/sci/ - Science & Math

first

>>11829106
second

>>11829106
third

>>11829106
fourth

benis
Seeing OPs pic, anyone happen to have access to Joyce's complex geometry course videos?

>>11829181
damn, can´t do induction anymore

For any one with a masters/PhD, how strong are your basic problem solving skills. Like can you pick up any undergrad basic calc (Stewart-like) or LA (Strang) book, open to random page, and do any problem?
I have a mental block when studying that if I run across a hard problem out of like the 150 at the end of the chapter, I halt and cannot move on. Self-study is hard. Tips on powering through?

Brainlet here.
Can someone help me with this?

>>11829284
what is this circle operation

>>11829278
>For any one with a masters/PhD, how strong are your basic problem solving skills. Like can you pick up any undergrad basic calc (Stewart-like) or LA (Strang) book, open to random page, and do any problem?
No.

>>11829292
Composition of relations.

>>11829278
>Like can you pick up any undergrad basic calc (Stewart-like) or LA (Strang) book, open to random page, and do any problem?
Probably. Definitely for Stewart, Stewart does not have hard problems in it. Sometimes elementary books have wacky sleeper problems in them that need a trick to finish, but those make up like 1% of the book.

You're expected to be teaching that kind of basic stuff while you do your PhD, you're going to run into trouble if it's not literally completely automatic.

>>11829284
Go reread the definition of relation composition until you understand it. This will take one line once you do.

>>11829278
Can you do these?

>>11829313
>You're expected to be teaching that kind of basic stuff while you do your PhD, you're going to run into trouble if it's not literally completely automatic.
Lmao this happened to me when I was tutoring people. I'm glad I had the solutions.

>>11829333
Tutoring is one of the best things I ever did, honestly.

>>11829337
What did you like about it? I hated it. Hopefully the feedback was so bad I don't have to do it again.

>>11829173
You're mathematician dude
Now do the average IQ of mathematicians, physicists, engineers even

>>11829341
I just like helping people understand concepts that they couldn't get before. Seeing them have those 'click' moments was innately satisfying for me. It also allowed for me to better engage with the material, since being able to do it and being able to teach are two different things, so I felt like I had a better understanding after teaching it. Lastly, it paid better than most alternatives at the time.

>>11829348
Average IQ of engineers has unironically got to be in the double digits.

>>11829278
Strang's book is shit
Nothing else to add

>>11829358
Name a better alternative, then.

>>11829349
I get what you mean by those click moments, they are nice and seeing people understand stuff is really motivating as the teacher. The opposite is true, also. Out of the 40-50 human shaped things I was teaching, only maybe 3 showed any signs of life and interacted. The rest were complaining that I don't answer their questions, which is true in the sense that I can't read anybody's mind so I can't just answer unspoken questions. Ironically, people who(se parents) are paying for the studies were less motivated to learn anything than 8th and 9th graders who went to a free public school when I was teaching them during my master stuff back home.

>>11829369
It probably helped that I was working with a university. So the kids I worked with were a lot more serious and willing to put forth the effort into the material. Even the ones who struggled the most gave very little resistance when it came to actually learning the material and putting forth effort. I'd probably never do it for an average public school because, while there are undoubtedly good students there, I know a lot of those kids could not care less about the material and it just ends up being both a waste of my time and theirs. I also don't have any sort of formal pedagogy training, so I wouldn't even know where to begin with students like that anyways.

>>11829387
Sadly, I was in a uni as well and they were 2nd year students.

>>11829313
OK thanks. It seems like the examples I had in class were the most cherry picked easy examples. Anything that was difficult the professor kind of stumbled through and made some leaps in logic that were hard to follow (granted, this was at a community college).
The book I used was Larson and they had some Putnam problems that I found impossible to do although this was probably more due to me not cranking through hundred of problems in pre-calc.

>>11829362
Friedberg, Hoffman and Kunze, Linear Algebra Done Right. Strang is a meme if you want to do any serious mathematics. Only engineers and other computation-oriented students should use Strang

>>11829362
No idea, I just used one from my uni. I just didn't like how Strang went about things. Random examples and tangential comments, it's a mess of a book.

>>11829420
Strang also has (or had, maybe fixed in an edition newer than the one I used) a terrible habit of just freely using terms, sometimes in nontrivial ways actually involved in the mathematics, several chapters before he defines them
Doing that kind of thing is poor form in material intended for graduate students, it's totally unacceptable in a book intended to be read by freshmen.

>>11829427
Exactly. His OCW classes aren't that much better either. It's just badly set up, I was in shock after how often I saw them recommended.

>>11829278
I teach calculus out of Stewarts book. I can do most problems off the top of my head, sometimes I have to think for a minute. The problems plus sections at the end of the section can be fun, and sometimes require thought. As for linear, I could probably do pretty well, but it has been a while since I solved computational linear problems. I did a grading gig for the proof based linear class last year. I could do some of the homework problems off the top of my head, but not all. The best advice I have for you is to think about the problem you just did. A lot of difficulties my student have is that they do a problem and then just move on, they don't about the steps they just took and try to generalize. Change the numbers and do it again, change the numbers to arbitrary letters and do it again. If the algebra is tricky, you just have to bash more, and get used to it.

>>11829284
What are you stuck on?

>>11829387
Tutoring highschool students is easy but lame. They dont give a shit but the material is easy enough. You basically babysit them for an hour.

>>11829284

Study this book.

>>11829497
The thing with pre-uni students (high or elementary school) is that you have to make sure beforehand they actually care enough that it's even possible for you to do your job.
A lot of times tutors are hired by parents for kids who are failing not because they're struggling but just because they don't give a shit without any input from the kid. Then when you show up it's like trying to teach a sack of potatoes since he's not even interested in looking in the rough direction of the page, which isn't good because the parents will then blame you when he keeps bombing his tests because he doesn't give a fuck.

