Research in Mathematics


Hello. We are a pleased to have with us Prof. Arindama
Singh from the Department of Mathematics and he will discuss with us you know, research
in mathematics and aspects of research associated with you know student life and how it interacts
with you know their research at in their department and so on. Prof. Arindama Singh has a PhD in mathematics
from IIT, Kanpur and he has been here at IIT, Madras, as a faculty for more than two decades
now, since 1995 and has a lot of you know a rich experience in working with students
in actually various capacities because he has also held several positions in the institute
which deal with you know critical aspects of a student life here. And incidentally you should also look him
up on the internet. He is a very interesting personality, I had
the opportunity of looking up lot of information on a about him. So, if you get a chance please do look him
up he has a written a lot of things about his experiences in life in generally in addition
to his provisional activities. So, thank you for joining us. So, I would like to start by looking at this
aspect that you know at least in engineering background. We tend to have you know in any engineering
division, we have areas of activity which are considered traditional areas of research. In mathematics, is there such a thing, is
there such a concept like you know these are the traditional areas of research which are
there and then, and which have been there for a long enough time, but there is still
research going on it and therefore, there is a lot of literature that people can look
at and you know engage themselves against. Yes, as usual mathematics is in fact, living
traditionally so obviously, the old areas never die. OK. But new areas being added due to applications
and some other programs coming up in daily life. So, like we have the geometry we started from
Euclid or so, it is still living. OK. Research is going on in geometry in various
aspects of it. Similarly we have analysis which is very traditional,
algebra. So, these are some of the branches. In fact, these comprise the whole of mathematics. Any branch of mathematicians you take it is
somewhere related to one of this. One of this. Or even all of this. OK. So, they are still living have, however in
India sometime back fluid dynamics too care of almost everything. Any department you go there will be some people
working in fluid dynamics. Fluid dynamics. That is an engineering subject. So, slowly it is dying from mathematics departments. OK ok. And some pure math, that is being established
everywhere. OK. So, that is the trend now. So, new areas of research of would be. Yes. I mean in what would be cover? What would constitute like you know areas
which have sort of come upon you very recently that well, it may be say let’s say the 5-10
years time frame that many may be in their many groups interested in looking at. So, after this advent of computers, new areas
like numerical series. OK. Then computer science related mathematics. For example, discrete mathematics, data structures,
theory of computation, then image processing and anything related to numerical like – numerical
linear algebra, for example. So, these areas have come up recently. So, you yourself in fact, expert in Numerical
Analysis. Yes, I am also related to one of those. Yeah, Computer Science, Theoretical computer
science kind of activities. Okay so, these are the newer areas that in
mathematics the people work on actually. Okay In the sense in fact, if we look at may
be students coming into mathematics department what sort of backgrounds do they come in I
mean are they only are they almost uniformly you know bachelor or B. Sc in a mathematics
kind of background or you see different, do you see enough engineering students moving
to mathematics in the PG programs. Not many engineers coming to mathematics,
but there are one or two. OK. In every one or two years, we get one or two
engineering students who is so interest in coming to mathematics and they also do good
research after that we find, but uniformly it is M. Sc from mathematics. OK. That is our intake
OK. So, in some of the places where mathematics
and statistics both are there. So, M. Sc statistics people also come. OK. For doing research. OK ok. So, in terms of the students coming in they
probably come with an wide range of different institutions from which they have been educated
for their B. Sc and M. Sc and may be as you said you know one or two engineering students
and what not. When they come in, in terms of settling into
doing a research kind of a program here in mathematics department here, are there a specific
issue that you students facing as they settle in it may be the early part of their graduate
or post graduate life here in terms of technically adjusting to what is required here and so
on. Yeah. There is in fact, our interns should be able
to take care of this issues. OK. But it does not because of various reasons. We have to load or narrow down this scope,
so that it should be accessible to many people. So, in that sense we keep our interns in such
way that it is come on to all almost all the universities in India, which are doing in
the B. Sc programs. So, that do we get students from almost all
the places and then we have the problem of bringing that standard of, so that they will
be almost equal in 1 or 2 years and that’s a gigantic task, in one year it’s not possible
we know, but then we have to give some courses which will be very basic to them. So, that is the idea. OK. And then during this course work of period
they take the courses which are useful for the research also not only on the general
mathematics, but also narrowing down to their research area. So, at least 1 or 2 courses are given from
the research area so that they will be going faster. OK. This idea of course work is really very important
for the research students. So that they will be equalized to you over
1 or 2 years and then they will also be earning some expertise in their narrow down area. In terms of any other preparation in terms
you know. So, basically you are saying may be the rigger
is what they have to pick up on. Yes. When they come in and it takes some may be
a year or two to settle into this regard rigger, of course, when we think of I know basic sciences
you know including physics, chemistry, mathematics and so on, especially with respect to mathematics,
