My Time at the University of Arizona

I got my BS in mathematics from the University of Arizona, in the beautiful city of Tucson. I didn’t always think education was important, in fact when I grew up, I joined the military instead of going directly to school. I thought that a degree was just a piece of paper. Then in the Air Force, I saw how people with degrees were treated like gods, while people without were treated like scum. I didn’t like being treated like scum.

I began going to community college full time while working full time as a USAF weather forecaster. A kind of passion for knowledge and education had been kindled in my heart. The local Pima Community College went out of their way to make it easy for servicemembers to take classes, and I’m deeply indebted to them for making it possible for me to complete my gen ed’s while still enslaved by Uncle Sam. But attending community college was like climbing on a small hill, in the shadow of a giant mountain. The giant mountain was the University of Arizona, tugging more and more at my heartstrings as I become more and more restless wearing the Uniform.

Ever since junior high, I’d been passionate about mathematics. During my later teens, that passion smouldered down and almost disappeared, but between issuing tedious weather watches and warnings to bases around the western U.S., the old equations and theorems began dancing through my head once more. I’d browse the U of A’s math department webpage idly while I was supposed to be watching radar screens. Reading the descriptions of advanced high math courses filled me with the same wonder and awe that I experienced so many years ago gazing at the profoundly beautiful illustrations in Euclid’s Elements.

Ever the autodidact, I began teaching myself some higher math. I taught myself the basics of abstract algebra out of Herstein’s book, which a sympathetic mathematician sent to me when he heard about my plight on a math newsgroup. The clerks at the tiny base library got to know me as one of the few airmen taking advantage of the free inter-library loan system, requesting obscure tomes on Galois theory and topology. At work I was that guy who’s always reading a textbook. But I wasn’t satisfied, my hobby was incongruent with my lifestyle.

Suddenly, I was set free, when Congress decided the Air Force was overmanned. I volunteered to turn in my stripes, getting a super-rare honorable discharge from the AF after only 2 years of service. The timing was such that I was barely able to register for the Autumn semester. In fact, I didn’t even make the deadline, but by working with the office of admissions, I was able to get in. They needed my transcripts from community college, but because I was taking classes there until the very end, the transcripts wouldn’t even be ready until after the official deadline. I ended up biking all over Tucson so that I could hand-carry my transcripts from the community college to the U of A admissions building, just because snail mail would be too slow.

First Semester

Before my first semester even began, I was busy running all over campus on various errands. First, they had me enrolled as an out-of-state student, meaning the tuition, instead of being around $2000/semester, was more like $10,000/semester. I had to go through my voluminous Air Force paperwork and find all my paycheck forms indicating I’d been paying Arizona state taxes while I was stationed there. I was very relieved I’d payed my taxes to AZ– in the military, you have some leeway to pick what state you pay taxes in. Lots of people try to claim Alaska, to cash in on pipeline pay. If I’d done that, I would’ve ended up screwed As it was, for awhile I was afraid Uncle Sam was rewarding my service by making me out-of-state in all 50 states. When I finally got cleared for in-state tuition, I was so happy I was walking on clouds.

Similarly, I had trouble initially with the financial aid department. I filled out the FAFSA application, checking “prior military, honorable discharge” where it asked how I could prove my independence from my parents. I guess the people at the finance department thought that must have been a typo or a lie, cuz how could someone as young as me be prior military with an honorable discharge? And have two years worth of community college to boot? They had so much trouble believing it, I had to bring in paperwork proving my status. It’s a good thing I was able to prove myself independent, because I’d end up getting quite a lot of free money from Pell grants later.

Because I’d done so much community college, I was entering the University of Arizona as a junior. My gen ed requirements were totally taken care of, putting me in the very wonderful position of being able to pick classes based on my major and on whatever made me happiest That first semester, I took real analysis, numerical analysis, nonlinear dynamics, graph theory, engineering physics, and just for fun, an upper level history class about the art and architecture of ancient Crete. Initially, the math department put me in an “introduction to proofs” course, but after talking to the professor, he decided I should skip past that class and go straight into the real analysis class. All the self-teaching paid off: I managed to do all the intro-proof homework (the whole semester’s worth) in one evening, giving the professor all the confirmation he needed to bump me up.

