I completed my BTech 2 yeas ago. I want to go to Maths. How can I ???

There are many people who want to shift from BTech/BE to Mathematics. They are either looking for MSc in Mathematics or Direct PhD.

First I will post here a mail I got yesterday :

Dear Sir,
I’m extremely delighted and thankful to you that you replied to my comment in just an hour.
Sir, I was a very brilliant mathematics student in my school and till 10+2 I couldn’t study any other subject, because of my obsession of mathematics.
However, after my 10+2 exams, I did a biggest mistake of my life that has almost costed my career.
Sir, I got selected for B.tech metallurgical engg. in NIT XYZ. With absolutely no interest in metallurgy, I chose to pursue my career in Metallurgy,  just because of the crave for NIT in my area.
After I went through, I realized what I had done, but too late. Due to lack of interest, I just studied for passing the exams and got mediocre grades. After completing my exams, my pointer was around 6.9, and I came out of NIT without placements.
Due to lack of scope of this subject in my area (XYZ), I couldn’t find any job here either. I couldn’t opt for M.tech in the same feild because with passing time, I started to hate this field.
It has now been 2 yrs since I took my B.Tech. degree and I feel like my career is destroyed by none other than my own self. I feel depressed.
I am doing a small job in a private firm. So, I really took it, as an end of my career.

Recently, I came across an fb page titled ‘I love Mathematics’ and I hit the like button. I came across many mathematical problems of calculus or trigonometry that remembered me of my past days. The desire, along with the feeling that I can’t solve these problems now, dejected me but at the same time, I saw a glimmer of hope, at the end of the tunnel.
An idea struck my mind that I might pursue a career in Mathematics. I went to Web and there I found you. In your blog I read that I can prepare for Gate and go for direct PhD. I also have another option, for doing M.Sc in Maths in our XYZ University but I’m not sure whether they take B.tech students for this program.

But Sir, I now have great challenges ahead of me. I have almost forgotten my 11th or 12th class maths. I also am in need of financial support not for just my studies, but also for my family.

I will be very grateful to you if you can help me to let me know which books should I study, how should I make myself ready for Gate 2018, and how can I get financial support.

I have tried not to reveal the identity of the person who sent me this mail. While writing answer I am aware that this answer will play very important role for the future of him and many others like him.

Here is my answer:

Dear Sulatan,

Let we discuss how can you qualify GATE-2018. Today is 1st August 2017 and GATE exam is in first week of February 2018. You have six months. I am not much sure that in Six months you can qualify GATE with good rank but I can tell you that in 1 and a half year with 3 hour daily spending, you can qualify this exam with good rank.

I am sure that you have studied maths for 3 to 4 semester in your BTech. (No problem if you forgot this also)

GATE Syllabus:

Since you have not did BSc, I will suggest
Real analysis:
R.G. Bartle and D. R. Sherbert, Introduction to Real Analysis
Linear Algebra:
Linear algebra done right by axler.

Abstract Algebra: joseph A. Gallian by Contemporary Abstract Algebra


Complex Analysis:
Joseph Bak and Donald J. Newman, Complex analysis
Ordinary differential equations
Theory of Ordinary differential equations by E.A. Coddington
If you do above topics nicely you can qualify GATE, CSIR, JAM easily. Bellow are additional subjects
topology by munkres
Functional Analysis
Introductory Functional Analysis with Applications by Erwin Kreyszig
How to read mathematics books:
Start from first page. There will be definitions. Then there will be some theorems and examples. Try to prove theorems your self ( I try each theorem. In some trivial theorems and results i get success. In some more difficult theorems I get success in 25% cases). If you try and try but cant understand a sentence then ask for help who are good at mathematics. If there is no one near to you then skip it. later visit that sentence again.  Exercises are very important. Try to solve at-least 50% exercises. Thats all.. 🙂
If you get into PhD by GATE or by CSIR-UGC NET or by NBHM you will get 25000 around per month. If you go to MSc and if you clear NBHM-MSc scholarship test then you will get 6000per month for two year of MSc.
I suggest you to continue your JOB and spend two-three hours daily to read above books. Dont take all the subjects once at a time. take one or two book at a time. give your best.

