A comprehensive question about personal statement

Question

I have some questions regarding my personal statement for graduate school (US/Canadian universities) in math. My question(s) are comprehensive and long, as the title suggests, thus I have numbered and sub-numbered the questions.

Note that these questions are targeted at schools that do not allow me to upload a CV otherwise I think half of these questions would go away.

1. Courses

   • 1a) Is it silly or a waste of space to talk about your math background? Or should I assume the graduate committee already has this?

   • 1b) Some schools I have checked out actually asked me to list out all my junior/senior courses along with their books, I guess for those schools I don’t need to? What about those who do not?

   • 1c) Should I write or mention courses I have self-studied? Or is this completely irrelevant to them?

   • 1d) Should I also bother explaining one W and one ‘bad’ mark that happened in the summer?

   • 1e) Should I mention my math department is understaffed and I tried to take as many “hard” classes as possible? How understaffed? We have only at most four math classes at the senior level every year. We are so small that most junior/senior classes stop only at the introductory level.

     For example, we only have: introductory PDE, introductory Number Theory, introductory Algebra, and Topology does not even exist at my university.

     Very rarely do we get continuations to those courses. In comparison with all the other areas, we have quite a lot of Analysis courses, but all of them are focused in Optimization (excluding Real Analysis, we usually have one to two Analysis classes).

     We have no Calculus of Variation, no Measure Theory, almost nothing.

     I had to go out my way to bug a professor to request an extra Analysis course this year to the unit head and even then I am short on Math classes next year.

2. TA experience

   • 2a) Should I talk about this? How will they even verify me? Because I have done some things that most TA don’t do at my university – writing exam solutions. The prof I TA’d for left everything for me to do, except the teaching and actually writing the midterms/finals. I never had a class with him, so I am not so sure about asking him to write a letter for me.

   • 2b) I also TA’d for another prof at another campus during one summer term (same university, but different Math department), should I mention this?

     I can provide a link of my exam solutions through the prof's site. I think he will give me permission, should I include this?

3. Research Experience

   I have very very little experience, so much that I could probably only write one or two short sentences about it. I also have no publication, but I think the prof I worked for can
   confirm that I did do research under him.

   By the way, the “research experience” I had was a problem the prof had written by hand on a math paper and he asked me to answer the question he posed. It was not an analytic problem, it was coding, graphing, and writing a report.

4. Area of Interest.

   • 4a) I already know my area of interest, I am wondering if it is a good idea to write why I got interested in the first place or is this completely irrelevant to the graduate committee?

     My reasons are rather absurd, I am going into my desired area because of a textbook writer and the textbook I read by him isn’t even the area I was interested in, although the writer did write a book in the subject and I was simply in love with his style of writing.

     I later found out the writer’s background and plus some neat stuff I read on the Internet sealed the deal for me. If people think this reason isn’t silly or “cliché” (e.g. “I liked puzzles when I was young”), then please tell me.

   • 4b) Also one major problem is that I can’t talk too deeply about my area of interest. I can mention specific subfields, but that's about it. For instance, if I liked Number Theory, I could mention "Analytic Number Theory" and the "Riemann Zeta" or if I liked Differential Geometry/PDE, I could mention "Geometric Analysis".

     So would it be better to omit the details if I can't comment too much on the details of the subject and simply write "Number Theory"?

5. Thesis Advisor

   I can find people and mention their names easily on my personal statement. I am just curious if I should narrow it down to only ONE person? Does it look bad that I am just listing out the people whom I want to work with instead of writing down just one name?

6. Scholarships/Award

   I have never liked the word 'Award', so I am going to use 'Scholarship'. Do I need to mention about a scholarship I got from a professor? Again, how can I be verified for this? I think I could ask the prof who gave it to me (whom I did research for) to mention/confirm this?

