/mg/ - maths general

[Anonymous No.10864149]

Previously >>10841541
Talk maths.

[Anonymous No.10864156]

Why has /sci/ not created a curriculum?

[Anonymous No.10864176]

>>10864156
>Why has /sci/ not created a curriculum?
/mg/ already has one.

[Anonymous No.10864188]

>>10864156
check the wiki

[Anonymous No.10864462]

Whats the importance of compactness outside of general topology?

[Anonymous No.10864470]

>>10864462
It shows up a solid 90% of the time in analysis and slightly less in differential geometry.

[Anonymous No.10864473]

>>10864176
Lol no c'mon, show us the real one

[Anonymous No.10864578]

>>10864149
Who's the old man?

[Anonymous No.10864657]

>>10864578
>Who's the old man?
Gromov

[Anonymous No.10864687]

>>10864657
I see

[Anonymous No.10864718]

>>10864462
Perturbation by a compact operators keeps the kernel finite dimensional. This is what the field of analytic index theory is based on.

[Anonymous No.10864860]

>>10864657
Based Gromov. I think he was Perelman's Waifu at some point but now Perelman is picking mushrooms and having a blast.

[Anonymous No.10865005]

>>10864149
why did he lose? is it because he is a brainlet and normies think he is a creep?

[Anonymous No.10865227]

Should I go for a PhD?

The idea of doing mathematics 8 hours a day 6 days a week sounds more appealing to me than slaving away at some software developer job. I want to be in an environment where I can discuss interesting problems with like minded people.
My issue is that I will probably be the dumbest person there, can perseverance get me through it?

[Anonymous No.10865321]

>>10864473

[Anonymous No.10865325]

>>10864149
Who is the guy holding the mic?

[Anonymous No.10865326]

>>10865325
Cedric Villani (might have spelled it wrong)

[Anonymous No.10865327]

>>10865325
Cédric Villani

[Anonymous No.10865330]

>>10865325
Cedric Villani

[Anonymous No.10865334]

>>10865326
>>10865327
>>10865330
Thank you!

[Anonymous No.10865361]

Pugh, Lang, or Rudin?

[Anonymous No.10865364]

>>10865361
Royden.

[Anonymous No.10865423]

>>10864462
You need it sometimes in algebraic topology, for example in van Kampen's theorem.

[Anonymous No.10865434]

>>10864462
It makes infinite objects essentially finite, so you can do actual mathematics on them.

[Anonymous No.10865447]

if Villani wanted to be president, would you vote for him?

[Anonymous No.10865452]

>>10865447
fuck no, people form academia are not fitted to rule

[Anonymous No.10865459]

>>10865321
>>10864176
These are garbage.

[Anonymous No.10865861]

>>10864462
The categorical notion of compactness often correctly picks out the "finite" objects.

[Anonymous No.10865871]

>>10864718
based fredholmbro

[Anonymous No.10865873]

>>10865361
Pugh, with Rudin as a supplementary text.

[Anonymous No.10865876]

I'm reading Villani's book now, Birth of a Theorem, and it's a really wonderful read. He doesn't hold back the mathematics, but he also does a really good job of depicting his life outside of math. He also writes pretty well.
Highly recommended.

[Anonymous No.10865994]

>>10865361
Zorich is the Dummit Foote of analysis

[Anonymous No.10866006]

>>10865452
Think about it anon. More tax money will go to research in pure mathematics. Wouldn’t you want that?