>>11829490
So, the diagonal of the Cartesian product, X x X, will be all pairs (x,x), right? I'm not sure where to go from there, though.

>>11829573
do you know what composition of relations means

>>11829576
It forms a third relation from two already existing ones, right?

Like if A = {0,1} and B = {2,3} then A o B = {0,3}.

>>11829583
>It forms a third relation from two already existing ones, right?
Yes, but how?
>Like if A = {0,1} and B = {2,3} then A o B = {0,3}.
No
please go read the definition

[math]\sum{\mathbb{R}}=0[/math]?

>>11829610
[math]\zeta(-1)=\frac{-1}{12}[/math]

I understand why all parallelepipeds P have the same volume. But why does the argument (underlined in red) uses a ball here?
I don't really get how it's related to proving that they all have the same volume.

>>11829610
>>11829634
can't into mathmode :|

>>11829610
The reals are uncountably infinite, what makes you think you can add all of them together?

>>11829681
Not him. But isn't summing all elements of Z causes fucked up things, such as when you arrange them in a different way, you get a different sum?
Can you do the same for integrals from -inf to inf?

What is the most efficient way to study textbooks? I feel copying a bunch of stuff onto my notebook is incredibly innefective. If it's a book I got from a library I can't make annotations on it, either.

Just realized there's some voice recordings of Grothendieck online,

here at 18:05
https://youtu.be/LFV4FpfdwEw?t=1085

>>11829701

>>11829610
nah [math] \sum \mathbb{R}=\mathbb{R} [/math]

>>11829700
Read each line over until you understand it. When you finish a paragraph, take notes on it. Focus on doing the more challenging examples over the trivial ones.

>>11829700
Try the Feynman method if you have time. That is, try to explain a chapter to an imaginary audience. You will have a vague feeling which part you don't truly understand.

Is combinatorial geometry a thing?

>>11829719
Of course! First and foremost algebraic topology used to be called combinatorial topology but, you know, algebra=difficult=cool so yeah we are stuck with AT for now. There is also discrete differential geometry, and graph theory might also fit what you have in mind.

>>11829700
Make examples of definitions, remove assumptions from theorems and make counter examples, add assumptions to theorems and look for simpler proofs. Are you doing the exercises? Also this >>11829717 is great.

>>11829719
is google a thing?

>>11829731
Yes, why?

>>11829667
The sum of the volumes of the translate parallelepipeds is given by the volume of the fundamental parallelepiped chosen times the number of elements of the lattice in the ball(which independs of the parallelepiped chosen). As the ball gets arbitrarily large, this number gets very close to the ball's volume. However, this is true for any choice of fundamental parallelepiped, so they need to have the same volume.

>>11829292
no you fool its 4 the answer is 4. every pleb with a bachelors knows the answer is 4. it doesnt even matter what the major is. english lit faggots with a bachelors know the answer was always 4

>>11829728
>Are you doing the exercises?
Planning to. I'm not following any textbook strictly right now because I have some more immediate things to attend to, but my goal with textbooks is doing them cover to cover, so exercises are a given. Growing up I wasn't the studying type, but now I'm trying to take the reins of my own learning.

Is there any guide with useful bullet points like "remove assumptions from theorems and make counter examples"?

>>11829711
So simply attempt to sum up each paragraph instead of straight away copying it?

>>11829727
I was looking at this problem and its followup papers in recent years:
https://en.wikipedia.org/wiki/Happy_ending_problem
It's combinatorial geometry, isn't it? I wasn't entirely sure, sorry.
>>11829731
Well, apart of a few books and some courses with closely related titles, I feel like no one actually works on it anymore. Take a look at all scholar profiles with the combinatorial geometry label:
https://scholar.google.com/citations?view_op=search_authors&hl=en&mauthors=label:combinatorial_geometry&before_author=IgR6__sBAAAJ&astart=0
There are like < 30 people who have been working on it, including older people like Ronald Graham.
So I was thinking that people call it with a different name now.

>>11829745
That's what I do. It's actually a technique that I adopted from reading philosophy texts, but I found that it translated well to maths. The biggest takeaway is that you can't read a textbook like you would a normal book and advancing without having a really good understanding of each bit is only going to hurt you.

I'm currently reading this book and I was doing alright until I got to factor groups.
Lads, I think I might be a brainlet...

>>11829755
If you don't understand an abstract definition take a look at examples of its applications. In your case check how representations of factor groups look like.

>>11829755
Consider the groups Z and 12Z, and then consider your alarm clock and its face.

Between the west coast and the east coast of the US, which side has a stronger Math community?
What about the mid west?

>>11829774
>Math community
lol. Place doens't matter honestly as long as you find a dedicated thesis advisor to work with.

Senior undergrad here.
Is learning about elliptic curves outside of my scope or are there some good introductory texts than an undergrad could grasp?

>>11829774
Princeton > *

>>11829745
I wouldn't say there is a guide. In general when there is a theorem in a book with assumptions A1, A2, and A3 with conclusion C, there usually will be a situation where A1, A2 are true and C fails. And you can figure that out by finding a counter example. Theorems in books rarely add unnecessary assumptions. Coming up with these counter examples will help you remember theorems more, and your intuition when solving future problems.

>>11829797
look at the thread from Sunday, this exact question was discussed

>>11829719
Yes, there are plenty of things that could qualify as combinatorial geometry

>graph theory
>geometric group theory (especially for discrete groups)
>tropical geometry
>toric geometry
>invariant theory
>homotopy theory in some sense

>>11829800
Ok, I think I understand what you're saying. If my memory serves me right, there were counter examples in Spivak's first chapter. That was my first encounter with more rigorous math and I realized I wouldn't be able to make the most out of the book if I didn't have a better background first, so I was recommended to do a book on proofs, which I haven't begun yet due to time constraints. I imagine the counter examples you speak of are the kinds done in proofs, especially since you mentioned assumptions in theorems.