The I mean atleast the perception is that you know may be the industry general industry
that is out there, which has a lot of people to what degree does that industry I mean see
show interest in graduates of a mathematics or in what you know aspects of industry is
there you know nice fit between people who are doing an advance degree in mathematics
an MS or PhD degree and the what the industry might desire or even say some section of the
corporate world may decide. Yeah. So, in the traditionally people are thinking
that industry might take who are doing well in fluid dynamics. But that is not happening in India. OK. So, there are many industries who use these
concepts and foods products are even their process can be optimized by using these methods,
but they don’t ask for it. And when we go for them they are also reluctant. OK Ok. Because there is a fear of losing their jobs,
or some such. OK Ok. But, in computer science areas our students
are really doing some good job they are going for R&D sections. Recently one person who graduated in a complexity
theory went for this job, for example, in Dell systems. So, there are some areas like this where they
are able to go, but it is really again a confine to the R&D sector. It’s not going to the productive sector. R&D sector. In the industries. But what about let’s say I mean let’s
say the world associated with you know all these stack markets and things like that. Yeah, Finance. Finance. We are not having any expertise in that. OK. There is nobody in actuarial sciences. But. That is one area where math 27 can be useful. But in abroad they are really. Yeah, they seem to be using that I mean even
from what I even say physicists and work not get absorbed by the financial sector because
they seem to be doing a lot of analysis or I think the tools may be they learns are suitable
for those kinds of positions. So, that is not something that you are saying. That is not at (Refer Time: 09:21). OK. You see just a there I mean is the just a
not aware that there are enough people here with that kind of expertise. We do not have expertise. In our department, for example, there is no
person who is expert in the actuarial sensors. OK, fine. Let us say in our experience which looking
at students over all these years. In generally know in the institution we have
some metrix of you know how people are progressing, what causes they have done, what grades they
have got, what type of publication they made etcetera. But in generally, in a more holistic sense
especially for someone who is just you know considering coming in and so on what would
you suggest are good ways to measure their progress in research, so that for their own
satisfaction also they understand in fact, they are progressing in research especially
let’s say with respect to mathematics for example, did you think there are ways in which
they should think of themselves analyze their situations. There is one objective factor which is well
public essence in good journals. OK. So, though it looks very objective, there
is objective factor in terming which one is good and which one is bad. OK. So, that is almost settled. OK. If you ask any general person whether this
journal is good or not he will be able to tell you. Even he publishes in that he may say also
it is bad enough. OK. So, there is some set of understanding. Understanding. So, number of papers that come in good journals
that is a. Good metric. Well. OK. But individually when a person discusses with
supervisor the supervisor knows how much progress he has taught. OK. About that, it’s basically not only that
area fair he is doing research, but the peripheral areas. OK ok. How much he has acquired about the null is
about the peripherals. OK. So that after he finishes his PhD, he will
be able to really do research on his own. OK. There are some measures like one publication
there is a measure factor they are in the publications. So, one is whether somebody has solved a long
stunning problem. OK. That is a good measure of thing or how far
he has progressed towards that. Another is if he has not solved any long standing
problem, whether he has done something which will give rise to a long standing problem. Fine, either solved a long standing problem
or created a long standing process. Yes. Problem there is stands for. So, these are the two things which are very
good. OK ok. And the third one is anyway we have to use
always which is the number of the papers in good journals
Ok. So, these are some. Yes. In especially with respect to mathematics
on a sort of a mundane thing concept you know when students come in they have come from
a you know academic setting where they do courses and so on, they come and they are
now getting into research setting. Generally you know all areas of research we
always feel that you know interaction is a very important, technical interaction is a
very important way in which people grow as researchers and in that you know working with
the people in the group, working with the guide, meeting the guide etcetera plays a
very important role. In mathematics where you know there is a lot
of thought processes involved, lot of you know it’s a very in many ways a very internal
thing we are not often not running an experiments sort of how important do you see this role
of a student adviser meeting? How often should you think they should meet? Ideally they should meet every day over coffee. OK. Because then mathematics do not have any labs,
where they can interact with the things of the work. OK. It’s really only communicative. It’s a linguistic entity. OK. So, they have to go on communicative. OK. By that only they will get experience, there
is no other way. OK. But what we find is usually they are giving
some jobs and they come to meet the supervisor after one or two weeks. And then they spend 1 or 2 hours, get some
ideas and go away. OK. That way it will not happen, mathematics will
not happen. OK. But sometime you may need that seclusion because
if some ideas really stuck you need certain answer time to get it into work. OK. So, sometimes it may be OK, but not always. OK. Ideally it should be everyday one should meet,
tell something about what has happened. And then go back. Ok ok and what sort of characteristic you
think people should have to be good mathematicians, I mean in the sense how can how can someone
you know of course, you have seen one is an inclination you tend to solve some problems
