Baby one-woman math squad
I want to start figuring out what area of math to study. I’m not sure if any mathematicians read me here, but if they do I’d love to hear about how you chose what to write your PhD thesis in and about what it’s like to study what you study.
In the absense of any grown-up mathematicians, maybe I can just use this blog to collect my thoughts. Here are some vague ideas around what I’d like to study:
1. I want it all! Specifically I don’t want to choose between being “pure” and “applied”. I want to prove theorems of exceptional beauty and have those theorems turn into astronaut dinosaur robot-cheetahs that run revolutionary preschools.
2. As far as I can tell, I’m not so much into differential equations. I might not be into analysis at all, really, but it’s too early to make that call. Certainly since applied math involving diff Eqs seems to grow on trees, I need more help finding applications from other fields.
3. Topology seems pretty cool jus’ sayin’.
4. I always like number theory too. And group theory.
5. But really that’s just a list of the things I’ve studied the most; I could probably like anything. So it’d be best to decide to like something that’s being studied by a really smart, dynamic professor at the U of M who would be a good mentor for me.
6. I think I like topology because I like using my geometric and algebraic intuitions in concert. I like seeing the same thing multiple ways, or seeing how different things are really the same. Making connections between two apparently different structures and using those connections to tell you more about each. Category theory just freakin’ delights me.
Okay that’s enough. Everyone tell me about applied topology. Or applied anything other than Diff Eqs. Also the application has to be something I’d actually care about helping to create; not weapons or stock portfolios.
How many hours a week do you work?
Do you feel like it is enough?
Do you feel like you can have anything approximating a work/life balance?
I work about 15 hours a week at my non-school job, or closer to 30-40 during school breaks. The important context is that I’m in…
I’ve been trying to track this for myself, recently. I think it’s about 18-25 on teaching (a 20-hr-per-week appointment that I think we’re expected to spend more like 15 hours per week on), and 20-35 on my own education.
What I feel is expected of me is more like 40 to 50 hours a week on school stuff, but I don’t know how much that’s in my head or actually coming from my program. I don’t want to work that much and don’t feel capable of it.
Maybe I’ll update this later when I’ve collected more data. It’s important to me to work on the ole work-life balance, and I appreciate hearing about how others manage it.
(via untidyfurrows)
In the sense that Margarita was always my Spanish name in school, and I AM THE MASTER of my modeling homework!
Okay I’m not doing one part of one problem. Whatever! I’ve gotten like 50% or below on everything else in this class so far, so by comparison, this is awesome.
My favorite part was learning about the connection between the smoothness of a periodic function and the decay of its Fourier coefficients.
No Joke, this is why I study math: doing homework is a quasi-spiritual practice of sitting with not knowing what to do. And usually from sitting with not-knowing long enough, knowing just appears out of nowhere.
Hoping if I get good enough at it, I’ll be able to sit with not knowing how to save the world until SHAZAM I figure it all out and everything is perfect for ever from then on.
(Source: kaleidoscopicchromatism)
Or so I assume. But not in the bad way. The class is ridiculously over my head and I’m going to keep trying to catch up part of the way. If I have to drop it, I’ll just drop it. As long as I feel like I’m learning cool stuff and making some kind of movement towards finding a specialty and they’re not taking my stipend away, grad school is going as planned!
Sure gives me empathy with my students, though. And with my professors. I at the same time think it’s silly how we’re expected to teach calc just because we know it and think that no one should ever be a student or a teacher without simultaneously filling the other role.
For those of you playing along at home, I’m now trying to work on a dimensional analysis problem, which are supposed to be easy but which I didn’t understand when we did them on the last homework. I think it’s because my linear algebra is rusty. So here are some linear algebra facts:
You can think of a matrix as a function that takes in a vector and outputs a different vector. Because when you multiply a vector by a matrix, you get a vector (wikipedia will tell you how!). Like a rotation matrix in three dimensions or something, I multiply my point in 3 dimensional space (which counts as a vector) by some 3 x 3 matrix, and I get a different point in 3 space. If I did this to every point in say, a 3-d image, and I really had a rotation matrix, the result would be the same image rotated into a different orientation.
Now when you have a function like that, also often called a map, it’s kernel is the set of everything that the function sends to 0. Like if f(x,y,z) = (0,0,0), then (x,y,z) is in the kernel. So the kernel of a matrix is the set of all vectors that are “sent” to 0 by the matrix. I.e. if v is a vector and M a matrix and Mv = 0*, then v is in the kernel of M. The kernel is also called the nullspace.
Now I’m trying to find the nullspace of a matrix formed by expressing the dimensions of quantities in terms of mass, length, and time, because the way my matrix is set up, the things this matrix sends to 0 will be dimensionless quantities. There’s something more I need to remember about free variables before I can do this. One-woman math squad away!
*here 0 is a vector all of whose entries are 0
But not in the probability sense! I’m apparently learning to take derivatives of functions that I’ve always been told weren’t differentiable. Because apparently now differentiability is not the point. It’s all about integration, baby.
I’ve been told before that integration is a mathematically deeper, more fundamental concept than differentiation, even though they were invented in the opposite order.
I find this part of the course a lot more exciting that the jam on a plane, so far. Maybe I am really a pure mathematician.
Maybe I just like the things I understand.
But seriously, a step function has a derivative? This is sillyness and nonsense! I am very excited.