Sorry if I misinterpreted something, my background in more rigorous math is null.

>>11829808
Will do.

>>11829797
no, it is not outside your scope

>>11829634
>>11829699
[math]\mathbb{N}\neq\mathbb{R}[/math], nor is [math]\mathbb{N}[/math] a field.
>>11829681
Is this a redundant question to ask? As far as I am in my studies, isn't this implied by the properties of all fields? Keep in mind my book requires additive inverses/the additive identity property for fields.That is, where [math]\mathbb{F}[/math] is any field, [eqn]\forall x \in \mathbb{F} \exists (-x)\in \mathbb{F},x+(-x)=0[/eqn]
[math]\mathbb{R}[/math] is a field, so all elements must have an additive inverse. Then... shouldn't the sum of all such elements equal zero? Even though [math]\mathbb{R}[/math] *is* uncountably infinite.

>>11829749
Google scholar is a pretty crappy resource. I wouldn't put too much faith in conclusions drawn from it. For example Karoly Bezdek isn't even listed in what you posted and he's a very big name in the field (enough that I know him and I don't even work in it).
You'll also find it often (I think more often nowadays) called discrete geometry, and there's also geometric combinatorics which conveys something a bit different in flavour but is extremely alive (there are a lot of people working in it right now and most of them are young). This isn't what you're referring to, but there are also multiple different ways you can use combinatorics in algebraic geometry, and that mixture's really only a couple decades old at the very most.

To be fair I'm not sure how popular those classic Erdos style points-in-the-plane autism puzzles still are, but there's a lot more people do than just those.

I love math so much, bros.

>>11829868
gay.

>>11829814
I see. If you are giving a counter example you still have to prove that it shows what you are claiming.

>>11829810
>>11829856
Thanks. All of those you posted are definitely related.
I will take a closer look.
>To be fair I'm not sure how popular those classic Erdos style points-in-the-plane autism puzzles still are, but there's a lot more people do than just those.
Not a lot. Well they are mainly just recreational math that some people do in their pass time.

>>11829739
Thanks anon. That makes sense.

When speaking about cohomology of sheaves, what does [math]H^k(\mathcal F)[/math] represent? Does it just leave the space implicit? For example, I could imagine [math]H^1(\mathcal O_X):=H^1(X,\mathcal O_X)[/math], but when seeing something like pic related, I'm at a bit of a loss

Is an IQ of 114 enough to get a B in Calculus 1 and 2?

>>11829983
>Falling for the IQ meme
Calc 1 and 2 are 90% computational. As long as you have a basic conceptual understanding, put forth actual effort in the HW, and do lots of practice problems, you'll get at least an A-.

>>11829983
No, at best you'll get a D

>>11829983
IQ is irrelevant. It's the age that matters. After you turn 24, it's over.

Is there a proof by contradiction that there are no consecutive odd integers?

>>11829992
>Calc 1 and 2 are 90% computational.
Which school for brainlets do you go to?

>>11830031
UT

>>11830027
no

>>11829946
The Cech differential takes local data and gives localler data, and the k-th cohomology shows up as the localler data that can't be glued together into local data at the k-th step.
Sheaf cohomology is best visualized in analogy with Cech cohomology.

>>11830032
>UT
Never heard of it, good luck getting into a decent grad school

>>11830027
>Is there a proof by contradiction that there are no consecutive odd integers?
suppose n and n+1 are consecutive odd integers
then (n+1) - n = 1 is even, a contradiction

>>11830061
I'm speaking strictly notational though - in every reference I've seen, cohomology has two inputs, a space and a sheaf. But now I'm seeing just cohomology of a sheaf, or perhaps a bundle, and no space to speak of

>>11830027
Suppose there exists two odd consecutive integers and note that every odd interger can be written in the form of [math] 2k+1, k\in \mathbb{N} [/math]. Therefore there exists [math] k\in\mathbb{N}[/math] such that [math] 2k+1-(2k-1)=1[/math]. However, we know that [math] 2k+1-(2k-1)=2[/math] and so [math]1=2[/math], a contradiction

>>11830069
If the context is clear, it probably just means that the space is implied

>>11830069
Oh. He probably wants to emphasize that it's the entire cohomology sheaf.

>>11830083
>sheaf
Presheaf, actually. I think.

>>11830079
>contradiction

>>11830066
>>11830079

But doesn't the fact that an odd number is of the 2k + 1 a result from the inductive proof to begin with? Before using this I would have to also prove that I can't find an odd number that is not wriitten as 2k + 1

>>11830109
You could just say that [math]\{2k|k\in\mathbb{Z}\}\cup\{2k+1|k\in\mathbb{Z}\}=\mathbb{Z}[/math] and if [math] x=2k \Rightarrow 2|x [/math] thus the set of all odd integers is a subset of [math] \{2k+1|k\in\mathbb{Z}\} [/math] (or in other terms all odd integers are of the form 2k+1)

>>11830128

I see. Maybe I should actually read some category theory to understand this stuff ...

>>11829708
is this a mogpost

>>11830169
no
don't
don't fall for it, read a number theory book instead. if you want a fuckload of arrows get into graph theory.

>>11830185
There's nothing wrong with graph theory.

>>11828598
Any idea on how those compare to those on the >wiki? Or to vector geometry?

>>11830193
I didn't mean to imply that. Graph theory is vastly underrated, I wish there where more cooperations between analytic geometers and graph theorists.

>>11830185

my problem is more philosophical than anything, I want to know how to understand foundational stuff that can't be proved how my autism wished they could

>>11829835
For one,
if I desperately try to make your idea of "pairwise cancelation in successive addition" work, I must first order the positive reals, i.e. find the uncountable ordinal of cardinality [math] | {\mathbb R} | = | 2^{ \mathbb N }| [/math].

