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How to improve graduate school application?

Current Junior at a non-target school with a 4.0 GPA and not much else. I am majoring in actuarial science and math. I thought I wanted to be an actuary so I passed 5 actuarial exams, got an actuarial internship last summer, and then realized I wanted more.

This year I applied to trading internships. Made the final round of Akuna, Optiver, and IMC and got rejected by all three, now I have no idea what to do this summer.

I want to be a quant. What can I do over the next year to get the attention of top schools? What additional opportunities are there over the summer?

I enjoy reading textbooks and self-learning. I've read/studied books on machine learning, option pricing, real analysis, python, C++, etc. and I have a lot of random extraneous knowledge about statistics/math/finance from my actuarial exams but I feel like I can't put any of that on a resume. I have loads of free time as maintaining a 4.0 here isn't difficult or time-consuming. So, assuming I can dedicate 6+ hours a day to it over the next year - what should I do to build a strong resume?

Thanks in advance.
 
Why not apply to more internships for the summer? It is only September, most companies have not locked in their interns. Actually, most companies have not even started interviewing. You have plenty of time. Find and apply to more internships.

If you are concerned about grad school, try taking the GRE and getting high scores. High GRE plus your GPA and some quantitative experience makes for a good application.
 
Why not apply to more internships for the summer? It is only September, most companies have not locked in their interns. Actually, most companies have not even started interviewing. You have plenty of time. Find and apply to more internships.

If you are concerned about grad school, try taking the GRE and getting high scores. High GRE plus your GPA and some quantitative experience makes for a good application.
GRE is a given. I want to get into as good of a grad school as possible; I'm assuming top schools want more than just GPA and GRE.

What kind of internships should I apply for? Quant internships require you to be in a master's/PhD program AFAIK, so I figured the best thing I could do was to get a trading internship. Should I apply for Data Science? Anything else?
 
Data science internships work. You can even consider alternative asset classes like energy--go work as a quant at an utility. Even though you got rejected, the fact that you made it to the final round is still a good sign. Maybe do some research internships where you can analyze data using machine learning, Python (preferred)/Matlab (used a lot by academics) and SQL? Machine learning and data science are honestly very popular right now. Good skills to have whether you work in finance, tech, healthcare, etc.
 
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