[Anonymous No.10866025]

Make cédric the mayor of Paris pls
Say no to LREM cucks

[Anonymous No.10866029]

>>10865227
I mean, clearly you want to do it. Don't assume you'll be the stupidest person going in. If you can't handle it, they won't let you into a PhD program. Have faith that if you get in you can do it. Most people drop out because perseverance is hard when you have no idea what you're doing constantly, so if you feel strongly you won't get discouraged, you're better than most who probably assume it won't be "that bad"
Good luck

[Anonymous No.10866220]

>>10866029
>don't assume you'll be the stupidest person going in
to be fair, a good piece of advice in general is to always assume this especially in mathematics communities. or maybe assume you'll be the second stupidest person. when you think you're the stupidest person, you have a reason to try and learn from all the people around you. when you think you're in the middle of the pack, you only have a reason to learn from half of the things you hear (roughly). i don't care who's actually smarter or less smart than who. what i care about is learning from others and their mathematical experiences, not so i can be smarter than them, but so i can be smarter than myself from a day ago. i find that asserting to myself that i'm probably one of the dumber people in a given room (when that's not a completely outlandish assumption) has helped me to focus on my own growth rather than on other's.
of course, for some this can backfire and lead them to lose encouragement. in fact, i think this only works if you know in the back of your mind that quite a lot of people are much, much dumber than you will ever be (which is pretty easy to accept if you're studying any kind of higher mathematics)

[Anonymous No.10866228]

>>10866220
>when you think you're in the middle of the pack, you only have a reason to learn from half of the things you hear
No, fool. Find a stupid hard worker and steal their bone deep insight.

[Anonymous No.10866430]

>>10864156
Good question.
I'm thinking about making an autistic guide exclusively about complex numbers.
That means:
>Conway's two volumes
>a good Riemann surfaces text
>several complex variables
>quasiconformal mappings
>kahler and hyperkahler manifolds(mix some Verbitsky in for the references)
>complex manifolds (Kodaira's good)
>Teichmuller (Papadopoulos's five volumes)
>symplectic geometry and topology
>pseudoholomorphic curves
Anything else?

[Anonymous No.10866469]

>>10866430
Sounds nice. I'd like to see a guide like that.

[Anonymous No.10866488]

>read Baby Rudin
>get through first Chapter
>"hell yeah lets do some exercises"
>can only do exercises 1 and 3

I'm not gonna make it bros.....

[Anonymous No.10866489]

I'm someone who's trying to learn math from scratch so i can eventually study physics. When i look at maths i fail to see for what we use it for. Why do we use algebra? Why do we use calculus? Why do we draw all those graphs with all of those functions? I know this seems like a brainlet post, but i'm willing to learn. I just want some guidance.

Where do i start?

[Anonymous No.10866502]

>>10866489

Those things model real-world phenomenon. As in, they represent real life. So instead of dealing with the massive chaos that is reality, you deal with numbers.

[Anonymous No.10866519]

>>10866502
So you could say math is used to break down the inner-workings of our reality?

[Anonymous No.10866538]

>>10866488
>>read Baby Rudin
Rudin is a meme.

[Anonymous No.10866560]

>>10866220
True enough, I suppose I should have said "don't assume you're too stupid to do it." I agree your attitude can be helpful, and I generally assume I know the least about anything in most situations, if only because it's a more constructive attitude.
However, going in thinking "I'm the stupidest person here and shouldn't be here, so I can't do it" is pretty destructive. That's the attitude I was trying to warn against.
I do appreciate your point, though.

[Anonymous No.10866623]

>>10866519
The ancient Greek "standard model" (in Timaeus) consisted of four elements: fire, air, water and earth. They were modeled on geometric planar and spacial shapes. From what I remember the basic building blocks were the 1-sqrt(3)-2 and 1-1-sqrt(2) triangles, and that they were combined together to form the actual elemental particles. The different interactions between the four elements, producing more complex forms of matter, was said to be governed by how those shapes could and could not fit together. Fire (aka light), for example, was said to consist of acute angles, hence it has heat.

Though for us today their model seems ridiculous, at the time it was correct because there was no evidence to disprove it. My guess is that, for the Greeks, this model was an attractive one because it used the latest research-level mathematics. The story of gravity is similar: first Newton describes motion in terms of calculus, then Einstein comes up with relativity after the discovery of non-Euclidean geometry. So I think it's fair to say that maths is used to understand nature.

tl:dr; >>>/lit/

[Anonymous No.10866679]

>>10866489
Mathematicians do math for their own self gratification and could care less if it has any use in reality.