>>11830027
I doubt there exists a proof of something this basic that's actually a real contradiction argument. Assuming n and n+1 are both odd and then proving from scratch that at most one of them is odd is not a contradiction, it's just wasted breath. You could just as well delete the contradiction and the proof would still work.

>>11830197
What do you mean? Just download them from libgen and check them out

>>11829284
>>11829500
i learned from this too but honestly i don't think it's very good. it gets very boring very quickly. i would instead reco starting a freshman level proof-based math textbook like Linear Algebra Done Right axler concurrently with "An Introduction to Mathematical Reasoning" by Peter Eccles

>>11829755
Factor/quotient groups (or any other kind of object) are rather misnamed imo. Something like gluing/relation group would be better, but I can't think of a name that rolls off the tongue.

>>11830200
Then read a book on formal logic. Category theory is a language. It makes only sense to learn if the stuff you're working on gets too complicated to write down in a "classical" way. This in particular implies that it does not make sense to devote too much time to cats if you don't already know a LOT.

I spend most of my time here, but I don't do any maths haha

>>11830270
>gluing

>>11830234
>It's a goat episode again
Oh no

>>11830305
fucking goats
how do they work?

>>11829983
It's too high to get a B. One standard deviation higher and you would probably fail

>>11830305
wew

>>11829755
Think of factor groups as declaring a certain relation in the group to be true.

For example, take a noncommutative group G and we want to consider, for no specific reason, the relations [math]aba^{-1}b^{-1}[/math] for all possible elements in the group. When we quotient by the subgroup generated by those relations, we are formally declaring that in this new factor group, the relation [math]aba^{-1}b^{-1}=e[/math] is true for all a,b in the group. In particular, [math]ab=ba[/math] for all a,b. So in this new group formed by taking the quotient, all elements are commutative.

>>11830234
First book is first year graduate level

I love this general so much.

>>11829292
In general, composition, right here it means comp of relations.
Wikipedia explains it pretty well desu.
The question is asking to prove that I is a relation where R is left unchanged under composition.

>>11830765
die

>>11830810
We all do eventually.

>>11830765
Let’s all love Lain instead.

>>11830844
dubs 'o truth, you may have my entire bounty of dubloons

>>11830930
wtf I hate maths now

How should I study combining textbooks with yt videos? I'm currently studying 8 hours a day, I'm going through basic mathematics and I expect to finish it until ~19july to start Calculus 1.

My mainly doubts are, it's better to read and practice problems, and if I don't understand some concepts, trying to go watch some prof Leonard videos? (That's what I'm doing now)

Or watch the lecture videos speed up and after that, going to read superficially and do a lot of problems? I've been improving a lot in just a week, but I'm worried if my study plan to get calculus until early September will works

>>11829769
So then one factor group would be all the times of the form 12:xx and another would be of the form 1:xx and then 2:xx and so on, and in total there would be 12 different factors?
Damn that's a really good way of explaining that.
I think you might've gotten me to understand these saucy lads.

>>11829762
>>11830270
>>11830380
Thanks lads. I had lost faith in /mg/ after encountering an anime posting bully, but now I'm feeling good about this thread.

>>11830994
Shut up.

>>11830998
y-yes ma'am,
s-s-sorry...

>>11830765
What prompted this in you?

>>11831106

How does one categorize and characterize the type of sets from different fields of mathematics? This typically becomes a major part of when beginning to learn a new field. I just realized I never understood analysis because I never figured out how to characterize, categorize and work with sets in analysis because to me it always seemed arbitrary. The moment I started thinking about this was during Analysis Yawp's lectures when he builds an open cover from open neighbourhoods and stated something like "Open sets in R are characterized by open balls". Is that always true? He does this and states every open cover is built from open balls, or something like that. How do you build sets in analysis and work with them? It always seems so arbitrary.

>tfw could understand every single proof of Rudin
>tfw couldn't do any of his exercises

Guess I'll reread Rudin again haha.

>>11831273
>>tfw could understand every single proof of Rudin
Rudin is a meme.

>>11831212
I do not understand the question.

>Open sets in R are characterized by open balls
If you know what "open" means this should be extremely intuitive.
Open *literally* means that around every point you can find a ball also in that set.

>How do you build sets in analysis and work with them?
Unions and intersections. Or differences or symmetric differences. And a million different other ways depending on the problem.

>>11831156
memelist

>>11829681
>what makes you think you can add all of them together?
It certainly is well defined, you can do sums over uncountable index sets.
IIRC it's just boring, though.

Is there a good, comprehensive basic real analysis book?

>>11831305
Rudin (unironically).

>>11831305
Principles of mathematical analysis
>>11831308
No (that book is pain)

>>11831305
Real and Complex Analysis by Rudin

>>11831156
My community college is focused more on the application than the theory. For example, my elementary linear algebra class is linear algebra and it's applications. How do I prepare for more rigorous math beginning with calculus I?

>>11830994
Basically it would be just the hours, but yeah Z/12Z is essentially the clock.

>>11831305
Three volumes of 'Differential and Integral Calculus' by G. M. Fichtenholz are a bible of real analysis (if you can read Russian, Chinese, German, Persian or Polish).

>>11830242
my man eccles taught me in first year

>>11831417
That's weird. Why is there no English translation when there is even a Persian one.

>>11831511
:something something: Iron Curtain, perhaps? Released in Soviet Union, Poland. China, East Germany...

>>11830994
in the case of Z/12Z, you can think of it as declaring that 12 = 0 in Z, so in your new factor group, indeed, 12 + 12Z = 0 + 12Z

Any tips? >>11830959

I'm 16 and speedruning ap calc bc, did the first half on khan academy in a week. I'm looking for something to supplement khan, so what's the best calculus book? Preferably something I can get on library genesis

>>11830846
Been rewatching Lain for the third time. It gets better with each viewing.

