How Should I Write My Statement of Purpose for Grad School in Mathematics?

[caffeinemachine]

Hello MHB,

I'll soon be applying for Masters and PhD programmes in mathematics to universities in the US. I need help with my statement of purpose. I am not sure what I should put in it since I am largely self taught (in math) and have little formal research experience. (Formal research experience means projects undertaken and internships). Please give your suggestions based on the following.

1. I am an undergraduate majoring in mechanical engineering. I'll graduate in 2014 with a master's degree in mechanical engineering.

2. My B. Tech and M. Tech thesis both are on mech. engg. topics.

3. I have done exactly one internship under a professor in mathematics. My guide for this internship has a PhD from UChicago and he has agreed to give me a strong letter of recommendation.

4. I have done Abstract Algebra, Computational Number Theory, Graph Theory and Linear Algebra courses at my institute. I have self studied a lot of undergraduate mathematics and I think my knowledge and skills (as an undergraduate) are decent.

5. I have not published anything in mathematics or in any other discipline.

6. My area of interest broadly is Graph Theory, Combinatorics and Algebra. I don't have any particular problem in mind right now on which I'd like to work during my PhD.

Any other advice regarding applications are welcome.

 

[Ackbach]

For graduate work in mathematics, the Big Three are abstract algebra, real analysis, and topology. If you haven't taken those courses, I'd strongly recommend you do. They are important for all mathematicians, pure or applied. Numerical analysis is also very helpful if you're at all interested in applied mathematics. Complex analysis is nice as well, but not as important as the Big Three.

 

[caffeinemachine]

For graduate work in mathematics, the Big Three are abstract algebra, real analysis, and topology. If you haven't taken those courses, I'd strongly recommend you do. They are important for all mathematicians, pure or applied. Numerical analysis is also very helpful if you're at all interested in applied mathematics. Complex analysis is nice as well, but not as important as the Big Three.

I can take topology next sem. But there's no way I can take real analysis before graduating. Anyway.. I have to apply by the end of this sem.

I know both these subjects at the undergraduate level quite well.. my analysis skills(esp multivariate) are not great though.

Does it make sense to apply without these courses on my transcript?

 

[Ackbach]

I can take topology next sem. But there's no way I can take real analysis before graduating. Anyway.. I have to apply by the end of this sem.

I know both these subjects at the undergraduate level quite well.. my analysis skills(esp multivariate) are not great though.

Does it make sense to apply without these courses on my transcript?

Sure you can. I had abstract algebra, real analysis, and numerical analysis, but no topology. I'm just putting forth what the most important courses are. Really, when it comes down to it, abstract algebra and real analysis form the core of the graduate mathematics education. Everyone should take those. If you don't have it on your college transcript, that just means you should take it in grad school. I had plenty of colleagues who took senior-level real analysis before jumping into the graduate-level version.

 

[caffeinemachine]

Sure you can. I had abstract algebra, real analysis, and numerical analysis, but no topology. I'm just putting forth what the most important courses are. Really, when it comes down to it, abstract algebra and real analysis form the core of the graduate mathematics education. Everyone should take those. If you don't have it on your college transcript, that just means you should take it in grad school. I had plenty of colleagues who took senior-level real analysis before jumping into the graduate-level version.

That gives me hope. But still I can't figure out what should I write in my SOP. On some websites I have read that one is required to talk about his research experience during his UG studies. I have not done any projects or internships (except one). What should I write? That I have read this and that on my own?

 

[Dustinsfl]

Why are you going from Engineering to Math? Are you planning on Applied Math?

I ended up switching from Applied Math to Mech Engineering in Grad school when I realized I was spending more time in pure math courses due to the requirements. Then there was a second specialization I needed to master; that is, 3 classes is another speciality. Considering I had more mandatory pure course as is and the only other specialities would be more pure math, I went to Mech Eng where I take more applied math, physics, programming, numerical analysis, and engineering courses than in the Applied Math program.

 

[caffeinemachine]

Why are you going from Engineering to Math? Are you planning on Applied Math?

I ended up switching from Applied Math to Mech Engineering in Grad school when I realized I was spending more time in pure math courses due to the requirements. Then there was a second specialization I needed to master; that is, 3 classes is another speciality. Considering I had more mandatory pure course as is and the only other specialities would be more pure math, I went to Mech Eng where I take more applied math, physics, programming, numerical analysis, and engineering courses than in the Applied Math program.

No, I am not aiming for applied math. My area of interest is Combinatorics, Graph Theory and Algebra. I want to pursue math because I like math. I want to produce highly non trivial results in mathematics.