I am a sophomore who took abstract algebra for the first time. Started out with Bs, just learned that I failed the course, which is to be expected given the fast decline of my mental health.
However, after getting such a grade, I'm too afraid of even thinking about getting back up. How can I even consider graduate studies in mathematics when I can't even pass such a class. Is it even possible to rise again.
Anyone had a similar story, or some motivating facts from their personal lives to share?
It just seems a reach to even consider grad school after such a failure, and someone sharing stories similar to this one would be of great comfort.
Get back up. This is precisely why mathematics is such an excellent field of study. You are presented with ideas that truly challenge you. Eventually, the light comes on and the sense of accomplishment you get when you finally own an idea you couldn't previously understand is like being high.
I never failed a course but, as an undergraduate, I took a course in Mathematical Logic. We used the book, "A Mathematical Introduction to Logic" by Herb Enderton. I was not used to this level of abstraction and I had a better chance of getting through Finnegan's Wake than that book.
A couple years later, I was in graduate school and I took the graduate version of this course. At some point I got stuck on something and I tried to look it up in my copy of Enderton. Not only did the text not cover the material that I was looking for, but it was too basic. This book that seemed so esoteric at one time now read like a high school text.
Mathematics is a discipline. You can spend the rest of your life doing it and you will always be exposed to new ideas. Go for it.