Since my last post before the JMM in January, I’ve begun a new semester. My goals are ambitious, as I am taking two course, finding an advisor for my Master’s thesis, and starting a new blog.
In some ways my new courses seem old. I am taking algebraic geometry and algebra. Two of the main topics of these courses – rings and algebraic (especially elliptic) curves – were introduced to me in a previous algebraic number theory course. I am looking forward to cementing my understanding of these topics and learn some new concepts. I think I am on the road to becoming an algebraist.
My search for an advisor has begun with a professor who taught my undergraduate algebra course, my algebraic number theory course, and who is teaching my current algebra course. I’ve also reached out to two professors on the analysis side. What I know about analytical number theory interests me, but I don’t know if there are any open problems in this area that are accessible to me or that are appropriate for a Master’s thesis. Most professors with whom I’ve interacted have several thesis topics at the ready for their students. In contrast with the above, I have often heard that graduate students need to choose their own topic. However, at this stage of my life in mathematics I am comfortable with adopting a research topic and personalizing it as I progress toward a thesis.
Finally, I have started a new blog with mathematical content. I got this idea from another blogger, Matt Might, and one of his several posts about success in graduate school. Since I haven’t begun my research yet, my first posts have been and will be based on what I have learned in my courses and independent reading. For example, my first post was on the finiteness of the ideal class group. My second post, based on a proof of the transcendence of , was on sequences of rational numbers that converge to powers of .
I plan to make the most of these new opportunities. Thus my goals for the semester are: Ace my two courses, find an advisor and research topic, and make posts to my new blog. What are your goals for the new semester?