*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

*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

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.
   

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.