/sci/ - Science & Math

>>10090014
i might fail my stat inference course

Why is arithmetic/number theory so fucking hard?
I keep studying and when faced with an exercise I can't do it. I don't have this problem with other branches of math.

>>10090014
I have my last one in two days and i can't study help me reeee

why french math colleges are the best in the world?

I know I failed Linear Algebra
It's because I don't have a work ethic
You already know the story, it's the classic one, don't do shit until the last week, study somewhat hard the last week, then fail because not prepared enough
It was min first tenta

>>10090089
>failing statistics
Y'all niggas insist on disappointing me.
>>10090107
I feel you desu.

>>10090133
How do you fix this?
I'm kinda in the same boat, during primary and half of my hs I went to a nice school, then moved and switched to a technical hs which I kinda breezed through and now I'm getting rekt in uni

>>10090129
Aside from ENS and l'X we're not that good. Number of Fields medalists != overall quality of math education.
A French math major at a decent university is probably as good on average as an American math major at a similarly ranked college.

>>10090014
never live with your girlfriend, even if you dont fuck her, its entirely a distraction, fuck man

>>10090135
>I feel you
It's frustrating. But at the same time, when I do find a solution, it feels so good (that is, when it wasn't obvious all along, then I feel like a retard).
Is number theory so hard because there aren't really any "methods" to speak of that can be generally applied to most problems, unlike with analysis or whatever else?

>>10090156
Number theory essentially relies on figuring out unrelated theorems and borrowing from other fields. The axioms are useless.
Always try to keep the theorems in mind when solving problems. In a test, if you get stuck on a question, try to solve another one and see if you can borrow that result for the previous one.

>>10090174
>the theorems
I know them all by heart, but most of the time, the answer is unrelated and requires a unique method. Sometimes I manage to bruteforce everything with induction proofs, but that doesn't always work.

>>10090133
this is why im failing stats desu im writing on thursday and have yet to finish the textbook>>10090135

>>10090144
correct post
having teachers who participated to bourbaki is pretty comfy though desu

>>10090150
Damn tell us more anon

>have to take an applied class to graduate
>hours a week that could have been used on my honors thesis
JUST

>>10090014
Instructor flat out said he isn't giving a midterm cause he doesn't want to grade it, grad school is comfy sometimes.

>>10090279
Probability is fun

What are some tricks for an abstract algebra exam?
inb4 study

>>10090301
What material is it on?

>>10090305
Basic group and ring theory. Things like quotient groups, group actions, Sylow's theorem, Euclidean domains, Ideals etc.

>>10090014
>98% on real analysis midterm
>62% on stat theory midterm
I think my stat theory professor put some shitty questions on the midterm though. We were asked to prove pic related, but we explicitly skipped the chapters on multivariate distributions (in fact, the prof said we wouldn't even touch multivariate distributions until the second semester stat theory course). I posted this in /sqt/, but I got a stupid response. Should I ask the prof about this? Or should I have been able to solve it.

>>10090321
Stupid response here, you've posted this thing fifteen times now, go fuck yourself.

>>10090333
Excellent digits, shame it was wasted on a shitpost.

>>10090333
Were you the one that responded in /sqt/?
Still waiting to see that proof that uses the "first rule" of integrals, btw. Bet it will knock my fucking socks off.

>>10090150
>living with a woman you haven't married
wew lad you dun goofed

>anons talk about midterms
>for me its the second week
>got >93% score on the homework
You could say I am ready for my bachelor thesis, noobs.

>>10090345
Didn't even see your post. BTW, my mistake, you also need the constant one.

what does the graph of a function from R^2 to R^2 look like? I understand what graphs from R^m to R and from R to R^n look like but what about R^m to R^n?

>GRE subject test on saturday

>>10090382
Hard to describe four dimensional objects desu. It looks like a two dimensional surface thrown on four dimensional space.

>>10090388
so the tangent surface of a function from R^m to R^n always has the "dimension" m?

>>10090395
Yup. Imagine you took the cover of your bed and threw it into four dimensional space. That's what a continuous R^2 to R^2 function looks like.

>>10090107

This is a mood. There's no powerful tools in elementary number theory at your disposal like other fields of math. It's one of the first placws where it comes down to raw IQ

>>10090409
>raw iq
Literally the field where IQ matters the least, raw creativity.

>>10090301
always try passing to the quotient, especially if you have a maximal/prime ideal, or normal subgroup

>>10090414
Creativity is associated with iq, though weakly compared to most other cog traits.

Was at an alg geom seminar earlier today. The following was an essential step in it: prove for positive coprime integers a,b that there exists unique integers 0<u<a and 0<v<b such that av+bu=ab+1

>>10090301
Same question for distribution theory desu
This shit is interesting but i feel retarded as soon as i try to practice.

>>10090429
>coprime
Literally never heard anyone use that before. Anyways:
Let u=a-i and v=b-j. Then a^2-ia+b^2-jb=ab+1
a^2+b^2-ab-1=ia+jb.
Fuck I started this and now I feel super lazy, sorry.

>>10090429
>>10090453
It's pretty simple now that I'm back home. I just didn't remember if there were bounds on the Bézout identity coefficients, which makes it very simple:

[math]\gcd(a,b)=1\iff \exists\text{ unique integers } r,s\text{ such that }ar+bs=1[/math]. In the particular case of [math]a,b>0[/math], we have that [math]|r|<b, |s|<a[/math]. Due to the symmetry of the problem and the positiveness of [math]a,b[/math], we can consider WLOG that [math]s<0[/math].

Now [math]ab+1= ab + ra+sb = b(a+s)+ra[/math], and in particular, [math]0<r<b[/math] and [math]0<a+s<a[/math], so we have the stated form. Uniqueness comes from uniqueness of the Bézout coefficients.

>>10090421
Thank you kind sir.

>>10090588
to add to that, always keep in mind the correspondence {ideals/normal subgroups} <-> {kernels}. You should know like the palm of your hand the first isomorphism theorems and the correspondence theorem of ideals/normal subgroups (google it if you havent heard the name, you've done it 100%) and their proofs (they're trivial). You should know the orbit-stabilizer theorem, its proof and its consequences. Of course, Sylow theorems are very important if theyre in your course, there will definitely be a counting argument proof.

It has finally been done: Introduction to Commutative Algebra following Atiyah-Macdonald thread.

>>10090674
>>10090674
>>10090674

how do i get good at proofs

>>10090679
I'll do it but I may have to tap out depending on my other work

Fuck everything I'll transfer to math next semester and follow my dreams even if it means I'll have endure a world of humiliation and pain.

