Three years ago around this time, I was applying to Princeton, and I had no idea what I wanted to study.

Before we graduate, Princeton students complete a little something called the senior thesis.

Among undergraduates, mathematics is perhaps one of the University’s most polarizing subjects. For the quantitatively inclined, the rigors of mathematical reasoning provide both a fascinating challenge and an indispensable tool. To these students, numbers bring clarity — and a reward. Though the mechanics of calculation can prove difficult, the sense of accomplishment is well worth the struggle; few things are more satisfying than the feeling of achievement upon completing an arduous problem set.  

To others, though, the specter of mathematics is far more frightening than it is inspiring, and many a humanities major has been known to avoid quantitative courses at all costs. For these students, high school math was more than enough. Here at Princeton, they’d rather spend their hours deciphering Adorno than proving theorems.

Yet even for the English major, the value of mathematics is hard to deny. After graduation, the quantitatively adept are in high demand. In our increasingly digital world, the ability to reason mathematically is useful in a seemingly endless range of contexts. 

Personally, I’ve always been stuck between these positions. Though I fared well in math prior to Princeton, I’ve never enjoyed it enough to even vaguely entertain the notion of studying college-level mathematics. 

Thankfully, Keith Devlin, a professor visiting from Stanford, is offering just the course for people like me. Welcome to Math 195: a class designed to teach the tools of mathematical reasoning without the attendant intricacies of advanced theoretical math. In our first class, Devlin tells us that the world is full of people who can do advanced mathematics competently and accurately. Far rarer, though, are those in the humanities and other non-STEM disciplines who can reason with the precision of mathematicians. It is at these kinds of intersections, where the rigor of mathematics is brought to bear on the challenges of other areas, where things get interesting.

Half a semester in, it’s been a whirlwind of discovery. Devlin is as engaging as they come: a former consultant for the CIA, a wildly popular guest on NPR, and a prolific author, he breaks from the stereotypical mold of the bookish academic. Classes are punctuated with anecdotes drawn from his decades of pedagogical experience. Over the course of his career, Devlin seems to have done mathematics in every context imaginable: government consulting, the private sector — even a popular television program. For us, a group of math students consisting almost entirely of non-quantitative majors, these creative applications of mathematical methods are a revelation. In one particularly striking lecture, Devlin tells us about a formula that’s been used to catch murderers. Hardly the dreadful stuff of 12th grade calculus.

Even more interesting, perhaps, is the way that the course has been delivered. Alongside our group of about 20 Princeton undergraduates, 30,000 others are simultaneously taking the course online. Introduction to Mathematical Thinking is offered as a MOOC, a massively open online course. Around the world, many, many others are learning about the issues that we grapple with in class. In fact, we watch the very same online lectures as every other student, and are graded on identical problem sets. What is different, though, is that we get the ‘VIP version’ of the course, so to speak. Alongside the online lectures, our class also benefits from three hours of in-person class time a week to ask Devlin questions and work together on the more challenging problems. Witnessing this against the backdrop of thousands of other students who would relish such an opportunity, every class feels like a luxury. It’s a sense of gratitude worth cultivating.

As we near the end of the semester, we are meant to be thinking about a final project. Fascinatingly, we’ve practically been given carte blanche — pick a subject we’re personally interested in, Devlin tells us, and he’ll help us find a mathematical angle to approach it from. As soon as I heard that, I knew exactly what I’d be writing. One of my more idiosyncratic passions is collecting credit card and airline miles, and figuring out how to best optimize my spending, booking my flights strategically, and signing up for new credit cards where lucrative bonuses beckon. Until now, my approach to all of this has largely been ramshackle. I usually meander around the Internet until I find a few opinions on which award schemes are superior to others. Confronted with dissenting opinions, I tend to go with what seems superficially most plausible. With this class, though, I’m excited to add a bit more rigor to what is admittedly a rather strange hobby.

Thankfully, Devlin is no point-neophyte himself, having flown more than 2 million miles on United, a landmark he hit during one of the first weeks of class. Having him advise my project then, seems particularly fitting.

Ultimately, this class has motivated a desire to dig deeper and go farther in the pursuit of mathematical knowledge. It’s a result I hardly ever thought would be possible in college, but an outcome, I think, worth being excited about.

While the amazing food may bring many through the doors of the CJL, our engaging activities and the incredible relationships made within our walls are what keep hundreds of students connected to Jewish life here on campus.

With the beginning of my senior year upon me, the inevitable has come: thesis. I meet this reality with a strange feeling. I actually got a chance to sort of start my thesis a few months back because my super awesome adviser took me into his Princeton lab as an assistant over the summer so I could learn the ropes. So in a way I should be familiar with how this goes, right?

