Wait, Which Notation Do I Use?

Being a math/atmospheric science student with a background in engineering is really cool most of the time. But unsurprisingly, it has some less pleasant moments. In particular, conventions have been making my head spin.

I’ve known for a long time that physicists and mathematicians use a different notation for which of theta and phi is the inclination angle and which is the azimuthal angle in spherical coordinates. And now it gets better; geophysical fluid dynamics uses yet another convention with regards to spherical coordinate notation.

In a fluid dynamics class, the streamfunction is usually defined with the x-velocity u equal to the partial derivative of the streamfunction with respect to x, and then the y-velocity v is equal to the partial derivative of the streamfunction with respect to y. In geophysical fluid dynamics (or at least my book/class), those signs are reversed.

Fluid dynamicists refer to the material derivative and write it as Dy/Dt; dy/dt implies that y is a function only of t. Physicists call the material derivative the total derivative and write it as dy/dt.

Why do I know about all of these, and why do I care? Because I’m either in classes now or was in classes last semester using all of these conventions, and courses or disciplines using each of these conventions will be on my qualifying exams. It’s fun, by which I mean very, deeply confusing. The joys of being interdisciplinary.

Knights, Knaves, and Normal People

I first heard of Raymond Smullyan when I was ten years old.

I had just started taking an online formal logic class, and the beginning of the class had two modes: introductions to the formal meanings of things like and, or, and implies, along with truth tables, and Raymond Smullyan (and similar style) puzzles.

In particular, I made my way through what seemed like dozens of knights, knaves, and normal people puzzles. They were so much fun, and I was fascinated. My mom checked Smullyan’s The Riddle of Scheherazade out from the library, and we did some of the puzzles in it, as well.

I know a lot of people who grew up loving math who lived on puzzles. Physical puzzles, Martin Gardner puzzles, Smullyan puzzles. I did Smullyan puzzles young, and I enjoyed them, and then I didn’t do them anymore, not really. Not for a number of years.

But fast forward to the summer I was seventeen. It was the summer before college, and I was spending it at home, working as a grader for Art of Problem Solving, watching lots of sports (live and on TV), and taking a few dance classes. I had one other major project: in June, I participated in Camp NaNo, something like National Novel Writing Month (run by the same group) with a bit more built-in flexibility and a different online social structure.

I didn’t have a particularly strong plot idea, like I sometimes did going into NaNo and similar challenges. I just wanted to write. Somehow, I ended up with the plan of writing about a group of friends who discovered and fell in love with logic puzzles. In particular, they happened upon a copy of Smullyan’s “What Is the Name of This Book?”

So, yes, I have written thousands — over fifty thousand — words largely inspired by Smullyan. (It’s not a good piece of writing, and it would be an odd thing for anyone else to read. It gives away the answers, which is just wrong. But it was an interesting piece to write, and that’s what was important at the time.) Even though, before that June, I hadn’t really done Smullyan puzzles in a number of years, that experience stayed with me.

I don’t really have a strong story to tell about Smullyan or his puzzles. They weren’t big or defining for me. But they were present, and they were part of my mathematical journey; they’re part of my love for math and for logic in particular, enough that I thought it was natural to write about other people discovering and experiencing that love. And with Smullyan having died this past week, I wanted to remember even these small ways in which he and his work mattered in my life.

Thank you, Raymond Smullyan.

Wanderings in Prealgebra

A few interesting math subjects — topics that we think about as fairly advanced, usually — came up in my Art of Problem Solving Prealgebra class tonight. I actually think they’re fairly normal things for students taking Prealgebra to think about, at least fleetingly, and that perhaps we don’t usually tell them how interesting these questions and thoughts are.

Manhattan Mathcounts

Part of what I wrote in the community involvement section of my NSF Graduate Research Fellowship application was about teaching math, science, and engineering topics to students. I’ve written about the math modeling classes I taught at Splash at Columbia and MIT last fall. I’ll be teaching at Columbia Spring Splash (classes to be determined) and at MIT Spark (one class about atmospheric soundings, one about Soviet ballet).

Teaching is definitely the kind of outreach I find most exciting. I like interfacing directly with students, even though there’s still a lot that I’m figuring out about how to teach these kinds of classes well. This weekend, though, I participated in a different kind of math volunteering by working at Manhattan Chapter Mathcounts.