Mathematics - 2020-10-02

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geocalc33

00:07

can you have a hyperboloid of revolution with finite surface area?

Edward Evans

00:19

-2

Q: Algerba 1: Abelian Group

(a,b)(c,d)=(ad+bc,bd),on the set {(x,y)∈ RR:y≠0}. (a,b)(c,d)=(ac,bc+d), on the set {(x,y)∈ RR:x≠0}. Same operation as in part 2, but on the set R*R. (a,b)(c,d)=(ac-bd,ad+bc),on the set RR with the origin deleted. Consider the operation of the preceding problem on the set R*R. Is this a group?Exp...

abstract-algebra group-theory abelian-groups

algerba

Thorgott

algerbic numba theoyr

Edward Evans

If you can raed tihs you are samtrer tahn 95% of poeepl

if I have a decreasing sequence of open subgroups of a compact group, does it necessarily terminate at $1$?

actually scrap that

dumb question

i mean not a dumb question, but not relevant

Thorgott

what if the sequence is constant

Edward Evans

ah ye

If I take an intersection of all open normal subgroups of a compact group, why is that trivial?

Or rather, if you can gimme a hint for why that's true

Ted Shifrin

00:45

That seems false.

Thorgott

I don't know this stuff lol

Ted Shifrin

Hard to have nontrivial open subgroups, in general.

Edward Evans

I guess I'll just struggle on my own instead of spamming here hahaha, I'm missing hypotheses

Thorgott

every open subgroup in a compact group has finite index

Ted Shifrin

Make the group connected. ;)

Edward Evans

00:56

If I can assume my group is Hausdorff, I think it's possible to show that the group has a fundamental system of open neighbourhoods of $1$ consisting only of open normal subgroups

and then that would work

those hypotheses are written the wrong way round, I mean if it's possible to show that the group has a system of open nbhds of 1 consisting only of open normal subgroups, and if the group is Hausdorff, then that would work

rofl

1 hour later…

anakhro

02:00

@TedShifrin what was your simplification of the proof?

Ted Shifrin

02:24

Consider using circles intersecting tangentially rather than in two points. However, this may require knowing angles are preserved, which needs linear algebra, most likely .

skullpatrol

02:38

Professor @TedShifrin have you seen the latest collection of "Classics" on MathEd.SE?

skullpatrol

02:49

nvm

geocalc33

hi?

Jack Rod

@skullpatrol hi pal!

skullpatrol

hi pal

How are you? @JackRod

7 hours later…

Adam L

09:40

Did anyone know that the unabomber was a math prodigy? another victim of the CIA's LSD pranks.

They didn't even need to offer him free top shelf prostitutes either, taking part in a psychology study was his carrot on a stick, so I guess he deserved it

user91500

10:09

@Stupidquestioninc page 10 in third edition and page 27 in fourth edition

@Stupidquestioninc In third edition the author says he discovered but in fourth edition says he observed!

Adam L

10:45

It's the same thing really most things that we discover are observations of things previously observed, I would go as far as to say everything we just observe it's not as if things get named by the original observer anyway, most of the time that is not what happens

Stupid question inc

11:10

@user91500 ah ok I see i will read it in break time

Edward Evans

11:22

@Thorgott wie viele ECTS nimmst du normal pro Semester?

Alessandro Codenotti

11:33

@EdwardEvans you should get around 30 if you want to have a full semester for your thesis

Edward Evans

Yeahhhh, I'm doing 36 this semester and that would mean I only need to do like 13 each semester for the next 2 semesters

It'd be cool to split it up some more, but the courses this semester probably won't be offered again for a while lol

Alessandro Codenotti

36 is heavy but doable depending on how they're divided

Like 36 credits of courses are madness, but with a couple of seminars should be doable

Edward Evans

Yeah right, I have 3 lectures and 2 seminars, but one of the lectures is Modular Forms which i've done before and for which I have the Zulassung for the Prüfung, so I don't have to worry about giving in psets on time

Alessandro Codenotti

Nice

How many credits are seminars/courses worth in Heidelberg?