Maybe.

This summer, I would safely say I had an experience I don’t think I could ever repeat. Like I said, I worked on campus in a lab, but that was only half the picture. This came hand-in-hand with a whole strange mix of other crazy adventures that make just sitting in Princeton and plugging away at research seem like a confusing new experience.

I spent about half my time this summer on a bike. I’ll explain.

Basically, I was planning to spend this summer off campus getting some pre-grad school logistics out of the way. I planned to do that back home, but when I got the invitation to stay at Princeton, I knew I had to find a way to make it work. I took a look at how to make that possible, and realized that it meant getting from Princeton to West Windsor, where I had a daily commitment. This is sort of tough to do when you don’t have a car, which I don’t (because, as I’m learning in my Urban Sociology class, public transportation in the suburbs is...not so great).

Luckily, my adviser lent me his wife’s bike. It casually meant biking 60 miles a week, though. My adviser sat with me for almost an hour trying to find the safest and most efficient route on Google maps. Like I said, the coolest.  

So I had a lot more work going on than thesis when I started it, and am still sort of learning to disassociate the dread of thesis from the other ridiculousness that I got accustomed to this summer. I wonder which will be more tiring, but for now, I am happy to say I haven’t touched a bicycle since August.

 

During move-in and the start of classes last week, I saw and heard fellow '16ers saying things like, "The last first day of move-in!" or "The last first day of class!" or "The last first time I sleep past my new semester's class!" 

Congratulations to everyone recently admitted to Princeton! You probably have some big choices to make this April, and I sympathize, since I have just completed making my own decision about where to attend graduate school in physics.

The graduate school decision process is a little different than the undergraduate one, but just as difficult and exciting.  It starts at the beginning of February, when decisions arrive. Many undergraduate schools give you advance notice about when they'll post decisions, but physics graduate school applicants have no such warning.

For about three weeks starting at the beginning of February, decisions arrive in your inbox at seemingly random times. These times are sometimes quite strange; I received acceptances on Saturday afternoon and at 2:55 a.m.  Even worse, many schools send out acceptances and rejections to different applicants at different times, which means that a friend might hear from a school before you do, and you may have no idea what that means. Given all this uncertainty, my friends and I were very stressed during February.

Luckily, however, we all did very well, and ended up with some wonderful schools to choose from. Though it was nice to have this variety, it did make deciding which school to attend harder. Most graduate schools pay for you to visit them and meet with their professors to help with this decision.  I decided to visit four of the schools that admitted me: UCLA, UCSD, MIT and Princeton itself.

I started with the California schools. I left New Jersey on a wet, cold, nasty morning, so when I stepped out of the airport in Los Angeles that afternoon, I seriously considered picking UCLA just because of the weather. Walking around UCLA's campus a few hours later reinforced this initial, favorable impression. UCLA's campus is filled with fountains, grass and open, elegant architecture that takes full advantage of its California setting, and the result is stunning.

The next day, I talked with several UCLA plasma physics professors and toured UCLA's plasma physics facilities, which were very impressive. These meetings helped me to better understand UCLA's offerings, but they also helped me better understand my prospective field. Plasma physics is currently facing some funding challenges, and the UCLA professors had opinions about why these challenges are happening and how to work through them.

I left L.A. that evening for San Diego. This trip again impressed on me the beauty of California: My train raced past beautiful beaches and majestic hills, and I could easily picture myself moving to San Diego, buying a surfboard and juggling physics research with new, ocean-based hobbies.

The next day, I went to UCSD's campus. The UCSD professor with whom I would have worked was away from campus to give an invited talk. But I spoke with many graduate students and other professors, and I Skyped with this professor later in the month.

I left California that evening completely exhausted, but with more understanding of the two schools.

My next "visit" was to Princeton, which admittedly wasn't much of a visit, since it entailed only taking a shuttle to the Princeton Plasma Physics Laboratory (PPPL), where I would do my graduate work. I already knew a lot about the research facilities, so I spent most of my time meeting with Princeton professors I didn't know well and talking to other prospective students who were visiting at the same time.

My final visit was to MIT. This was also my longest visit; the MIT physics department's graduate open house starts early Wednesday morning, and ends midday on Friday. Even with all this time, I didn't feel like I got a full understanding of the department or of the school as whole because MIT is a very large and busy place. However, I was impressed enough with what I did see, and with the prospect of moving closer to my Vermont family, I decided to commit to MIT.