It just so happens that some things mathematicians do have been discovered to be useful.

[Anonymous No.10866713]

>>10865459
let's see your meme list then

[Anonymous No.10866714]

Here’s one sad toss pots

23 x (7+1.4) +<2x

??
Fuck you

[Anonymous No.10866864]

>>10865361
Wheeler

[Anonymous No.10867079]

>>10866488
>he can't do 4
Nigga you're actually retarded, might as well drop maths.

[Anonymous No.10867159]

>>10867079
>>he can't do 4
I'm not a "he".

[Anonymous No.10867183]

>>10867079

I actually meant to write 1, 3 and 4. I can do 4, thankfully.

Also this isn't me
>>10867159

[Anonymous No.10867196]

>>10867183
That's good.
Did you try rereading the chapter while trying to abstract the proof techniques used in the proofs given? That's usually how books like this are meant to be read.
Essentially, just keep the problem in mind, and look through the text for inspiration.

[Anonymous No.10867228]

The books in these guides are so awful.

[Anonymous No.10867250]

>>10867196

I have not put so much focus in abstracting the proof techniques, moreso trying to understand the definitions and the logical steps of given theorems. I've noticed patterns in some proofs, but I'm honestly pretty discouraged because it feels like its out of my ability to comprehend, even when the proofs is blatantly written in front of me.

If I struggle to understand a given proof, how the hell am I supposed to be able to create one myself? It's a harsh blow to my ego, but I persist for better or worse.

[Anonymous No.10867288]

>>10866488
2 follows almost directly from 1 and 5 follows from the definitions.

[Anonymous No.10867298]

>>10867288
>2 follows almost directly from 1
I don't see a way of proving 2 from 1 that isn't extremely convoluted, please share with the rest of the class.

[Anonymous No.10867305]

>>10867298
1 says that if r is a nonzero rational and x is rational then rx is irrational, right? And 2 asks you to prove that the square root of twelve is irrational, right? So, since 12=3*2^2 using the magic of arithmetic we compute that root 12 equals 2 times root 3. Now, if one proves that root 3 is irrational, then the product of the rational 2 and the irrational root 3 is still an irrational, and since 2 times root 3 equals root 12, we'd be done. All that's left is to prove root 3 is irrational, which is pretty much identical to the proof that root 2 is irrational and that the root of any prime is irrational.

[Anonymous No.10867311]

>>10867305
Yup, that goes in the extremely convoluted folder.

[Anonymous No.10867313]

>>10867311
>Yup, that goes in the extremely convoluted folder.
If you actually think a three line proof is convoluted, then you might as well give up on analysis right now.

[Anonymous No.10867319]

>>10867183
Are you allowed to use Rational roots theorem? Also using Eisenstein Criterion would be funny. (Problem 2)

[Anonymous No.10867321]

>>10867313
No, the "we have a proof of the irrationality of the root of three but we can't repeat it for the roots of random other numbers that don't have natural roots" part is convoluted.
You solved the problem in a simple way from a convoluted set of theorems.

[Anonymous No.10867330]

>>10867321
Not the person you replied to, but I think the proof they gave was the one implied in the problem. I think it's pretty straightforward and I hate analysis.

[Anonymous No.10867348]

>>10867321
>No, the "we have a proof of the irrationality of the root of three but we can't repeat it for the roots of random other numbers that don't have natural roots" part is convoluted.
I mean, you can write a more general proof, it's just that for instructive purposes it was broken down into multiple parts. Further, the applied this to a simple case where it's not hard to see how this would be generalized. It's a touch long, but straightforward.

[Anonymous No.10867583]

>>10864860
He looks like Perelman from the future so this is now what I choose to believe.

[Anonymous No.10867878]

>>10866029
You are right, I really do want to do it. Thank you for your response.

