TEACHING 
Courses taught at the Department of Mathematics 
No. 
Year/Semester 
Title of Course 
Credits 
Taught alone/jointly 
1 
1992/AugDec 
MA211: Linear Algebra 
3:0 
with Prof. P. Prasad 
2 
1992/AugDec 
MA311: Algebra 
3:0 
Alone 
3 
1993/AugDec 
MA211: Linear Algebra 
3:0 
Alone 
4 
1993/AugDec 
MA311: Algebra 
3:0 
Alone 
5 
1994/AugDec 
MA211: Linear Algebra 
3:0 
Alone 
6 
1994/AugDec 
MA311: Algebra 
3:0 
Alone 
7 
1995/AugDec 
MA212: Discrete Structures 
3:0 
Alone 
8 
1996/JanApril 
MA312: Commutative algebra 
3:0 
Alone 
9 
1996/AugDec 
MA331: Topology 
3:0 
with Prof. B. Datta 
10 
1997/AugDec 
MA311: Algebra 
3:0 
Alone 
11 
1998/JanApril 
MA314: Algebraic curves 
3:0 
Alone 
12 
1998/AugDec 
MA331: Topology 
3:0 
with Prof. B. Datta 
13 
2000/AugDec 
MA311: Algebra 
3:0 
Alone 
14 
2001/JanApril 
MA223: Functional Analysis 
3:0 
Alone 
15 
2001/AugDec 
MA213: Algebra II 
3:0 
Alone 
16 
2001/AugDec 
MA226: Complex Analysis II 
3:0 
Alone 
17 
2002/AugDec 
MA302: Advanced Calculus* 
3:0 
Alone 
18 
2002/AugDec 
MA218: Number theory 
3:0 
with Prof. H.Wiebe 
19 
2003/AugDec 
MA219: Linear Algebra* 
3:0 
Alone 
20 
2003/AugDec 
MA312: Commutative Algebra* 
3:0 
Alone 
21 
2004/AugDec 
MA231: Topology* 
3:0 
Alone 
22 
2007/JanApr 
MA217: Discrete Mathematics* 
3:0 
Alone 
23 
2008/JanApr 
MA312: 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/AugDec 
MA211: Linear Algebra 
3:0 
with Prof. P. Prasad 
2 
1992/AugDec 
MA311: Algebra 
3:0 
Alone 
3 
1993/AugDec 
MA211: 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 Geometry^{1} 

Alone 
2 
2000/SeptDec 
Riemann Surfaces^{2} 

with Dr. T. Bhattacharrya 
3 
2003/MayJun 
Basic Algebra^{3} 

Alone 
4 
2005/SeptDec 
Long CourseAAG05^{4} Algebra, Arithmetic and Geometry 

Alone 
5 
2006/JanApr 
Long CourseAAG05 – Contd...^{5} Algebra, Arithmetic and Geometry 

Alone 
6 
2006/OctDec 
IAG06^{6} Introduction to Algebraic Geometry 

Alone 

 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.
 During SeptDec 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, SpringerVerlag, Heidelberg, 1977. Many students and faculty colleagues attended this course of lectures.
 During MayJune 2003, I offered the special summer course on “Basic Algebra”. This was a selfcontained course without any prerequisites and was attended by many students from various engineering departments.
 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 classroom. 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 settheory, 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 ExerciseSets are avaliable on my HomePage :
http://math.iisc.ernet.in/˜patil/courses.
 As there was a very good response to this “Long CourseAAG05” which started in September 2005. After a break
of two weeks in December 2005, the course continued during JanJune 2006. During this course there were “Seminars
by Participants” on some interesting topics.
 This course was a continuation of the Long Course AAG05.

Courses Taught Outside the Institute 
No. 
Year/Semester 
Title of Course 
Institute / University 
1 
198788 
Algebraic Geometry –Language of Schemes^{1} 
School of Mathematics, TIFR, Bombay, India 
2 
1990/AugDec 
Algebraic Geometry^{2} 
Department of Mathematics,
Panjab University, Chandigarh, India 
3 
1992/July 
Introduction to Algebraic Geometry^{3} 
Department of Mathematics,
University of Poona, Pune
India 
4 
1998 Oct1999 Feb 
Projective Modules^{4} 
Department of Mathematics
Ruhr Universi¨at Bochum,
Germany 
5 
1999/AprilJuly 
150206 Erg¨anzung zur Linearen Algebra und Geometrie^{5} 
Department of Mathematics,
Ruhr Universi¨at Bochum,
Germany 
6 
1999/AprilJune 
Settheoretic Complete intersections^{6} 
Department of Mathematics, Universi¨at Leipzig, Germany 
7 
2001/AprilJune 
10010611 Ordinary Differential Equations^{7} 
Department of Physics,
Universi¨at Leipzig, Germany 
8 
2004/AprilJuly 
150 239 An Introduction to Commutative Algebra and Algebraic Geometry^{8} 
Department of Mathematics, Ruhr Universi¨at Bochum,
Germany 
9 
2008/JuneJuly 
Koszul Complex and Regular Sequences^{9} 
Department of Mathematics
Universi¨at Leipzig, Germany 
10 
200809/OctFeb 
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 
200809/OctFeb 
Linear Algebra*^{10}
(32 Lectures of 90 Minutes and 16 Tutorials of 90 Minutes) 
Department of Mathematics Universi¨at Leipzig, Germany 
12 
200809/AprilJuly 
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 

 This was very long course based on the book : [Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, SpringerVerlag, New York, Heidelberg, Berlin, 1977, xvi + 496 pp.]
 During the semester AugDec 1990 I was invited to give this course.
 During the visit I gave this course.
 This course was based on various research papers and the book : [Lam, T. Y., : Serre’s Conjecture, Lecture Notes in Mathematics, 635, SpringerVerlag, New York/Berlin, 1978.]
 The main aim of this course was to prove Hilbert’s Nullstellensatz and give its applications.
 This course was based on various research papers and the book : [Mandal, S ., : Projective Modules and Complete Intersections, Lecture Notes in Mathematics, 1672, SpringerVerlag, New York/Berlin, 1997.]
 A course (BachelorAusbildung) given in the International Studies Programme of the Department of Physics, University of Leipzig, Germany.
 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.
 This Course was given while I was on Sabbatical Leave from the institute during June 2008July 2009.
 The courses marked with * are core courses for BachelorPhysik, 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 2008July 2009.