>>10090825
That's the spirit anon, we're all going to die from climate change anyway

>>10090382
Such functions are often graphed by showing the transformation of a regular grid. Another option (common for complex functions, C->C) is a 3D surface plot where the height is proportional to the magnitude and the surface colour shows the argument (angle).

failed all my midterms, for some reason couldnt think properly during the entire midterm week and got a lot of easy problems wrong. finna jump off a tall building!

>>10090998
Hey it's alright anon, I've fucked up many a midterm and I still managed to pull decent (or at least non-terrible) grades, get research opportunities, etc. Go make a warm drink and relax, and accept this virtual hug <3

>>10090683
By doing them, particularly doing them in the field you're working in since an, eg, group theory proof has a much different feel than an analysis one.

>>10090998
>finna jump off a tall building!
A guy at my school did this last semester. I walked by like 10 mins later wondering wtf happened. He wasn't a math major though.

>>10090139
Drugs

>>10090679
LMAFO
https://www.youtube.com/watch?v=zJTU6mMeIXs

please don't let this thread die >>10090674

>>10091011
thanks. your comment made me feel a lot better, no sarcasm

I'm having real trouble understanding why d, according to the answers, isn't a linear function. I mean it has a slope and a y value and it's in no way quadratic. Am I missing something, or is the book just incorrect?

>>10091898
And of course the picture has to end up upside down

>>10091903
you can't divide by x

>>10091906
Ahh, yeah that makes perfect sense. Thanks anon!

>>10090290
>Probability is fun
This, you're officially my favorite /mg/ anon.

>>10090290
>>10092006
Applied math is more fun and comfy in general.

How do I integrate this game theory feedback? I got some initial criticism for this essay I have to do (basically we have to create our own model for a RL situation and I picked Dubya's Iraq invasion) but I've got no idea how to integrate it, I thought I was doing fine (dynamic game since Iraq moves first, then the US after) but lecturer seems to disagree.
Game theory has to be the most bullshit thing involving maths I swear to god

>You can replace it with a constant, and discuss the equilibria for different ranges of the payoff, but the United States must know its own preferences (or, replace it with a probabilistic payoff, but then you still reduce that to one number [the expected value]).
>At a glance, I don't know what the justification for "Allow UN inspections" is, since it is decoupled from the actual decision whether or not to have a nuclear program (and, it is strictly dominated).
>It's not a "Bayesian game", since there is no real preference uncertainty. The game structure does imply using the PBE as the equilibrium concept, since there is only 1 subgame. But, since Allow UN Inspections is strictly dominated, the game simply reduces to a 2x2simultaneous move game.

I'm having trouble with this question involving lagrange multipliers. The problem asks to maximize f(x,y) = xy(s-x-y) on the constraint x+y+z=s (s is constant) with x, y, z > 0 and show that this implies xyz <= (s/3)^3. I'm not sure how to use lagrange multipliers for this, should I treat just treat z as a constant when finding the gradient of the constraint? Wolfram gives the maximum as (1/4)(z)(s-z)^2 at x = y = (s-z)/2 as the maximum. However I'm still not sure how to prove the inequality, and I'm not sure that the max I got was correct, since when I expand xyz and plug it into Wolfram it says that that the inequality (s-sz-z^2)z/4 <= (s/3)^3 isn't always true. Thoughts?

>>10092010
Applied is just taking all this nice comfy pure math and trying to find a way to wring a profit out of it, change my mind

Not sure if this belongs ITT but I'm trying to get good at newtonian mechanics and my professor told me I should be have a solid understanding of derivatives and what they represent mathematically.
I'm a freshman in college so I'm not very far into calculus yet, but are there any good resources you could recommend?

I'm going to enroll in college next year for physics. What kind of math should I focus hardest on prior to prepare? I enjoy doing math, I just want to know what I should really zero in on.

>>10092396
Calculus and Linear Algebra. Feel free to sleep on everything else except geometry and topology(rare).

>>10092411
Doesn't theoretical physics sometimes rely on some pure math concepts?

brainlet here. taking my first abstract algbera course and there are so many theorems and results. how the heck do I organize all of this, I feel so lost.

>>10090366
you wrote all that with your mouse didn't you?

>>10090107
Is number theory important for other branches of math or other subjects? I’m really shit at it

>>10092689
Quantum stuff does but the physicists usually fuck it up

>>10092700
Yes and no. Number theory is centrally important to modern math, but at the same time not much other than pure number theory actually depends on number theory as foundation.
What makes number theory a unique subject (and I think part of why many people like it) is that you can work on it using literally any tool in all of mathematics.

Is pic related any good? I want to learn about QM with as little classical physics as possible. I know that's retarded but work with me.

What looks worse on a transcript?
- dropping a math unit
- failing a math unit

>>10092697
What are you doing? Groups/rings/fields?

In groups and rings, you should know like the palm of your hand the first isomorphism theorem and the correspondence theorem.
For groups, you should also know Lagrange's theorem.
For group actions, you should know the orbit-stabiliser theorem, and the sylow theorems if you've done them in class.
For rings, you should know the hierarchy of ED implies PID implies UFD, and Gauss lemma, perhaps R ufd implies R[x] ufd, and others if you've done noetherian stuff, including chain conditions.
The rest are easy corollaries of these

>>10092724
Failin you reterd

>>10092689
If you have a course on linear algebra and it's mathematically rigorous, it will set the stage to abstract algebra and pure math you may need to learn in due time. That anon is correct, the math needed in physics is easy as fuck, the hard part are the tricks you have to employ and gaining intuition using math in physics

>>10092733
Guess I'll drop it then.
I'm probably going to fail it no matter how much I try to study for it anyway. May as well save myself the pain.

>>10092712
I don't know but learning QM without putting it in a physics context will be more painful than taking the time to learn the important physics concepts that precede it

>>10092712
Mathematical Foundations of Quantum Mechanics by von neumann.

