May 2013
3 posts
Things I know so far
So what’s the point of higher category theory, and weak n-categories and (weak?) infinity categories? What do I know so far?
Well category theory is a concise way of describing a bunch of seemingly different mathematical ideas. A category has:
-objects (these could be sets, or numbers, or dots on a paper)
-morphisms, (these could be functions between sets, or arrows between dots on a...
Tumblr will you be my accountability buddy?
So funny thing about math grad school—at some point a switch flips and after a LIFETIME of being told what to do, academically, you’re supposed to become an independent researcher who finds her own problems and figures out what’s important and how much depth to go into things and so forth.
This is, you can probably guess, really really really hard.
Hilarious!
So as an attempt...
Accidental math poetry for Geddes
From one of my professors, talking about homotopy theory and higher category theory:
“At each stage, you’re never asking for an identity. You’re always asking for a witness for some fact.”
April 2013
11 posts
Math Crush
I have the world’s biggest math crush on Eugenia Cheng of The Catsters.
https://twitter.com/DrEugeniaCheng
http://cheng.staff.shef.ac.uk/
Prelim Prelim Prelim
I can calculate fourier series, but I can’t yet use them to compute infinite sums unless I’m using the fourier series of x^2 to compute the sum of 1/(n^2).
I’m pretty sure I can show the supremum of the fourier transform of f is the L-1 norm of f, and that it’s acheived only at x=0. Some classmate was trying to tell me a really fancy way of doing this yesterday, but today...
One-Woman Math Squad: More Lipschitz continuity →
thingsendinginphysics:
mathsquad:
physicsphiends:
mathsquad:
Geddes told me that she reads my mathiest posts as poetry, so here is an update on Lipschitz continuity, for your literary pleasure:
It turns out that I need two things to do this proof: the Stone-Weierstrass theorem, and compactness of X. The Stone-Weierstrass theorem is about when you have a…
Compact Metric Space
-
It...
One-Woman Math Squad: More Lipschitz continuity →
physicsphiends:
mathsquad:
Geddes told me that she reads my mathiest posts as poetry, so here is an update on Lipschitz continuity, for your literary pleasure:
It turns out that I need two things to do this proof: the Stone-Weierstrass theorem, and compactness of X. The Stone-Weierstrass theorem is about when you have a…
Compact Metric Space
-
It turns out that I need two things:
...
More Lipschitz continuity
Geddes told me that she reads my mathiest posts as poetry, so here is an update on Lipschitz continuity, for your literary pleasure:
It turns out that I need two things to do this proof: the Stone-Weierstrass theorem, and compactness of X. The Stone-Weierstrass theorem is about when you have a collection of functions that form a sub-algebra of C(X, R), the continuous real-valued functions on X,...
Drinking from the fire hose
I went to that conference and it was great, because I like being overwhelmed with way more math than I could possibly understand. I like the discipline of trying to pay attention and seek for understanding even when I’m not finding it. It feels like really important practice for life: just being alive in the world is often Too Much of a Good Thing for me and I try to shut out some of my...
Math joke
I’m going to the graduate student topology conference this weekend. I’m excited! And I have high hopes that this could be the first time I go to a conference and actually understand some of the talks.
But I’ve been studying so much analysis with the prelim coming up…what if I don’t fit in? I’ll be like “how far is it to the banquet?” and everyone...
More studying
Yesterday and today I’ve been trying to prove that Lipschitz continuous functions from a compact metric space X to the real numbers are dense (in the uniform sense) in the space of continuous functions on X.
There are three different notions of distance hiding in what I just said—the distance between real numbers, the distance between points in X, and the uniform-norm distance between...
pegghetti:
dream-passi0nately:
my current mentality is “im sad and i hate myself but i have to get good grades”
that’s how I feel
is there any other way to feel to quote an original song from the cinematic masterpiece, School of Rock, “got good grades but don’t got no soul”
I don’t feel this anymore, but I remember it from high school, and I bet a lot of my students are in this...
Grandma Got STEM!
So cool, so cool! Stories of grandmas and grandma-like people who are or were badass scientists, engineers, and mathematicians: Grandma Got STEM.
More scheming
I had a birthday and am now in my late 20’s! Which means a lot of great things, but also that Grace Llewellyn didn’t write a handbook for my liberation. So I have to write my own. First step, finding people out in the world who are moving in the direction I want to go. Have some links!
exco
The Open Master’s Program
Zero Tuition College
The Public School
Citizen Circles
...
March 2013
8 posts
Scheming and Studying
I’m studying for prelims again—real analysis this time. It’s fun except when I get discouraged because it seems like too much to learn (my analysis background is limited).
And at the same time, I’m scheming about alternatives to grad school for people (me) who want to learn math at the highest level and do math research, but don’t want to participate in the...
Secrets of Circles at Minnesota Children's Museum
Happy Pi Day folks!
Yesterday I went to the Minnesota Children’s Museum with two of my housemates. They have an exhibit, called Secrets of Circles, that’s visiting from the Children’s Discovery Museum of San Jose.
My favorite part of the exhibit was the Exploratorium-style turntable, but that thing is my favorite part of any exhibit it’s in. It has all the play value of...
Logic puzzle with Geddes
You have 3000 apples that you want to transport over a distance of 1000 miles, but your truck only holds 1000 miles AND whenever it has any apples on it, it loses 1 apple per mile. How many apples can you get to your destination?
We solved this problem over the phone and it was fun! We talked more about how much to interrogate the boundaries of the universe described by the problem (e.g. the...
Set →
My super-cool big brother is starting a website about games, and the first step is a newsletter. This issue talks about Set, which is a great and mathy game. See if you can spot me in the text!
