PROFILE
 
TEACHING
Courses taught at the Department of Mathematics
No.
 Year/Semester  Title of Course
 Credits
Taught alone/jointly
1
 1992/Aug-Dec  MA-211: Linear Algebra
3:0
 with Prof. P. Prasad
2
 1992/Aug-Dec  MA-311: Algebra
3:0
 Alone
3
 1993/Aug-Dec  MA-211: Linear Algebra
3:0
 Alone
4
 1993/Aug-Dec  MA-311: Algebra
3:0
 Alone
5
 1994/Aug-Dec  MA-211: Linear Algebra
3:0
 Alone
6
 1994/Aug-Dec  MA-311: Algebra
3:0
 Alone
7
 1995/Aug-Dec  MA-212: Discrete Structures
3:0
 Alone
8
 1996/Jan-April  MA-312: Commutative algebra
3:0
 Alone
9
 1996/Aug-Dec  MA-331: Topology
3:0
 with Prof. B. Datta
10
 1997/Aug-Dec  MA-311: Algebra
3:0
 Alone
11
 1998/Jan-April  MA-314: Algebraic curves
3:0
 Alone
12
 1998/Aug-Dec  MA-331: Topology
3:0
 with Prof. B. Datta
13
 2000/Aug-Dec  MA-311: Algebra
3:0
 Alone
14
 2001/Jan-April  MA-223: Functional Analysis
3:0
 Alone
15
 2001/Aug-Dec  MA-213: Algebra II
3:0
 Alone
16
 2001/Aug-Dec  MA-226: Complex Analysis II
3:0
 Alone
17
 2002/Aug-Dec  MA-302: Advanced Calculus*
3:0
 Alone
18
 2002/Aug-Dec  MA-218: Number theory
3:0
 with Prof. H.Wiebe
19
 2003/Aug-Dec  MA-219: Linear Algebra*
3:0
 Alone
20
 2003/Aug-Dec  MA-312: Commutative Algebra*
3:0
 Alone
21
 2004/Aug-Dec  MA-231: Topology*
3:0
 Alone
22
 2007/Jan-Apr  MA-217: Discrete Mathematics*
3:0
 Alone
23
 2008/Jan-Apr  MA-312: Commutative Algebra
3:0
 Alone
         


*Details of the Syllabus, Lectures and Exercise sets prepared for these courses can be found on the
Homepage: http://math.iisc.ernet.in/˜patil/courses

Courses taught at the Department of CSA

No.
 Year/Semester  Title of Course
 Credits
Taught alone/jointly
1
 1992/Aug-Dec  MA-211: Linear Algebra
3:0
 with Prof. P. Prasad
2
 1992/Aug-Dec  MA-311: Algebra
3:0
 Alone
3
 1993/Aug-Dec  MA-211: Linear Algebra
3:0
 Alone
         


*Details of the Syllabus, Lectures and Exercise sets prepared for these courses can be found on the
Homepage: http://math.iisc.ernet.in/˜patil/courses