[Anonymous No.10867980]

>>10865452
https://en.m.wikipedia.org/wiki/Paul_Painlevé
Paul Painleve was a mathematician and the prime minister of France

[Anonymous No.10868030]

>wanna get a PhD subject
>website says you can if it doesn't list prerequisites
>it doesn't, but I've read the first chapter of a book on the subject, and worst case scenario I'll have to review Fourier and Diff eqs
>website says you need the professor's signature
>professor vanishes into thin air
>ask some lads in the department when is he there
>they ask for what
>signature for a subject
>that's on this other website
>the other website doesn't fucking work
I'll see if he's there again later. Wish me luck lads.

[Anonymous No.10868219]

>>10866489
Algebra as you learn it in school is the language in which you can express general facts about numbers.
Literals such as ‘x’ are used to represent arbitrary elements in a collection S.
Formulas involving an x in a collection S are general statements about elements of that collection. Proving such a formula amounts to proving that the statement holds for all members of that collection.
For example the formula (x+y)^2 = x^2 + 2xy + y^2 holding for all real numbers x and y means that I can substitute any real numbers to x and y and get a true statement.
For example, setting x = 1000, y = 1, I get 1001^2 = 1000^2 + 2000 + 1 = 1002001.
tl;dr: variables allow you to easily express general facts about numbers. There was a time when there was no algebra as we know it and people would just write really long sentences for what we write in one line. Proofs were even worse.
Calculus is a tool that allows you to analyze variations in quantities, in a very precise way. A function is a process that inputs a "thing" (usually a number, but not necessarily) and outputs another "thing" according to a fixed rule (ie. a given input will always lead to the same output).
The graph of a function is a visual representation of that process. If you input numbers and output numbers, then you will have the possible values of the input along one axis, the possible values of the output along another axis, and put a point at all points (input, corresponding output).
You can usually see on the graph if the output increases with the input, or decreases, or neither, but calculus allows you (for suitable functions) to quantify the change of a function via the derivative, and get even more precise information.
This is used in physics to formulate general laws. General principles of physics are classically formulated as differential equations, ie. equations relating physical quantities and their derivatives.
This allows you to relate quantities to the change of other quantities.

[Anonymous No.10868312]

>>10867980
>https://en.m.wikipedia.org/wiki/Paul_Painlevé
we are talking about modern mathematicians, you really don't want them to rule.

[Anonymous No.10868663]

In a proof I did recently for uniform convergence of series, I relied on associating terms in an alternating sequence to use Weierstrass M test. For example [math]1-1/2+1/4-1/8+\cdots =(1-1/2)+(1/4-1/8)+\cdots [/math]
This does not change the series, right? In the sense that I know that reordering the terms in the series may change it if it doesn't converge absolutely. Also, can anyone tell me why intuitively changing the order of the terms changes the series?

[Anonymous No.10868696]

>>10868663
It does.
See:
1-1+1-1+1...
Compared to:
(1-1)+(1-1)...
Which converges.
>intuitively changing the order of the terms changes the series
Because you can switch from something like
>one positive term, one negative
To something like
>five hundred positive terms, one negative
Which is usually larger.

[Anonymous No.10868703]

>>10868663
>This does not change the series, right?
Right, because it converges absolutely
Now, as to why the value can change if the order of the series changes, it is a bit hard to grasp intuitively (because we, or at least I, usually imagine finitely supported permutations), but the idea is that if your series is convergent but diverges in absolute value, then you have a lot of leeway in what you can do to your sum. The sum of positive terms and that of negative terms must both diverge to infinity so intuitively, you can steer your partial sums arbitrarily far in some direction, and then use the fact that the series converges in the first place to justify that you can cancel out the rest of the terms (this is really really sketchy)

[Anonymous No.10868707]

>>10868312
why

[Anonymous No.10868710]

>>10868696
Oh, I'll add something quick.
Associating doesn't change the values if it converges, but it can change whether or not it converges, and two different ways of associating a given non-converging series can give different results (see: Eilenberg swindle).

[Anonymous No.10868786]

>>10868696
>>10868703
Thanks, I'm glad I asked and fixed my way of thinking.

[Anonymous No.10868788]

>>10868710
Ohhh thanks for the follow up, that actually fixes my problem since it was easy to check that it converges point wise a priori.

