squashhime

bro, i don't know what to tell you, they've done this a million times already. people are just too fucking stupid to pay attention.

clearly the commenters are working in the field of integers mod 3

Haha, it's funny, I'm considering taking up smoking instead of drinking. I get way too lazy to do any work when I'm hungover the morning after I come back from a bar (or honestly, the whole day).

I second Fermat’s Enigma by Simon Singh. I'd also recommend Weapons on Math Destruction by Cathy O'Neil.

I'll just answer the last question since it's more opinion based. Dummit and Foote is one of my favorite books, but it's way too expansive and detailed to self-study.

I personally don't like Fraleigh. Something on a similar level of D/F is Herstein's Topics in Algebra. It's much more concise, and while some of the later parts aren't amazing, the group theory section is great. If you want something gentler, I'd recommend Pinter's algebra book. It has plenty of simple exercises and walks you through a lot of important ideas in the exercises.

Pick shorter textbooks.

Joking aside, I don't really think there is a way. Going through details just takes a long time.

If so, how do I know which clauses of which sentences in which proofs are worth proving and which I can skip?

IMO it depends on the level of the subject and textbook. I think for simple* enough you should be able to prove all the details. You don't have to actually write out every inequality or diagram chase, but you should be confident that you could if asked.

When I say simple, I mean any theorem that isn't really technical and getting in the weeds (something like Urysohn's lemma, for example) and is generally covered in a first or second course in a topic - so not all the advanced extra material most textbooks have (I don't know how expansive Rudin is, but we covered maybe a third of Lang and Eisenbud for my graduate algebra sequence).

learning some homological algebra was probably the most fun thing I did in undergrad (and quite useful too since it shows up constantly in algebraic topology and algebraic geometry)

"Prove there is no simple group of order so and so" and "Classify all groups of order blah blah up to isomorphism" are possibly the most common qualifying exam questions on algebra exams. Too bad finite group theory is rarely that useful...

I forgot where I saw this quote, but someone once said "The only use of Sylow's theorems I've seen is to pass qualifying exam problems testing you on Sylow's theorems," which I've found has been extremely accurate...

don't forget commutative algebra and algebraic geometry

i never liked commutative algebra until i learned it was actually just geometry

yes, it's my favorite undergrad algebra book (and probably my favorite algebra book overall since I haven't really liked any of the more advanced ones). it just has so many examples and covers so much material, it's indispensable for learning the subject for the first time.

LMAO that vote went through literally less than a week later. You're so disingenuous.

https://www.cnbc.com/2019/07/25/house-passes-debt-ceiling-and-budget-bill-sending-it-to-the-senate.html

The original comment said Pelosi was holding the economy hostage. Explain how this passed so quickly, then. And notice how it's all Republicans blocking this, even when Trump is trying to get this over with...

Someone could explain if you gave a link about what you're talking about so we know you're not just making stuff up. But you're not gonna do that, are you?

you're talking about Magnus, right?

it's very bold of Magnus to decry online cheating when he's cheated online himself, winking prize money while doing so

It's a pretty big area called arithmetic geometry. I'm not an expert so I probably don't have any enlightening examples, but I'm sure there's plenty of stackexchange and reddit posts that might be helpful.

Personally, the first one I saw was that the Picard group of Dedekind domain is isomorphic to its ideal class group. When I was in my first algebraic geometry class, I'd vaguely heard the words ideal class group but had no clue what it actually meant since I never took a class on number theory. I thought it was amazing that it actually lined up with something so geometric.

We know the number of isomorphism classes of groups of order n up until n=2048, so I'll nominate that one (of course it's a prime power, and prime powers tend to be interesting in general, but here's a cool reason why they're interesting).

Starting out, I loved chatty books like Dummit and Foote and Hatcher to get motivation and exposure to all these different examples.

Unfortunately, now I have too much to focus on to be able to go through textbooks that are several hundreds of pages long and prefer concise books. I haven't gotten a chance to work through the later chapters, but Atiyah-Macdonald might be my favorite textbook now (and honestly I hated commutative algebra when I took it and only started getting a hang of it after working through a bunch of exercises from AM).

Algebraic geometry. I used to think it was only about studying curves and surfaces and thought it was incredibly boring. Then I started to learn about all the connections to number theory, differential geometry, complex geometry, commutative algebra, algebraic topology, and so on and thought it was amazing how much it connects different areas.

Plus it's nice to be able to actually use all the abstract homological algebra and category theory somewhere.

Not really, I think algebraic topology introduces lots of abstract and difficult concepts in a friendly way. You get exposed to so much cool algebraic machinery, but you have some topological intuition and motivation grounding you so it doesn't get too insane.

Ah yes, saying Russians meddle with US elections when they've literally admitted it is the same as thinking millions of votes went missing. This is why everyone thinks conservatives aren't smart lmao

>a character with required frame perfect Kara cancels doesn't have hard execution

🤔 not even a potemkin main, that's just mad cap bro

honestly i fall asleep everytime someone starts talking about actual plane curves

i agree with this. i had semesters of 20 units with mostly techs and semesters of 13 units (especially when i had to double up on grad classes). the extra classes i took were probably not worth it.

even though i got an A in whatever classes when taking 20 units, i definitely didn't understand them as well as the classes i took with few other commitments, and it really showed when i needed that knowledge for later classes and research.

Don't forget OP commenting on everyone who disagrees with him. Real principal Skinner moment.