Some background context: Because of a lack of information and other variables outside of my control, my first round of applications (fall 23) did not go well. Although I got into every single Master's program I applied to (a mix of public and private, prestigious and non-prestigious), I got rejected to every single Ph.D. program (Only top-tier private schools: Stanford, brown, etc.).

Here are some of my Info:

Undergrad Institution: Top Public University (In U.S.)

Major(s): Pure Math

GPA: 3.86 out of 4.00

Type of Student: International, Asian, Female

Any Other Miscellaneous Points: First Gen,

**Transfer Student**. The GPA above is the GPA after I transferred (It doesn't include my community college GPA).

Master's Institution: Non-prestigous (at all) Public School (US News Ranking 100+, QS 300+), has thesis option. allows Master's transfer to PhD. Not a lot of class choices (But I feel like this is quite universal among schools?? A lot of classes won't be offered regularly even if they are on the catalog).

GRE General Test:

169/170 (93%) on the Quantitative Part

Pretty low on the Verbal Part (52%), and Writing Part (around 40%)

GRE Subject Test in Mathematics: None taken

Program Applying: Pure Math

Research Interest (not changing): Algebraic number theory and representation theory. Langlands's Program (would like to focus more on elliptic curves stuff), arithmetic geometry.

Research Experience:

**None**. Only have done two reading courses relevant to my research interests. No publication. No papers of any sort.

Other experiences might help: Some math tutoring and English tutoring.

Before you ask why I had no research experience, here are some reasons:

1. I am not qualified for REU (or any similar opportunities) because I am an international student.

2. I was short on time in my undergrad institution because I am a transfer student. I only had two years to take advanced math courses and completing other degree requirement, which doesn't go well with the fact that the bar of pure math research is very high (and need a lot of time to reach). To put it into perspective, while my non-transfer-student peers were taking grad-level math courses, I just began to take Intro to Proofs. Moreover, the Profs at my undergrad institution typically don't give undergrad research opportunities unless they are extremely far ahead (at least a year of grad-level math courses experience and some relevant topic courses).

3. My academic interests are strictly in pure math, which just makes it harder in general to get research opportunities compared to applied math.

Math courses:

(undergraduate upper-div) : Abstract Algebra, Real Analysis, Complex Analysis, Differential Geometry, Number Theory, Mathematical Logic, Graph Theory, Cryptography, Linear Algebra.

(graduate) Planning on taking real analysis and abstract algebra sequences in my first year. I may take (or audit) topic courses about algebra if time allows.

**Edit:**Adding Information of letter of recs in my fall23 application round:

one from a lecturer who knows me very well

one from an associate prof.who I have taken a class related to my research interests

one from an assistant prof. who I have taken a class in math but unrelated to my research interest.

About getting letter of recs: I feel this is very difficult in a sense that I only had one year in my undergrad to form relationship with any faculty (since I am a transfer student); and now I am essentially facing the same situation again (because of the length of the master's program). Any advice on making connections with faculty and getting letter of recs would be appreciated!!