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Written test/Interview experience at IISER Pune, IIT Madras and IIT Bombay

This post will cover more than what its heading says.

When my CSIR-NET result published, I got 47th rank. I contacted my professor. I was informed that now I have JRF, getting into IITs will not be a big deal. So I decided to get into IISc, IIT-Madras, IISER-Pune, IIT-Bombay in this order. This order was based on my subject in which I was interested to do PhD. I was thinking that to get IISc will be somewhat tough but IITs will be easy since I am a JRF qualified(it was true in early days).  Thus I applied for this four institutes only. To my surprise I was below cutoff for IISc to appear for interview. Cutoff was 35 rank in JRF and 850 score in GATE. Later I came to know that IITs and IISERs don’t care if you have qualified JRF or GATE or INSPIRE. I got surprised when I came to know that IISER Kolkata has also set cutoff. Two of my friends with not much good score in JRF are not called for written test/interview. Although they were called at IIT-B, IIT-M, IISER-P, IIT-Indore, IIT-Guwahati, IIT-Gn, etc…

Now I was having written test/interview at IIT-B on 9th-10th/may, at IIT-M on 15th-16th/may  and at IISER-Pune on 17th/may .

IIT Bombay:

Written test was in morning on 9th May. I did some silly mistakes and my name was not there in the list published on the same day 2pm and consisting of 33 students (out of around 150 who came for written test) who were shortlisted for interview. 😦

If you are looking for getting into PhD in IIT Bombay then you should look at written test papers of previous years. Here it is with syllabus. Written test of IIT-Bomaby consists only Linear algebra(40%), Real analysis(30%) and Probaility(30%). Probability is for those who applied for Stats.

IIT Madras:

Written test started at sharp 9:30am of 15th May. Result declared at 14:00. There were around 100 students. I was in those list of 40 who was selected for Interview. We were asked to gather in a classroom at 14:30. Then they asked us to choose one from two committees for interview.

1st committee consist of analysis(real and complex), ODE/PDE, and few more

2nd consist of Algebra(Linear and Abstract), Topology and discrete maths(I am not sure about last one)

I was interested in Topology and set theory so I choose 2nd committee. Interviews  were going to last for 2 days. Many students were having interview at IISER Pune on next day and they were requesting to arrange their interview on same day. Around 80% of them got same day. I was in no hurry so I choose 2nd day.

My interview started around 4pm. There were around 12 faculties in panel.

I entered in classroom.

There were smiling faces looking friendly. One faculty asked to introduce my self.

Me: My self Ravi. I did my MSc from NIT Warangal. ( I stoped. He said finised.? I replied yes by moving my head. 🙂 )

Then one aged professor asked about my primary Interest.

Me: I like topology and Set theory.

Intr: Do you mean point set topology?

Me: Yes sir. (they got surprised. May be I was so specific)

Intr: We have not much people working in this field. What is your 2nd preference.?

Me: (I was taking so-much time to answer. My facial expression was saying that I don’t want other field)

Intr: We dont have people working on this.

Me: I like self study. (They laughed. They said you need some guide during your PhD.)

Intr: So what if we give you number theory or algebraic topology? would you like to work?

Me: (I was taking time)

Intr: We will not ask you questions from number theory. Just tell us if you can work in other field if you get.

Me: (after taking some time) No. ( I was thinking wtf I just said)

Intr: Why? (One senior faculty was not happy with this question. Maybe he was thinking that this question will make me uncomfortable or nervous in interview)

Me: (after taking some time)I like many subjects in maths like Probability, Analysis, graph theory etc… But I will be spending 4 years in this particular subject. Thus I should go to the subject I find most interesting. Okay, My second preference is algebraic topology.

Intr: So which theorem in topology you like most?

Me: (Taking so-much time. Not coming one single theorem in mind)

Intr:(With smiling face) Just tell us one theorem that you find interesting…

Me:(After taking a little time) Convergence class theorem (This one is given in General Topology by John Kelly. I was good at all the terms that appear in this theorem like NET, DIRECTED SET)

Intr: What is this theorem.

Me:(stated it but not precisely. Below pic consisting definition is from General Topology by John Kelly)


Intr: what is Net

Me: (defined)

Intr: What is directed set.

Me: (defined)

Intr: What is relation between Continuous functions and NET.