7. Skills

   How much will it add to my application if I tell them I can use LaTeX (honor's thesis not required for honors degree at my university. I asked one of my profs why and even he doesn't know.), high proficiency with Mathematica, Maple, MATLAB, etc...? I was going to add Photoshop, but then I realize how pointless and irrelevant that is. I can also use Python, but since I am postponed my 1st year computer science requirements till my last year I do not think they will buy this. Also my school teaches Java.

Thank you very much for reading and taking this time to read this ridiculously long question(s)

Answer 1

Some ideas on your statements/questions:

(1a)-(1b)-(1c): It seems to be your undergraduate university is not a very well known one and/or even not considered strong in mathematics. Graduate schools may be wanting to be sure you covered what they consider necessary as undergraduate mathematics. Upon being asked I'd consider sending along a short syllabus of the courses you took. I'm almost sure your university must have these things.

(1d)-(1e) Don't even mess with this unless specifically asked, which I think it's unlikely to happen.

The lack of any topology/measure theory (and perhaps more) courses in your university (or college...?) is a rather serious one, imo, and it may point, again, at some lack of elementary basis most mathematics depts. are supposed to have. in fact, I think it is likely some universities could require from you to complete several courses before they considere you as an actual candidate for graduate school in mathematics...are you sure that what you studied in that school of yours was "mathematics"? Perhaps it was something like "applied mathematics"?

I don't think serious graduate schools require TA from undergraduates. In fact, mentioning you TA'd some course before being a graduate could be considered as (another) sign of a low mathematics level in your school.

To require research? From an undergraduate? I don't think there's such a university. What could be required, imo, is good skills to "hunt" for books, papers, etc. in a mathematics library and, in our days, perhaps also in the web.

No need to dwell a lot with your area of interest. Perhaps mentioning some of the wide areas (analysis, topology, algebra) could be enough, though imo most decent graduate schools require from graduate students to take two or more rather hefty, year-long course in some of these areas, and only later you begin to drift towards your love... The same applies, imo, for thesis advisor.

Please do mention any scholarship-award you got that's connected to your studies. This may be rather important.

About skills: I don't think anybody will really care about it. Most probably schools will be more interested in finding out about your seriousness, love for the subject, responsibility, etc.

Good luck!

Answer 2

Responding to questions approximately in order:

It is not a waste of space to talk about your mathematics background. Mere course titles tell almost nothing, so it's good to explain more. Telling the authors of the texts used explain a lot to experienced mathematicians.

Especially if your school has a relatively weak program, and even if not, telling what self-study you've done is very important. It is all the more important as an indicator that you take initiative, are driven by curiosity about mathematics, independent of grades and structured programs.

Explaining briefly that you've had TA experience is a small plus, because almost all grad students in math are supported by TA work, so knowing in advance that you can communicate will ease the minds of admissions committee members.

Despite the contemporary pretense that undergrads "do research" between their junior and senior years, it is very rare that any sort of genuine research occurs. Sometimes, but rarely. After all, if research only takes 8-10 weeks in the summer, with almost no prior background, why does a PhD takes years? :) (There is a good purpose served by the summer programs, though, of giving undergrads the idea that mathematics is not confined to a classroom and textbooks, as well as creating social connections with other undergrads seriously interested in math. But these situations don't really produce cutting-edge research.)

About "specific interests": of course it is vastly better to have tentative, ill-formed, and inevitably ill-informed, "interests", rather than not. :) I'd encourage you to tell how these interests arose, giving the admissions committee some insight into your approach to mathematics.

It's good to mention scholarships. People will not be so skeptical that you need to document it.

Computing skills are a positive, and deserve a brief mention. Again, there is little need to offer "proof".

In summary, it is a mistake to think that one's transcript explains what the admissions committee wants to hear or needs to know to make a reasonable decision. An informative personal statement makes a huge difference, especially in communicating your motivations and learning outside classrooms. Also, letters of recommendation from mathematicians well-acquainted with you, from contexts of relatively advanced mathematics (rather than elementary) are very important to give an idea of how well you'd fare with more advanced/sophisticated work. (After all, many people do well-enough in undergrad material, but find that graduate-level mathematics has a slightly different nature... of less interest...)