and you feel comfortable with idea that I understand, but over and above that is there
some visualization capability that you I mean what should a person see in themselves and
say okay this I am able to do this, probably I am good at mathematics other than just being
able to solve the problem. Well, if you look at mathematicians there
are all sorts of people in that community. OK. We cannot say that for mathematics one should
be like these. OK. But certainly they are not fools. OK. That is one characteristic that they should
be intelligent. OK. They should try to find out if there is something
to go differ or not. OK. So that is one characteristic which really
characterizes them. OK. There are not satisfied just looking at the
surface. They would like to go deeper. OK. What is the pattern behind it? Right. See one has that interest. Then probably it can be happened. OK. But, if you doesn’t have that interest he
cannot be a mathematician. So, that thing that you know you should not
be a superficial thing. Yes. Okay much, much deeper into the thought process
behind that the solution. What sort of I mean I know you touched upon
this little bit, what sort of especially with you know in both certainly in engineering
and I am sure in mathematics too when you say an MS or a PhD kind of a degree automatically
the thinking is that this person is now an expert in a narrow area. So, there is some kind of a specialization
associated with it. So, in that sense what sort of positions are
people who create MS or PhD degrees from mathematics department and what sort of positions you
see them going to in recent times and where do you think are the possibilities for such. See at least from IITs when you get one PhD
in mathematics, you do not expect him to be very narrow because there are associated with
the tutorial classes with the B. Tech process. OK. So, they are having a lot bigger background
than other process. OK. Where this HTTA concept is missing, probably
there the students are also missing. Those students are also missing. Ok, fine they are missing that. So, here it is a nice learning experience. It is nice learning experience and they get
firsthand experience of teaching also. OK. Have to communicate mathematics by Vernon
communication. So, that is important they can write, but
they are not able to speak sometimes. OK. So, this helps them to speak that way they
are better compared to other process, but then that is not everything. So, they have to once they really narrowed
down because IITs there are only 17 or 18 IITs and we get a less number of students
compared to the other process. So, everywhere it is not possible. So, there, there is an expectation, they are
narrowed down to some particular area, but then it should be possible for them to take
up when the other thing later, because once that is what one person asked me once that
if I come to do M. Sc here what will I gain, I am not going to get any job directly after
M. Sc. So, at that time there was no job even in
the market for the mathematics students. Now at least there are some employment for
doing research or something at that time there is no possible term research also, very few
places where having the research compositions. So, my typical answer was whatever job they
go they will be able to do it. OK. Provided they have the interest. OK. So, these mathematicians pick up this nasty
habit that they want to reinvent everything. OK. See, if something is done in the book. They will not be satisfied. They would like to do themselves again, though
that will be a guideline. OK. So, this reinvention is also hated in some
of the industries. OK. Because they have the particular process. OK. And if this person does’nt follow the process
tries to topple with it or create problems then lot of things gets disturbed. OK. So, that is the only thing they have to be
conscious, when they go to do any other job outside the academia. OK, but what all. But usually the position is academic position. Academic position is the most teaching positions. And then in industries R&D positions. R&D position. These are the. These are the best ones. OK. Best fitted for them really. Okay Fine and okay may be a sort of enclosing
I just wanted to get a sense of you know a lot of students I mean in fact, there are
students who finish you know even high school who consider mathematics as a something that
is very interested and passionate about maybe under grads who consider it in greater you
know enthusiasm for it. Is there some, what sort of advise you would
give for people who are aspiring to become MS and PhD students to go on to get higher
degrees in mathematics, what sort of advise would give you them? Well, once they do their M. Sc, just to able
to find out in which area they are really interested, if they are really interested
in some area they should be able to produce some such new things, which may not be very
weak thing which expert sees in that area I will say it is nothing, but it should be
a deviation from the usual curriculum. OK. One such a thing is there I would encourage
him to go for doing research in mathematics. If it is not there then it may not be worth
doing because I will do the usual things you will for teaching and so on. OK. But not we will be able to really contribute
to mathematics. So, you are saying this would be one nice
way for them to gauge whether they are you know in the right process to be going ahead
for. Yes. Higher degrees in mathematics. Yes. So, they would have to at least for small
number of new things. Yes. They should start dabbling with, so that an
expert feels that they are you know comfortable with that. Yeah. So, you would like to see the playing thing
that he really plays with mathematics. OK. Not only does the conventional things. OK. But he is very comfortable with it and he
does something there. OK ok. So, that is your advice, before he just jump
in to an. Yes. Master degree or a PhD degree they should
first gauge. Yes. Whether are you know sort of in the right
frame of the mind for it and then on that basis proceed. Okay Thank you Dr. Arindama Singh. Welcome. Enjoyed meeting you and I think a very nice
advise for, because mostly people we look at engineering students more often and think
a lot of people considered mathematics, but they don’t where to take it and I think
these are nice words for advise for them to pointer about before they make their decisions
and look at their life in graduate school here. Thank you so much.