# ATML School on Algebra & Number Theory (2009)

Venue: |
PU, Chandigarh |

Dates: |
15 Dec-31 Dec |

Convener(s) |
Speakers, Syllabus and Time table |
Applicants/Participants |

Name |
Prof. Madhu Raka | Prof. Gurmeet K. Bakshi |

Mailing Address |
Department of Mathematics, Panjab University, |
Department of Mathematics, Panjab University, |

Advanced Training School in Mathematics for Lecturers (ATML) in Algebra and Number Theory is being organised in Department of Mathematics, Panjab University, at Chandigarh in December 2009 on behalf of NBHM.

#### 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. UFDâ€™s, PIDâ€™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; Minkowskiâ€™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.

Selected Applicants |

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