If you begin good in functional analysis.

if i become obsessed with a problem do i finish it even if i`m stuck or i just move on to different ones until i have inspiration for that one
help pls i feel like it is pushing in a depression

>>10092712
Looks good
cite preface
>Quantum mechan- ics books in the physics literature are generally not easily understood by most mathematicians. There is, of course, a lower level of mathematical precision in such books than mathematicians are accustomed to. In addi- tion, physics books on quantum mechanics assume knowledge of classical mechanics that mathematicians often do not have. And, finally, there is a subtle difference in “culture”—differences in terminology and notation— that can make reading the physics literature like reading a foreign language for the mathematician. There are few books that attempt to translate quan- tum theory into terms that mathematicians can understand.
>This book is intended as an introduction to quantum mechanics for math- ematicians with little prior exposure to physics. The twin goals of the book are (1) to explain the physical ideas of quantum mechanics in language mathematicians will be comfortable with, and (2) to develop the neces- sary mathematical tools to treat those ideas in a rigorous fashion

Other notes.

https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.020/fackler/SS15/qm/lnotes_mathematical_found_qm_temp.pdf

>>10092762
I guess if you have some sort of interest in that particular problem and the answer you're gonna get is gonna influence you one way or the other, and you have lots of time on your hands, you might as well keep at it. Unless you get completely stuck, in which case you might wanna look into other things.
If it's on an exam or something, fuck no, skip it.

>>10092737
Are you 100% sure you can't recover? If you are, drop it, if you are not sure study a fuckton and see if you can pass.

>>10092762
>inspiration exists, but you had to find it working
>t. pablo picasso

Working in diferent thing,rest and made habit read or analysist problems from different point of view end if you don't had inspiration.

going to self teach linear algebra, is this a good book for it?

>>10092807
If you want Lineal algebra for engineers yes.
If you want learn pure math.
Lineal algebra shilov
http://store.doverpublications.com/048663518x.html
Or
Lineal algebra Hoffman and kunze.

>>10092727
Basically just group theory right now. Basic stuff, not too advanced. We did Lagrange the other day. I'll keep this in mind.

>>10092770
Yeah I'm pretty sure judging by so far, and I don't think I have the motivation to study hard for a difficult subject that I know I'll probably fail anyway, and it's too stressful. Also the lecture notes and lecturer are fucking trash and I don't even understand the solutions to exercises. How the fuck am I supposed to salvage this in the little time I have before the exam.
Even if I did study a lot and "passed" I would probably end up with a pathetic just-above-failing-threshold mark anyway.
I'd rather study for units I can actually succeed in and get high marks in.

>>10092699
Yah.

>graduate with a phd in math
>haven't even studied 90% of the shit that US students learn to pass their fucking quals and be considered for a phd
why is maths education so shit in the UK. at least I'm done with a phd at age 25 though, but it still sucks because I know fuck all.

>>10092883
What was your thesis on?

>>10092883
>phd knows fuck all
Same in Brazil desu. Niggas don't see linear analysis, measure theory, non-euclidian geometries, or just about anything beyond basic topology and real analysis without going for optional classes.

>>10092883
Leave that cat alone!

>>10092892
I'm about to enroll in mathematics in Brazil. Is there anything I should know before hand? Do you have any tips? I'm assuming you're Brazilian as well.

>>10092889
met a nice prof who was doing applied stuff, ended up doing my thesis about some cool convex optimisation methods used in that field.

>>10092892
yeah. people will say "well you can just study these things on your own", but it's not the same as now I have to fight for postdoc positions / tenure / etc. so I can't dedicate a whole fucking year to studying measure theory, even though I wish I could.

>>10092912
Second semester here, I know fuck all. One thing I'd have to recommend is checking PAM out.

>>10092914
>convex optimisation methods
milk meme learning

>>10092925
>PAM
Nigga, see you next semester, then. Unless there's another advanced program with the exact same name in other universities. Besides, it's second semester, you just passed the introductory stuff.

>>10092939
Pretty sure it's just UFRJ and UFSC, and I'm assuming you mean the latter.
But seriously, the curriculum is a joke, make sure to go for optional classes.

>>10090107
Im deaping with this. Im just practicing A LOT and understanding for real every problem it gets to my hands.

What is the matter w u. The lack of vision at proving or the subject itself?

You could be making bank doing engineering, but instead you're wasting your potential studying abstract garbage, why? WHY?

Your future self will regret not using your mathematical ability for something useful and profitable.

>>10092953
because some people would rather do what they enjoy the most as their job.

>>10092944
Yes I meant the latter, and I'm definitely taking the optional classes.

>>10092957
>still doing math but get paid a fuckton for it
Are you just deluding yourself into thinking that studying weird bullshit is more enjoyable than any other math-based field?

>>10092914
Is dropping out of academia to study math while on autism bucks then harassing your former colleagues to referee your papers the true patrician choice?

Seriously though how's your postdoc hunt going? I want to know how fucked I am if I continue on this course.

>>10092953
Because engineering is just begging your capitalist overlords to exploit you and engineers are just about the worst people on this earth. Math people may be autistic but they're nice autists.

>using your mathematical ability for something useful and profitable
There's basically no overlap between higher math and applied engineering math.

>>10092961
math has many completely different subfields, most of which are as close to engineering math as you are to someone who's not retarded.

protip: you should wait until after you graduate high school to make decisions about what to study and what to do with your life

>>10092966
>tfw too smart to have financial security
Is what you just said

>>10092962
>Is dropping out of academia to study math while on autism bucks then harassing your former colleagues to referee your papers the true patrician choice?
I know a guy who was a reasonably good assoc prof. he married a rich as fuck asian lady, left his job, and just kept doing research while living with her. obviously not quite comparable to living on autism bucks, but it's not impossible in general
>Seriously though how's your postdoc hunt going? I want to know how fucked I am if I continue on this course.
I did applied stuff so it's not terrible, and postdocs are reasonably easy to get (tenure is a whole nother story). I didn't quite do meme learning like the poster above implied, but as long as you find a field in which there's a non-zero amount of funding it should be okay.

>>10092969
That's not what I said at all, I said that engineering was unpleasant and that the skill-sets don't overlap that much. Math people should become codeslaves if anything.

>>10092990
>wishing codeslavery on anyone
You do know you're going to hell, right?

>>10092848
I felt like this the first 3 weeks. Then i read everything from the beggining again. But with confidence. Believe me that makes really the difference sometines. U dont lose anything. Dropping will really be a burden in the future.

>>10092991
If I'm going to hell you're going to one of the fucked up tibetan buddist hells for wishing engineering on people

>>10092994
I'm not 3 weeks in though, I'm about 3 weeks till the end of the semester.

>>10092947
Every problem is different so that the same thing doesn't usually work twice, you have to work around that shit and be creative with proofs, and I'm not good at that yet I guess.
I have no issues with other things like analysis, algebra or whatever. But number theory just fucks my shit up.