Me: (I stated something else. After I explained they asked same question again)

Me: (I answered this question. I learned this time that We should listen them carefully)

Intr: Which topics you are good in Topology?

Me: Connectedness , Compactness etc…

Intr: Give an example of a set which is connected but not path connected.

Me: (I gave example of Topologists SINE curve)

Intr: Is it locally connected?

Me: (I was not having Idea of what is locally connected. I was taking time)

Intr: How a neighborhood looks at (0,0) (They asked to draw ).

Me: (answred)

Intr: Now you can answer. (I was taking time) Do you know what is Locally compact set?

Me: No sir.

Intr: is this set compact?

Me: (I was trying to prove by definition)

Intr: is it closed?

me: Since we are adding all limit points of graph (x,sin(1/x)), this set is closed.

Intr: Now answer previous question.

Me: Yes. It is also bounded (They asked reason. I gave) Thus it is compact since R^2 is euclidean space.

Intr: Here is one last question. Are you comfortable with metric spaces? ( I said yes) So Let X is a connected metric space with at-least two points. Prove that it is uncountable.

Me: (I was trying. I was doing rough work on board. I was trying to prove that there will be a point for each real no. on some interval. I was trying and trying. I was getting nervous. I knew that I was trying in right direction but since i was not getting answer , I changed the the approach and started  trying to prove that I will have a perfect subset. they asked what is perfect set. I answered. They stopped me as time was over for interview.)

I left the room. This last question was very easy. I was near to the answer and I changed my strategy and this could reduce my chance of selection. I was 50% sure about getting selected.


Infrastructure of IISER-P is beautiful and academically also this institute looked nice. I reached here early morning around 6am. Booked a room in hostel. Did breakfast in mess. Then written test started around 8:30 am. A good point about IISER-P is that all students were not asked on same day unlike IIT-B and IIT-M. Students were distributed over 3 days. I was invited on the last day. Here we were not shortlisted unlike IIT-B and IIT-M. We all were having interview on the same day. There were three parallel panel for interview. My was in 1st panel after lunch. Interviews were running from 30 minutes to 70 minutes. Maths dept. of this institute has a beautiful waiting room. Here is a pic of a painting I captured.

Books appearing on right side of pic are great classical books. Do read them if you get time. Here is pics of that side.

My interview started around 4pm. When I went to that classroom, one of the three panel member were outside of class. Let we call him Mr. A. He said that other panel members went outside and coming in two minutes. He was really very very friendly with smiley face. He asked about myself and my degree. I said I am from Gujarat. I said I had completed my MSc this year and result of 4th sem announced just two days back. I said I got 7.55. He asked how mush is 7.55 in your institute NIT W. I said not much good. There are students with 9 point also. He asked if i had appeared for interview anywhere  and how was it. I said I had interview at IIT Madras and it was somewhat good. He asked about my interest. I said I want to work in any of set theory, mathematical logic and topology. He looked surprised. He asked if I had read Naive Set Theory by Halmos for axiomatic set theory. I said this book is soo much descriptive and I didn’t like this book. I liked appendix of General topology by John Kelly. He felt good. Meanwhile two other member came and we all four went into classroom. That sir introduced my self to two other members with mentioning that I am interested in Set Theory.

Mr. A: So do you know godel’s incompleteness theorems? ( I said no)

Mr. A: Do you no ZFC? ( I said Yes sir. He said ‘Ohhh every one interested in set theory knows this.’ He didn’t asked any question further in set theory or logic)

Intr: So since you are interested in topology… can you give an example of continuous function f from X to Y  such that f is bijective, f inverse of each element is connected set and Y is connected and X is not connected.

Me: Let X is [-2, -1) union [0,1]. Y is [-1,1]. f is identity on [0,1]. f(x)=x+1 on [-2,-1).

Intr: What is topology on X and Y.

Me: Subspace topology of R^2.

Intr.: Yes. You are right. Here X is not connected. what condition we should add such that X becomes connected (She didn’t exactly said this but trying to say this).

Me: (I was not getting question properly. I said extra condition is f inverse is also continuous. I should not answer this because then f becomes homeomorphism and there is no fun)

Intr.: (She was not satified. She knew that I am not getting question. She tried a lot.) Do you know quotient sapce? (I said yes). Define it.

