Arindama Singh
Department of Mathematics

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Research Guide

Wrting Paper?

Industrial Maths, Kaiserslautern

Dept of Computing, Macquarie Univ

Maths, IIT Kanpur

Maths, IIT Kharagpur

CS, Univ of Hyderabad

Indian Math Soc

Ramanujan Math Soc

AMTI

ISTE

Singular Perturbation

The image on the top right is the Hogsmeade Village.

 

Extras

Though administration is an integral part of education, I am a bit averse to it; my personal taste. It so happened I could not refuse the responsibility of JEE. In 2010, I took the responsibility of organizing vice-chairman of JEE. Then there was no escape. In 2011, I did the job of vice-chairman again, and in 2012, I managed the JEE job as chairman. I have been a member of many confidential committees; but I canot mention them here!

Some other topics relevant to education, that you may not have found in other sections, are here. Please feel free to browse through this section. The following are the topics covered:

Guidance
    Ph.D.
    M.Phil.
    M.Sc.
Assignments Abroad
    University of Kaiserslautern
    Macquarie University
Invited Talks
    At Conferences
    At Short-term Courses
    At Institutions
Unpublished Articles
    Conferences
    Others
My Views on Research, Teaching, and Professing
    On Research
    On Teaching
    On Professing I concurr with this view.
Membership in Professional Bodies

 
Guidance

During my career as a teacher I had guided many students for their research work. The works that led to Ph.D. degree were carried out in collaboration with the respective students. The works for the M.Phil. degree were usually survey of literature with some work-outs done by the students. I had but a little contribution in terms of the work-outs. Basically I had to suggest the body of relevant literature, and then help in working out the details so as to put the matter in a unified and coherent manner. The guidance involved in M.Sc. focuses more in letting the student understand and present a topic centred arround four to five papers. Here are the respective lists:

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Ph.D.

  1. Student: M. Ravibabu
    Topic: New Algorithms to compute Eigenpairs of Large Matrices, Awarded degree in 2016
  2. Student: S.Surya Prasath
    Topic: Image Processing and PDEs, Awarded degree in 2010
  3. Student: Jajati K Sahoo
    Topic: Mathematical learning Theory, Awarded degree in 2010
  4. Student: M.K.Rout
    Topic: Computing Prime Implicates of First Order Formulas, Awarded degree in 2005
  5. Student: S.Sheela
    Topic: Regularization of Singularly Perturbed Elliptic PDEs, Awarded degree in 2003

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M.Phil.

  1. Student:G.Chinna Babu
    Topic:Heuristic Methods for Singular Perturbation, 1992
  2. Student: K.Radhika
    Topic:Finite Element Methods for Singularly Perturbed Two-point Boundary Value Problems, 1993
  3. Student:T.Bhavani
    Topic:Euler's One-step methods for Singularly Perturbed Two-point Boundary Value Systems, 1993
  4. Student: G.S.Mini
    Topic: Splines for Singular Perturbations, 1994
I guided these M.Phil. students during my stay at University of Hyderabad.

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M.Sc.

  1. Student: K.Kavitha
    Topic: A Heuristic Method for Singularly Perturbed Two-Point Boundary Value Problems, 1996
  2. Student:G.Janaki
    Topic: Computing Prime Implicants, 1997
  3. Student:J.Sangeetha
    Topic:Adequacy of Equational Calculus, 1997
  4. Student: S.Masoothu
    Topic: A Uniformly Convergent Numerical Method for A Singular Perturbation Problem, 1998
  5. Student: Deepa Nagarajan
    Topic: An FEM for A Problem With A Small Parameter, 1998
  6. Student: R.Sunitha
    Topic:Representing And Reasoning About Motion in a Two-Dimensional World, 1999
  7. Student: N.Subhashini
    Topic: Subgoal Strategies for Solving Board Puzzles, 1999
  8. Student: M Smitha Unny
    Topic: Numerical Methods for the Solution of Stiff Differential Equations, 1999
  9. Student: Ann C.Jose
    Topic:Default Reasoning, 2000
  10. Student:K.Deepa
    Topic:Surprise Examination Paradox, 2000
  11. Student: Delphin Lizzy
    Topic: Adequacy of Calculational Logic, 2001
  12. Student: O.K.Raja Mohamed
    Topic: Hypergraphs for SAT, 2001
  13. Student:K.Vijaykumar
    Topic:Automated reasoning with OTTER, 2002
  14. Student: R.Ushanandini
    Topic:Analytic Tableau for Sentential and Predicate Logic, 2002
  15. Student: R.Srilakshmi
    Topic: A `C' Implimentation of Gentzen's sequential Calculaus, 2002
  16. Student: V.Seethalakshmi
    Topic:The Search for Satisfaction, 2002
  17. Student:M.Mutyala Rao
    Topic: Examples of Categories, 2003

