At Institutions

Numerical Solution of Singularly Perturbed
Boundary Value Problems, University of Kaiserslautern, Germany,
June 1998.

Satisfiability Problem, DST Course on Current
Problems in Mathematics, MS University, Tirunelvelli, July 1998.

Computing Prime Implicants, IIT Bombay, Mumbai,
September 1998.

Prime Implicants, Institute of Mathematical
Sciences, Chennai, March 1999.

Theory of Equations, Mathematics for School Children, Cultural and Mathematical Foundation for Children, Chennai, February 2004.

Contextfree Languages,SNM Jain Engineering College, Chennai, June 2004.

Mapcode Computability Institute of Information and Integrated Systems, Griffith University, Brisbane, November 2005.

Cantor Schroder Bernstein Theorem Indian Institute of Science Education and Research, Thiruvananthapuram, August 2014.

Goedel's Incompleteness Theorems M.S. University, Thirunelvelli, Tamil nadu, India, April, 2016.
My Views on Research, Teaching, and Professing
It is a permanent debate how and what should be taught at which level. What topics are to be researched upon, and so on. Here are my views on research, teaching, and professing, in general, and on why I took up to my own research and teaching interests. This is not uptodate. That is, currently, I may be adhering to slightly different opinion than written here; it is in flux!
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On Research, My Interests
It feels divine to loose one's identity in seeking the path of
artistic pursuit. As of that matter any scientific discipline has
such a spiritual angle for the scientist. Also, in the context of
our social existence, one feels the urge to pursuing the kind of
art that contributes, however small, towards the progress of
society. One must consider both the aspects and exhibit a balance between these dual aspects while doing research.
Such duality and unity of the abstract art of reasoning
and of its concretization is in the heart of mathematics and
computer science. The thrust is not only on looking at how the accumulated knowledge might come of help, but also on the creation of knowledge that is felt too required for improving our way of life. The latter is achieved through the translation of a real life problem to a
formal language, the activity, often called as mathematical
modelling. Experience shows that models of most practical
problems pose challenges to the existing mathematical and
computing practice. This is aptly described by the modern terms of
illposed problems, hard problems, etc. My research interests include subproblems in these general classes.
With the commonality of computation, I am also interested in the
application of Logic to various branches of computer science. In
advanced AI applications such as hypotheses synthesis, truth
maintenance systems, etc, knowledge compilation plays an important
role. Knowledge compilation involves in transforming a knowledge
base to an equivalent one but with (computationally) nice
properties such as primeness, etc. I have developed an efficient
algorithm for computing prime implicants of a propositional
knowledge base competing with (also complementing) the method of
consensus and subsumption. I had extended the notion of knowledge
compilation to first order logic.
As I mentioned earlier, I have changed my topic of research almost every five years. I also worked in image restoration, mathematical learning theory. Currently I am working in approximating eigenvalues and eigenvectors of large matrices, which comes under Numerical Linear Algebra. It looks that my research interests have looped around the broad theme of mathematics behind computation.
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On Teaching, My Interests
We, human beings, form perhaps a unique species; we have
premeditatively set up very elaborate and comprehensive programs
to educate our young ones.
I believe that the primary objective of an educational institution
is teaching. By that, I do not assert that research is an
appendix. On the contrary, in order to teach well one must be an
honest researcher. Research is a prerequisite, a preparation. It
is the long and meticulous preparation of a Odisi performer who puts in ten years of continuing effort for the ten
minutes show. The inquisitiveness and the enquiries equip one with
the necessary metaknowledge of the subject for clearer
understanding and thus for better teaching. It enhances a
teacher's abilities to share with his students the taste of
knowledge accumulated and that is yet to be born.
Coming to teaching the subject of interest, one must explain why
a particular piece of knowledge fits where in the zigsaw.
Laterally, one must sharpen the eyes of the young ones to percieve
the underlying beauty that is hiding in seemingly different
disciplines. Most effort must be directed towards understanding
and explaining what, but slowly and steadily. Young ones need to
acquire knowledge and also to reason about them. Both exposure to
information and active participation are essential at this stage.
Only when one actively participates, one realizes what he thought
to have understood, he did not. So the teacher challenges his
students with problems so sliced out that they should feel the
thrill of discovering while being driven towards the goal. The
teacher slowly takes the role of a guide and aims at the
nullification of his own role, guiding, which must ultimately come
from the students themselves.
The way to perform teaching well lies in the understanding that
the subject must become a commonality between the teacher and the
taught. In case one fails in communicating the message of sharing,
one must try it from different angles, until the communication
channel becomes free, where thoughts and ideas would flow freely;
until the illuminating sparkle of understanding shines vividly in
the eyes of the students. This sparkle is the best reward of a
teacher, because only then he knows that his job is accomplished;
only then he knows that he has made a difference in one's life,
however small it may be.
My teaching interests include Scientific Computation, Formal
Languages and Machines, Data Structures, Logic and its application
to Program Verification, Program Construction, Linear Algebra, and Differential equations. Besides these courses, I also taught
courses including Calculus, Numerical Analysis, and Discrete
Mathematics.
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On Professing (I concurr with this view.)
THE ROLE OF THE PROFESSOR
by Walter Noll, Professor of Mathematics Emeritus, Carnegie Mellon University
August 1992, revised April 1997
This essay is intended not only to help professors better understand
their own role, but also to help the public at large better appreciate this role.
Although the essay is written from the point of view of a professor of
mathematics, its essence should apply to professors in any field.
When I am being asked what I do for a living and then answer that I
am a professor, the next question invariably is: "What do you teach?" This
shows that to most people, a professor is just a glorified teacher. The
university administration expects me to do research as well as teaching, and
it is assumed that these are the only important duties of an academic. In fact,
