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 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 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 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.

Also visit below link where you will find some important links