Me: (Defined it nicely with two different approach. One with partition of a topological space X and one with given function f from topological space X to set Y)

Intr.: prove or disprove that if f is a quotient map from X to Y such that f inverse(y) is connected for each y and Y is connected than X is also connected.

Me: (Did Some rough work. Tried for few minutes. Proved. I was surprised that I proved it. She was asking her doubts about proof. Mr. A. was explaining my proof to her)

Intr.: Which other subject you are comfortable with?

Me: Algebra.

Mr.A.:  (He asked something related to conjugacy classes. I said I don’t know about conjugacy classes) He asked what is group of rotaions of CUBE.

Me: (I tried to rotate vertically, Horizontally, Diagonally but I was not getting answer. Mr.A. gave me a lot of hints. but i had never spent time on this topic. I was not able to answer)

Mr. A.: How many members are there in this group? (I was not getting answer. )

Mr.A.: Can you give a lower bound ?

Me: 12. since there is an element of order 3 and an element of order 4.

Intr.: Prove or disprove: If V is a vector space then that there exist finite number of proper subspaces of V such that Union over them is V.

Me: (I was trying and trying to prove that it is false. looked obvious in R^1, R^2 and R^3. I was trying to solve using induction on something I don’t exactly remember now. She said use induction on dim(V). I tried. Was not able to solve. Time finished. Total duration was around 70minutes)

I left Pune on next day morning.


I didn’t in IISER Pune. I got selected in IIT Madras. I will be joining IIT-Madras from 10th July.

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CSIR NET-JRF Mathematical Science Exam

Official website is http://www.csirhrdg.res.in/

past year papers with key at http://www.csirhrdg.res.in/AnswerKeys.html


Cutoff marks of previous years: June2015 , Dec2015, June2016

Pattern of Paper:

Section 1: Aptitude. Total 20Q. Answer maximum 15Q. 2 for correct. -0.5 for incorrect.

Section 2: Total 40Q. Answer maximum 25. 3 for correct. -0.75 for incorrect.

Section 3: Total 60Q. Answer maximum 20. 4.75 for correct. No negative marking.


Total 200 marks. Cutoff stands near to 55% for JRF and 50% for NET every year. Means one need to score at least 110/200 for JRF and 100/200 for NET.


See the unit wise weightage of marks in above pic. Notice that in Section C, you have to answer maximum 20 question and unit-1 of C itself contain 18 questions. Though C section has no negative marking, you need good concept of the subject, since C section is multiple select type.

My goal for Dec-2016 was


and I am getting


It is very very important to make a strategy for this exam.

If you are saying that you are gonna answer 17 answers correct in section B then from which unit of section B you gonna try this 17 question.?? We need to write 25 questions in B but you should not try 25 questions and you should try only around 17 questions in those units you feel confident and after answering this 17 questions in a prefixed interval of time, you should move to section C. Here also you do not need to try all 20 questions out off 60 questions but try around 14 questions only out off 60Q. Distribute time section wise. Keep your eyes on watch.

Books to follow: Below list mentions two books for each subject. If you are not worried about marks in Exams and just doing math for fun then I suggest 2nd book. If you also want marks then after reading theory and doing exercises of 2nd book, go to the 1st book and do exercises after each chapter. (You can also completely ignore 2nd book. )

Linear algebra:

  1. Linear algebra done right by axler
  2. Linear Algebra by Hoffman and Kunze

Abstract Algebra :

  1. Algebra by Michael Artin
  2. Algebra by Serge Lang (If you are reading abstract algebra first time then I will suggest Undergraduate algebra by serge lang)

Real analysis: Principals  of mathematical analysis by Walter Rudin

Complex analysis :

  1. Foundations of Complex Analysis by Ponnusamy
  2. Complex analysis by Walter Rudin ( You should read this book after reading Principals  of mathematical analysis by Walter Rudin )

Topology :

  1. Topology by munkers
  2. General topology by John Kelly

Do at least 50 percent exercise with your self and rest remember the results.

Good Luck friends. Feel free to ask in the comment section.

