# 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.

hi sir…. i completed engineering and iam interested to pg in mathematics. What can i do for that… exams

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Sir I am done my education in m.sc mathematics .how to choose my research area

What's the most trending issue in math today?

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These advices are worth life changing for someone like me who aspires to do researchs in Mathematics.

I have completed my engineering and now want to work for MATHEMATICS, How to proceed!?

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https://youtu.be/0z2rlz5D-J0

finite dimensional vector space key points

Thanks for posting an instructional video. I need online help because I was coming up with ideas surpassing many professors at my university and people didn't like it. I also technically didn't finish my bachelors because of financial issues needed to finish my foreign language requirements.