[Anonymous No.10869100]

Given two (nontrivial, i.e.holding at least an uncountable ordinal) models of ZF, consider their smallest inner models of them, i.e. the constructable universes they contain.
Are they the same / isomorphic?
I.e. is the constructible universe always the same? Can we speak of "the" L of Zermelo Freankel set theory?
Thanks

Related links
https://en.wikipedia.org/wiki/Axiom_of_constructibility
https://en.wikipedia.org/wiki/Constructible_universe
https://en.wikipedia.org/wiki/Inner_model

[Anonymous No.10869249]

I'm finishing up my undergrad degree and am starting to choose my "elective" math courses. Which classes piqued your interest?

So far I'm planning on:
Optimization [math]\rightarrow[/math] ML
Game Theory

[Anonymous No.10869419]

>>10869249

memes.

[Anonymous No.10869863]

>>10866029
>If you can't handle it, they won't let you into a PhD program.
This is nice fluffy motivational talk but it's flagrantly not true. At every university I've ever seen (even very, very good ones), less than half of admitted grad students finish. Some of these students have extraneous circumstances but for a lot of them it's simply that they either couldn't handle it or did not want to handle it.

[Anonymous No.10869898]

>>10864149
what's james randi doing with hila klein?

[Anonymous No.10869994]

Which one of you recommended a rotating mechanical pencil? I asked if it was a meme and was told 'no'. This thing is a total meme.

[Anonymous No.10870071]

>mfw arbitrary products

[Anonymous No.10870227]

>>10866488
oh come on now. all the listed exercises are braindead obvious. go bait somewhere else.
>>10866538
you're a moron.

[Anonymous No.10870238]

>tfw realizing mathematics was just a phase and I don't want to spend my life doing it
I really hate myself. I wish I was cool and autistic like you guys.
What the fuck do I do with this degree now?

[Anonymous No.10870272]

>>10870238
>Yes, he's saying that he wants out. Take care of him.

[Anonymous No.10870283]

>>10870238
huh? i don't get it. how is that possible?
maybe you just need a break.

[Anonymous No.10870310]

>>10870283
I've always been like this, I can't commit to any passion or interest long term. Maybe I'm just burned out, but I haven't voluntarily picked up a math book in months and don't feel like that's going to change.

[Anonymous No.10870314]

>>10864176
> galois theory in high school.

Go fuck yourself.

[Anonymous No.10870329]

>>10870314
>> galois theory in high school.
>Go fuck yourself.
I don't understand your point. Are you insinuating that Galois theory is nontrivial?

[Anonymous No.10870337]

>reading https://www.wiley.com/en-us/Algebra+and+Number+Theory%3A+An+Integrated+Approach-p-9780470640548 because my community college has a wiley subscription and I wanted to into the topic
>author very clearly uses fraktur for sets of sets
>get to chapter 1 exercises
>A, B, and C are sets
>shit about A and B being elements of C in plain serif font, while also using A and B as subsets
did I pick a bad introductory text, or am I just retarded (options not mutually exclusive)

[Anonymous No.10870427]

>>10870329
this board is retarted.
Why do you guys feel the need to anonymously larp?

The geniuses certainly cover a lot of material young, but if your one of them, your not on this board.

Yes its non-trivial you have to learn group theory, ring theory, field theory, field extensions, etc first. That's at least two semester of serious study for those who never have touched these subjects.

You aren't impressing anyone.

[Anonymous No.10870442]

>>10870427
>this board is retarded
Are you projecting your own insecurities onto our board?
>anonymously larp
No one is "live action role playing."
>"your" not on this board
Where is your evidence to support this claim? Plenty of "us" are right here in /mg/. I'm not sure I agree with the classification "genius" unless that is your word for "has a base competency in mathematics."
>group theory, ring theory, field theory, etc.
>non-trivial
I'm not certain that you have much experience in any of the above fields, given your persistent assertions that the elementary results in said fields are nontrivial. Could it be that I am speaking with an 8th grader?
>for anyone who has never touched these subjects
When did we ever say anything about such children?
>You aren't impressing anyone.
Well, that wasn't the goal, was it?

