(Sponsored by National Board for Higher Mathematics)

December 15 - 31, 2009

Principal Speakers :

Algebra

Professor J. K. Verma, IIT Bombay
Profesor A. K. Bhandari, Panjab University, Chandigarh
Dr. Gurmeet K. Bakshi, Panjab University, Chandigarh

Number Theory

Profesor S. D. Adhikari, HRI Allahabad
Professor Madhu Raka, Panjab University, Chandigarh
Profesor A. K. Agarwal, Panjab University, Chandigarh

Guest Speakers :

Professor I. B. S. Passi, Panjab University, Chandigarh
Professor R. J. Hans -Gill, Panjab University, Chandigarh
Tentative Tutors : Dr. Anuradha Sharma, Dr. Saurabh Bhatia, Ms. Harpreet Grover, Ms. Pooja Grover, Ms. Shivani Anand.

Syllabus

Algebra:

Groups of Symmetry, Group action, Finitely generated abelian groups, Sylow Theore Solvable groups, Jordan-Holder Theorems. UFD’s, PID’s and their application Number Theory, Chain Conditions, Free modules, finitely generated modules over a P Rational canonical form & Jordan canonical form. Review of Basic Field Theory, separable and normal extensions, Galois extensi cyclotomic extensions, cyclic and abelian extensions, solvability by radicals, calcula of Galois group.

Number Theory:

Primitive roots and indices, Quadratic reciprocity, Theory of Partitions, Herm estimates on the minima of positive definite quadratic forms and their application sums of two squares, three squares and four squares; Minkowski’s Theorem in Geom of Numbers and its applications, Distributions of primes, Prime Number Theor Combinatorial Number Theory.

References:

1. S. Lang, Algebra, 3rd Edition
2. M. Artin, Algebra
3. Luthar and Passi, Algebra Volume I, II, III
4. Niven & Zuckerman, Number Theory
5. T. M. Apostol, Analytic Number Theory
6. Andre Weil, Partitions.