>>11830079
You’ve proven by contradiction that consecutive integers can’t both be odd.

>>11829284
i don't even know what you're supposed to write besides "it just is" ? that seems like the most obvious thing ever

>>11829755
this >>11830380 is a good explanation, but i think it can be confusing to someone new to factoring. factor (or quotient) constructions are a prominent pons asinorum in algebra, so don't worry about not getting it at first. if you understand modular arithmetic (Z/nZ), factor groups are the same, but in abstract generality. i like to think of it this way: factoring is a "gluing" relationship, that "glues" together all of the elements that have "something" in common. so in the case of modular arithmetic you take the integers and you glue together all the numbers that leave the same remainder when divided by some "n". there are only n possibilities when it comes to remainders, namely 0,1,2,...,n-1, so by gluing together the integers in this way you are left with a 12 element set, each element of which represents all of the integers that leave a fixed remainder when divided by n. in the case of general groups you take the "in common" thing to be a some normal subgroup, which you then factor out. so all the elements of that subgroup are glued to together and become the identity, and the rest of the group is mapped to certain representatives (like how the integers are mapped to one of the n remainders)

>>11830270
>>11831839
i didn't notice someone else had already replied with my analogy
yeah, "glue" group sounds kind of silly, but then again factor/quotient makes sense, you are "factoring" out the subgroup and are left with "the remainders"

>>11830200
any direct proof can be turned into a proof by contradiction: suppose hypothesis holds, but conclusion does not -> apply direct proof to show that hypothesis implies conclusion -> contradiction.

>>11831839
>there are only n possibilities when it comes to remainders, namely 0,1,2,...,n-1, so by gluing together the integers in this way you are left with a 12 element set
woops, n* element set, i must've been thinking of Z/12Z
the most basic example for factor groups are the even and odd numbers. you know from school that there are certain additive (including multiplication would make it a ring) relationships between them, right, namely, even+even=even, even+odd=odd and odd+odd=even. what you've done is you've sorted all the evens and odds into 2 sets, E and O, and now you're naturaly lead to defining addition on these 2 sets, making E+E=E, E+O=O & O+O=O. so by glueing together integers based on their parity you've produced a 2 element group, {E, O}. mathematically speaking you've factored Z by its normal subgroup 2Z (consisting of elements of the form 2n, where n is an integer), producing Z/2Z, 2 element factor group

>>11829755

>>11829610
inf-inf is undefined
any proof dependent on the order of adding is bs

>>11831280
>IIRC it's just boring, though.
a necessary condition for the sum to exist is that all but countably many summands are zero. so yeah.

>>11830063
>never heard of UT
Also, there's different kinds of calc courses; I wouldn't expect a non-STEM calc course to concentrate too much on theory.

>>11829797
https://ocw.mit.edu/courses/mathematics/18-783-elliptic-curves-spring-2019/
This seems up your alley.

>>11830032
University of Texas?

>>11829610
>>11831969
Not the question answered, but up to the jump of limit ordinals (which i don't know how to handle), once could maybe at least do something with the idea.

Let [math] b:\alpha \to {\mathbb R}_+ [/math] be a bijection between the positive reals and an uncountable ordinal [math] \alpha [/math] (this decides the continuum hypothesis, though).
For all smaller ordinals [math] \beta < \alpha [/math], define [math] s(0)=0 [/math] and [math] s(\beta+1) = s(\beta) + b(\beta) + (-b(\beta)) = s(\beta) [/math] (and something similar for limit ordinals?).

Then, in an artificial way, I squeezed all reals in a transfinite sum and we should be able to prove this is 0.

Are you guys happy with how good you are at math for your age? I'm finishing my 2nd year of undergrad and I don't feel like a failure or anything but I hoped I would be further along in my journey by now desu. I just wanna be able to read a grad-level book without wanting to bash my head in every 20 min.

>>11831622
>>11830959
>and if I don't understand some concepts, trying to go watch some prof Leonard videos? (That's what I'm doing now)

That's good, generally an efficient strategy is to try hard on the stuff that challenges you and use easier sources like YT videos only when you get stuck.
Don't spend much time passively reading theory, 90% of learning is done when you engage with the problems and try to solve them by yourself. Visit the parts of the theory needed to solve your problem and think about how they relate to it and help you solve it.
Don't feel like you must finish basic mathematics before going further and don't burn out anon, gl

>>11832161
>Are you guys happy with how good you are at math for your age?
I'm a total failure, as is expected at my age. Hence I am indifferent.

Teach me Math

>>11832129
Yes, University of Texas - Austin.

>>11832196
[math]f(\vartheta)=sin^2(\vartheta)+cos^2(\vartheta) \\f'(\vartheta)=2sin(\vartheta)cos(\vartheta)-2cos(\vartheta)sin(\vartheta)=0 \\ f(\vartheta)=f(0)=0^2+1^1=1[/math]

>>11832244
Sin?
Cos?

S-Cinco?

Two 5's - two 5's = zero?!

oh wait, thats actually right...

i'm starting a PhD this autumn
i have literally zero interest in learning any more mathematics, i'm just in it for the money
please end my suffering

>>11832260
>i have literally zero interest in learning any more mathematics, i'm just in it for the money
are you sure you didn't mean to write, you know, the exact opposite ?

>>11832260
Where?

>>11832266
Kek

>>11831156
That man probably hasn't read all those books. Regardless the first line is true. I hate lists that have you go through 3 proof books, basic mathematics and the like before you touch Spivak or Apostol.

>>11832260
>doing a PhD for the money
In the 3 to 6 years you do it, you can just as well ramp up on something you'll directly use to gain that money.

