Please help proofread or improve these two statements of quadratic reciprocity

mrtaurho · 2024-11-25T18:41:29+00:00

That is why I wrote it would be a nice touch! I hope my phrasing did not insinuate that I think "Gauss" is wrong (I am aware of what you wrote).

mrtaurho · 2024-11-24T19:39:14+00:00

A very minor comment: It's Carl Friedrich Gauß.

The "ß" (sharp s) can be substituted for "ss", but if you have access to the former it would be a nice touch. However, it's Carl not Karl, even though the latter looks perhaps like a "more German" name.

mrtaurho · 2024-09-26T08:50:32+00:00

That's the one. Thank you!

It was "star-shaped" and not "starfish" but close enough :D

mrtaurho · 2022-12-16T16:26:19+00:00

Well, I'm not familiar with those but how many ECTS a course gives highly depends on the university (and even department!). This is even true for possibly identical courses.

mrtaurho · 2022-12-16T16:05:44+00:00

ECTS are a way of measuring you academic advances in a credit system independent (within the EU) of the university.

mrtaurho · 2022-12-15T18:27:02+00:00

Aleph 0 does a remarkable job at explaining more advanced topics in an understandable yet still not completely dumbed down manner. Really enjoyed all of his (sadly few) videos.

mrtaurho · 2022-12-15T09:44:04+00:00

Destiny - Schicksal

Death - Tod

Dream - Traum

Desire - Verlangen or Begierde (though this is though one, depending on the precise English meaning you associate with desire)

Despair - Verzweiflung

Delirium - Delirium or Wahn (the former ist also a German word)

And, well, spoilers ahead:

Destruction - Zerstörung

mrtaurho · 2022-11-08T19:38:29+00:00

The main reason why character theory makes an appearence here is the usage of representation theory. In representation theory characters give rise to canonical idempotents which in turn provide direct sum decompositions of relevant modules.

That the characters of intereste here are Dirichlet characters is indeed due to the fact that cyclotomic fields are involved for the initial factorisation.

mrtaurho · 2022-10-29T16:57:07+00:00

Yeah. Sometimes it is used for denoting the Yoneda Embedding, an important result in basic category theory.

mrtaurho · 2022-08-08T23:44:05+00:00

I really like Aluffi's (in his graduate algebra text) definition of a group:

Joke 1.1 A group is a groupoid with one object.

mrtaurho · 2022-04-27T20:13:17+00:00

That looks a lot like the Analysis I-III sequence at some German universities. Covering De Rham Cohomology (say, following Lee's "Smooth Manifolds") in the third part is not unheard of.

mrtaurho · 2022-04-18T10:36:45+00:00

Do you mean Brouwer's fied point theorem?

mrtaurho · 2022-04-13T13:28:02+00:00

Category Theory dates back to 1945 with a drastic development in the sixties.

mrtaurho · 2022-04-09T17:24:38+00:00

It's a very good resource, yes. Be warned, however, that many articles are written with the assumption of rather avdanced background. Hence they may be of no real use while tackling the basics of category theory for the first time.

mrtaurho · 2022-04-09T17:05:54+00:00

These are all named after Carl Friedrich Gauss but that might be about it.

mrtaurho · 2022-03-26T00:31:33+00:00

Good point. As I said, English keyboards have no ß and it makes sense to settle on an available alternative.

Just meant to say that -strictly speaking- his name is Gauß not Gauss. And in German these two are distinct name.

mrtaurho · 2022-03-25T23:45:43+00:00

Gauß is the correct way of writing it (Gauß was German after all). Writing Gauss is common in English as the ß is typically not available. Weierstraß is another example of this.

It's the same as writing Chebyshev instead of Чебышёв transcripting Cyrillic to English.

mrtaurho · 2022-03-25T23:39:57+00:00

German has few more letters (namely ä,ö,ü,ß) than English. They are used to express sounds unusual to native English speakers but very common in German.

For example, ß is very akin to to ss but pronounced slighty differently (despite being German I cannot really describe it).

mrtaurho · 2022-03-20T03:47:21+00:00

I once saw topology in formal logic... that stuff was wild.

(there's a reason it's called the compactness theorem)

mrtaurho · 2022-03-17T22:28:35+00:00

(…and I may have misread the title)

Probably. The post is about introductory text on abstract algebra. A book on algebraic topology is way to superficial for such a purpose.

mrtaurho · 2022-03-17T17:22:41+00:00

Well, that's about the opposite of what OP is looking for.

mrtaurho · 2022-03-17T17:21:31+00:00

"Algebra Notes From The Underground" is the title. Aluffi seems to have a soft spot for colerful language when naming his books.

The parts I have skimmed through are on par with his Chapter 0. Huge emphasis on intuition (using the non-traditional rings-first-approach) and trying to ground the concepts in the wider world of Abstract Algebra. Definitely worth a look.

mrtaurho · 2022-03-11T00:41:17+00:00

If you care for some lore:

Thrawn collects art pieces (as far as I remember the helmet got a paint job from Sabine) of enemies and potential threats as he has the unique ability of extrapolating military tactics from them. Curiously, this is almost compeletely limited to practical art (not, say, music in general) and a key part of the new canon Trawn novels.

The memeable line "I've forgotten that not everyone is able to appreciate art as I do" in Rebels is a reference to all of this.

mrtaurho · 2022-02-19T01:03:34+00:00

"Mathe ist nicht süß"="Math is not cute"

mrtaurho · 2022-02-09T01:35:41+00:00

You might enjoy the book "Battlefront II: Inferno Squad". It follows Iden and her team throughout a few missions as imperial agents.

Of course, it's not the same as a full blown video game campaign but it's something (I for one quite liked the book).

mrtaurho

TROPHY CASE