How Can I Strengthen My Graduate School Application for Mathematics?

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In summary, the individual is a mathematics graduate and has been working as an actuary for a few years. They are considering returning to graduate school for a PhD in math, but have concerns about their application. These include lack of upper level math courses, research experience, and strong recommendation letters. They are wondering if there are any ways to improve their application and if there are non-degree math courses available for someone working full-time. They also mention the possibility of taking courses at a nearby school and getting involved in research to strengthen their application.
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regginbrow
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I graduated the middle of the last decade with a BS in mathematics. I've been working as an actuary since graduation, and completed all the exams just a few years after graduation. The money is very nice, but I find myself completely uninterested in business, and am kicking around the idea of returning to graduate school for math, ideally on a PhD track. There are a few problems with my application, however, and I'm interested in seeing if there are any ways to make myself a stronger candidate. I don't plan to return for at least a few more years to save up some cash, so there is time for me to improve myself.

First, I never really planned on going to grad school while an undergrad, so I did not take every upper level math course I could (missing complex analysis, topology, number theory). I am very skilled at self-study, so I am confident that I will be able to teach myself this material on my own time, but I don't know how to demonstrate this to admissions. Since I'm working full-time, ideally I'd be able to take courses at night, on weekends, or online and rock an A on all of them, but that doesn't seem to be possible with upper level math courses. The best I seem to be able to do is rock the GRE instead.

Second, I don't have much in the way of research. I did a senior-level honors thesis that did have original research in it, but I am definitely not published anywhere (no REU, etc.).

Third, recommendation letters. I can probably still count on a strong letter from my thesis adviser, but I don't know what to do for the other two letters. I've been out of school long enough that I can't just ask random former professors and expect to get strong letters from them.

I was as strong student, with 3.9/3.6 math/cum GPA, at a top tier liberal arts college. However, I did not gear myself towards grad school, and my CV reflects that. Given that I will not apply for at least 2-3 years, is there anything I can do to improve it? Are there any kind of non-degree math courses that would be available to someone working full-time (nights/weekends/online)? My ideal situation would be to take courses at a nearby school of this variety, ingratiate myself with some professors, and start helping them out on research. Is this even possible, without returning to school full-time for a second bachelors degree?

Thanks
 
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I don't know how much things have changed, but about 25 years ago I was in a similar situation. I had been working for about five years (and was ten years older than most grad students, since I started college after military service), and had virtually nothing to show grad schools except very high grades and very high GRE scores. I had gone for breadth rather than depth as an undergrad, so I had a BA in Math, a BS in CS, and a minor in EE, but pretty much the bare minimum in upper division courses, from a mediocre state university. No research, nothing relevant from my job. I doubt that my letters of recommendation, from profs who probably barely remembered me, were more than boilerplate. One of them made it pretty clear that he was not thrilled that I had asked him, but I had no choice.

Despite all that, I got several very good offers (full tuition and a generous stipend) from some top CS PhD programs, including Berkeley. And I'm a white male. So, it can be done, as of 1986 anyway.
 
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I think that, right now, I could probably get into a PhD program at a decent enough school. Possibly an unfunded masters program at a top 25 school and try to transfer to the PhD program if I live up to it, although I am not 100% confident in that. But, since I do have time before I plan on applying, I would like to work on and improve my application. Like I said, research, letters, and volume of coursework are my biggest hurdles, but I don't know if it's possible to do anything at this point.
 

1. What safety measures will be in place for students returning to school for math classes?

Safety measures will vary depending on the school and local guidelines, but some common measures include social distancing, wearing masks, frequent hand washing, and regular cleaning and sanitizing of classrooms and equipment.

2. Will students be required to wear masks during math classes?

Again, this will depend on the school and local guidelines. Some schools may require masks to be worn at all times, while others may only require them when social distancing cannot be maintained.

3. Will there be any changes to the curriculum for math classes due to the pandemic?

It is possible that some adjustments may be made to the curriculum to accommodate for any missed instruction during remote learning. However, the core concepts and skills will still be covered in math classes.

4. What options will be available for students who are not comfortable returning to school for math classes in person?

Many schools are offering a hybrid or fully remote option for students who are not comfortable returning to school in person. This may include live virtual instruction or recorded lessons and assignments.

5. How will students be able to catch up on any missed math instruction from the previous school year?

Schools may offer additional support or resources for students to catch up on missed instruction, such as tutoring or review sessions. Teachers may also provide extra help during class or offer office hours for individual assistance.

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