PS, money is a meme.

Why do you guys keep recommending Rudin? I read it once and it made me want to shoot myself in the head.
It's the same tier as Terrence Tao's book.

>>11832266
>>11832332
i worded my previous post poorly
i got scholarships n shit secured so i will at least earn my living, and i think doing a phd requires much less effort than a 9 to 5 job, so that's why i'm doing it
>>11832269
a mediocre university in europe

>>11832356
Europe-Europe or UK?

>>11832359
europe, the poor eastern part

>>11832362
Then I will not have a motivational chit chat with you.

>>11832353
What do you like

>>11832196
An operation is a map [math]\mu : S \times S \rightarrow S[/math].
An operation is abelian if [math]\mu (a, b) = \mu (b, a)[/math].
For example, addition is abelian, because 2+2=2+2.
>>11832260
Based bizarro /sci/ poster.

>>11832413
I dont undertand

Let's all have breakfast first

>>11832353
>It's the same tier as Terrence Tao's book.
So, god tier?

>Laplacian
>Composition
>Cartesian product
>d'Alambertian

Hey guys I just finished my undergrad with a Math major and CS+Physics minors. Although I wish I had taken the more rigorous math courses I feel like I learned a lot.
Anyways, would any of you recommend books to learn data science? I am looking for a nice mix of formalism and applied examples. Thanks.

>>11832467
>Hey guys I just finished my undergrad with a Math major and CS+Physics minors.
Congrats!

>>11832417
I've already had lunch.
>>11832439
Which Laplacian?

I don't know about you guys, but I love Dover books.

>>11832534
[math]\Delta[/math]

>>11832543

>>11832356
>and i think doing a phd requires much less effort than a 9 to 5 job
peak kek

>>11832161
I did (rising senior) but now I feel like I'm catching up. I built up an impressive amount of math immediately after high school and during freshman year but after that for two years I was averse to studying math. I think it was because of career anxiety and a massive dose (somewhere around [math] 1000 \mu g [/math]) 25i-NBOME trip (I thought it was acid) kinda fucked me up for a while. Anyway I'm back at it now and it feels nice.
>>11832543
Me too, except I hate most of them.

>>11832627
>Phoneposter
You have to go back.

>>11832543
Do you actually like the physical books?

I need to draw a shape with symmetry group Z/4Z and I don't know where to start

reposting from previous thread

I wish that more textbooks would go through more examples instead of including a thousand exercises that I don't even know how to begin solving. I understand the point of having to do things myself, but if I'm just unable to do most exercises, then I learn fucking nothing. Call me a brainlet, but if the authors bothered to go through some of the exercises first then I'd have a much better time solving the rest of them myself and would learn a lot more from the book. It doesn't help that my lectures are fucking useless.

Is there a functional analysis textbook that takes a more explanatory approach like that?

>>11832708
I'm not sure if this works, but try a cube with one face removed.

>>11832701
Yes, I have a stack of them right next to me.

maths.

If complex numbers come as a solution for
[math]x^{2}=-1[/math]

Could you define a whole new set of numbers by defining some x that satisfies
[math]e^{x}=-1[/math]

>>11832776
it's the same set

>>11832776
Unironically the same set.

>>11832776
[math] e^{\pi i n} (n = 2k + 1 and k \in \mathbb{Z} [\math] satisfies that and it’s not a new set of numbers.

>>11832776
[math] e^{\pi i n} (n = 2k + 1 and k \in \mathbb{Z} [/math] satisfies that and it’s not a new set of numbers.

>>11832708

>>11832776
[math] e^{\pi i n} (n = 2k + 1 \text{ and } k \in \mathbb{Z}) [\math] satisfies that and it’s not a new set of numbers.

>>11832708
Think of a square - it has symmetry group D_4, consisting of rotations about the centre and reflections about some axis. The rotation subgroup is precisely Z/4Z. So think of an object similar to a square that has no reflection symmetry

>>11832799
i was literally about to post this picture lmao

>>11832799
Based.

>>11832778
[math] e^{\pi i n} (n = 2k + 1 \text{ and } k \in \mathbb{Z}) [/math] satisfies that and it’s not a new set of numbers

>>11832714
Google, unironically.

>>11832814
sure, I thought of it as IR(i) in both cases

is asserting non-commutativity the only way to extend the complex to quarternions?

>>11832807
>D_4
[math] D_{4} [/math] has order 8

>>11832543
I'm low-key a whole for Dover books. They're so comfy in how they vary wildly from classics to craptastic. I love collecting them. Don't judge me, guys.

>>11832898
Whoops I meant whore. I'm a whore for Dover books.

>>11832883
yes, but for deep reasons

>>11832887
what does that have to do with anything? i specifically said the rotation subgroup of D_4, which has order 4, and is precisely Z/4Z

>>11832919
my bad misread

>>11832467
>>11832478
thank you bub

Hey lads. I've recently been studying eigentheory and fixed points, and I've noticed some very interesting patterns, so I'd like to make a conjecture: Every linear endomorphism of a Banach space has at least one fixed point.
The best I've been able to do is show that, for isometries on finite-dimensional spaces, Brouwer's fixed point theorem gives us the result immediately, since the linear isometry fixes the unit ball.
I think that the essence of the problem is framing it in its proper categorical context. Any suggestions?

>>11833043
T(0) = 0

>>11833043
>I think that the essence of the problem is framing it in its proper categorical context.
well done my friend you gave me a chuckle

>>11833053
That was fast, I was hoping for at least one shitpost before someone bothered.

>>11829362
https://link.springer.com/book/10.1007/978-3-319-91041-3

>>11832898
I wish I was enough of a richfag to collect AMS books
The physical quality of GSMs is absolute kino but anything remotely recent is like $70-80USD a piece, they're way too expensive to buy just because you want one.