That semester, I made some close friends who would remain my closest comrades throughout all my time at the university. All math majors of course, people as passionate about mathematics as I was. We would hang out and joke about math. Or do homework together. My “reality” was very small, my whole world consisted of proofs and theorems and equations. Perhaps it was my body’s way of recuperating after the stressful couple years I’d spent slaving away wearing Air Force blues. If so, it was a much-needed recuperation. My interests wouldn’t start to open up again until my last months at the school. For a long while, I would live, eat, and breathe the abstractions of pure math.

I continued the precedent I’d set at the easier community college, managing to pull in straight A’s despite being enrolled in almost double the full-time course load. Interestingly enough, the most difficult class to ace was actually the lowest-numbered class, the only “freshman” class of the bunch, the engineering physics class. Taught by a really demanding physicist, this course was totally intense. I think only seven or eight students out of the whole auditorium managed to pull off an A, so I was more proud of my A there than in, say, the real analysis course I tested into. I would later realize the counter-intuitive pattern holds more generally: the higher level the course, the easier it is to ace, as you rise out of the “filter” classes and into stuff in your major.

Straight A Student

After getting that first semester’s grade reports, I kind of “locked into” the straight-A path. In other words, I was deteremined I was gonna graduate the University of Arizona with a 4.0. Looking back on it now, I think this was ultimately negative. The intensity with which I studied and performed assignments prevented me from working much on my social life, which was very much stunted. Besides, I’ve come to suspect that a 4.0 isn’t even the best grade to show to grad schools or potential employers. Whereas, say, a 3.7 or 3.8 would suggest a very intelligent applicant, I think a 4.0 actually sets off alarms: “Who is this guy, doesn’t he have a life, is he autistic or something?” What’s more, in the later semesters, I actually ended up dropping a couple classes to maintain my unspoilt GPA, including a work-intensive course on Game Theory, a branch of math which is very popular in popular culture these days. It would’ve been better to sit that course, even if it meant eating a B or something. In short, my high grades would eventually cause me to lose sight of why I was attending the University in the first place.

There was one definite benefit to my high grades, though: after the first couple grade reports came in, full of A’s, Uncle Sam suddenly couldn’t stop giving me money. Thanks to financial aid, I barely had to pay any tuition at all after the initial semesters. I guess someone in Washington saw me and thought, “This guy is headed straight for the NSA!” Good thing they didn’t know I’d end up lazy and hedonistic

Urban Exploration

In my later semesters, my interests finally loosened up a little. I got into the highly non-mathematical hobby of urban exploration, the art of going where you’re not supposed to go. Suddenly, the world became much more full of wonder, as every door, every window became a possible portal to adventure. I’d spend evenings wandering the gorgeous campus, finding cool places to go: I saw many a mechanical room, many a rooftop, many a construction site. Near the end of my time there, I even found an entrance to the steam tunnels, a system of really awesome tunnels that served to provide heat to all the different campus buildings from one central steam plant.

Urban exploration was important in my development as a person because it represented a certain opening up, a certain reality expansion, which widened my world beyond the narrow realm of sets and numbers. While not strictly necessary, this no doubt helped me to pick up some of the other diverse interests I’ve since acquired.

Homeless By Choice

When I first got out of the Air Force, I took up residence in a very cheap studio half an hour’s walk from the school. However, because I was so devoted to school, this proved to be basically just a place for me to sleep and eat, and less and less even a place to eat. During the Winter, when I had an 8 AM class in the physics building, I grew rather tired of waking up at 7AM for the morning “Hell march”. Though Tucson doesn’t get all that cold relatively speaking, I’m a San Diego guy, and those early Winter mornings seemed cold as the gaze of death. Besides, I usually stayed on campus very late, working in the computer labs or hanging out with other math majors. The homeward trek seemed totally pointless: I’d spend half an hour walking home in the evening, sleep, and then spend another half-hour walking back to school. So, I experimented with sleeping in the physics undergraduate lounge on the nights before the early morning physics class. Oh no!, isn’t that like being homeless or something?? Well, all I know is, it was a whole lot more convenient!

I gradually became aware of how little point there was to having my little studio apartment. If I could sleep on campus when I wanted, and if I spent most my waking life on campus anyway, then why was I paying a highly non-significant amount of my savings to some landlord somewhere? So, quietly and with little fanfare, I went homeless by choice, and started living on campus. You can read the main article here: Homeless By Choice.

Taking Graduate Classes

In my senior year at U of A, I began taking graduate level classes, having pretty much already advanced past everything the undergraduate mathematics courses could offer. My first graduate level class was a very advanced linear algebra class. When you hear “linear algebra” you probably think matrices and vectors, but I’m talking more about tensors, universal diagrams, Clifford algebras, that kind of thing. I was a little nervous filling out the paper to get in the class as an undergrad, wondering whether I’d be able to handle it. Well, it was definitely a big step up from the undergraduate material in terms of difficulty, but I really liked it and learned a lot.

