/sci/ - Science & Math

>>10118033
first you have to calculate the energy from the specific heat to change ice from -41.7 to 0 degrees, then you add to that the energy from changing from ice into water

>>10117999
i know it's not technically bad, but I dont have much to show for it. Also a lot of the time was wasted in putting up polished solutions, but oh well.
>>10118001
thanks, sadly this is the least "advanced" topic im going to be doing in the near future so i cant really do any other thread of this style that's accessible
>>10118003
im still going to be doing the problems, so if you're stuck on something just ask here, im always lurking

Welp, took a nap for too long and my comm algebra thread died... well, im not gonna start a new one because i've barely gotten through 3 chapters in 2 weeks at this rate with the posting and all

>>10112951
a lot of time, but I take too many breaks honestly, mostly because of lack of sleep makes it hard for me to concentrate.

>>10112790

>>10112787

>>10112783

posting some chapter 3 now

>>10111444
f(x) is bounded for all x implies f(g(x)) is bounded for all x since any single value of g(x) is bounded, and hence is in R

>>10109789
I know a bit about Ext_1 that I learnt in my algebraic topology class but since we didnt use tensor products, I didnt learn Tor (and I didnt learn about Ext_n) so it would be too much for a digression for me right now, but I'll be getting into homological algebra right after commutative algebra

>>10110015
This is a very different type of algebra. If you're referring to the type of algebra "solve for x when x^2-4=3x+1" then you should probably go on Khan Academy, or perhaps Gelfand's Algebra followed by Axler's precalculus

This is the last answer to chapter 2 that I'm posting. 23 is trivial and I don't know about Tor yet although I will eventually get to it. These last few questions are a lot of symbol pushing, but they do define important notions. Direct limits are also called in category theory "colimits", so you can expect that this idea has a dual notion.

Anyone that knows is welcome to post answers of the rest of the stuff. I'll be passing to Chapter 3 soon but doesn't mean you can't post about previous chapters

>>10108664
No matter if a ring has or doesn't have unity, it doesn't solve the problems that modules solve, that is, making rings an abelian category.

Also no identity means Z can have more than one ring structure which is just disgusting

>>10109180
Also to note: exercise 13 in chapter 1 is essentially constructing the algebraic closure as the direct limit, and you can see it by applying exercise 17 in chapter 2

>>10109181
the derivative of 1/x is -1/x^2

>>10108843
An exhausting question honestly, mostly because A/M just glance over the fact that you have to first prove regular products commute with the direct limit.

A satisfying chase

>>10107680

>>10106885
I wouldnt use a wedge when speaking about linear algebra when you mean "and"...

and its obviously not true. Consider [math](1,1)\not\in \langle (0,1)\rangle[/math] and [math]\not\in \langle (1,0)\rangle[/math], but clearly [math](1,1)\in \langle (0,1),(1,0)\rangle[/math].

>>10105733
At a number theory seminar I had the other day, someone was speaking about L functions and he mentioned (jokingly) that what he did would disprove RH, and someone else said "with apologies to Atiyah" and they all laughed. idk what it means tho

>>10107412
To me it's the other way around. I find it so much more satisfying when something doesn't just work because of a clever map, but because the universe decided it was meant to be (or something of the like, I'm not the best at expressing myself).

And yeah, perhaps it wouldnt work past the first chapter, but I could expect it to last several threads where half the pics are anime avatars

These last few questions remind me of my times reading Aluffi's algebra book. Something tells me that a thread like this for category theory would have been more popular if only for the larping categorytheoryfags

>>10105605
Well, what I had planned was for us each individually read a chapter, and perhaps if there's something in the book that we don't understand, to ask each other for insight. Then to also do the exercises in a similar fashion. I've been posting my solutions to the exercises so other people might have solutions to compare to, or perhaps so that others might tell me if I'm wrong somewhere.

However, chapters 1+2 are relatively straightforward standard material (perhaps a first meeting with the tensor product and exact sequences for some), so it's less likely that someone might have a question about them.