[Anonymous No.10870462]

>>10870442
KEK.

So tell me, are all undergraduate curriculums across the nation just memes? The norm is starting with graduate school huh? Just right out of the gate?

[Anonymous No.10870476]

>>10870462
If by that you mean that the norm is to begin in undergraduate coursework using textbooks which are labeled as "graduate texts" and using a syllabus which anticipates a base competency in the most basic algebraic and analytic facts, then yes, of course.
I'm not sure we disagree, do we? Why the condescending tone?

[Anonymous No.10870490]

>>10870476
>I'm not sure we disagree, do we?
Mathematicians use "We're", not "I'm".

[Anonymous No.10870552]

>>10870238
Same. I'm currently doing in undergrad in math, and I don't know how much further I can keep this up until I become completely demotivated. My peers are far more invested in this subject than I am, and it really shows. I'm not sure if I have the passion required to proceed into academia. Maybe its just a lack of motivation, but I've been spending a lot of time this year feeling this way. Maybe I'm in this particular funk because of the shit I've been learning in class recently. There are a lot of things I enjoy in mathematics, so maybe this will pass.

[Anonymous No.10870555]

>>10870462
>So tell me, are all undergraduate curriculums across the nation just memes?
Yep

[Anonymous No.10870664]

>>10870238
>tfw realizing mathematics was just a phase
This is a very confusing notion. As soon as I learned what math is beyond high school computations, I couldn't stop. This anon >>10870283 summarizes my sentiments.

[Anonymous No.10870888]

>>10867305
Not him but this sounds like a shitty proof.

[Anonymous No.10870892]

>>10870664
not that anon, but what is your position ? undegraduate/graduate student or phd ?

[Anonymous No.10870962]

>>10870442
ok mr smarty pants. Derive the roots of the general quintic for me.

[Anonymous No.10871002]

How does one define the mapping operator in algebra and where does it get it's commutative property from?

Is the distributive property of the mapping operator an a-priori condition for a group automorphism?

[Anonymous No.10871008]

>>10864156
Because they can't decide on what's the best way to be a tryhard. And even if they did, that russian mathematician that works in Rio already has them beat.

[Anonymous No.10871013]

>>10871002
what's "mapping operator" ?

[Anonymous No.10871092]

>>10871013
I used the wrong terminology, I just mean the map. For example let's say we have a group z defined with an operation That's an addition mod 6 (using symbol +)

Then if you take map(x + y) do you get map(x) + map(y) always or only if you define it that way and call it a group automorphism.

[Anonymous No.10871112]

>>10871092
what have you tried ?

[Anonymous No.10871124]

>>10871092
Incomprehensible-tier question.

[Anonymous No.10871248]

>>10870314
>>10870427

I read the book "Abstract algebra" by Charle's C. Pinter in highschool. It has a couple chapters on Gallois theory and a proof that there is a polynomial with an unsolvable Gallois group.

>>10870462

Well, they're all pretty much the same. You won't be able to find a university that lets you focus on theoretical math that I know of. You'll have to take a bunch of calc courses that are designed for scientists and engineers. Undergrad curriculums are a huge meme because they are designed with the fact that math majors are likely to switch engineering or science in mind.

Gallois theory and abstract algebra doesn't depend on being able to solve integrals and prove limit theorems. But this is all you'll be doing for your first 3 years of uni according to the normal curriculum. So it's totally possible for a highschooler to pick up an abstract algebra book and read it.

[Anonymous No.10871292]

>>10871248
>You won't be able to find a university that lets you focus on theoretical math that I know of.
in europe an undergraduate degree in pure math is a normal thing

[Anonymous No.10871336]

>>10871292

I doubt it's much different in Europe.

Are you saying that if I was a math major in Europe, I wouldn't have to take any calc classes to graduate and I could start freshmen year with abstract algebra?