In the next semesters, I pretty much took exactly the classes I would’ve taken if I was a first-year grad student. Pretty much the only differences between me and a first-year grad student were that I wasn’t teaching and that, well, I was an undergrad. There were three core grad level sequences: real analysis, algebra, and topology (the latter which was split into differential topology one semester, and algebraic topology the next). If I’d thought that the mathematics was challenging in the first semesters at the university, those bygone days were nothing compared to what I had gotten myself into in senior year. And still, I loved the classes and aced them.

Undergraduate Research Paper

Though it wasn’t required, I published an undergraduate research paper during my senior year. Around that time, a deep thirst came upon me to publish, publish, publish. Since I was still technically an undergrad, I submitted a paper to the Rose-Hulman Undergraduate Mathematics Journal. The topic was computability theory; I dispatched a question which had been interesting to me since long before I even enrolled at the university. The problem of finding a formula for an arbitrary function. I handled this using machinery from the field of computability theory, as well as a lot of machinery I came up with on my own. The big result, in English, says: “Any function that can be programmed into a computer, has an explicit formula” (with lots of qualifiers on what “explicit formula” actually means).

This paper would foreshadow the path I would later take in graduate school: mathematical logic. The work I put into that paper seemed to confirm that I’m born with a knack for logic. Not only that, but I also love logic, so much so that I want to do some work to further the field as a whole. That’s where I’m at right now, in grad school.

Graduating from the University of Arizona

Based on my GPA, I was chosen as the outstanding graduate from the math department among my graduating class. But I would not end up “walking” at the official graduation ceremony. Here’s what happened. In order to crunch the last week of the year down as much as possible, because grad students generally don’t attend the undergraduate commencement ceremony, some graduate courses at UA actually have their final exam scheduled during the big event. Such was the case with the graduate algebraic topology class I was taking. Now, I could’ve gotten permission to take the final at a different time in the professor’s office, but honestly I didn’t care that much about the ceremony, and didn’t really mind missing it.

But then when some of the staff at the undergraduate math department were asking me about it, I didn’t want come out and say all that. To this day I dunno why I did it, but I told a rather ridiculous lie, saying that I wasn’t going to attend because I couldn’t afford the cap and gown! Before I knew it, the staff had chipped together and gave me the $20 necessary to buy the outfit. That put me in an awkward position, and I really regretted saying what I did. It was kind of too late to ask the professor to give me a special exam session. I hoped that I would be able to hit the ceremony, walk up and shake the dean’s hand, and rush off to take my algebraic topology final. There was about a half hour of ceremony time before the final actually started, and my last name starts with ‘A’, so I figured I had a pretty decent chance. Unfortunately, some guy noone ever heard of was giving some big speech, and I had to rush out to catch the final without ever using the robe the math department staff had paid for. As far as I know, the robe and cap I bought are still tucked away in a corner in the physics undergraduate lounge

I graduated with a four-point-ohhh, though it didn’t end up being as big of a victory as I imagined it would be. The requirements to graduate “summa cum laude” were only a 3.8 or 3.9, and there wasn’t really any other kind of special distinction to mark the perfect list of A’s. I had sacrificed some of my social life for, essentially, not a whole lot.

After Undergraduate

The math department offered to let me continue toward my PhD with them, even offering me a very generous stipend (one of the perks of majoring in mathematics is that you never hurt for money during your grad program). But there’s a kind of community wisdom that you shouldn’t do your undergraduate degree and your graduate degree at the same institution, and I ended up going to the Ohio State University instead, which is where I’m still enrolled as I write this article today.

At the University of Arizona, Tucson, I learned a ton of mathematics, and I also grew and expanded as a person. The rarefied environment of the mathematics department was the perfect place for me to recuperate from my long tenure in the military, and I when I emerged blinking in the sunlight, I was a healed man. I met some really awesome people on campus and I had a lot of fun in the wonderful city of Tucson. All in all, my time at Arizona’s oldest university was one of the most fun times in my life.

FURTHER READING

My Experience in Air Force Boot Camp
5 Ways to be Better At Mathematics
Become More Intelligent by Doing New Stuff
My Time in the Seduction Community
Training Self-Discipline
Pictures from Japan