sometimes I get questionnaires in which I am asked how I spend my time:
what percentage on "teaching" and what percentage on "research". I am
very uncomfortable when answering such questions. Recently I realized that
I have spent most of my professional life neither with "teaching" nor with
"research" in the narrow sense: rather, I have been mostly occupied with
professing my subject: mathematics. There are important distinctions
between a teacher, a researcher, and a pure professor. Let me make them
clear.
The teacher's focus is on his students. His task is to convey a fixed
body of knowledge to his students and to worry about the best way to do so.
He normally follows a textbook and a "syllabus". A very important part of
his job is to assign homework and to give tests to find out how much his
students are learning. He pays attention to what the students think of him
and his performance. He sympathizes with his students' worry about their
grades.
The professor's focus is on his subject. He "lives" his subject and
cannot easily switch it off, even while lying in bed awake or on vacation. He
recreates the subject in his mind each time he lectures on it. He cannot
know, in the beginning of a course, exactly how and in what order he will
present the material. He may even, in the middle of the course, change his
mind about what material to include or exclude. He always tries to find a
new approach to and better insight into the subject of his course. He almost
never gives a course twice in the same way, and he considers it anathema to
have to follow a textbook and a syllabus. He is pleased if some students
follow and appreciate his efforts, but he finds homework, tests, and grades a
nuisance. As the famous British mathematician G.H. Hardy put it in his book
A Mathematician's Apology: " I hate 'teaching', and have had to do very
little,... ; I love lecturing, and have lectured a great deal to extremely able
classes;..."
The researcher's focus is on the discovery of new results. He is the
creator of new knowledge. His nightmare is to get stuck in his search or to
learn that what he has found has already been discovered shortly before by
somebody else. Priority is very important to him and will sometimes induce
him to rush into print prematurely.
The professor's focus, on the other hand, is on understanding, gaining
insight into, judging the significance of, and organizing old knowledge. He
is disturbed by the pileup of undigested and illunderstood new results. He
is not happy until he has been able to fit these results into a larger context.
He is happy if he can find a new conceptual framework with which to unify
and simplify the results that have been found by the researcher. Before going
into print, he lets his ideas ripen. Priority is not an issue for him.
I and most of my colleagues are teachers and researchers as well as
professors in the senses described above. Most are very good professors, but
many are only mediocre teachers or just adequate researchers. I know only
one who is very good in all three categories.
In the Faculty Handbook of this University, under "Criteria for
Faculty Appointments", I can find almost nothing that relates to professing a
subject in the sense described above. Such professing rarely gets much
recognition. Most of the rewards in academia go to those who excel in
research or in teaching. I believe this has had some bad effects.
The emphasis on research has led to the wellknown "publish or
perish" phenomenon. It has led to excessive specialization. A young faculty
member receives promotion because the letters of recommendation say that
he is "one of the best in his field"; but his field may be so narrow that there
are only ten people in the world working in it, and few outside this small
circle can understand the "new results" this faculty member has found. In
mathematics, it is easy to get a paper published that contains new results, no
matter how obscure and insignificant. Papers that present important new
perspectives often are rejected because they contain "no new results".
In recent years, young faculty members are more and more
encouraged to pay attention to teaching, especially since facultycourse
evaluations have become common. This has made teaching more and more a
popularity contest, and it has often led to lowering of standards and grade
inflation. Most students do not know the difference between a teacher and a
professor. They expect to be treated in college the same way as they were
treated in high school. They do not know that, in college, they should be
their own teachers.
The reasons for the push toward research and teaching alone may be,
at least in part, financial. Academics are encouraged to scramble for research
grants. The granting agencies want proposals that contain strategies for
obtaining specific "results". As to the push towards "teaching", the following
analysis by Camille Paglia in the Times Literary Supplement of May 22,
1992, although unfair to many parents and students, may contain some truth:
"As costs continue to rise, [the colleges are] locked into a strictly
commercial relationship with parents. Intellectual matters [take] a back seat
to the main issue: providing a 'nice time' for students with paying parents."
One may argue that we need only researchers and teachers, and that
professors are unnecessary. I do not agree because I believe that the
professor is the mediator between the researcher and the teacher.
Without influence from the professor, the teacher's curriculum would
soon become more and more outdated and lifeless. Even now, many of the
people who write textbooks for elementary courses in mathematics are hacks
who have only a very shallow understanding of the subjects they are writing
about. The teachers who select these books often do not know better, and the
sales success of these books depends more on the number of educationist
gimmicks used than on the soundness of the content. Academics are not
likely to get merit raises for writing elementary textbooks.
Without listening to the professor, the researcher would soon become
a narrow specialist who loses all contact with the rest of science. The
"results" found by the researcher, if not critically examined, sorted, and fit
into a coherent framework by the professor, would be of little value.
I believe that it is impossible to be a good teacher without being at
least a little bit of a professor in the sense of having some passion for the
subject. The sad state of the mathematics education in our secondary schools
is caused, at least in part, by the fact that too few teachers have any such
passion. I also believe that it is impossible to be a good researcher without
being somewhat of a professor, because research cannot be good unless it
relates to something larger than itself.
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Membership in Professional Bodies
I am a life member of the following professional bodies:

Indian Society for Industrial and Applied Mathematics (ISIAM)

Indian Society of Technical Education (ISTE)

Ramanujan Mathematical Society (RMS)

Indian Mathematical Society (IMS)

The Association of Mathematics Teachers of India (AMTI)

Orissa Mathematical Society (OMS)
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