Looks like the anon on /sci/ who provided a proof for a new solution to the superpermutation problem is getting some attention in news articles.

>>10093108
Fucking this.
Number theory is really tearing my anus apart this semester

>>10093187
Read other old threads, looks likes begin some IMO contest from an asian country.

IMO and IOI contest from china,taiwan,south korea,japan love anime.

>>10093199
https://www.theverge.com/2018/10/24/18019464/4chan-anon-anime-haruhi-math-mystery
https://web.archive.org/web/20181024190314/https://warosu.org/sci/thread/3751105#p3751197

>>10090014
I made a 101 on my Calculus III test. If I ace the next two, then I will excused from the final. This class is so easy compared to II.

>>10093238
I do it too, but ignore pure math like 10 years.
Begin some math area call analysis, formal proof concepts calculus.

If you love math, learn pure math

>>10093238
That's because they don't teach any of the theory and you're just doing calculus 1 but with multiple integral signs.

>>10093206
state of science journalism

How to draw integer set symbol? It always ends up looking like a banana

>>10093486
What? You mean [math]\mathbb{Z}[\math]?
I draw a normal Z then add another line to the right of the diagonal

>>10092712
Tahktajan is better.

>>10093486
If you mean "blackboard font", I always just draw two of the letter atop each other at a small offset, to emulate writing on a blackboard while holding two pieces of chalk.

>>10092712
>I want to learn about QM with as little classical physics as possible. I know that's retarded but work with me.

Too bad, learn classical physics. At least read "Physics for Mathematicians: Mechanics" by Michael Spivak

>>10092712
There are in general two approaches to QM
1. Geometric quantization via classical mechanics and symplectic geoemtry (Woodhouse, Guillemin-Sternberg, Marsden-Weinstein).
2. C*-algebraic and constructive QM via local operator algebras, e.g. GNS representation (>>10092747, Haag, Strocchi-Swieca).
Both have their pros and cons,
1. Geometric quantization makes explicit the classical intuitions behind QM and the implementation of gauge invariance is straightforward via the moment map. In addition, the topological effects (i.e. A-B effect, Dirac monopole quantization, etc.) are almost immediate. However, such "nice" properties rely on some pretty stringent equivariant cohomological conditions, and the continuum limit (i.e. QFT) is not obvious.
2. Operator algebras and the GNS representation is a purely C*-algebraic construction, namely it is completely independent of whether you're in a QM or a QFT setting. In addition, the QFT you obtain automatically satisfies all the Streater-Wightman axioms and the Euclidean reconstruction theorem can be obtained with relative ease. However, it is not clear how gauge bundle structure actually affects the operator algebra, which makes gauge symmetry elusive; and the topology begins to intertwine with the algebraic geometry, which is a massive headache.
These two approaches have been proven (Zhang-Baez) to be equivalent in free theories via the particle-wave duality theorem, however, but it is not clear how to bridge the two in terms of their pros can cons.

>Weyl equidistribution theorem
Math is a strange thing

>>10092712
>Is pic related any good?
Why don't you read it and find out?

>>10090107
>mfw number theory and abstract algebra were the only classes i didnt need to study for and just made sense, failed calculus several times

>>10090107
Number Theory is the only course I ever flunked.
Everything in arithmetic seems ad-hoc.
No way through the thickets.

>>10092953
>money money money
Fuck off

>>10093187
Proof that /sci/entists are 7 years ahead of everyone else.

>>10094258
>>10090107
>>10090409
>>10090135
Undergrad or grad level number theory? If it's undergrad then pick up Dudley Underwood's 'Elementary Number Theory' book. It's extremely methodical and does everything with one foot in front of the other in a way that feels like it's going somewhere (instead of some ad-hoc soup of theorems and techniques). Reading that book made my number theory class trivial and since it's actually pretty easy to read I was able to do it in a few days.

>>10093187
>>10093206
I still hate this general.

>>10092304
TC7

Got 60% calculus, 80% math with modulation, 100% programming.
God damn epsilon-delta proofs which the test almost consisted entirely od

>>10094347
Go back to your containment board.

>>10094527
I wonder what he meant by this.

>>10094573
The only people who get buttblasted over math discussion on a math board are pop-sci brainlets.

>>10094574
Were /mg/ filled with math it would have nothing in it to fuel my hate. Try again.

>>10094580
What about the [math]empty\ thread[/math]? It's not filled with math but I bet you'd still be buttblasted.

>>10094587
[math] \{ \text{post}\in/\text{sci}/ : \text{post}\in/\text{mg}/ \} = \emptyset \implies T(\text{my mental state} = \text{pic related}) = 1 [/math]

>>10093262
Based
https://www.theverge.com/2018/10/24/18019464/4chan-anon-anime-haruhi-math-mystery

>>10094430
Epsilon-delta proofs aren't hard, you're just stupid.

>>10092256
read "a stochastic model related to telegrapher's equation" by mark kac

>>10093943
classical physics is the most overrated crock of shit. here's why:
1) the main application areas are 19th/20th century technology, and recent advancement in these areas is mostly a result of more sophisticated optimization and numerical methods (i.e. commercially available finite element methods) and better computers, very little to do with better understanding of classical physics. also we are not building rockets anymore
2) classical physics theory liberally makes retarded assumptions like no noise, friction, air resistance, or god forbid significant higher order terms. (I add: people have this idea that physicists are masters of making intuitive mathematical judgements. this is incorrect. they are masters of ignoring terms that makes analysis hard. they are masters of truncating taylor series and assuming everything is a harmonic oscillator)
3) if you have two neurons to rub together, you can learn how to derive lagrangians in a day. but classical physics does not give you any tools to make qualitative judgements about the ridiculous ODEs you derive about these systems. unless, again, you make assumptions
4) similar statement holds for continuum mechanics. if for some reason you are greedy and masochistic enough to work in numerical methods, than maybe learning a bit of continuum mechanics is a good idea. but in terms of theory, the low-hanging fruit has all been eaten and shat out a 100 years ago. The current state of continuum mechanics (including fluids) is PDE models that consume the careers of mathematicians, that physicists are totally bored of, and that engineers can simulate without thought.

anyway. that's my rant. quantum mechanics is a beautiful area of physics, continues to have modern applications and theoretical developments, and shares an intimate relationship with pure math.

>tfw too many things to study
How do I just pick something and stick with it?

>>10094783
You pick something and stick with it. Forget about the rest.

