With the academic year drawing to a close, and having finished my Master’s degree in Mathematics at the University of New Mexico, I find myself with more time than I have had in, frankly, years. To those who know me, you will know that I am taking a gap year for (at the least) the upcoming academic year. For those who do not know me, this is in part due to the large role my aging grandfather has had on me. It was only recently, after my grandmother passed, that we realized how codependent they truly were, and we have chosen to spend more time with him. With that out of the way, I should say something of sustenance rather than just my plans for the foreseeable future. So instead, I will opt to reflect on my experience at the University of New Mexico.

My time in Albuquerque has been interesting, to say the least. Academically, my only interest is number theory. This makes me hard to advise, as my Master’s advisor Dr. Maria Cristina Pereyra (Cristina, from here on) will attest. However, it also makes me relatively self-driven. I came to the University of New Mexico hoping to work with Dr. Alexandru Buium due to his work in differential arithmetic geometry. However, upon arrival I learned (much to my disappointment) that Dr. Buium has not been taking students for several years due to his personal situation, which I will not mention here out of respect for him. However, suffice it to say that he was unsure of when he would retire, and he eventually announced that he would retire at the end of the 2023-24 academic year. Despite him not taking students, he was kind enough to provide me with a list of potential faculty advisors to work with. From this list I chose Cristina, and I was happy working with her. It taught me many things, including the fact that I quite enjoy the field of analytic number theory.

My coursework was also quite interesting, covering the basic topics (abstract algebra, real analysis, complex analysis, and differential geometry), as well as some more specialized topics (algebraic geometry, toric varieties, Fourier analysis, etc.) Some of my favorite moments, which I will save for later when I talk about my fellow graduate students, come from studying for those courses. But courses are hardly the point of graduate school. To me, the purpose is to learn to be a better academic, to learn how to do research on your own, and to learn how to study topics in detail on your own. The courses aren’t important, it’s the habits you build along the way that are.

But the academic situation is perhaps only a third of any graduate experience. There are also the interpersonal and work portions of the experience. The work was the easiest, as work comes faster than the tedious process of building social connections. I begin my work under Dr. Derek Martinez. Derek is a principal lecturer at the university, and primarily teaches calculus coursework. He is known (at least among the students) to be one of the best teachers in the department, and I was fortunate enough to teach recitations for Calculus 2, corresponding to three lecture sections which he was teaching. Teaching at a university level was an interesting transition from my previous work experience as a mathematics paraprofessional, and I have my own history with Calculus 2 (stories for a future post, I suppose). However, I quickly learned to appreciate the environment, and the material. During both of my years at the university, I was nominated for the university’s teaching award, the “Susan Deese-Roberts Outstanding Teaching Assistant Award”. Upon graduating, I was awarded the departmental teaching award, along with a number of exceptional graduating teaching assistants who were in the Ph.D. program.

To me, the teaching awards are somewhat meaningless. But it is the fact that mathematicians may be nominated that is miraculous to me. This is because, in some sense, it is closer to what I consider to be the spirit of mathematics. That one may compete with those who draw families closer together (as is common among the Spanish department and their teaching assistants at the University of New Mexico) with only the passion they have for the subject. That, to some degree, just loving your subject can elevate you to a position where you compete with those who change lives. I think in that way, while mathematics as a field may be defined as the study of consequences of presupposed axioms, or even the study of patterns, mathematics is not characterized by this. Mathematics is characterized by the way that mathematicians love the subject, and dedicate their lives to it.

This draws me to the part of my master’s program that I remember with the most fondness: the people. I would be nowhere near where I am today if it weren’t for the support of my office mates, or the encouragement of my friends. Quite possibly my favorite memories of school are from my graduate program, sitting in the department lounge every other Friday doing homework with Shandy Simpson and Mahyar Shafighi for our Complex Analysis courses. We would sit together and work on problems as we fought the clock to our deadline at midnight. Every week we would say, “We need to get an earlier start on this. Let’s not do this next time,” only to be back in the same situation on the next homework two weeks later. The moments where we would find a hole in a proof just minutes before the deadline, only to frantically patch it and barely get our homework in on time. These are the moments that define my master’s program to me.

I also got to explore my interests in crafting to some degree due to my friends. I was reminded (through reasons I will get into in a future post) of my interests in bookbinding. Much to my surprise my office-mate, Jose Garcia, had done some bookbinding before, and he encouraged me to bind a few books. This quickly grew out of control, and turned into me binding a new book any time I needed one. I would buy a PDF (or get one from the Author, with their permission), print it, stitch the pages, and glue the whole thing together. After some time of this, I got to teach my friend Sarah Poiani how to bind books. Several weeks later, Sarah taught me how to knit, and soon I was crafting when I should have been studying, just like her. This, combined with my course work, served as a wonderful distraction from my personal life while my grandmother passed. I am sure she would approve of the distraction, and I am sure I will be talking about her in a future post.