@KasmirKhaan hmm, the really introductory algebra books I've used were all German

... and none of hte conditions care about anything that depends on something finer than the isomorphism class of the sheaf in D^b(X)

@MatheinBoulomenos we never really had something as intro >< each class, we needed to work alot to be able to understand the book, our first encouter to algebra was linear algera then directly abstract algebra, there are no other intro courses

in the paper by Goresky and Mac-Pherson (math.mit.edu/conferences/geometryworkshop/references/GM83.pdf ) there is the following statement (page 107): (here AX2 is AX_p and the modification to AX2' should be the one to AX_p[S])

I Heard that in germany you had algebra 1 and 2

Well yeah, that was how it was for me, too. First linear algebra, then abstract algebra

yes, but algebra 2 is advanced stuff

like category theory, commutative algebra, noncommutative algebra, homological algebra

aha

so the same system =p

algebra 1 was groups, rings, fields, galois theory

but we did nto cover alot of topics, in both courses

algebra 1 we did only Groups and Little bit of rings

linear algebra was a joke >< compared to what needed

I read this and I know what every word means, but the dont make any sense at all to me, I dont see how that adresses the problems I had with the book

but the Courses were both 1.5 months

the theorems cited in my interpretation of your statement above all rely on this paper, so im confused

Our courses are longer than 1.5 months

like 2 lectures a week of 90 mins or lesss ><

that is better for understanding

well i took now 2 Courses that are 5 months long

this way at least i have time to think about stuff :D

Our courses typically go 14 weeks, so something over 3 months. 2 lectures a week of 90 minutes and one exercise session a week of 90 minutes

Hi @Mathei

Hi @AlessandroCodenotti

@MatheinBoulomenos I think kasmir will consider taking a semester in germany to study some algebra there :D

You can apply for Erasmus

ill google that

i was thinking to go france at first

since i know that language

That's very similar to Italy, we have two semesters of 14 weeks each

but hmm i think germany is far better :D

thanks Mathein :D

@KasmirKhaan if you're interested in going to Heidelberg: uni-heidelberg.de/international/erasmus/incoming/index_en.html

But you're going to need some German skills

they don't test you formally, though

oh :o

why would I need to speak german?

I took german in highschool but dont think i remember much :D

Well, almost all the courses here are in German

grrrr mathein -.-

"Ich hätte gerne Bier und Bratwürste, danke" that's some real important German to remember

hmm, well wont hurt to learn some german

@MonaJalal Yes, you will have to break it into $[-\infty, 0]$ and $[0, \infty]$. Complete the square with respect to $t$, and a lot of stuff will reduce to a constant power of e that goes outside the integral. Then it will reduce to a known Gaussian integral.

@AlessandroCodenotti that's all you need

i wont be doing this , this year anyway, so maybe next year :D

haha @AlessandroCodenotti

@KasmirKhaan look at this, though: uni-heidelberg.de/international/erasmus/incoming/… there's a 4 week intensive German language course before the semester starts, up to 8 hours a day

I should review some German, I'm forgetting all I knew

and weekly German courses during the semester, too

@MatheinBoulomenos okay thanks :D , I mean i do understand lots of it, since i studies some in highschool and also its somewhat similiar to swedish

@AlessandroCodenotti I should review my Italian, I never knew much, but I'm forgetting the little I know

8 hours a day neat :D

Some universtities in germany have english language courses if you are insistent about going to germany

But it's really rare at the bachelor level

Well I like to try something different , does nto have to be germany , but iv seen how smart mathein is , so that was my motive ><

German is hard too!

nope !

you know what is hard? chinease!

also french, ( grammatics )

@KasmirKhaan ah I think I misunderstood, it's not 8 hours a day

I thought so =p

maybe they have night / morning courses

@KasmirKhaan I think it would fine if you write your solutions in English, but the lectures and the problems will be in German

'Chinease' can be learnt with ease! :]

Okay i think the best plan is to learn some german Before going to germany =p

anyway :D i have to keep working on the HW that i need to be done with

you don't need to go to German, it's just an option

for tomorrow =p

I know ><

but we had many students here from germany, they are cool ppl

Maybe switzerland or belgium have english language bachelors, since these are countries with more than one official language

and i want to try something new =p so ill figure it out later :D

Any language is hard to be honest. Things can help of course, like if your mother tongue is from the family of the language you're learning (shared sounds etc).

@MatheinBoulomenos where did you learn it?

@KasmirKhaan Are you from the UK?