[Anonymous No.10871364]

>>10866713
what does this picture mean? what is [math]\pi(x)[/math] ?

[Anonymous No.10871401]

>>10871364
Prime counting function.

[Anonymous No.10871430]

>>10871336
you would have to learn calculus, because it's a general knowledge. but the treatment would be rigorous and your classmates will be only students of pure and applied math.

[Anonymous No.10871453]

>>10870892
I'm a PhD student in my early 20s. My master's and bachelor's are in computational mathematics.

[Anonymous No.10871492]

>>10864149
I used to justify the existence of pure math to people by explaining it works on problems that have no concrete meaning and that we never know what we will find in these abstractions. Then when I actually studied these fields in postgrad, I realised these fields don't have pure motivations at all, but they all essentially grew out of the simple monkey desire to solving equations (or finding sets fields and their properties etc which is the same thing even if we're pretending to be removed from numerical math). Algebraic Geometry at its core is just about solving polynomial equations. Differential geometry is just about finding vector field solutions to DEs. Even fucking group theory just deals with old methods we used to solve single variable algebraic equations.

Why the fuck do math researchers care so much about analysing these simple monkey problems? In any case all the best equation solving algorithms are developed by people in other fields. Computer scientists gave us the best convex solvers. Physicists found concrete methods for vector field decomposition/reconstruction. Engineers developed the best PDE solvers and even the best topology optimisation and shape optimisation algorithm etc.

We're talking about whether or not we can solve these problems while they're actually doing it (and on far more complex objects embedded in far more complex spaces than stupid shit like smooth algebraic varieties).

Is there any real justification to math other than supporting advances of citation webed researchers in dead end fields like String Theory? I'm honestly thinking about quiting my PhD to pursue more honest and meaningful fields.

[Anonymous No.10871512]

>>10864149
>math
Not math or science.

[Anonymous No.10871515]

>>10871492
>Algebraic Geometry at its core is just about solving polynomial equations.
No, it isn't. Algebraic geometry studies the topological and geometrical aspects of solutions of polynomial equations, or, equivalently, spaces that are locally the zeroes of a ring of functions.

[Anonymous No.10871516]

>>10871492
>Differential geometry is just about finding vector field solutions to DEs
where the hell did you hear this

[Anonymous No.10871521]

>>10871492

Math is not just algebraic geometry, topology and differential geometry. These are just the entry level normie tier fields.

[Anonymous No.10871531]

>>10871515
>or, equivalently, spaces that are locally the zeroes of a ring of functions.
That is literary what I just said.

>>10871516
This is the primary motivation for and starting point of the field in many graduate level textbooks.

>>10871521
Of course those are just the main branches, but virtually all cutting edge research fields grew out of them.

[Anonymous No.10871532]

>>10871492

Math is not just algebraic geometry, topology and differential geometry.

[Anonymous No.10871542]

>>10871492
>We're talking about whether or not we can solve these problems while they're actually doing it
One necessarily precedes the other.
Take an actual course on numerics to see why "just write an algorithm" is a bad approach.

The algorithms are the outcome of the understanding, one can not exist without the other.

[Anonymous No.10871543]

>>10871532
I left out analysis because let's face it, analysis is just a motivation for convergence of numerical analysis techniques. Functional analysis largely deals with spaces produced by PDEs.

[Anonymous No.10871553]

>>10871542
>Take an actual course on numerics to see why "just write an algorithm" is a bad approach.
Why are you assuming I haven't? I took it an undergrad and we weren't taught to "just write an algorithm", it dealt mostly with convergence in real euclidean spaces.

>The algorithms are the outcome of the understanding, one can not exist without the other.

This is my point. These fields are monkey work meant for physicists and engineers, we should be doing it for them we should be working on understanding more interesting things. There appears to be no (major) math field that doesn't focus on studying concrete problems.

[Anonymous No.10871597]

>>10871543
>>10871492

I would argue that "real math" is _especially_ the stuff that is considered "low brow" by the mainstream math community. And it makes sense that this stuff doesn't receive as much funding or attention.

