Hello everyone. I've applied to Fall 2018 PhD programs with the goal of studying graph theory. I'm quite worried that I won't get in anywhere. If anyone could generally evaluate how my application compares with others, I would be very appreciative. Thank you.

Applied: Berkeley, Princeton, Emory, South Carolina, MIT, Rutgers, Georgia Tech, Arizona State, Iowa State, Carnegie Mellon, Cambridge, Oxford, Waterloo, McGill, UBC, Simon Fraser, Birmingham, LSE

Undergraduate: State school, ranked 100ish in the USA

Major: Mathematics

GPA: 3.82, 3.80 for math (dragged down by one C-)

GRE: 170 Verbal, 169 Quantitative, 6.0 Analytical Writing

GRE Math: 790 (77th percentile )

Demographics: White male, 23 (I have been out of school for two years)

Upper level courses: Analysis I and II, Stochastics, Graph Theory, Linear Algebra, Abstract Algebra, Combinatorics

I received an A in all of these classes except for Analysis II (A-) and Combinatorics (C-). I took Combinatorics in Korea as a sophomore without any previous mathematical experience, and part of the course was instructed in Korean. I mentioned in my SOP that getting my ass kicked in this course contributed to my motivation for starting to study mathematics seriously.

Research experience: Nearly ready to submit a paper in which I prove a new complexity theorem for tripartite graphs. My graph theory professor has been helping me to edit this paper for almost two years now.

Awards: National Merit Finalist, Phi Beta Kappa, graduated with distinction

Work experience: By next fall, I will have two years of experience teaching Cambridge A-Level Math and Physics to high school students.

Recommendations: I believe that my graph theory professor gave me a very strong recommendation. I submitted my complexity result to him as a final project for his class, and he seemed very impressed by my result, and he took the initiative to work with me to get my result published. He has seemed very enthusiastic about helping me edit my paper. My other two recommendations are probably average.

Other: I have some other random qualifications. I have a Java Bronze Certification, and I have language certifications in Mandarin, Spanish, Korean, and Japanese.

I'm worried because I didn't decide to finally major in math until my last year, so I don't have many upper-level math courses. I wish I could have taken complex analysis and algebraic combinatorics, but my scholarship ran out after four years, and I had to graduate. My graph theory professor said that applying for top schools would be aiming too high, and he gave me a list of medium-level schools with good graph theory faculty, but he said that even these schools are extremely competitive.

I'm really sorry to flood the forums with another one of these. If anyone could give any insight about how my application compares to others who apply for PhD's to study combinatorics or graph theory, I would be extremely grateful. Thank you.

## Graph Theory PhD

### Re: Graph Theory PhD

My interests are primarily in Algebraic Geometry so I can only provide information regarding expectations for students such as myself. In the top schools, students interested in a certain area of mathematics are generally expected to have studied the first couple graduate courses in that area. There are cases where students pursuing research in Algebraic Geometry have not yet studied Algebraic Geometry but, they are able to study it in their first year. For schools ranked below 15, I would say you have a fairly strong chance because of your research and fairly strong GRE scores. Writing to professors from these schools will help a lot.

### Re: Graph Theory PhD

I really appreciate the information you provided since I don't really know what happen in top50 schools.djysyed wrote:My interests are primarily in Algebraic Geometry so I can only provide information regarding expectations for students such as myself. In the top schools, students interested in a certain area of mathematics are generally expected to have studied the first couple graduate courses in that area. There are cases where students pursuing research in Algebraic Geometry have not yet studied Algebraic Geometry but, they are able to study it in their first year. For schools ranked below 15, I would say you have a fairly strong chance because of your research and fairly strong GRE scores. Writing to professors from these schools will help a lot.

### Re: Graph Theory PhD

I appreciate your reply. I've been emailing professors with several different types of emails just to see what gets a reply. I've been sending emails mentioning specific things I liked about certain papers, and I've also been sending emails asking if certain techniques that a professor uses can be used to solve another kind of problem; I even took a gamble recently and sent a professor a list of errata for one of his preprints. (I made sure that they were actually errors; they were all just instances of using two letters to refer to the same variable or using a variable with no definition, whose meaning must be inferred from a later line of a proof.) I've only gotten a few replies, but I'll keep trying. Also, if you have any advice about how to send emails that catch professors' interest, I would appreciate reading that as well. Thank you.djysyed wrote:My interests are primarily in Algebraic Geometry so I can only provide information regarding expectations for students such as myself. In the top schools, students interested in a certain area of mathematics are generally expected to have studied the first couple graduate courses in that area. There are cases where students pursuing research in Algebraic Geometry have not yet studied Algebraic Geometry but, they are able to study it in their first year. For schools ranked below 15, I would say you have a fairly strong chance because of your research and fairly strong GRE scores. Writing to professors from these schools will help a lot.

### Re: Graph Theory PhD

I was under the impression not to try talking to them about their papers unless you were writing thesis level papers prior to applying. The emails I usually sent were generally along the lines of:

Hello Dr. ...

I hope you are doing well. My name is (name) and I will be applying to (school) for their PhD program in mathematics. I have some questions about (insert your fields of interest) and was wondering if you would be able to answer my questions about the general expectations of graduate students?

Best wishes,

(name)

Hello Dr. ...

I hope you are doing well. My name is (name) and I will be applying to (school) for their PhD program in mathematics. I have some questions about (insert your fields of interest) and was wondering if you would be able to answer my questions about the general expectations of graduate students?

Best wishes,

(name)