In addition to teaching these courses, I also
conducted the tutorials, as a Course Associate, for several
B.Tech. courses at IIT Bombay. Some of the M.Sc. courses
mentioned above have also been conducted, mainly as Self-Study, during the
summer.
For the CEBS, Mumbai as an Instructor (with classes were held at IIT Bombay)
1. M 802, Algebraic Number Theory, Spring 2013.
III. Short Courses taught at Summer Schools, Instructional
Conferences, etc.
``Galois theory and ramification theory'', A series of six lectures,
All India Summer School on Number Theory,
Bhaskaracharya Pratishthana-University of Poona, Pune, June 1991.
``Discriminant and ramification", A series of five lectures, UGC
Refresher Course on Algebraic Number Theory, University of Bombay, Bombay,
December 1991.
``Elements of the theory of representations of finite groups
with an introduction to Frobenius-Schur theory of characters of S_{n}'',
A series of five lectures, UGC Refresher Course on Algebra, University
of Poona, Pune, July 1993.
``Commutative Algebra'', A Series of six lectures, NBHM
Instructional Conference on Combinatorial Topology and Algebra, Indian
Institute of Technology, Bombay, December 1993.
``Symmetric functions and Galois groups'', A series of four
lectures, Refresher Course in
Mathematics, University of Poona, Pune, August 1994.
``Constructible numbers and field extensions'', A series of two
lectures, Workshop in Mathematics, Indian Institute of Technology, Bombay,
November 1994.
``Field theory and ramification theory'', A series of five lectures,
NBHM Instructional School on Algebraic Number Theory, University of Bombay,
Bombay, December 1994.
``Resultants and discriminants'', A series of two lectures,
Workshop in Mathematics, Indian Institute of Technology, Bombay,
November 1995.
``Elimination theory and Gröbner bases'' A series of three
lectures, Refresher Course in Computational Algebra and Geometry,
University of Bombay, Mumbai, December 1996.
``An algorithmic method in polynomial ideal theory and its
applications'', A series of three lectures, Refresher Course on Advances
in Algebra and their Applications, Aligarh Muslim University, Aligarh,
March 1997.
``Introduction to Algebraic Geometry'', An intensive short
course of twenty lectures, New Arts, Commerce & Science College,
Ahmednagar, August 1997 and October 1997.
``Introduction to the theory of equations'', A series of four
lectures, Regional Maths Olympiad Training Programme,
L.U. & M. V. College, Andheri, Mumbai, November 1998.
``Rudiments of Linear Algebra'', A series of three lectures,
Workshop in Mathematics, Indian Institute of Technology, Bombay,
December 1998.
``First and Second Fundamental Theorems of Invariant Theory'',
A series of seven lectures,
Winter School on Algorithms in Invariant Theory and Algebraic Geometry,
University of Pune, Pune, December 1999.
``Polynomials and their roots'', A series of four lectures,
Refresher Course on Fundamental Theorem of Algebra,
University of Mumbai, Mumbai, February 2000.
``Review of Classical Commutative Algebra'', A series of two lectures, Winter School on Cohomological Methods in Commutative Algebra, supported by
NBHM and IMU, Homi Bhabha Centre for Science Education, Mumbai, November 2000.
``Lectures on Algebraic Number Theory'', A series of ten lectures,
Christian-Alberchts Universität Kiel, Kiel, Germany, December 2000.
``Introduction to Coding Theory and Algebraic Geometry'', A series of
six lectures, UGC Refresher Course on Recent Developments
in Mathematics, Shivaji University, Kolhapur, October 2001.
``Bezout's Theorem'', A series of five lectures, UGC Refresher Course
on Elliptic Curves and Cryptography, University of Mumbai, Mumbai,
February-March 2002.
``Basic Algebraic Geometry'', A series of five lectures, Winter School on
Arithmetic Algebraic Geometry, Harish-Chandra Research Institute, Allahabad,
December 2002.
`Zeta functions of curves over finite fields'', A series of two lectures,
Mini Workshop on Curves over Finite Fields, University of Mumbai, Mumbai,
July 2003.
"Coding Theory'', A series of three lectures, Workshop on Coding Theory,
Mathematical Sciences Institute, Postgraduate Centre of Karnataka University,
Belgaum, November 2004.