>>11833084
>*pplied

>>11833091
Oh my God I know that exact feeling.
I spend too much time fantasizing about all the nice as textbooks I'd buy if I ever got rich.

>>11833091
>Why yes, I do have AMS books on Sobolev Spaces, Stochastic Analysis, and Riemann Surfaces sitting on my shelf. What made it so obvious?

>>11833103
Nice ass textbooks*

>>11833102
There's nothing wrong with applied mathematics.

>étale cohomology

>>11832898
>>11832898
>I'm low-key a whole for Dover books.
zoomer or tranny typed this, maybe both

>triple integrals

>>11833130
I'm a millenial by a few years and not a tranny.

>>11833130
Zoomers are not into math.

>>11830242
>i learned from this too but honestly i don't think it's very good.

The thing about Velleman is that it's thinly veiled book on applied classical Natural Deduction. So you can learn to do proofs on elementary set theory and other easy things in a rigorous, structured, almost formal way (I used to write them in Fitch style).

And once that 'clicks' basically there's no mystery about proofs anymore, it's just hard work (but you'll get annoyed over lazily written or disorganized proofs in other books). No doubts about contrapositives, no mistaking forall and exists, even constructive mathematics is understandable. That's the fabled "mathematical maturity" right here in book form, instead of trying to get it through osmosis.

Velleman is worth it.

>>11832916
whoah.....deep

>proof of the classification of semi-simple Lie algebras

>>11833175
Based.

>>11833175
>over [math]\mathbb{R}[/math]

How would you go about drawing the
[math]{z, e^{2 z}}[/math] transformation of this region?

>>11833238
just use polar coordinates bro

>>11833238
>>11832799

Is it normal to feel horny after solving a math problem?

>>11833244
[math]x=r\ cos(\psi) \\y=r\ sin(\psi)[/math]

>>11833255
Care to spoonfeed a bit more? Not sure how to follow. It's supposed to be a complex plane too

>>11833253
Yes.

>>11833253
no unless you are playing strip putnam

>characteristic 2

>>11833260
Sounds hot, but then again, all mathfags are male so it would be gay af

>>11833265
you just need to find the hot trannies and femboys

>>11833265
Well if you are a gay mathfag it's a win.

>>11833260
/mg/ is over, the greatest post ever has been made

>>11833270
>hot trannies
t. ranny

>>11833278
>t. new

>Infinite fields with non-zero characteristic

>>11833284
>Infinite fields with non-zero characteristic
Name one (1) example of this.

>>11833288
[math]\mathbb{Z} /p\mathbb{Z}[X] [/math] with prime
I'm pretty sure I'll fuck up the LaTeX somehow

>>11833288
[math]\mathbb{F}_3(X)[/math]

>>11833297
>writing [math]\mathbb{Z}/p\mathbb{Z}[/math] for [math]\mathbb{F}_p[/math]
this is not gigachad behaviour

>>11833288
[math]\mathbb{Z}/p\mathbb{Z}(X) [/math] with p prime
I'm retarded.

>>11833303
It's fine as long as you don't write it [math]\mathbb{Z}_p[/math]
People who use this notation for anything but the p-adic integers should be manually castrated.

>>11833288
[eqn]\overline{\mathbb F_p}[/eqn]

>>11833323
Doesn't exist.

>[math]((\mathbb{Z}/p\mathbb{Z}[X])/<X^2+1>)(X)[/math]

>>11833313
In algebra and geometry sure, but in homotopy theory and physics, no.

>>11832799
BASED

I have a 6 hour math exam tomorrow, how do I not fail it?

>>11833378
don't die in the next 24 hours

>>11833378
>6 hour math exam

>>11831663
>I'm 16 and speedruning ap calc bc, did the first half on khan academy in a week. I'm looking for something to supplement khan, so what's the best calculus book? Preferably something I can get on library genesis
LMFAO

>>11833391
Based.

>>11833388
We had those in the end of HS. Something like answering to 10 out of 15 questions within 6 hours and you would have questions from all sorts of stuff you've learned over the course of your high school career like basic differential or integral stuff, geometry, vectors, logic, number theory etc.

>>11833391
I'm a specialist on the product rule

>>11833514
For me, it's the logarithmic derivative

Is there a generalization for ζ(n) where n = 2k? I've been playing around with it and it seems that π^n shows up in all the terms, but I'm not sure if this is a coincidence or not.

>>11833524
https://en.wikipedia.org/wiki/Particular_values_of_the_Riemann_zeta_function#Even_positive_integers

>>11833528
Based.

>prove that if S is an isometry and R is a nonnegative operator, where T=SR, R=√T*T
Been stuck on this for a couple days but I don't wanna outright google the answer. Any hints?

>>11833403
CEGEP [math]\neq[/math] HS

>>11829278
Met Terry Tao at a PDE lecture at USC last year. He mentioned that he is pretty bad at basic problem solving and the lightning quick competition-style of mathematics. And he's definitely right - a lot of PhDs like to sit down and tackle one problem, from different angles, in their own time.

>>11833584
did you try writing down T*T?
do you know that every nonnegative operator has a unique nonnegative square root?

>>11833595
Never heard of that.

>>11833604
Dude Terence Tao was literally a child prodigy. He got a high putnam score at like 13. Either he is being insanely humble, or you are lying.

Is it normal for a first class in algebra to cover naive Lie theory or is my professor just a madlad?

>>11833647
Humility is a key pillar of Asian culture.

>>11833615
I know the second part
I know that ||Tv|| = ||T*Tv||, but that only tells me I can go from one to the other with an isometry.

>>11833670
Theres sqrt there but 4chan ate it

>>11833677
[math]\sqrt{x}[/math]

>>11833670
if T=SR
then T*T = (SR)*SR
simplify the right hand side and then think

>>11833652
The algebra sequence at my uni doesn't mention it, it def wasn't in algebra 1, but my school is also something of a shitter so...

