I am a Master's student in math who is doing pretty well so far. I aced my first two classes (real analysis) and my summer session in probability theory is going well, too. Even before my Master's study, I already thought of a PhD. Nonetheless, there are concerns:
My good grades were the result of grit, not brain, meaning that I had to spend time to understand what the book is telling me. Furthermore, a lot of times during exam and homework, I had to try and fail a few times before arriving at the solution.
I did not study math during undergrad. Before my Master's study, I gulped down three semesters of calculus, plus LA and DE in one year. So compared to other students, I am already behind. In the next two months, I will learn complex numbers on my own and review my linear algebra.
I am a professional in a field that has nothing to do with math or research. After the holiday, I will speak to my advisor about taking a thesis class. It's not an insurmountable obstacle, but, in an unrelated field, I do have less time to concentrate on math.
At the end, how big is the jump from Master's to Phd? Especially after what I said in (1), I do worry that it is beyond my ability. I do not hold anyone responsible for my decision. So, please kindly offer your best assessment of my situation.
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