Hello, everyone! I'm a mathematics graduate student from the United States. Almost two years ago, I was forced to leave my Ph.D. program because of some unfortunate circumstances, but starting in the Spring, I'll be returning to school to get back to work on my degree. I've been spending the past month brushing up on the math I learned in my first couple years of grad school so I can hit the ground running when I actually get back into classes. I basically joined this forum to have a place to discuss proofs that have been giving me trouble in my self-study, but once I get back into the swing of things, I'm sure I'll be motivated to talk about more interesting things.