Analysis and algebra, nature and nurture
There are two broad regions of the universe of math that are called analysis and algebra. I don’t know what they are or how to explain the difference between them, but they’re different. Part of the difference is that anaysis deals with things that are continuous, like ramps, and algebra deals with things that are discrete, like stairs.
The discipline seems to think that each...
Following my nose
I’m trying to find a problem to research. Well at this point, I’m still trying to find an area to learn about in enough depth that I can find a problem in that area to research. It’s a moment of specialization, and I’ve always been afraid of those. So I’ve been thinking a lot about what I like in math, how I’ve realized I liked it, and how I came to like it. And...
Doing things even when I don't feel like it, or...
My brain feels like sludge today, probably because I haven’t been dancing or moving much lately and my brain is a part of my body.
Historically when I’ve felt this way I haven’t even tried to do work, but today I am. It’s mostly unpleasant, but also feels like an experiment or a novelty, still.
It’s good to know that I CAN do math even when I’m not feeling...
February 2013
3 posts
Can we talk about the Hopf fibration?
Yes, later. Til then, look at this pretty picture from Wikipedia.
I hate school.
This isn’t news, I know. But I’m having a rough week with the whole deschooling advocate/grad student/math teacher contradiction I’ve involved myself in.
In particular, I’ve been feeling like a shitty TA this week. It’s small things—I graded an assignment too harshly, I’m having a hard time adjusting to the way my lecturer teaches, I’ve been trying...
Math professors talk about their jobs
My analysis professor was in a great mood today. He followed a probability example with “I don’t mean to oversell probability…even though it can make you happy for decades.” At the end of class, he said “isn’t it great to have a job where every day there are at least a few moments of fun?”
A professor I worked for once distinguished his real motivation...
January 2013
1 post
Products
I want a list of all the things that are commonly called “products” in math and whether they are category theoretic products, coproducts, or neither.
I don’t know if the internet is going to come through for me on this one, though. I guess the point of becoming a mathematician is that I should be able to answer my own questions.
December 2012
3 posts
What do math grad students do? →
“The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don’t really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you’re only allowed to use words that are four letters long or shorter.”
November 2012
4 posts
Follow-up
When I take this mathematical self-acceptance thing to heart and slow down and let my braaaaaaiiiins to their thing, it’s kind of amazing what they can come up with. When I wrote the previous post, I was freaking out about not knowing the definition of a Tor functor, or of several of the words in the first definition I read of it. But then I chilled out and within a couple of wikipedia...
An epiphany I have to keep having every few...
I have to do math at my own speed because that’s tautologically the only speed I can ever go. I have this brain and it does what it does, and there’s no point in believing that it ought to do something different.
September 2012
5 posts
A tidbit for my bosom friends. Maybe my super cool...
Tensors and other things I don't understand
I just talked to a classmate about the way we learn complicated ideas in math—it’s cheerful to remember that other people have similar experiences. We talked about tensors and tensor products and how even though we’ve been working with them for a couple of years and have been taught about them a couple of times in different ways, we still at the base of it have no real idea of...
And now my brain is exploding
The exterior algebra is…a space formed by sums of products of vectors? Or maybe vector fields. It’s a graded algebra, which is kind of like having subspaces of different dimensions. Kind of. And differential forms form an exterior algebra? Or is it the same “the” exterior algebra? And it’s dual to the space of alternating multilinear forms, which are the same as (or...
School's Started
I didn’t pass the complex prelim, but I learned a bunch of complex and I bet I’ll get it done in the spring.
This year, I’m taking commutative/homological algebra, real analysis, and algebraic topology. but the algebraic topology class is being taught by a geometric topologist: oh no it is a disaster!
Just kidding. At the department picnic last weekend, I had a good talk with...
August 2012
2 posts
Pretty →
Math life
I was in Ohio for G’s family reunion last week. People kept demanding logic puzzles, and I was happy to oblige. We did the 12 coin problem, the 10 hat problem, and maybe one other. It was funny to me the way people kept interrogating the problem for a trick answer, like in the coin problem asking if we could just bite the coins instead of using the balance scale mentioned in the problem. We...
July 2012
7 posts
Why Sally Ride's sexuality really matters →
My friend Lisa is the coolest science writer in town.
Complex function applet →
Fun!
Math in "real life" 2
Making 2/3 of a recipe for tofu scramble, because we wanted 4 servings and not 6.
Math in "real life"
I want to start recording times when I use middle or high school math to accomplish something that doesn’t itself have to do with math. Here are two high school algebra moments from the weekend:
A friend had designed a logo for a preschool and was now being hired to paint it on a sign. I helped her cross-multiply some fractions and solve for the factor by which the sign was scaled up, so...
(t.w. disordered eating) to brown gurls, whose...
subtlecluster:
blackgirldangerous:
by Janani Balasubramanian
There are some accepted ways for white girls to deliver poems on eating disorders. They might analyze their mirror and remark on the ugliness of the light refracted back, so thin and so cracked. They might struggle under the weight of a thousand magazines, feel the pressurized dig of Vogue Models’ heels into their backs. They might...
June 2012
3 posts
One-Woman Math Squad Makes a Dress
untidyfurrows:
mathsquad:
I’m making an extremely dorky wrap dress. I took apart a worn out wrap dress to use as a pattern, but the old dress was never quite perfect, and I’m making the new dress in a different fabric, so I’m making a lot of modifications. Mostly I modify things in the direction of increased dorkiness.
So I’d like to take this opportunity to tell you about some traditionally...
One-Woman Math Squad Makes a Dress
I’m making an extremely dorky wrap dress. I took apart a worn out wrap dress to use as a pattern, but the old dress was never quite perfect, and I’m making the new dress in a different fabric, so I’m making a lot of modifications. Mostly I modify things in the direction of increased dorkiness.
So I’d like to take this opportunity to tell you about some traditionally...