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Assignments Abroad

I do not like travelling. During travel, I must be worrying about my documents, mode of travel, paucity of time, and what to eat, safeguarding my money and the baggage. In return, I would get experience, which I usually forget within six months. Nonetheless, I travelled, may be, just to understand that it does not worth.

During both the visits, I came to learn that we must improve atleast on three counts:

  • General Hygiene
    I saw how well their roads are maintained and how well they dispose of garbage.
  • Self Respect
    Students there never copy their homework from a friend.
  • Seriousness and involvement in one's work
    In India, a common complain of the wives to their husbands, (I am fortunate not to have experienced it.) is -- `Only you are working for this much salary, or others are also working?. Look at so and so. He is also working in your office, but see how is he able to manage devoting his office time to his family.' This is our crime. On the other hand, our work environment is also equally a case for improvement. In general, the joke from a Tamil film may be cited -- 'One who works, loves his work, so he gets more work. One who does not work, gets promotion.' In general, one who does his intended job is considered a donkey, and one who gets around it, thus getting more from the society than his contribution to it, is considered intelligent. This social superstition must go.

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University of Kaiserslautern

University of Kaiserslautern, Germany : The department of Mathematics, IIT Madras wanted to start the M.Tech. programme in Industrial Mathematics. It sent me to the University of Kaiserslautern for obtaining first hand experience of a similar program which was being run quite successfully under the guidance of Professor H. Neunzert. I visited the university during May 05 to July 12, 1998. Delivered a lecture at the university and learnt a bit of Industrial Mathematics. The work environment was excellent. Just to mention, and not to offend any, I was not very much impressed by the programme. The sort of work that was being done over there were being done by our engineering departments here. So I could not appreciate their being done in a mathematics department.

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Macquarie University

Macquarie University, Australia : One of my old friends, Abhaya Nayak is currently working in Macquarie University as a faculty in the Division of Computing. His work focusses on belief revision in propositional logic. He wanted me to have some collaborative work on the topic and also visit their `Intelligent Systems' group. Moreover, Professor Norman Foo of University of New South Wales has adopted my book `Logics for Computer Science' as one of the texts for his course on logic. This invitation from Abhaya gave me a chance to meet Professor Foo. During October 08 to December 18, 2005 I visited Macquarie University. During this visit, I met Professor Foo of University of New South Wales, Professor Abdul Sattar of Griffith University, Professor Sanjay Chawla at University of Sydney, and Professor Aditya Ghosh of University of Wollogong. I also visited NICTA at Brisbane. I saw their manner of work. The work environment is excellent. However, the focus of work is slowly changing its direction from academics to business.

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Invited Talks

I had delivered invited talks in conferences, at the respective departments of institutions other than my place of employment, and to the participants of short-term courses. The topics range from basic mathematics to research topics. The paper presentations at conferences are excluded. I have forgotten most of them. Those I remember, are as under:

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Invited Talks At Conferences

  1. Do Euler's schemes commute with decouplings?, Annual Conference of OMS held at Utkal University, Bhubaneswar, March 1998.
  2. Space in Mathematics,National Space Seminar, IIT Kharagpur, September 1998.
  3. Sat and Hypergraphs, A series of 3 lectures delivered at Logic Colloquium organised by Calcutta Logic Circle, at Calcutta University, July 1999.
  4. Propositional logic via hypergraphs, OMS Annual Conference held at Utkal University, Bhubaneswar, March 2000.
  5. Regularization of Singularly Perturbed PDEs, Int. Conf. on Recent Trends in Differential Equations and Dynamical Systems, IIT Kanpur, December 2001.
  6. Towards a Topological Theory of Cognition, National Symposium in Cognitive Sciences, University of Hyderabad, February 2002.
  7. Creativity. Creativity! Creativity?, National Seminar on Cognitive Sciences and Creativity, University of Hyderabad, February 2004.
  8. Cantor's Little Theorem and its Corollaries, Indian Mathematical Association, Benaras Hindu University, December 2013.

