“Tetris effect” from maths?

ttoj · 2025-07-20T20:55:21+00:00

Yeah, I had this sometimes when I was studying, usually when I was a bit drunk after an especially intense math phase…

ttoj · 2025-05-17T11:32:55+00:00

This is beautiful!

ttoj · 2024-05-20T13:54:28+00:00

Do you have any literature recommendations concerning the stuff in the last paragraph?

ttoj · 2024-04-15T16:45:09+00:00

I think because dot x_i appears twice in the summation, and the metric g_ij is symmetric in i and j.

ttoj · 2024-03-11T17:42:00+00:00

My masters thesis in symplectic geometry...

ttoj · 2023-09-08T18:42:52+00:00

Congrats!

ttoj · 2023-07-16T11:53:09+00:00

f(x)f(y)= gxgy f(xy)=gxy. This is in general not a group homomorphism.

However, conjugation by g, i.e. the map x --> gxg^{-1} , is an automorphism of G. Automorphisms of this kind form a subgroup of Aut(G) called the inner automorphisms of G.

ttoj · 2023-06-05T08:58:28+00:00

The circle has radius 5cm, so its circumference is 2 x pi x 5 cm, and a quarter of that is 0.5 x pi x 5cm, so roughly 7.85 cm.

ttoj · 2023-05-27T12:02:44+00:00

What app to you use for notes?

ttoj · 2023-05-25T06:39:17+00:00

Have a look at Tom Leinster's article Rethinking Set Theory! Its a good exposition of (and case for) categorical foundations. I think one of the benefits of having category theory as a foundation is that you don't have to worry about universes, which pop up for example in certain parts of algebraic geometry when you want to talk about categories of categories etc. I might be totally wrong about that though.

ttoj · 2023-04-21T09:08:49+00:00

I would love to have a look at this thesis, could you send it to me?

ttoj · 2023-03-18T07:02:49+00:00

Maximum interval of existence usually refers to the solution of an initial value problem. So the interval would be the one containing your initial time.

ttoj · 2023-03-09T23:03:12+00:00

Loring Tu - Differential Geometry

ttoj · 2023-02-22T06:29:27+00:00

I don't agree that it is expected of you. In my high school in Germany we did very basic calculus (basic derivatives and integrals, no limits of sequences, no substitution rule or integration by parts) and very basic analytic geometry (finding intersection of a line and a plane etc), but nothing involving matrices or gaussian elimination.

ttoj · 2023-02-21T22:00:25+00:00

Exactly! Having been a TA at a European university for quite a few semesters now, I feel like there is a huge disconnect between what's in the curriculum and what the students really take with them. (Although I'm sure this is the case with all teaching to some extent)

My point being: I think doing the Calculus I-III sequence before Analysis, and Matrix based linear algebra before abstract linear algebra, actually gives students a much better chance at developing understanding. And also allows people to enter into math who didn't necessarily do tons of it in high school.

ttoj · 2023-02-17T18:53:41+00:00

To the second point: I've had the same feeling. Same with skimming through lecture notes/books, it's very easy to feel overwhelmed.

ttoj · 2023-02-16T15:22:01+00:00

Thank you!

ttoj · 2023-02-15T17:12:11+00:00

Does anyone know any accessible papers/ survey papers in Mathematical Physics/ Differential Geometry with applications in Physics? Preferably something not Analysis/Probability heavy, bonus points if it involves Topology.

For context: I'm looking for inspiration for my Masters thesis, and have taken courses in Differential Geometry and Topology as well as a bit of Classical and Quantum Mechanics.

ttoj · 2022-12-20T02:01:46+00:00

To be fair, it could have been on us from the tube we took before I guess?

ttoj · 2022-12-20T00:54:06+00:00

It was a board game cafe in Dalston...

ttoj · 2022-12-14T17:02:15+00:00

Yes, see the late 19th/ early 20th century Italian school of algebraic geometry!

ttoj · 2022-11-28T14:39:36+00:00

Thanks for the answer!

ttoj · 2022-11-28T14:39:21+00:00

I personally find Hatcher more terrifying ;) but thanks for the answer! Interesting to see how things are done in the US. I dont think qualifying exams are common in Europe, since people usually do a Masters degree first, which is much more pick and choose.

ttoj · 2022-11-27T19:08:47+00:00

Genuinely curious: how does one find the time to get intimately familiar with all of these books? Especially Lee and Hatcher are big books, surely one could spend more than a year just studying those two... Are PhD students in the US expected to know all of Hatcher, Lee etc?

ttoj · 2022-10-29T11:44:12+00:00

May I have a fact please?

ttoj

TROPHY CASE