``Dimension theory of affine algebras'', A Series of Six Lectures, Advanced Instructional School in Commutative Algebra and Algebraic Geometry, IIT Bombay, Mumbai, July 2005.
``Equations over finite fields'', A series of six lectures, Refresher
Course on Finite Fields and their Applications,
University of Mumbai, Mumbai, March 2006.
``Commutative Algebra'', A series of eight lectures, NBHM Annual Foundation
School (AFS)-II, Bhaskaracharya Pratishthana and University of Pune,
Pune, June, 2006.
``Field and Galois Theory'', A series of eight lectures,
First ATM School in Algebra and Linear Algebra for Lecturers,
Indian Institute of Technology Bombay, June-July 2006.
``Convexity, Concavity and Differentiability of Functions of Several
Variables'', A series of three lectures, ATM School for Lecturers in
Multivariable Calculus, University of Pune, Pune, November 2006.
``Introduction to algebraic geometry'', Short Term Training Programme on Advances in Control Theory, Veermata Jijabai Technological Institute (VJTI), Mumbai, October 2007.
``Introduction to coding theory'', Workshop on Mathematics for Engineers, D. J. Sanghvi College of Engineering, Vile Parle, Mumbai, February 2008.
``Hardy-Ramanujan-Rademacher Formula for the number of integer partitions'', A Series of four lectures, NBHM Advanced Instructional School on Complex Analysis, Pune, June-July 2008.
"Linear recurrence equations over finite fields'',
A series of five lectures,
Discussion Meeting on Finite Fields and Coding Theory,
Harish-Chandra Research Institute, Allahabad, November 2009.
"Fundamental theorem of calculus and its generalizations'', A series of two
lectures, Refresher Course for College Teachers of Mathematics, University
of Pune, Pune, November 2009.
"Gröbner bases and coding theory'', A series of five lectures,
Indo-German Workshop on Computational Commutative Algebra (NBHM Advanced Instructional
School), Indian Institute of Science Education and Research, Pune, December 2010.
"Finite fields'', A series of two lectures, School on Algebra, Analysis and
Topology, The Kerala School of Mathematics, Kozhikode, January 2011.
"Finite fields and their applications'', A series of two lectures,
Karnataka Science & Technology Academy Special Lecture Series,
Mangalore University, Mangalagangothri, October 2011.
"Algebra'', A series of six lectures, NBHM Annual Foundational School (AFS-I), Indian Institute of Science Education and Research, Pune, December 2011.
"Normalization and primary decomposition'', A series of four lectures, NBHM Advanced Instuctional School on Computational Commutative Algebra, NIIT University, Neemrana, Rajasthan, January 2012.
"Topics in elementary number theory'', A series of four lectures, UGC Refresher Course in Mathematics/Statistics,
Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, September 2012.
"Betti numbers of Stanley-Reisner rings and generalized Hamming weights of codes and matroids", A series of four lectures, Workshop on Syzygies and Free Resolutions, Chennai Mathematical Institute, Siruseri, December 2012.
"Linear feedback shift registers and their
generalizations", A series of two lectures, National Workshop on
Computer Applications based on Modern Algebra, Manipal Institute of Technology, Manipal, January 2013.
"Aspects of coding theory", A series of six lectures, Advanced Instructional School on Algebraic Combinatorics, Indian Statistical Institute, Bangalore, July 2013.
"Differentiation of vector valued functions of several real variables'', A series of six lectures, Teachers Enrichment Workshop on Multivariable Calculus, Bhaskaracharya Pratishthana, Pune, November 2013.
Matrices, linear maps, and canonical forms", A series of six lectures, Instructional School for Lecturers (ISL) on Linear Algebra, Centre for Excellence in Mathematical Sciences, Kumaun University, Almora, Uttarakhand, March 2014.
"Theory of equations", A series of six lectures, NCM Instuctional School on Galois Theory, SGGS Institute of Engineering & Technology, Nanded, December 2014.
"Determinants and characterisitic polynomials", A series of six lectures, NCM Instructional School for Teachers on Linear Algebra, SGGS Institute of Engineering and Technology, Nanded, November 2015.
"Basics of ring theory", A series of six lectures, NCM Instructional School for Teachers on Algebra, Malaviya National Institute of Technology, Jaipur, December 2015.
Lecture notes based on some of these short courses are available here.