Though I'm satisfied with my decision, remembering that these are now my last days in Princeton makes me sad. This sadness is amplified by the excitement of the pre-frosh, who discuss Princeton's qualities in their Facebook group and send me more questions via private message. Every time I talk to them about the incredible opportunities at Princeton, I remember that I'm about to leave these very opportunities behind, and that these opportunities are pretty incredible. One pre-frosh recently requested a "pitch" of the strengths of Princeton's physics and astrophysics programs, and I leave my response here so you know what I mean:

"Princeton University and the nearby Institute for Advanced Study together host arguably the most exceptional community of theoretical physicists in the entire world, and this can lead to some pretty cool encounters. For example, a few weeks ago, a visiting postdoc gave a presentation about the topic I'm working on for my thesis. I went, and ended up sitting a few feet away from Juan Maldacena, a physicist responsible for huge advances in string theory.

The University also has many astro/physics opportunities that are probably unique. If you’re interested in biophysics, or just in seeing how physics fits with other sciences in general, the Integrated Science program would be perfect for you. JPs (junior papers) and theses make sure that everyone gets involved in research, and some of these independent works are actually published (more common in astro than physics, I think). PPPL is probably the best plasma physics research facility in the entire United States, and possibly the world, and it’s very easy to do a JP, thesis or internship there.

Beyond all that, physics at Princeton is pretty fun as well. Physics majors tend to be close to others in their year, since they bond over problem sets. The senior physics majors are sad that we’ll be parting soon, so we’re holding a series of physics parties this semester. The astro department typically has very few majors, so it is known for offering lots of individual attention and support."

One of the most common questions I am asked is about Princeton's competitiveness: Are students here extremely competitive, or do they collaborate on their work? This was also a very important question for me, and is perhaps the thing about Princeton that has most pleasantly surprised me. Considering that most students in Princeton have come here after several years of a competitive environment in high school, I imagined the environment at Princeton to be cutthroat and fierce, but I couldn't have been more wrong.

Collaboration in Princeton is highly encouraged. In all my classes with problem sets, instructors have organized sessions for students to come together and discuss the sets. I have spent numerous nights working late with my fellow students, throwing chalk frustratedly at a chalkboard, trying to make sense of a particular problem. These sessions are incredibly helpful as we get to pick each other's brains and bounce ideas off one another, trying to figure out which approach would work, which wouldn't and why. This has helped me many times to understand the subject matter better conceptually.

It is also wonderful to play to each other's strengths.This was especially evident when I took the integrated science curriculum in freshman year. The questions drew from many different branches of science, and we were all able to contribute in different ways. Having a background in physics, I would always take the asymptotic cases, the biologists would try to make sense on a larger picture and the mathematicians would check for rigor.

In all science classes, while it is required for your work to be your own, instructors encourage, and often even pursue, the students to attend such problem-solving sessions and share ideas, concerns and questions. And students love attending these sessions, or working together in self-organized sessions, as otherwise they might hit a wall when tackling a problem unless someone nudged them in a particular direction. Nobody in a position to help me has ever denied my request for assistance with a problem, or notes or anything else.

In all my classes where we would be assigned projects, group work has always been highly appreciated by the instructors, whether in philosophy, computer science or history. Often, group projects go beyond the requirements of the course when some of the members of the group are incredibly passionate about the project and it catches on. This has led to some very memorable computer science and art projects that have become known to the larger student body, including many apps and art installations. In fact, you can even collaborate on independent work to produce joint-theses or papers.

I like to say that I have learned as much from my peers at Princeton as I have from my professors, and I strongly believe in that statement. One of the greatest things about studying at Princeton has been the opportunity to interact and work with so many amazing individuals, and learning from these individuals inspires me to work harder and understand the material better every day.

Last we left off in this awesome chapter of my education, I had told you all about my class on "Olmec Art", which I started taking because of my job at the museum. (Speaking of the museum, I’m giving a tour on April 28 for Princeton Preview at 2 p.m. If you’ll be on campus, come say hi to me!!!)

If you haven’t seen that post, I started working at the museum my freshman year, and fell in love with one object of Olmec origin, “Kneeling Lord with Toad Incised on his Head.” I joined the class about Olmec art to learn more about this piece at the beginning of this semester.

A few awesome things have transpired since then.

First, I got to hold the “Kneeling Lord” figurine that I raved about last time. I fan-girled. A lot. It was indescribably cool to be able to get up close and personal with something that, until then, I only got to look at behind glass.

And all that was just the first part in the list of exciting things going on right now in that class. 