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How GATE – Mathematics is helpful to BTech students


Unless other GATE papers, GATE-Mathematics exam is Specially for MSc – mathematics students.  ( If you see syllabus of this exam it is BSc-maths level syllabus. More BSc and a little MSc level syllabus)

BTech/BE and MSc students can apply for GATE-Maths exam.

If you qualify GATE, you can apply in any IITs- NITs and almost all CFTI for PhD program in maths. You can’t apply for MSc with GATE. You may have doubt that how a BE/BTech student can go directly in PhD. But since you have studied a little maths in BTech and a little while preparing for GATE, you know BSc lavel maths and PhD first one year or one and half year will be for course work , you will face no problem ( depends on institute. In some inst. u may face a little prob. )

Not just GATE but you should also appear for CSIR NET/JRF exam. This exam is really superb. If you prepare just Algebra and Analysis then you can easily qualify this exam. Reason is there is so many optional questions in this exam. This exam is conducted twice a year.

PS: while applying for CSIR-Net keep following things in mind.(Many people are facing prob bcoz of this mistakes)

  1. Dont do spelling mistake in your Name while filing the form.
  2. Put date of birth as in 10th std cert.
  3. If you come under other quota then don’t do spelling mistake in father’s name. put it as it appear in cast cert.

PS. Try to clear both- NET and GATE. Because CSIR-NET is very reluctant to give stipend on time and not responsive at all. While in GATE, u will get stipend on time and from the first month you start PhD.

Good luck friends. Feel free to ask any in comment section.

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If you are in BSc first year and thinking about how to prepare for Jam- Mathematics

So you are in BSc first year and so you are thinking you have a lot of time for preparation. That is not true. Reality is JAM exam will be 2 months away and you will realize that Ohh JAM is just Two months away and I am not ready yet… So start working from this moment…

Now I will explain how to work out :

First if you don’t have big screen phone then just get print of last two- three years papers and syllabus ( available on Jam – website). After looking at syllabus and past year papers that questions are not much difficult if you have studied that particular topic nicely.

If your professors are not good enough or if you feel that you are not getting any thing from attending classes you should not attend classes, thus you will save precious time and you will not start hating that beautiful topic of mathematics.( Or if attendance is compulsory then seat at last seat and do your own work. But don’t try to look at board or listen to professor. Otherwise you will start hating real analysis, algebra, topology, combinatorics and that is really very very sad…)

Use standard text books for preparation and if your professors ask questions from notes only in end semester exam than don’t worry about that. You will score enough in exams.

So start working from today… good luck friends:-)

And for standard text books, refer earlier post on this blog

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CCMN-2016 Counseling Portal is Active now…

To get admission in MSc in Most NITs , process is through CCMN portal. here is the link http://ccmn.in/

Now if you are a BE/BTech student and willing for MSc in mathematics then only NIT-Arunachal Pradesh is offering you MSc and that also not pure mathematics… 😦

If you are not getting any other institute for MSc then just participate in this counseling and fill all institutes which you like in choice filling… Then if you get admission in any NIT of your choice as per your choice filling , you have to pay fees (may be through DD or State Bank Collect). Then with receipt of paid fees and all documents you have to go to that respective NIT. When time comes to show your fee receipt and documents, they will notice that you are a BE/BTech student. The people who will verify our documents actually will not be aware of eligibility criteria and if they, just tell them that as you have studied Mathematics for Four semester you are eligible, since there is no special eligibility criteria like six sem study of math on CCMN portal… This worked for me last year at NIT Warangal…

I am sure that finally they will not cancel your admission… Stuck to your argument that since there is no special eligibility criteria, i am eligible…. 🙂

And if they reject your admission you will get your money back as per refund criteria available on CCMN portal…

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Job opportunities after MSc in Mathematics

Here I will discuss not only about job opportunities but also about how you can earn money after MSc in math.

After MSc, you have two options  (i) Further study-PhD  (ii) Job

i) Further study

You can go for PhD and earn 25000-35000 per month plus accommodation for four-five years.  After PhD you can go for Post Doctorate and earn 30000-45000 per month plus accommodation for 3-4 years.

ii) Job

Go for lectureship in good institutes and earn nearly 35000 per month. For other jobs, this may help you http://gonitsora.com/top-paying-mathematics-related-careers/

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