Am I just a mega brainlet?
>has crazy fear of Calc II
>for next upcoming test studies super hard
>actually starts to make sense
>feelsgood.jpeg
>actually thinks I’m gonna pass and conquer fear
>takes test
>mfw

>>10094965
I feel you

>>10090014
Midterms? Like finals for your course in the first semester of the year?

>>10094985
Burger schools generally have courses that are a semester long (four months or so). A lot of the time you'll have a mid-term half way through the semester (so after two months or so of instruction).

>>10094965
There are probably a few mathnerds in that class, just become friends with them and talk about the material with them. They like helping brainlets because it makes them feel either important (if they are narcissists) or appreciated (if they are autists).

>>10090014
Did decent on numerical analysis, considering I forgot we could use a cheat sheet entirely.

>>10090014
on my way to analytic/coordinate geometry test. Damn I hope I don't fail again, I know how to solve all problems I just can't write all down in time.
Edit: I'm sure I passed with 100% ok answers.
He put 4 problems instead of 6 so I finished and even had time to do a wizard solution. I'm sure I'm getting back my grades.
>>10090279
FUCK I HAVE 7 HOURS OF PHYSICS A WEEK BECAUSE I'M STILL IN THE COMMON BRANCH FUGGGFF

>Edit:

>>10095015
I tried to send this in the morning before the teat and it failed kek

I'm trying to understand differential forms. I get Garrity's explanation in "All the Mathematics You Missed" as far as it goes. I've been trying to work through chapter 6 of Hubbard & Hubbard, but I guess I am too brainlet. Munkres was even worse. Should I look at Spivak's Calculus on Manifolds or is there something with better intuition and examples out there?

>>10095425
I liked Dan Piponi's explanation
http://yaroslavvb.com/papers/notes/piponi-on.pdf

>>10095425
Cheer up, they are what they are. They are a mistical tool with applications, don't go crazy over them.

>>10090014
I actually nailed my engineering-math exam last semester. Straight A. No Idea how I did that, my professor did an amazing job at teaching tho.

>>10090014
>algebraic topology midterm
>it's another infinite torus question

>>10095453
Thanks fren

>start getting invited to seminars
>get to larp as a real mathematician even though I'm just an undergrad brainlet
sometimes life is comfy

Everyone failed the midterm. Yikes.

>>10090014
I'm grading them right now. Terrible. I don't even know what grade to give since so many people failed so much

>>10095647
>I don't even know what grade to give since so many people failed so much
just grade everything objectively based on the solutions
your professor will adjust the grade distribution manually if necessary

>>10095656
Nah I think I'm supposed to be the one doing the adjustments.. The prof seemed to be hinting at that.
The good thing is, since I made the test so "hard" (or so they thought), most students only did the computational part, which is very easy to grade (read the first and last lines)

Is there a category theory notion that unifies the ideas of normal subgroups and ideals of ring(-like) objects? They're both sub-objects that act somewhat like the additive identity, and I feel you should be able to formalize that.

>>10095737
kernels of quotient maps, whenever that makes sense ?

>>10092925
is she hot?

How do I get good at analysis. My intro to analysis class is fukin my ass hole hard and I am so confused by it.

>>10095936
What book are you using?
You should muddle along as best you can, then after you have some understanding go back through Rudin to git gud at it

>>10095656
The distribution of scores is also a score about your teaching faggot

>>10095950
depends on the class imo. That anon probably doesn't want to dox himself by elaborating but if its something non-math majors or even early math majors are taking teaching may be hopeless.

>>10095647
Give them half question points for effort and shit.

Is there a way to reformulate Euler's formula for planar graphs (V - E + F = 2) so that it works with surfaces of other genus? Eg, is there some notion of "planar graph" I can use such that in a torus V - E + F = 0?

>>10096037
Yes, it's called a CW complex. The Euler polyhedron formula is a special case of Euler characteristic [eqn]\chi(X) = \sum_i (-1)^i\operatorname{rank}H_i(X)[/eqn], which is related to the genus [math]g[/math] via [math]\chi = 2- g[/math] for closed compact orientable [math]2[/math]-manifolds.

>>10095954
If you don’t set the prereqs or the school!s admission policies, you have to work with the material you’re given.

>>10095737
Both normal subgroups and ideals are exactly the subobjects that arise as kernels of morphisms. The notion of kernel makes sense in any category with a "zero object", meaning an object which is both initial and terminal. (For example, this makes no sense in the category of sets). Once you have a zero-object, between any two objects there is a unique morphism which factors through 0, which we call the zero morphism. You can use this to define kernels.

There is one subtlety, and that's the fact that the kernel of a ring homomorphism (i.e. an ideal) is not necessarily a ring (by any gentleman's definition, since it doesn't contain 1), so kernels do not exist in the category of rings. They do exist in the category of modules over a ring though, which is one reason modules are nice. (They are even better: they are an abelian category.

This is all presented pretty nicely in Vakil's algebraic geometry notes, in the first chapter.

>>10096290
Not that guy but that's a very good explanation. You put it so well a baka like me was able to follow along.

>>10090825
based

>>10095944
I'm in UK so we get workbooks from the teacher. But I have been using guide to analysis by m Hart for our intro to analysis course. I imagine in term 2 we will be taught proper analysis and that'd when I'll read Rudin.

Alternatively, how do I get good at maths at the uni level. It's making me sad on how crap I'm doing.

>>10095647
Female: 85%
Islamic: 90%
Jewish: 100%
Xian: 60%
Asian: 70%
Hispanic: 80%
Black: 90%
Homosexual: 95% (only 75% for TERFs)
Transgender or gender nonconforming: 90%
Poor: 80%
Refugee: 95%
Crippled or mentally ill: 85%
Straight cis-gender white male: 50%

>>10096814
>Xian
what's that

>almost everyone failed the test
>professor gave a 20 point curve to everyone, average is now a 70
>test grade is now 120
thanks brainlets

>>10096827
https://www.urbandictionary.com/define.php?term=Xian

>>10096832
Exact thing happened in my CS classes

>>10095954
Yeah, it's a class for 2nd year math major, so their writing is mostly bad. Moreover the test was a bit too long for the allotted time, so many rushed and made stupid mistakes along the way.

They are good kids and competent but I think I pushed them a bit too much with this one heh. Thank god it is not that big a part of the final grade

>>10096840
why was this deleted

>>10096878
Because you touch yourself at night.

>>10097156
That’s a lie. I’ve been a good boy everyday.

Can I give a lemma without proof if it really is incredibly obvious? Not like the
>proof: think.
meme, I mean it's literally just a straightforward calculation.

