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I'm passionate about getting a PhD in Math for a career as a research mathematician and then as an educator working at a community college.

I got A's in community college. I transferred to our local University and for my 1st semester got a 3.67 taking science courses and 300 level math courses. The next semester I got a 4.00 taking more science and math courses. The next year I started exhibiting symptoms of bi-polar and my grades tanked pretty hard. After that I muddled through, graduated with a total GPA of 3.5 and started on a long journey of learning to live and thrive with bi-polar and depression. However, I did probably the dumbest thing ever. I convinced myself that getting a C.S. masters was a prudent idea and proceeded to re-enroll at our University and fail a bunch of CS classes. Now my overall GPA (despite already having graduated) is 3.19. Since then I went into the workforce, decided I really just want to get my PhD in math and teach a community college and have been pursuing that for a year now. In working toward that goal I took an independent study course with one of my professors to refresh my linear algebra and got an A. Then I took graduate level analysis (B+) and graduate level applications of linear algebra (A-). I'm currently in the 2nd semester of graduate level analysis and feel like I've gotten the hang of graduate level course work (I'm confident I'll get an A in this one).

So despite having early success in math (A's in the Calc series and A's in several 300 and 400 level courses) I have what looks like a really really confusing transcript because I tried CS, actually hated it, and go F's in two of those classes. To add to my transcript/GPA concerns I have C's in the undergraduate analysis courses from when bi-polar threw my life off the rails and around the same time got a D in diff-eq (which I retook for an A) and a C in combinatorics.

Now that I'm looking to apply for grad school in Fall 2020 (possibly out of my small state if the program is good) I don't really know how to communicate what probably seems like a very confusing academic record. For what it's worth I have 1 math professor that will write me a good letter of rec, a retired math professor that will write me a good letter of rec, and the P.I. from my internship at a big name research institute that might write me a letter. So at least I have that. But damn, my transcript looks like something that will hurt me without explanation. How do I explain it? Is it possible? Should I reconsider my path? I'm very dedicated to this path but I worry that despite my passion current and ability to pass graduate level courses it won't be enough. Any suggestions on how to explain my transcript would be so wonderful =)

TL;DR - I got good grades at my local Uni in nowhere USA. Then I got bi-polar disorder and so did my grades, then I graduated, then I tried CS and got even crappier grades still. But now I'm doing well and getting better grades in grad-level classes but have no idea how to explain all of this to grad programs I apply to =/

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    You will almost definitely have to choose between "research mathematician" and "K-12 educator." Those are two different full-time jobs. – user37208 Feb 7 at 14:42
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You need to focus. Why do you think you need a PhD in mathematics? If you plan to be a serious researcher, how do you plan to balance that with working in your under-performing school district? What specific area of math is your intended focus? Are you trying to get into a top 5 program or any program? That also makes a difference. If you can show that you are focused today and have doable plans with a PhD, telling your story won't be as difficult as explaining a low grade in an entry-level math course such as differential calculus. You will have a hard time living that one down. Figure out why you earned a D and how that changed your approach to understanding math. You might want to consider applying to a MS mathematics program and state your intention to seek the PhD at that institution.

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  1. A research level math degree is not needed or probably even beneficial for teaching in pre-college schooling. Instead of more subject matter schooling, you should be getting training at teaching.

  2. If you need more math, it will be an ed degree (or more hopefully) a year or so to get a certificate. The sooner you get into teaching the better. Rambling through more degree programs is avoiding where the rubber hits the road. But even though ed cert programs have parts that are a little daft (pop psych and questionable edufads), the do have one powerful learning area: substitute and trainee teaching. So you will be at the coalface.

  3. For school jobs, nobody will care about your varied past. They have people of all walks of life going into teaching. It is more about what have you done lately.

  4. (Not meant to cut, but serious direct advice.) If your requests for help or information are anything like this question (verbose, rambling, long paras), you will get little help in the real world. A big part of being a good teacher is being an efficient communicator. Make a little more effort--I bet you can do better.

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    A phd gives extra career options. Maybe OP will want to do a postdoc after it, or maybe they will want to teach at a university. I don't think it is a good advice to limit your prospects to teaching at school. – Alexey B. Feb 7 at 18:42
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Without knowing much about the American realities, I suspect that low GPA will hurt your chances to go to a highly-ranked fancy school, but you will still be a strong candidate for a mid-ranked one, given that you took extra classes and a research internship. First, since you are in touch with some math professors who consider you a good student, talk with them about wanting to do a PhD. They may give you advice or maybe even refer you to someone who is looking for a PhD student. Second don't be discouraged by the first few rejections that you'll inevitably get.

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