Edward Evans

A seminar is 6 credits and a lecture course is 8

Master thesis + Master seminar is 38 credits

Alessandro Codenotti

11:47

I see. In Bonn it was 6 for seminars, 5,7 or 9 for courses depending on the type of course (selected topic, advanced topic, standard course) and 36 for the thesis+thesis seminar

Edward Evans

Nice

I'm supposed to take 16 credits in applied courses but I think you can just ask not to do that

because fuck that

Alessandro Codenotti

I actually ended up with more credits than I needed because I cannot do basic addition

So I had one extra course in algebra and was missing one in analysis

(there were some requirements to take courses from at least three different areas and blablabla)

Edward Evans

hahaha stronk

I'm gonna ring the Prüfungsamt actually, because it says "The courses from the applied area can be replaced with pure mathematics courses", but it also says that I need to take at least one applied course

idk

Alessandro Codenotti

But it was fine, I took a PDEs course (which I barely survived) and AG didn't count for my final grade

Edward Evans

ah AG is gonna kick my ass

Alessandro Codenotti

11:53

Nah I think you'll like it

Edward Evans

Maybe, but it’s still gonna kick my ass

Alessandro Codenotti

Fair

When do lectures begin for the WiSe?

Edward Evans

2nd of November

When do you start in Münster?

Alessandro Codenotti

(do they use WiSe instead of WS to avoid having to call the summer one SS?)

Edward Evans

Loool I think they actually do but I never thought of that

Alessandro Codenotti

11:55

@EdwardEvans classes begin in November, I started yesterday officially, but I've been here a week already

Edward Evans

Ah nice, congrats

What courses are you taking?

Alessandro Codenotti

Dunno, I don't have to take any, but there are a couple that seem interesting, I'll most likely do the Descriptive Set Theory one even though I should already know half of the material being covered

Edward Evans

Nise, idek what that is but nice

Alessandro Codenotti

Very broadly the study of Polish spaces and their "definable" subsets

Edward Evans

What’s a Polish space hahaha

Alessandro Codenotti

12:00

Completely metrizable separable

Edward Evans

What do you mean by completely metrizable ? Like metrizable in such a way that the space is complete?

Alessandro Codenotti

Yes, there exist some metric inducing the topology of the space and wrt which the space is complete (but we don't actually fix one usually)

Edward Evans

Okay cool

Alessandro Codenotti

Like (0,1) is not complete in the metric inherited from R, but it is completely metrizable

Edward Evans

I see, sounds like an area of study that would kill me

Alessandro Codenotti

12:05

I will probably think about Polish groups and their actions during my PhD but that's still far from decided

Edward Evans

Nah man you’re in the first week, you should already have a title and 3 published papers

Alessandro Codenotti

I know, I know, I've been slacking off

Edward Evans

Poor attitude

Qi Zhu

12:26

@AlessandroCodenotti haha In Munich we do often call them WS/SS, though

Alessandro Codenotti

I'm not sure but I think it was always called SoSe in Bonn

Edward Evans

yeah it's called WiSe and SoSe here

Alessandro Codenotti

I see you'll be starting a Masters in Bonn too soon, nice! When will the lectures begin this semester?

Qi Zhu

Hm interesting, we use both

Yeah, thanks! They start on October 26

Alessandro Codenotti

I see, have you already thought about the courses you want to take?

Qi Zhu

12:31

Yes, I will probably be taking AlgGeo 1, Rep Theory 1, Algebra 2, Topology 1, Advanced Algebra 1 and a seminar in number theory

But my main focus will be on algebraic geometry

Edward Evans

tf

Alessandro Codenotti

Who's doing AG1 and topology 1 this time?

Edward Evans

in your first semester?

Qi Zhu

Huybrechts and Schwede I think

Alessandro Codenotti

I see

Qi Zhu

12:33

Yeah, first semester in masters, Edward

Edward Evans

that's a lot of courses

Alessandro Codenotti

I have no first hand experience, but Huybrechts's courses are said to be very though

Qi Zhu

I hope it won't be too much but in my undergrad I often did 50 ECTS semesters and I've sort of already taken algebraic topology and algebraic NT, so I'm thinking that will help

Yup, but I'm really looking forward to Huybrecht's class

Are you studying set theory in Bonn? (Judging from your MSE activity)

Alessandro Codenotti

Ah I should update my MSE description, I just finished my masters and I'm now doing a PhD in Münster

Edward Evans

Okay fair enough, still, it sounds like a crazy workload

Alessandro Codenotti

12:36

But yeah I'm interested mostly in set theory of various flavours

Qi Zhu

Ah I see, so you picked up set theory in Bonn?

Alessandro Codenotti

Yep

Qi Zhu

True but I can still just drop courses if it becomes too much, Edward :p

Nice! Does Bonn have a good group on set theory? I assume Münster does if you're going there for a PhD?

Alessandro Codenotti

But Koepke (the only set theory professor) retired at the end of the WiSe 2019/20 so there's no more logic group in Bonn (there were a couple of postdocs but they had to leave too)

Qi Zhu

Oh I see, that's a pity

Alessandro Codenotti

12:38

In Münster there's a lot of model theorists and some set theorists, the logic and set theory groups has almost 20 people now (counting professors, postdocs and PhDs)

Qi Zhu

Darn, that sounds like an amazing place to study set theory and logic

Alessandro Codenotti

I don't know who they hired to replace Koepke, they were looking for a new professor but not necessarily a set theory one

Qi Zhu

Maybe that's why they don't have a set theory lecture this semester? (Or was it even held every winter?)

