Applying for Applied Math PhD as a non-math major (Letters of Recommendation, etc.) This is my first post, so I'm not be fully familiar with the etiquette of posting on this forum, but I'll do my best.
I graduated Summa Cum Laude in May from a reputable university with a major in finance. During my final semester, I took Linear Algebra and I noticed that I might have an affinity for mathematics. So, I took Calculus II at a community college over the summer, and I self-studied some Abstract Algebra. I also noticed that from the financial courses that I have taken, ones that dealt mostly with data and probability theory were my favorite. I then decided to pursue a PhD in Applied Math and have been preparing my application, so it'll be ready by December.
So far, I took the GRE and got scores above the 90th percentile in both sections. I was supposed to take the GRE Math test, but last week ETS cancelled it for this year. I'm also planning on taking Calc III and Mathematical Proofs in the Fall, then Real Analysis in the Spring. As I was narrowing down the list of professors to reach out for recommendation letters, I got into some issues that I was hoping this forum would help me with.
At this point, a well-established professor of mine has agreed to write me a good recommendation letter after getting the highest grade in his class (which is considered to be really hard finance course in my school). I did an independent study with a history professor; when I thought of requesting a letter from him, I wondered whether he would be helpful considering I only did a qualitative research with him. I also was the TA for a Management and Organizations class, so I considered a recommendation letter from my professor. Lastly, I was considering asking for a letter from a professor whom I wrote an economics research paper for.
About the professors mentioned above, do you think any of their LOCs would be helpful for my application? I ask particularly because I am applying from a non-traditional background.
I apologize for this lengthy post. The application process is starting to stress me out particularly because most educational institutions have stopped major research until further notice. So I'm stuck with the experiences that I have done.
Thank you!
P.S. My undergrad degree is from the US, and I plan on applying for a PhD in the US as well.
Having some research experience is better than no experience.  I don't see an issue with having a history professor write a letter for you, especially since you got research experience under their guidance.  Same goes for the economics professor, since Applied Mathematics and Economics are two very connected fields (and also since you wrote a research paper with them).  I think you should be good on letters of recommendation, especially since you mentioned that two of your potential writers are from past research experiences, which is what PhD programs want since it's focused on research after all.  As far as the professors you choose, it's most important to choose the ones who think most highly of you in a research setting, as opposed to &quot;got an A in my class,&quot; since PhD programs are about research output and less about A's earned in coursework.
The finance major shouldn't be too much of an issue.  Applied mathematics, as far as I'm aware, overlaps with many disciplines, ranging from quantitative finance to computational science to biostatistics.  Many of the professors in my department come from a wide variety of backgrounds, such as chemistry, physics, and pure mathematics.  So long as you have the mathematical basics to succeed you should have no issue here.
Finally, as far as other issues go, generally this is either for your SOP (Statement of Purpose, for talking about your research fit/interests) or something you should contact your programs of interest with regards to (including for the issue with the Math GRE given the circumstances we are in).  If you want to keep doing research, I know some professors (at least at my institution), have shifted to virtual format for the time being, you could try and see if there are profs doing virtual research in your school.
Hope my answer helped, especially for the LOR's part since that was your main point in the question, and best of luck with applications.