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Advanced Training in Mathematics workshop on Instructional School for Teachers on Algebra 07/12/2015 To 19/12/2015

A National centre for Mathematics which is joint centre of TIFR and IIT Bombay, ATM (Advanced Training in Mathematics) workshop on 'Instructional School for teachers on Algebra' is organized by the Department of Mathematics, Malaviya National Institute of Technology Jaipur during December 7-19, 2015.
The first day of the workshop started with the welcome of the experts and participants. The guests of the honour of the occasion were Dr. Sudhir Ghorpade and Dr. H. Ananthnarayan, from IIT Bombay. The programme started with the lighting of the lamp and invoking the blessings of Goddess Saraswati. The guests were welcomed by presenting bouquet. Dr. Vatsala Mathur, HOD, Mathematics welcomed the guests and delegates and told about the department, its courses and activities. Prof. Sudhir Ghorpade told about the origin and scope of ATM Schools. He also mentioned about the objective and utility of these Schools. Dr. Hariharan told the participants about the best ways of learning and things to remember during the workshop. Dr. Ritu Agarwal, local organizer of ATMW proposed vote of thanks.
IST on Algebra covered the theory of groups and rings with applications to geometry, group symmetries and number theory. The venerable and learned speakers from IIT Bombay and IIT Gandhinagar delivered lectures in the workshop. Each day two 90 minutes sessions were followed by two 60 minutes tutorials. The participants are NET qualified teachers and research scholars from various parts of the country
During the first week of the event, lectures were delivered by Prof. Sudhir Ghorpade and Dr. Ananthnarayan H., IIT Bombay. Prof. Ghorpade delivered a series of six lectures (of one and half hour duration each) on ring theory. The topics covered included the following: Basic definitions, examples of rings, ideals and residue class rings, homomorphism theorems, construction of quotient field of an integral domain, maximal and prime ideals, Hilbert's Nullstellensatz and its applications.
Dr. Ananthnarayan delivered a series of six lectures (of one and half hour duration each) on group theory. The topics covered included basic definitions; examples of groups, including cyclic, dihedral, quaternion, permutation and alternating groups, and matrix groups; subgroups, and quotient groups, homomorphisms. There was a discussion on group actions, the orbit-stabilizer formula, and class equation; Sylow's theorems were proved using group actions, and as an application, groups of order 12 were classified.
During the second week of the event, Prof. J. K. Verma from IIT Bombay and Dr. Indranath Sengupta from IIT Gandhinagar delivered a series of six lectures each . Prof. Verma made students aware of the interesting topic of isometries and finite groups of rigid motions of plane, Orthogonal matrices and rotations of space, Groups of symmetries of Platonic solids and the Finite subgroups of SO(3).
Dr. Indranath Sengupta from IIT Gandhinagar discussed Unique Factorization Domain, Prime Ideal Domain, Euclidean domains and primes ideals in imaginary quadratic fields with applications to number theory. They all delivered their best and explained the confusing concepts with so ease, that every participant was satisfied. The Speakers also explained the relevance of these topics in various fields of sciences.
In addition, all the lecture sessions were followed by tutorial sessions (of two hours duration each) everyday, where a number of pre-assigned problems were discussed. The speakers were assisted by the tutorial assistants Mr. Mrinmoy Datta and Ms. Parangama Sarkar from IIT Bombay, who were always available for solving the problems of participants.
Stay arrangements for participants and speakers was made in the nearby places so that most of the time can be utilized for discussions on the subject. Prof. Rashmi Jain and Dr. Ritu Agarwal, Convener of ATMW stood on their feet for 13 days for the good arrangements and making sure that students get the best of knowledge.
At the end of the School the participants were asked to fill a feedback form. More than 90% attendees reported to be satisfied in the programme and hoped that such courses are organized on regular basis in near future. During the valedictory function Certificates of participation were awarded to participants.
The workshop comes out to be a success in terms of quality of lectures, organization of the syllabus covered and participants understanding of the subject and positive feedback.

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