Alessandro Codenotti

@QiZhu They are also said to be good, the two things are not incompatible haha

the masters set theory courses were held every other year so there shouldn't be any this semester, but I suppose there won't be any in the next WiSe either

Qi Zhu

I can imagine haha I don't mind the class being hard (I hope I won't regret saying this), I simply want to learn as much as possible

Oh I see I see, that is also a pity, I did want to take it

Alessandro Codenotti

12:44

I know a guy who is starting his PhD with Huybrechts this semester, we used to be classmates for the bachelor

Qi Zhu

I'm guessing a PhD with Huybrechts is a lot of work but also very rewarding?

Alessandro Codenotti

I don't know, I'll ask him in a while I guess haha

Ice Wizard

13:04

Number of solutions of $$e^x=x^{2020}$$ in the real domain is?

Astyx

It's 3

Ice Wizard

@Astyx then find the largest :)

Astyx

Huh it's probably some ugly special function

And very large

Ice Wizard

Does there really exist some special function...I couldnt find one yet

110179 is a number having only 2 prime factors $\neq$ 1 , the number of coprime numbers to it are 109480 , find the sum of the prime factors

Astyx

According to Mathematica it's $-2020 W_{-1}(-1/2020)$

Ice Wizard

13:13

W is lambert?

Astyx

Probably

But $W_{-1}$ is the other branch

I mean Lambert is the solution to the simplified equation

Ice Wizard

Ohh so there exist a method to find such things, impressive

The prime factors question is just for fun...(answer is 700)

But it is not found by factorising 110179

Apply wilson's theorem and see how it unfolds

Astyx

If $pq = n = 110179$, then the coprime numbers $\le n$ are of the form $pk$ or $qk$, and there are 110179-109480 = 699 of them. There are q factors of the form pk and p of the form qk, and only one is in both sets (pq). Therefore 699 = p+q-1 ie p+q=700

What does Wilson's theorem state ?

Ice Wizard

13:30

@Astyx Not Wilson...The theorem which says 109480=110179(1-1/p)(1-1/q)

Euler Totient oops...

4 hours later…

geocalc33

17:34

if you take a hyperboloid of one sheet of finite height and identify the ends, is there a name for it?

Ice Wizard

Does anybody see any symmetry here

skullpatrol

Perhaps, y = x

Try counting the number of points on either side of y=x.

Ice Wizard

17:57

@skullpatrol Go ahead and use linear regression y~mx+b, if you get the line y=mx, it's symmetry, but in this case it's not

I am not talking about trivial/visual symmetries

2 hours later…

AMDG

20:23

Good evening!

So, I realized that if I want to get what I want, I actually needed to find a system that is not the complex numbers, not vectors, and is simpler than the concept of axes relating direction.

Well, turns out the solution is very simple: just make the axes be defined as diagonals such that along the diagonals, the value is zero.

As a plane, it may be defined as infinitely many views of the set of real numbers where, given some $\epsilon$ that is infinitesimally small which satisfies $0 < \epsilon < \frac{1}{x}$, then a point along the diagonal is $\mathbb{R}[N - \alpha\epsilon]$ for some real value of $\alpha$.

With this definition of a plane, I only need one value to represent both magnitude and direction without using a complex number, polar coordinates, or vectors as there aren't truly any defined axes. Perfect!

Oh, right, and N is some constant in $\mathbb{R}$.

AMDG

21:08

Is this a good and clear way of putting it? $$\{\text{constant }N\in\mathbb{R};\alpha\in\mathbb{R};0<\epsilon<\frac{1}{x}\}\mathbb{R}[N-\alpha\epsilon]:=\mathbb{A}_{N} : \{\mathbb{A}_{N} \mapsto \mathbb{R}^{n}; \mathbb{A}_{N} \cong \mathbb{R}^{n}\}$$

Then a Euclidean plane's axes may be defined with $\mathbb{A}_{x}$ and $\mathbb{A}_{y}$ for $x$ and $y$ respectively.

2 hours later…

Thorgott

23:04

@Edward ECTS?

Astyx

23:41

European Credit Transfer and Accumulation System, a European system for equivalence of formation between universities

You need to fulfill a certain amount of ECTS to get into some formations, etc

@Thorgott

Thorgott

ah, he means the credit points

uhh, I haven't kept track

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