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At Short-term Courses

  1. Singular Perturbation, Three lectures at UGC Refreshers course on Differential Equations, University of Hyderabad, March 1992.
  2. Numerical Linear Algebra, Six lectures at UGC Refreshers course on Linear Algebra and Applications, University of Hyderabad, December 1993.
  3. Turing Machines, Nine lectures at UGC Refreshers course on Mathematics in Computation, Sambalpur University, Sambalpur, March 1994.
  4. Algorithms, Nine lectures at UGC Refreshers course on Discrete Mathematics, Utkal University, Bhubaneswar, March 1995.
  5. Metalogic, Nine lectures at AICTE Short-term course on Logic, Graphs, and Automata, IIT Madras, Chennai, October 1997.
  6. Quantification Theory, Nine lectures at ICPR Short Term Course on Logic, ICPR, Butler Palace, Lucknow, December 1998.
  7. Logic and Problem Solving, Six lectures at UGC Short Term Course in Maths, Kasargod College, Kerala, August 1999.
  8. Linear Algebra, Series of lectures at MTTS-level-0, IIT Madras, May-June 2000.
  9. Linear Algebra, Series of lectures at MTTS-level-0, University of Pondichery, May 2001.
  10. Mathematical Logic, Three lectures at UGC Short Term Course in Discrete Maths., Ramanujan Institute, Chennai, February 2003.
  11. Linear Algebra, Series of lectures at MTTS-level-1, IIT Guwahati, June 2003.
  12. Stability of ODEs, Three lectures at UGC Short Term Course in Differential Equations, Pondichery University, October 2003.
  13. Context-free Languages and PDA, Six lectures at QIP-STTP on Research Trends on Formal Language Theory and Automata, IIT Madras, September 2005.
  14. Propositional Logic, Six lectures at the First Conference on Logic and its Relation with Other Disciplines, IIT Bombay, January 2006.
  15. Foundation of Mathematics,Twelve lectures at Mini-MTTS, NIT Agartala, October, 2013.
  16. Linear Algebra,Twelve lectues at MTTS, IIT Guwahati, July 2014.
  17. What is a real number?,Two lectures at APU-RMS workshop, Chennai, August 2014.
  18. What is pi?, Two lectures at APU-RMS workshop, Chennai, October 2014.
  19. Linear Algebra, Six lecturs at a short-term course for college teachers, Ramanujan Institute for Advanced Studies, University of Madras, October 2014.
  20. How many?, One lecture at a one-day workshop for school children, Institute of Mathematical Sciences, Chennai, November, 2014.
  21. Ordinary Differential Equations, Twelve lectures at TPM, NISER, Bhubaneswar, May-June 2015.
  22. Foundations of Mathematics, Twelve lectures at TPM, NISER, Bhubaneswar, May-June 2016.

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At Institutions

  1. Numerical Solution of Singularly Perturbed Boundary Value Problems, University of Kaiserslautern, Germany, June 1998.
  2. Satisfiability Problem, DST Course on Current Problems in Mathematics, MS University, Tirunelvelli, July 1998.
  3. Computing Prime Implicants, IIT Bombay, Mumbai, September 1998.
  4. Prime Implicants, Institute of Mathematical Sciences, Chennai, March 1999.
  5. Theory of Equations, Mathematics for School Children, Cultural and Mathematical Foundation for Children, Chennai, February 2004.
  6. Context-free Languages,SNM Jain Engineering College, Chennai, June 2004.
  7. Mapcode Computability Institute of Information and Integrated Systems, Griffith University, Brisbane, November 2005.
  8. Cantor Schroder Bernstein Theorem Indian Institute of Science Education and Research, Thiruvananthapuram, August 2014.
  9. 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 ill-posed 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 pile-up of undigested and ill-understood 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 well-known "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 faculty-course 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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2015   Arindama Singh