>>10096832
This is why you change the grad scaling instead of curving

I fear the future

>>10097200
>Can I give a lemma without proof if it really is incredibly obvious?
Yes, but just make sure that you explicitly state you're omitting it because it's just a simple calculation with no tricks.
Nothing's worse than that guy who writes
>skipped cuz obvious lol
on everything and each time it takes 2 days to figure out why it's obvious.

>>10097200
if it's so straightforward, why not take the two lines to write it?

>>10097305
What is it about math that causes these situations? No one has problems learning basic chemistry or biology or history or writing, why is rudimentary math seen as such a hurdle? Is it the comparative rigidity of the "rules"?

>>10097322
memorization vs application

>>10097325
I just don't understand. These people can't be that dumb (if they are I can't imagine how dumb someone who can't get into college is). At least when stem people are bad at writing you can blame a lack of creative, subjective skills, but no one is unable to follow rudimentary logic, right?

>>10097322
It's because college prioritize mindless usage of formulas rather than understanding the damn thing. Those sons of bitches lectures.

Looking for a picture I’ve seen on /sci/ before
It’s basically just a flowchart for how to into math with different books and subjects

>tfw you prove a result but don't use all of the conditions of the premise
>tfw you know they're all necessary
>tfw don't know why

>>10097350
Post a sketch of the proof or the theorem here. We might be able to ease your fears.

>>10097350
Probably used them implicitly.

>>10097305
>they call the quadratic formula "abstract algebra"
Hoo boy.

>>10097592
This was indeed the case

>>10097305

>>10090139
A number of sick strata have saved me, and not all of them entitled unprecedented amounts of physical effort;it was all a matter of experimentation in which case it required unprecedented amounts of thought
>sweet spots
Find a location you study best in
Ironically I study best outdoors/public places because I feel like I have to look like a good boy and not some slacker so it was more playing to insecurities
>sleep schedule
Don't sleep when you feel tired, sleep so that when you wake up you feel awake, else you aren't sleeping right, but sleep consistently and you'll squeeze 2-3 more active hours into your day, and that could be for business or leisure
>pray for a good lecturer
To my experience a good learner is interested or determined, but a good lecturer knows his to present material, and leaves a ton of practice material or has the resources on hand, some of the best lecturers I've ever had had me writing notes furiously or drilled me enough that the study time I had to devote outside of class was mainly devoted to classes with more subpar lectures, note formats, or traditional drilling courses like the ones where they force you to do basic algebra fast by hurling problems at you until you're quick at them

In the end it boils down to psyche and how much thought you put into how you learn is arguably more important than bruteforcing via flashcards or reading the particularly painful portion of a textbook

>>10096878
Code monkeys belong in the >>>/g/hetto

>>10095647
Are you going to curve it? What class did you teach?

>>10097320
it is obvious, but you have to use transfinite induction and Zorn's lemma in two different ways, and just thinking about writing that all down just gives me a headache

>>10097344

Sorry if I sound like a retard asking for this but how do I find the complete solution to an easy partial differential equation ?

>>10098253
Unironically guess and check

>Nobody in class finished the test on time

>>10098259
>class of brainlets

>>10094965
>Doing homework
>Feel like an expert
>take test
>Feel like a brainlet

>>10097350
>>10097636
literally just did this on an exam, i was fucking flipping out the entire time since it was the first problem and when i finished the exam i went back to see how bad i was fucking up and i realized one of the things i'd always taken for granted in topology was not actually true for general topological spaces
turns out it was true for hausdorff spaces, which was the condition i hadn't used. but man i was lucky i saw that, cause proving hausdorff spaces had that property was the more meaty bit of the problem. there's a chance the prof would just assume "oh it's hausdorff so he must know that property holds" but most likely i would have been buttfucked

>>10098253
probably separation of variables or some fancy factorization trick (like with the 1d d'alembertian)

>>10097344
>>10098137
Be warned that many of these charts are memes. This one looks like it could be ok, but don't follow any guide religiously. For example, Apostol is a questionable choice for an intro to calculus if you just want examples or the knowledge of how to "do" calculus like you would need for physics or something else.

Books on proofs might be ok, but my preference (at least the way I learned things) is to pick a more beginner-friendly book on some other more specific topic like abstract algebra, so you can get to the point quicker, rather than proving "obvious" things for a while.

Axler is a "controversial" choice for linear algebra, since he bends over backwards to avoid determinants. A popular "conventional" introductory book is Hoffman and Kunze. This could also function as a good "first rigorous math" book.

Dummit and Foote is also a pretty thick book for a first course. Personally I have a hard time sticking to a book that long and daunting. This is good as a reference as you go into more specific subjects, but you might want something lighter to start off, so you can get a feel for what makes the subject interesting without getting burnt out. Honestly I'm surprised this guide wants you to read this and then Lang's Algebra, which seems very redundant.

After that, keep in mind these things don't have a specific order. Linear algebra, abstract algebra, analysis, and point-set topology don't really have an order you need to follow. Each will get motivation and examples from the other, but in theory you can learn them in any order. (One exception: learning point-set topology without a first semester of analysis would be difficult, since most of the abstract ideas in topology are meant to generalize concrete things in analysis.)

A last word of advice: I like short books: Sarancino's abstract algebra, Fulton's book on curves, Atiya & MacDonald's commie algebra, Serre's "A course on arithmetic", etc.

>>10098281
>Dummit and Foote is also a pretty thick book for a first course. Personally I have a hard time sticking to a book that long and daunting.
It's all in your head. You can make the book less intimidating by dividing it into many small parts and focus on understanding the small parts one by one. It's easier to turn a wheel by 1 degree than turn it by 180 degree.

>>10090014
i showed up late, but actually could of used those extra like 5 minutes

but then again thats usually true in exams anyways that you need to use every last minute in the most valuable way possible !!!!

>tfw freshman in Computer Organization course
>tfw all of the juniors in the course are struggling with fucking Boolean logic of all things

Thank God I had credits transfer in from high school and am overloading, otherwise I'd have to stay all four years at this place

>>10098564
>Taking the CS Computer Organization and not the EE/CpE Computer Architecture class

You fucked up. Computer Organization shouldn't be teaching Boolean logic or basic gate constructs in the first place.

>>10098536
I'm aware of that since I finished a two-semester sequence using nearly all of it. But it sounds like the person asking for this was trying to self-study, and 1000 pages is a lot to sift through if you've never seen the subject before and you don't have an instructor to guide you.

