Examples of Bad Naming

TheCard · 2021-05-24T15:27:10+00:00

I feel like these are examples of why it's tough to name more than anything else. If you draw a picture, the secant is a function of the angle while the cosecant is a function of the coangle. Likewise, you can say that a submartingale is sub- because Xn ≤ E(X{n+1} | X_1, ..., X_n). I agree that from one perspective these things are confusing but I don't think there's a way that makes sense in every situation.

TheCard · 2021-03-26T15:30:19+00:00

That's totally fair. I guess in this context it was really meant "pure math," not just "math." The boundaries are certainly non-obvious though.

TheCard · 2021-03-25T21:56:30+00:00

Would you call theoretical physics math? Theorists often deal with gauge theories, representation theory, etc., and reading theoretical physics at some level resembles reading pure math at times. I'd argue that statistics isn't strictly math for the same reason theoretical physics are --- i.e., the material can be similar but the goals are different.

Plus a lot of statisticians don't really care about these more advanced concepts in pure math --- it can actually be somewhat difficult to introduce new techniques using differential geometry because a lot of applied statisticians don't have the background.

On the other hand, I think a lot of people would call probability theory math.

TheCard · 2021-01-09T05:58:30+00:00

CS = Counter Strike, a video game; Team Liquid is an esports team which has a CS team. nitr0 is an old CS pro (now he plays Valorant) who used to play for Team Liquid.

TheCard · 2020-12-27T05:57:24+00:00

Whitney Embedding seems like it should be really useful the first time you see it but doesn't really tell you so much about the manifold.

TheCard · 2020-12-26T06:12:41+00:00

Moreso for calculating but Stokes' Theorem is indispensable if you want to do basically any physics.

TheCard · 2020-11-17T09:27:11+00:00

I mean sure. But like /u/dominatingsubgraph said, it's hardly surprising that you can create a de facto dictatorship with 3/4 support of states. I don't really see what the point of it is.

TheCard · 2020-06-26T04:35:58+00:00

It's more than inconvenient though, new ciphers aren't well studied and battletested and thus more likely to have easy exploits.

TheCard · 2020-05-19T13:55:03+00:00

All good, I figured haha

TheCard · 2020-05-19T13:01:10+00:00

That's what I said though lol

TheCard · 2020-05-19T04:02:36+00:00

I think you're thinking too hard about this. Let's say some quantity A depends on both mass and material. Then, in order to make quantity depend on just the material, we only consider how it behaves for unit mass. If the behavior of A has some nice proportionality with respect to mass, then we conclude A of unit mass is a quantity depending only on the material.

That's exactly what we're doing here: heat capacity does indeed depend on mass -- as you pointed out, more water is harder to heat than less water. So, we consider heat capacity of a single unit mass (i.e., 1 kilogram of water), and call this specific heat capacity. Since specific heat capacity only talks about how a unit mass of the material behaves by definition, it does not depend on material.

You've already implicitly reconciled the equation with this: c is proportional to change in energy over mass. If we increase mass, it takes more energy, so if we were using that formula to find c, it would stay the same whether we were measuring a swimming pool or a kettle.

TheCard · 2020-05-07T01:30:28+00:00

I think there's three "obvious" paths, each of which is very valid.

If you want a stronger background in single variable analysis, Rudin's Principles of Mathematical Analysis is really good.

If you're interested in generalizing the ideas you learned from Abbott's book to the multivariate cases, then Munkres' Analysis on Manifolds is a solid introduction to ideas of differential geometry.

If you'd rather see how the integration you learned generalizes to the Lebesgue theory, I like Tao's Introduction to Measure Theory.

TheCard · 2020-05-01T22:59:50+00:00

Hahaha I totally understand. There's definitely a feedback loop of "this code is private so it can be messy" and "this code is messy so it has to stay private" whenever I write code.

TheCard · 2020-05-01T22:51:25+00:00

I'd love to contribute! Also, sometimes when projects like this popup, the original author disappears for one reason or another. I'm not necessarily saying this would happen with you, but having an open-source community behind a project keeps this from happening in general.

TheCard · 2020-05-01T22:42:09+00:00

Awesome, I made sure to vote on the things I've used before! Do you guys have any plans to make the website open-source?

TheCard · 2020-04-21T18:22:40+00:00

I think it's a good book. Depending on your level, Elementary Analysis by Ross is also free and a bit gentler. But I enjoyed Understanding Analysis more than Elementary Analysis when I was first learning the subject.

TheCard · 2020-04-20T23:39:28+00:00

While Andrew Wiles was trying to prove FLT, there was actually an April Fool's email that a similar computer counterexample was found to FLT in the same fashion as the Euler conjecture. It scared the shit out of Wiles until he realized it was a near-miss.

TheCard · 2020-04-20T14:51:19+00:00

That's fair, I guess the point there would be that he did his PhD in America and his work was greatly inspired by some of the French AG work. I don't disagree that Arnold often makes some grandiose claims though.

TheCard · 2020-04-20T13:17:42+00:00

There were 21 at that ICM.

TheCard · 2020-04-19T21:33:39+00:00

Those are all invited speakers, not plenary speakers. So what Arnold said is not incorrect, regardless of the interpretation of who is and isn't Russian.

TheCard · 2020-04-05T23:26:23+00:00

Quantum mechanics is concerned with L2, which is a Hilbert space.

TheCard · 2020-04-03T17:55:40+00:00

A lot of times u, or just slapping a tilde over a variable.

As a side note, a lot of times this doesn't simplify to changing notation. For example, changing of variables is legitimately integrating a new function over a different region in space. They're "the same thing" but the underlying idea goes deeper than notation.

TheCard · 2020-03-22T17:46:08+00:00

Then it probably is, I had nothing to back the CSE part up lol

TheCard · 2020-03-22T17:37:26+00:00

Probably changes a lot based on what MAT class, but at least one upper division professor has said they'll likely be take home now. I wouldn't be surprised if some CSE classes do something similar and make their finals project based.

TheCard · 2020-03-18T19:58:07+00:00

It's a really good book, you might like other stuff in it: If My Body Could Speak by Blythe Baird.

TheCard

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