Special courses taught at the Institute

No.
 Year/Semester  Title of Course
 Credits
Taught alone/jointly
1
1993/Dec Basic Algebraic Geometry1
 Alone
2
2000/Sept-Dec Riemann Surfaces2
 with Dr. T. Bhattacharrya
3
2003/May-Jun Basic Algebra3
 Alone
4
2005/Sept-Dec Long Course-AAG-054
Algebra, Arithmetic and Geometry
 Alone
5
2006/Jan-Apr Long Course-AAG-05 – Contd...5
Algebra, Arithmetic and Geometry
 Alone
6
2006/Oct-Dec IAG-066
Introduction to Algebraic Geometry
 Alone
  1. This short course of 10 lectures (of 90 minutes) on “Basic Algebraic Geometry” was introduced for the two talented students (Ms Veena Adiga, IIT, Bombay and Mr. R. Jayendraraj, Mayiladuthurai) who were selected (sponsored by NBHM) from the MTTS Programme 1993, to spend one month December 1993 with me to learn “Algebraic Geometry”. Many students and researchers from various engineering departments attended this course of lectures.
  2. During Sept-Dec 2000, this was a seminar/course on “Riemann Surfaces” (Jointly with Dr. T. Bhattacharrya) based on the book : Forster, O. Lectures on Riemann Surfaces, GTM 81, Springer-Verlag, Heidelberg, 1977. Many students and faculty colleagues attended this course of lectures.
  3. During May-June 2003, I offered the special summer course on “Basic Algebra”. This was a self-contained course without any prerequisites and was attended by many students from various engineering departments.
  4. 4A very special “Long Course” entitled “Algebra, Arithmetic and Geometry — With a View Toward Applications” from September 2005. The main aims of this Course were to make students think, stimulate them into active learning, show them the excitement of doing mathematics on their own, enthuse them into learning more advanced topics with confidence, assist them to realize their potential, nurture their Mathematical talent and appreciate the deep effects on the application world. Special effort were be made to encourage the participants to ask questions, raise doubts and seek clarifications in the class-room. The course was be taught very much in the spirit of a mathematical “guided tour”. Volunteering as the guide, I took upon myself the task of charting a route through beautiful mathematics surrounding the above three classical branches and led the audience through the route pointing out the beautiful sceneries and historical landmarks along the way. The emphasis was given to motivate the development of important concepts using as many examples as possible. These examples were ranged from routine to fairly sophisticated theoretical ones.
    This course presupposed ONLY a basic knowledge of Elements of set-theory, Elementary abstract algebra and Linear algebra. The first stage of the course was the foundations of “Algebra”, “Arithmetic (Number theory)” and “Geometry” and interplay among them. Class Notes and Exercise-Sets are avaliable on my Home-Page : http://math.iisc.ernet.in/˜patil/courses.
  5. As there was a very good response to this “Long Course-AAG-05” which started in September 2005. After a break of two weeks in December 2005, the course continued during Jan-June 2006. During this course there were “Seminars by Participants” on some interesting topics.
  6. This course was a continuation of the Long Course- AAG-05.
Courses Taught Outside the Institute
No.
 Year/Semester  Title of Course Institute / University
1
1987-88 Algebraic Geometry –Language of Schemes1 School of Mathematics, TIFR, Bombay, India
2
1990/Aug-Dec Algebraic Geometry2 Department of Mathematics, Panjab University, Chandigarh, India
3
1992/July Introduction to Algebraic Geometry3 Department of Mathematics, University of Poona, Pune India
4
1998 Oct-1999 Feb Projective Modules4 Department of Mathematics Ruhr Universi¨at Bochum, Germany
5
1999/April-July 150206 Erg¨anzung zur Linearen Algebra und Geometrie5 Department of Mathematics, Ruhr Universi¨at Bochum,
Germany
6
1999/April-June Set-theoretic Complete intersections6 Department of Mathematics, Universi¨at Leipzig, Germany
7
2001/April-June 10010611 Ordinary Differential Equations7 Department of Physics, Universi¨at Leipzig, Germany
8
2004/April-July 150 239 An Introduction to Commutative Algebra and Algebraic Geometry8 Department of Mathematics, Ruhr Universi¨at Bochum,
Germany
9
2008/June-July Koszul Complex and Regular Sequences9 Department of Mathematics Universi¨at Leipzig, Germany
10
2008-09/Oct-Feb Calculus 1*10 - Analysis of one variable
(32 Lectures of 90 Minutes and 16 Tutorials of 90 Minutes)
Department of Mathematics Universi¨at Leipzig, Germany
11
2008-09/Oct-Feb Linear Algebra*10
(32 Lectures of 90 Minutes and 16 Tutorials of 90 Minutes)
Department of Mathematics Universi¨at Leipzig, Germany
12
2008-09/April-July Calculus 2*10 - Analysis of one variable
(32 Lectures of 90 Minutes and 16 Tutorials of 90 Minutes)
Department of Mathematics Universi¨at Leipzig, Germany
  1. This was very long course based on the book : [Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York, Heidelberg, Berlin, 1977, xvi + 496 pp.]
  2. During the semester Aug-Dec 1990 I was invited to give this course.
  3. During the visit I gave this course.
  4. This course was based on various research papers and the book : [Lam, T. Y., : Serre’s Conjecture, Lecture Notes in Mathematics, 635, Springer-Verlag, New York/Berlin, 1978.]
  5. The main aim of this course was to prove Hilbert’s Nullstellensatz and give its applications.
  6. This course was based on various research papers and the book : [Mandal, S ., : Projective Modules and Complete Intersections, Lecture Notes in Mathematics, 1672, Springer-Verlag, New York/Berlin, 1997.]
  7. A course (Bachelor-Ausbildung) given in the International Studies Programme of the Department of Physics, University of Leipzig, Germany.
  8. The main aim of this course in to introduce the language of algebraic geometry by using commutative algebra and prove the basic theorems in both commutative algebra and algebraic geometry, e.g. Hilbert’s Nullstellensatz, Noether’s Normalisation lemma, Localisation, Primary decomposition, Zariski- topology, Algebraic varieties, etc.
  9. This Course was given while I was on Sabbatical Leave from the institute during June 2008-July 2009.
  10. The courses marked with * are core courses for Bachelor-Physik, International Physics Studies Programme of the Department of Physics, University of Leipzig, Germany. These Courses were taught while I was on Sabbatical Leave from the institute during June 2008-July 2009.
 
 
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