>only did applied maths in high school
>taking linear algebra in college
no words can describe my suffering

>>10098651
>only took applied
>got into college
???

>>10098651
Linear Algebra can be a real bitch, but enough study it'll click sooner or later so don't sweat it.

>>10098652
Europe needs to be glassed

>>10098664
>The UK* needs to be gasses
FTFY

Is there a point in taking a course in algebraic geometry if I have no interest in number theory?

>>10098878
String theory,statistics algebra,Model theory and Quantum mechanics use AG.

How long should it take to learn the entire game theory syllabus for this exam to the point where I can score 90%, assuming limited prior knowledge of the content? I have three weeks where I can go absolutely balls deep in exercises

>>10090014
I messed up my diffeq test, expecting a ~30% result. Now that I have an idea for what kind of test it is I'll do better with the end-of-semester re-do though.
My applied analysis test went somewhat better but my mistake there was overconfidence, should've went in order of difficulty, didn't have enough time in the end.

>>10090089
>>10090121
>>10090150
>>10095480
>>10098549
>>10098920
Jesus Christ, I'm surrounded by brainlets.

>>10095495
Wait until the imposter syndrome sets in. I used to attend seminars but I got too busy with my coursework and fell behind. Eventually I just felt embarrassed to show my face there. I've graduated now and want to get involved again and do grad school with these people but I can't help feeling ashamed. Feelsbadman.

>>10090014
>take a course on theoretical CS, about turing machines and computability, really interesting imo
>most of the course point are on some gay practical programming project

Last time I'm advertising my own thread but: If you're interested in introductory commutative algebra, take a look:

>>10090674
>>10090674
>>10090674

>>10099004
Sorry Anon, I'm not at that level yet. Give me at least 2 more years to catch up.

>linear II exam yesterday
>orthogonality, question on normal equations
>forgot if I needed to make matrix A have orthogonal or orthonormal columns
>still get the wrong x values every time
This man understands that adversity and existence are one and the same

>>10091903
d isn't even a polynomial

Went rather poor. Manged to get all the proofs done correctly but fucked a calculation on 2 computational problems which brought me from above the average to below. Wish partial credit was a thing.

Never put that shitty edition ever again. Holy fuck the amount of fucking high schoolers in this thread

Is it possible to have a number with exactly 3 distinct real roots?

>>10099222
how can a number have roots? It's not a tree nigga
>nice digits

>>10099222
No, because roots are on a circle in the complex plane, and each root is evenly spaced out on this circle. This circle only coincides with the real line twice so you can have at most two distinct real roots.

Can someone help me out here with p-adics. I'm trying to follow some langlands bullshit and at one point it says:
Let F be the p-adic rationals
Let O be the ring of integers of F (the associated p-adic integers)
Let P be the maximal ideal of O (this is just p multiplied by the p-adic integers)
....Then |P/O| is some power of p???

Why is it not just p? How can it be any power of p other than 1? Surely I just get the values 0 through to p-1 when I take P/O, how can I get anything more?

>>10099387
>Surely I just get the values 0 through to p-1 when I take P/O
Why?

>>10099387
>I'm trying to follow some langlands bullshit and at one point it says:
Post the page

>>10098662
at least it's not DiffEqs where it's just like pic related

I get that groups have just the necessary properties to represent symmetry or something
But what is the point of rings? Why were they created?

>>10099218
Undergrads are part of our little community too anon. We must give them a voice from time to time and exam season is the ideal time for that.

>>10099558
Because sometime you want to pretend you're in [math] \mathbb{Z} [/math]. (To be honest I find your question very odd. I think about these things in a very different way.)

>>10099149
> 1/3 *x^-1 + 5 isn't polynomial
???

>>10099596
Yes, exactly. If it doesn't have integer coefficients, it isn't a polynomial. Inverse might be one tho.

>>10099562
There are only like five people who aren't undergrads in this thread, anyone who says otherwise is kidding themselves

>>10099558
Rings historically came first, abstracting commonalities between the integers, matrices, and polynomial rings.

Abstract algebra itself didn't really exist until around a century ago. The way it's taught today makes it seem like groups would have been conceived of first, being simpler in structure. But the structural properties we require for them were originally motivated by analogous properties of the integers. The algebraicists at the time weren't interested in studying algebraic structures in their own right, but in things like systematically solving polynomial equations. The search for a quintic formula is what ultimately led to our modern notion of a group through Galois theory.

>>10098973
Computability theory by Cooper is great. You want to see computability from a mathematical perspective not some lame theory of comp shit.

>>10099387
for F = Q_p, O/P is F_p, but for finite extensions (which would still be called p-adic fields) you might get a finite extension of F_p

How do I be successful in Real Analysis if I have a terrible memory? My prof probably thinks all the definition and theorem reciting questions on the exams are freebies, but that’s just not how I’ve succeeded in math classes before. I mean, I did pretty well in abstract algebra but it was less focused on this sort of memorization task.

Should I just train myself for rote memorization? I’ve never been able to learn math this way. Always just by doing it until it makes sense.

>>10099697
How many theorems and definitions have you possibly covered that this is an issue?

>>10099697
You will never be able to get ahead in math if you are not able to remember definitions and assimilate new concepts.
If you cannot remember the definitions in real analysis, that is just because you do not understand them well enough. Definitions model real phenomena. You should relate these definitions to the intuitive notions that lie underneath.

>>10099697
Get Out multitask hell
https://medium.com/thrive-global/what-all-that-multi-tasking-is-doing-to-your-brain-and-memory-ed55b0848027

>>10090107
lol try combinatorics babby

I'm working on my final proyect for a course and I'm relating this course with some topics that I'm interested in but it's getting super long (It's going to be about 50 pages). Is the prof even going to accept it? Should I edit out the more niche topics? Or is it good because it shows that I'm interested in the course?

Hi brainlet here.

Since, [math]e^{\frac{2πi}{n}}[/math] is a root of unity, Is [math]e^{\frac{πi}{n}}[/math] a root of unity too? Or does it have to equate +1?

>>10099756
>Since, [math]e^{\frac{2πi}{n}}[/math] is a root of unity, Is [math]e^{\frac{πi}{n}}[/math] a root of unity too?
* Since, [eqn] e^{\frac{2πi}{n}} [/eqn] is a root of unity, Is [eqn] e^{\frac{πi}{n}} [/eqn] a root of unity too?

>>10099760
It looks worse now.
Anyway, no.