@AlessandroCodenotti I took a course at university due to a formal requirement for my former major. I liked it, so I went to Rome for 3 weeks to a language school

@Bennett nope! sweden

@KasmirKhaan Oh, in that case you got this under the belt. I don't know if I've fallen for a stereotype, but I'm convinced people from Sweden are linguistic wizes!

@Bennett haha that is very common idea but it is not quite true =p, most of swedes do know English well but nothing more than that =p

I once met a Brit who was convinced that people from the UK can't learn foreign languages due to genetics

haha ><

@MatheinBoulomenos your former major? You didn't begin with maths?

Haha!

@AlessandroCodenotti no, I started with philosophy and ancient Greek

Oh, that's a surprise!

@KasmirKhaan Yeah, I think that's what it was. Everyone in Sweden spoke English so well it was amazing!

I remember having a great time pondering about the delicacies of the Ancient greek grammar or translating from German to ancient Greek

Makes sense though, the philosophy uni in Heidelberg is very well known

yes because we learn it at very Young age, also we dont Watch anything but English Movies,series ect

@MatheinBoulomenos I believe that condition is called Brexitexia.

Germans are not really well known for being good at English

we're better at it than the French, I guess

Really? My dad told me that Germans are among the best ones in Europe at English. Though he also said that Germans tend to not have accents which I'm not sure is the case

We have no trouble communicating (unless you go to rural areas), but a lot of people have accents and make some small mistakes

Demonark: That would be erroneous.

Hi @Daminark @Ted

Hi Mathein

In the netherlands people speak really good english, sort of surprising since their own language is such an absolute mess to listen to

Hey Ted, Mathein, and sharp!

@TedShifrin Ted :D

To me, Dutch sounds like a parody of German

hi Kasmir

But yeah the situation in the latter case was funny, someone in my group chat last year found a video of our analysis prof last year (we thought at the time he was German, turns out he's Austrian) where he made some joke. Now ny dad was with me when I pulled it up and he was in pure shock that the guy had an accent

The Netherlands, Sweden, Denmark, and the English speaking parts of the UK (exceptions being Liverpool and Manchester where they speak Scouse).

"English speaking parts of the UK" LOL

@Daminark I don't get why your dad thinks that we don't have accents. Don't you even have people with German accents in some American movies?

what about wales?

@Daminark yh, you can't call what they speak in Liverpool/Manchester English. I know English but that ain't no English I ever heard before. xD

@BalarkaSen there’s a very slick GMT proof

Yeah I'm not sure, maybe he met a few people without accents and was just like wow

And I've never heard people from those areas talk but I will say there was a teacher at my high school from Wales and I couldn't understand a word

Most Germans can't speak English without an accent (myself included)

Hi @Ted

Hi demonic @Alessandro

Hey Alessandro!

And lol I see

I once met a guy who I was certain was American (midwest sounding accent). Later on I found out that he was German. My mind was blown. He explained he went there on holiday.

@BalarkaSen Modulo details, the coarea formula gives $$\mu(t)=\int_t^\infty \int_{\Sigma_s} \frac{d\mathcal H^{n-1}}{|Du|} \,ds$$

THERE IS A CAR IN ORBIT AROUND THE EARTH AND THERE IS A CAMERA ON IT

checking that one can apply the coarea formula is a pain in the ass though because $Du$ could be zero

Stop yelling, DogAteMy!

it then follows that $\mu(t)$ is differentiable a.e.

DogAteMy, if the car lands on the street in front of my apartment, is it mine?

@0celo7 one of my friends who is a physics major is thinking about taking the second part of a one year differential topology sequence next semester, but he is unsure about the relevance for physics. The topics that will be covered are Morse theory, a short intro to Riemannian geometry, characteristic classes, bordisms and h-bordisms. The other option would be taking intro diffrential geometry, which would have more on Riemannian geometry, but also some overlap with the diff top he already took

@AkivaWeinberger Aka Satellites? I suppose the International Space Station is like a glorified truck/lorry with a camera.

No, I think there's actually a Tesla up there ... or so I've heard.

@0celo7 do you have an advice?

looool that's insane!

@MatheinBoulomenos I'm not a physicist

but if I were, I'd say both

@Mathein: If he's interested in learning advanced math physics (like mechanics or relativity), I'd opt for a Riemannian geometry course. Characteristic classes show up in physics, for sure, but I doubt bordism does.

@TedShifrin cobordism does

But characteristic classes show up via curvature matrices of 2-forms, not in terms of topologists' ways of doing them.

@MatheinBoulomenos characteristic classes are used in string theory/supergravity anomalies, but as Ted says, it's the geometric version