Last Sunday, we took a trip to New York City to go see museums and galleries that house nice collections of Olmec material. We went to the Museum of Natural History, the MET and to a private collection. At the private collection, we had an opportunity to talk to the collector, see her art and were each assigned a piece to research for a final project.

Tonight, just before starting this post, I must have walked up and down the stairs in the art library on campus about 15 times getting books to start the research process. But, in doing so, I found things out about an object that I had never known. We weren’t given a fact sheet to accompany our piece, so we just had to flip through catalogues, find pictures that matched our objects and research backwards from that point.

And guess what? The piece I have is related in style to my oh-so-favorite “Kneeling Lord.” It’s kind of funny how because of that piece, I found it important to join the class, and now, I am finishing up my class writing a report (kind of) about it. 

That works out nicely :)

 

After what has doubtless felt like a long spring, March 31 has finally come and gone. For many of you, this means that you now know where you’ll be headed for college. A lucky number of you will be headed to Princeton—but even for those going elsewhere, you are on the cusp of embarking on some of the most exciting years of your life. Here are some of my thoughts as you begin to navigate the whirlwind few months you have left before summer.

First, spend some time carefully thinking about your college choice. Talk to your friends, family and teachers about your options; having multiple perspectives is always better than merely having one. Visit campuses if you can, talk to students if you know any and really try to look beyond a school’s website; often, the most useful information comes from the unlikeliest places. At the same time, though, avoid having this decision overwhelm your life. The hard part of the college admissions process is already behind you, and in my experience at least, people invariably end up happiest where they ultimately choose to go to school.

On the issue of the dreaded senioritis, resist the tendency to bow out of academics. You’ve made it through most of high school and, for a number of reasons, it’s worth finishing as strong as you started. First, the teachers who’ve worked so hard to mentor you over the past four years want to see you succeed—in fact, in some international systems (like the International Baccalaureate), the congruency of your achieved and predicted scores might even affect the credibility of their future recommendations. You’ve doubtless worked hard to earn the respect of your school and academic mentors; use these last few months to leave them with a lasting and positive impression.

There’s also a pragmatic side to this, and I think you’ll find that finishing high school ambitiously will prove useful in your first few months at college. Starting university can be stressful, and you don’t want to be spending hours holed up in your room teaching yourself material that you neglected to learn at the end of senior year.

Moving on though, as the year draws nearer to a close, be sure to step back and take stock of your surroundings. It can be easy to take your high school friends and hometown experiences for granted, but you shouldn’t. In all likelihood, your life is going to change radically once you start college, and you may very well find that you sometimes miss the relative simplicity of senior year. You’ll certainly miss the people. This isn’t to say that you’ll entirely lose touch with home once you head off for college, but it’s worth being intentional about how you spend the final months of what has doubtless been a formative four years.

Part of this has to do with gratitude. Make sure to say thank you to everyone who helped you get through high school. In spite of your best intentions, it will be difficult to stay in touch with teachers and mentors once you move away from home. Take them out for coffee, drop them a note or simply take time to tell them how much you’ve appreciated their guidance. You’d be surprised how rare of an occurrence this really is. If you had interviewers for your college applications, shoot them a message of thanks as well. To this day, I continue to correspond with my Princeton interviewer, and I've found it uniformly refreshing to have someone to call upon for advice with a bit more perspective.

Beyond the school year, though, this summer will arrive faster than you know it, and you should start thinking about what you’ll do right now. For many of you, the summers of high school were largely occupied with camps, programs and part-time jobs. Unsurprisingly, the periods between the years of college are likely to get similarly filled with employment or academics of one type or another. In some sense, this is really the most boundless summer that you’ll have for some time, so you should make full use of it. Whether it’s taking a meandering road trip across the country, conquering the entirety of Proust’s "In Search of Lost Time," or simply spending more time with your family before moving away, have a clear plan in mind. As tempting as it is to spend months aimlessly hanging around the local shopping mall with friends or playing video games in your basement, these aren’t good uses of a summer that otherwise has so much potential.

In a similar vein, it’s probably a pretty good time to set goals for the next four years, too. Once you finally arrive on campus, you’ll probably find yourself spending a lot of time adjusting to the new context. At Princeton, orientation week can feel like trying to drink out of a fire hose—so much to do, with so little time to do it. While you still have the mental space to think carefully about what you expect to get out of college, consider making a list of concrete things you hope to accomplish. While these will inevitably change once you start to experience the university landscape for yourself, having an idea of how you want to shape your experience will invariably prove helpful as you’re deciding how to get involved freshman fall.