>>10099409
Because the elements in O are any number which doesn't have a unit part, the elements in P/O (I actually meant O/P) are just 0 or any unit (1 through p-1)

>>10099655
I think I get you. So I could have a p-adic field which is, say Q_5 along with the quadratic extension of (x^2-5)? At which point the algebraic integers are Z_5 + sqrt(5) Z_5 ? So the maximal ideal here is (I think) 5Z_5 + 5sqrt(5) Z_5 and O/P is....isomorphic to Z_5^2 so its order is a power of p. That does feel right just checking this is what you meant. Thank you.

>>10099761
Thank you. Excuse my autism. I meant to type pic related.

>>10099756
Try n=3.

>>10099756
Yes. If e^x is a primitive nth root of unity then e^(x/2) is a primitive n/2th root of unity

>>10099765
Tbqh I won't arse myself to use Latex for anything less than integration.Literally just write exp(2πi/n), or exp(2 pi i/n) if using pc.

>>10099697
What real analysis are you talking about? Like first year undergraduate ones?
I know that feeling, every course has at least 50 important propositions and might even not make all that sense. And the thing is, after you have given the exam and studied things build upon it (or more general), it will seem trivial and indispensable. But right now your job is to get through it, to adapt to the language, solve the exercises and review the material few times.

>>10099765
>>10099771
is this a new version of LaTeX?

[math]e\times p(\frac{2\pi i}{n})[\math]

>>10090014
i am on the brink of death

>>10099791
Now that's old.
OPTIMIZATOR, WE BELIEVE IN YOU.

>>10099639
thanks, looks exactly like what i'm looking for. Sometimes I wonder if uni is even worth it if some of my courses are being half-assed like this. glad I can get some good recommended readings on here.

FUCK WHY IS SHOWING SURJECTIVITY SO HARD

an explicit form for the inverse is not possible with the morphism I'm working with in general, I think, so I'm struggling to derive a contradiction from the existence of an element outside of the image

>>10100212
>an explicit form for the inverse is not possible with the morphism I'm working with in general
Which morphism?

>>10100219
I can't say I'll dox myself

Does a notion of a matrix (as in a representation of a linear transformation) make sense for vector spaces other than F^n?

>>10100226
Really doubt you will. I'm kinda curious about what kind of morphism is both not explicitly subjective but still necessarily subjective.

>>10100241
>Does a notion of a matrix (as in a representation of a linear transformation) make sense for vector spaces other than F^n?
It makes sense up to vector spaces of countably infinite dimension.

>>10100241
>F^n
Is that some new-fangled way of saying R^n or are you referring to fields in general?
If the first, yes, if the second, a vector space is necessarily over a field.

>>10100241
>>10100419
F^n refers to a finite-dimensional vector space over an arbitrary field. He's asking if matrices still make sense without a finite basis. The answer is sort-of: if you have a basis indexed by the set A then your "matrix" would have a row and column for each element of A, where each row contains only finitely many nonzero elements. For a countable basis you could imagine drawing it out with "..." in either direction. For an uncountable basis the concept still works but you can't really draw a nice picture.

>>10100431
You assumed the amount of dimensions is countable.

>>10100439
My mistake, a thousand apologies.

>>10100439
Where did I assume that? The data of a linear transformation [math] F^{\oplus I} \to F^{\oplus I} [/math] is a map [math] F \to F^{\oplus I} [/math] for each element of I. Since a map out of F is determined by where 1 goes, this is the same as an element of [math] F^{\oplus I} [/math], which is an element of [math] F^I [/math] with finitely many nonzero entries. The "composition law" for matrices still works as well, since each sum involved has only finitely many nonzero terms.

https://en.wikipedia.org/wiki/Generality_of_algebra

>>10100212
showing surjectivity outside of contradiction is usually a constructive proof... i get your feel tho, very much

>>10100212
It usually falls into the realm of existence proofs, which is the hardest type of problems.
There is no reason to think it would not be hard.

>>10100212
Just give an element of the preimage mapping to any element. Surjectivity is easy.

Failed everything. Im gonna kms

>>10101242
>an explicit form for the inverse is not possible with the morphism I'm working with in general, I think

Brainlet here, if we have an F-algebra is there always a copy of F sitting inside of it?

>>10101714
>Brainlet here, if we have an F-algebra is there always a copy of F sitting inside of it?
No.

>>10101714
no, consider Z/nZ as a Z-algebra

Hi Hank. Im doing machine learning, real time systems and some front end programming. Need to review LA, probability and stats and information theory. I can understand the machine learning materials as I read them but I feel like I get lost in the abstractions sometimes. That's why Im reviewing what I listed

>>10101714
if the algebra is over a field and unital, you can always assume that the field is fixed by any algebra homomorphism f (since for any element a in F is taken to f(a)= af(1)=a) hence, not only do you have a copy of the field F, it stays invariant under homomorphisms.

>>10101728
Z isn't a field though

>>10101741
Aw, excellent. A ring in my world is a ring with unity so it looks like all is well.


Who do I believe?

>>10101759
>Who do I believe?
Fuck, that was my original post before I noticed Z wasn't a field.

>>10101759
>tfw in my ring theory class rings do NOT have 1 or COMMUTE

Matrix operation an linear system equations saved my ass. I'm pretty sure that it's thanks to them that I'll pass, even if it’s with the smallest of marginals.

>>10101774
>do not have one
That's part of the definition.
>commute
That isn't.

>>10101788
95% of classes you go to, they actually both are part of the definition.

>>10101798
>95% of classes you go to, they actually both are part of the definition.
Which school for brainlets do you go to?

>>10101800
a school that doesnt just have intro to rings class and that's it

>>10101798
If you require rings to be commutative you lose the cute definition of an algebra being a vector space that's also a ring

wtf Lang's Basic Mathematics is actually a pretty good book.

>>10101759
>>10101741
forgot to mention (it was implicit), but the fact that a k-algebra contains k also follows from the fact that any homomorphism from a field to a non-zero ring must be injective since a field has no nontrivial ideals

>advisor asks me to find a simpler proof of a restriction of a theorem to a specific case
>can't figure out how to do it without proving the general result first
life is suffering

>>10101894
additionally
>tfw its sunday afternoon and you're still fucking stuck on this

>>10101733
>LA, probability and stats and information theory

https://www.wiley.com/en-us/Elements+of+Information+Theory%2C+2nd+Edition-p-9780471241959

http://sgsa.berkeley.edu/current_students/books/