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?