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I went to college right out of high school not really knowing what I wanted to study. I ended up with medical issues about two and a half years into my degree, lost motivation, and dropped out. After taking the occasional class at a community college, I helped open a math tutoring business with my parents. I've always been good at math, but I have absolutely fallen in love with it now, often spending most of my free time going through early graduate level textbooks and staying up all night reading proofs. I now hope to pursue a PhD. in Mathematics. I have been accepted as a transfer student to finish up my bachelors degree in mathematics, which is quite different than my original intended major of theology. I graduated from high school in 2007 and will likely finish my undergraduate degree around 2018.

**QUESTION: ** as a result of being unmotivated in my years right after high school, I have some F's which have resulted in around a 2.5 GPA, although I do not know if that will be shown on my transcript, since it came from a different institution. If I show motivation and a passion for constantly striving to push my knowledge in mathematics and receive over a 3.7 in my 300-400 level math courses, can that overcome my failures in the past?

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What matters most to be accepted into and succeed in a PhD program is an advisor who values you and your work and will vouch for you. Grades only matter if you're applying through the front door in a pile of 1000 applications, which you want to avoid.

During your remaining years in undergrad, look up and seek out the Mathematics professors at the college or university you want to attend. Read their research, journal publications, conference presentation, research agenda, etc. and figure out how you can contribute to that and build upon it. Then reach out to a select couple of them and have coffee with them, discuss your plans, volunteer to join one of their research projects as an undergraduate research assistant (sometimes it's even paid), and so on. If you demonstrate aptitude, particularly when it comes to novel research and deep understanding of the subject material AND you have found the right advisor who wants to work with you, that person will help you with the application process and take you on as their graduate student.

Good luck!

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    I'd also recommend smashing the GRE math subject test. – CKM Feb 2 '16 at 19:30
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    This comment might make a lot of sense in other fields, but there are many aspects that don't apply to mathematics. (For example: advisors don't admit students to work with them, there aren't undergrad research assistants, professors' publications are not readable by undergrads, etc.) Plus picking one university that you "want to attend" for grad school is a terrible idea. However, the basic advice here is good; you should just apply it to faculty at your insitution. You need to find a faculty member at your institution who will advocate very strongly for you in their letter. – Tom Church Feb 3 '16 at 4:35

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