Is a Phd in pure mathematics a viable option for an engineering graduate?

[marellasunny]

Getting into a Phd-good or bad??

Hi,this might sound familiar.I quit my masters in automotive engineering from a very reputed university in Germany.I had finished all my course-work in 2 years,had 1 year of thesis and internship left.But,I couldn't take the emperical dominated engineering stuff.So,I decided to pursue my long-lost dream of taking-up mathematics,although I took a lot of applied math electives during engineering.The main reason for mechanical engineering was because of family tradition.I still love mech.engineering but I love math more.So,right now I am giving the integrated phd. entrance exams for applied and pure math programs in India.Unfortunately,I failed in the first attempt.
Would you advice me to continue down this path?I am now 24 and most proff. I meet suggest I first gain work-experience and secure my future.This is what is bothering me a lot.
Q. If I score well in the GRE subject test,would it help boost my phd application for a university abroad?

My main interests in mathematics are:

Abstract algebra,multivariable calculus,topology,financial calculus,complex analysis and I love fractals and non-linearity models.

As a hobby,I design and analyse physical models using FEM and other tools.

Thank you.Your advice is greatly appreciated.

 

[chiro]

Hey marellasunny and welcome to the forums.

I guess the question I have is 1) How many attempts can you take for the entrance exam? 2) Do you have priorities other than education that are more important? 3) How badly do you want this new pursuit (and are you willing to do whatever it takes to get there)? 4) Are there other institutions that you can apply for which have similar programs?

Without knowing anything detailed about your situation, it's hard to give any kind of specific suggestions.

Also I'd would be helpful for the readers to know the feedback from your entrance examination if you got it. You should have received some feedback on what went wrong and if you didn't get it, it would be a good idea to see if you can get some kind of detailed information.

Also it might help if you outlined the content and the nature of the exam itself so that we know what was involved.

 

[marellasunny]

Chiro:
1) How many attempts can you take for the entrance exam?

There is no limit,either in age or number of attempts.(The entrance exam(s) do have a caste-quota system though.This means I am at a disadvantage because my cut-off mark is higher as I belong to a particular caste.)

2) Do you have priorities other than education that are more important?

Technically yes,I have to clear-off a small debt from my previous degree.It would take me about a year's work to clear it off.But,I'm 100% certain I won't be capable of financing my next degree without a scholarship.But the good thing is most math masters and phd programs have scholarships in India and Germany.

3) How badly do you want this new pursuit (and are you willing to do whatever it takes to get there)?

I've quit my masters degree just for mathematics.I'm already making sacrifices.I study 13-15 hours everyday and teach math in a local college part-time.Yes,I'm willing to do whatever it takes but I do have a time limit.I want to be financially and career-wise secure after 7-8 years time.

4) Are there other institutions that you can apply for which have similar programs?

This is where I'm falling short of advice.There are only 4 reputed mathematical institutes in India.The other ones are not worth looking into.Abroad,the German universities I've approached insist I start of with bachelors(which is ridiculous because I have credits to show I'm math worthy).The only other closest option is mathematical finance in India which requires GMAT.

Feedback on results:
I did miserably in abstract algebra-went horribly wrong in word problems involving rings and isomorphisms and vector spaces.I amazingly fared badly in multivariable calculus.The positives are that I scored high in linear algebra and topology.I was trying to pass an exam which required 1 year prep work,I had 4 months.

The exam is divided into 4 sections:
1.Algebra
2.Topology
3.Complex analysis
4.Calculus and real analysis

 

[jedishrfu]

Math is far different than you can imagine. Abstract algebra and point set topology are basis of so much current research. Proofs and how to do them are what matters most. I also tried to get into math grad studies here in the US but ran into you're not a math major issue meaning go back and study math at the undergrad level as a math major.

 

[marellasunny]

Math is far different than you can imagine. Abstract algebra and point set topology are basis of so much current research. Proofs and how to do them are what matters most. I also tried to get into math grad studies here in the US but ran into you're not a math major issue meaning go back and study math at the undergrad level as a math major.

"Your'e not a math major issue doesn't seem to exist in India",thank God!I understand the concept of going back to undergrad for 'pure mathematics',but it seems ridiculous to start-off again with a bachelors for 'applied math' even after having a degree in engineering.I took courses like multivariable calculus,linear algebra,complex analysis and operations research during engineering.I'm sure I'll be taking them again for a bachelors in applied math.Is there no university in the world where applied math and pure math are considered the same?Why do they have to separate these two?They are so connected.Okay,proofs are a more integral part of pure math but that's the best part of math.So,it looks like my chances for getting into a pure math phd are slim.Thanks for the reply jedishrfu.