>>11833687
Hehehe
Math is strange
You can look all over and delve into caverns of complexity and be confused
Or you can take a couple steps to the left and you're at the destination

Is logic a non euclidean geometry?

>>11829278
No. I teach both calc and la but there are a lot of problem types I have not bothered with since my undergraduate years.

Should I do my post-doc in IUT or should I transition and live like a woman?

>>11833738
Both?

Anyone here interested in leavitt path algebras?

>>11833604
Because being able to solve relatively simple problems fast is not what most mathematicians do.
Also I would think that "pretty bad" means for him not being in the 0.0001%.

>>11833712
don't worry
the situation "wow the solution is just 2-3 simple steps, and I spent few hours on the problem" happens to me especially often with that kind of functional analysis

Any good books for someone looking to get into Clifford algebra?

yoo is this a sneed thread?

>>11833759
It is now.

>>11829278
You need to spend a lot of time on these problems. They are not designed to be plowed through.

I'm going to have sex with Gauss in Dungeon AI and there's nothing you can do about it.
(Should I pick a modern mathematician?)

>>11833820
Like Serre?

>>11833652
What the fuck is Naive Lie theory, did your professor just construct the classical matrix groups and do some analogies for their Lie algebras or something?

>>11833828
Gauss is definitely in the database (the AI knows that he has some relation to differential equations). I'm not sure about Serre, I will try later.

Is Tao's analysis book really that bad or is hating on it just an /mg/ meme?

Well I'm 20 years late in solving the Poincare conj.

I finished 1st year of software engineering and about to start a degree in mathematics too. how fucked am I?

>>11833874
Can you solve this?

>>11833883
no

>>11829278
>For any one with a masters/PhD, how strong are your basic problem solving skills. Like can you pick up any undergrad basic calc (Stewart-like) or LA (Strang) book, open to random page, and do any problem?
Yes. That is basically how I do my TA sessions. I go over a problem set during my commute, do it in my head then go ask my students. If there is some difficulty, I do it during the session.
But honestly, this has more to do with my undergrad training and very little to do with my PhD work.
I went through French class prepa and we were basically expected to do these exercises standing on our head if we were to enter the best unis. I also passed an advanced teacher certification, which was basically prepa 2.0, so all my undergrad material is drilled in my head for good.

>>11833976
What course(s) do you TA?

>>11833990
I TA’d a semester-long linear algebra sequence that covered duality in finite-dimensional spaces, bilinear algebra, euclidean/hermitian spaces and Hilbert spaces

bump limit and only one poster mentioned the OP said "maths", and nothing came from it. Did /mg/ finally mature?

>>11834042
maths is for illiterate people (aka britbongs)

>>11834048
No country has done more for the advancement of math than the UK.

>>11834053
Haha, that's funny (Germany, France, Russia, Austria), all you have is Wiles

>>11834053
Does "UK" stand for france or for germany?

>>11834067
>>11834070
>No Greece
Actual cringe.

>>11834080
Wasn't at the same time as the UK, but yes. Just don't mention the greek people on Vixra

For the anon who was concerned about the superpermutations article and the editorial disruption taking place there:
>Tendentious editing. The continuous, aggressive pursuit of an editorial goal is considered disruptive, and should be avoided. Editors should listen, respond, and cooperate to build a better article. Editors who refuse to allow any consensus except the one they insist on, and who filibuster indefinitely to attain that goal, risk damaging the consensus process.
https://en.wikipedia.org/wiki/Wikipedia:Consensus

It looks like there's stuff on here that could be leveraged to start a dispute/complaint.
I'm not sure how to start a dispute or any of that, but I do agree that it's inappropriate to hold that article hostage to prove a point to some other unrelated argument one editor was having.
I'd like to see it reverted and would support the effort someone else starts, but I can't really/don't know how to spearhead it myself.

>>11834098

if superpermutations anon cared about recognition he wouldn't have posted his proof here, just let the redditors have their wikepedia page

Is conway's real analysis book good?

>>11834344
Why don’t you read it and tell us anon?

i'm trying to go throught this book, but the setential logic chapters are so fucking boring. can i simply skip to the sets and variables section?

>>11834388
Of course.

>>11834098
>I'd like to see it reverted and would support the effort someone else starts, but I can't really/don't know how to spearhead it myself.
pathetic.

>>11834353
>Why don’t you read it and tell us anon?
Because I am retarded!

>>11834434
>Anime poster
Checks out.

>>11834391
what's even the point of including that in the book then

What is the formula for cuteness?

>>11834502
[math]\mathcal{C}(x)=(qt) \int_0 ^\tau sin^2(x)dx [/math]

>>11834502
[math]f:\text{people}\rightarrow \text{cuteness}/10[/math] is defined as: [math] f(x) =
\begin{cases}
10, & \text{if $x$ is female (female)} \\
10, & \text{if $x$ is female (male)} \\
0, &\text{if $x$ is male}
\end{cases} [/math]

Help with my PDE homework? I'm not sure what is meant by infinite series here, I don't think its taylor, idk how to do fourier. I believe lambda_n are the eignvalues for the DE.

>>11834534
Also, don't know what radiation and absorption are, couldn't find it online.

>>11834530
Is this a bijection?

>>11834563
I see what you're going for, doesn't quite work. The tranny poster will seethe nonetheless.

>>11834563
uh, no?
>>11834576
I'm confused what do they mean?

>>11834591

I want to get some opinions from other mathematicians here on the JQ. My thoughts are that they do have an undue amount of influence on america and Europe and the holocaust was largely exaggerated. You?

>>11834600
I believe that /sci/ should be an ethnostate with everyone sans /pol/tards. You have to go back

>>11834614
ave sujet