[Anonymous No.10871624]

>>10871597
>I would argue that "real math" is _especially_ the stuff that is considered "low brow" by the mainstream math community.
Yes, you are right. It does exist, it is just not prominent as you say.

> And it makes sense that this stuff doesn't receive as much funding or attention.
I understand this, and why it doesn't receive much funding (and therefore even less attention), but I just want professional mathematicians to be truthful about it. They aren't monks taking a salary cut out of some commendable desire to peer into the Platonic realm. They are unlicensed engineering professionals and theoretical scientists who happen to work in the math department.

[Anonymous No.10871714]

>>10871248
>>10871336
dude literally everyone does this in college in the US because we take the fucking ap calculus exam
who the fuck bothers with calc? lmao

[Anonymous No.10871719]

>>10871714

multivariable is still calc
linear algebra and differential equations is still calc

[Anonymous No.10871731]

lol imagine being partway through your phd and still completely misunderstanding the point of math
it's not about "solving equations" just because that's the motivation. the motivation is not the same as the result. it's about drawing connections and conclusions about a wide variety of abstract systems and structures. it is only secondarily about using those connections and conclusions for concrete results. sure thing, you can talk about how people implement topological data analysis all you want, but someone needed to find the mechanism for homology connecting geometric and algebraic objects before anyone can implement an algorithm for this sort of analysis. okay, yeah, maybe pure number theory isn't for you. but don't throw the baby out with the bathwater because you are tunnel visioned on the first page of a number of introductory """graduate""" level texts.

[Anonymous No.10871732]

>>10871719
>linear algebra is still calc
lmao
anyway i did all the computational classes in high school because i took BC as a junior (totally achievable) and finished multi, introductory lin alg, and diff eq in senior year. started with discrete and axler lin alg in college, have never taken a computational college course. what i am saying is easily achievable for anyone with even a modicum of interest in studying mathematics.

[Anonymous No.10871748]

>>10870238
>>10870552


teach until something new comes along

[Anonymous No.10871800]

>>10871732

I don't think most highschools offer multivariable or linear algebra and diff eqns.
But that's really beside the point. I'm saying the curriculum has a design flaw.

Your typical person who has passed calc BC has the ability to learn abstract algebra, but they usually don't for about 2 years because the incentive is for them to take a bunch of cuckulus and analysis

[Anonymous No.10871987]

>>10871731
First of all quote me directly you goddamn beta. Secondly I'm reading reviews and papers and I'm fully up to date with 3 different fields including one I publish in and not including the ones where I've only dabbled with. So stick your proposal up your ass. You have no idea how slow these fields are moving and how trivial most of the work currently being produced is.

If you don't agree with my previous posts you almost certainly haven't even started delving past classical results.

[Anonymous No.10871992]

>>10871553
>it dealt mostly with convergence in real euclidean spaces.
Than actually learn how engineers deal with ODEs and PDEs.

>These fields are monkey work meant for physicists and engineers
What is that even supposed to mean? PDE theory can be interesting purely by itself, saying it is "monkey work" because engineers and physicists make use of it is kida dumb.

>There appears to be no (major) math field that doesn't focus on studying concrete problems.
There are things like set theory and foundations, but that pretty much misses the point.
I think there are diverging answers to the question "what is the point of math", both mine and the historical view makes mathematics out as an abstract description of reality, it is inherently inseperable from the question it likes to answer.
And I know that this is probably something that is seen as quite controversial, but I honestly do not think that is the case, all the most basic notions in mathematics are born out of the way we perceive reality.

[Anonymous No.10872015]

>>10871992
>Than actually learn how engineers deal with ODEs and PDEs.
Assuming you meant then*, I have. In fact that story is part of my disgust. If you must know my entire grant was rendered pointless because it turns out that the lab funding our work didn't even really need the work they funded us for. They just weren't aware that there's a simple numerical algorithm that can very efficiently solve their problem that was developed 30 years ago by some IBM industry engineer. Not only that, but it has stronger guarantees than the toy spaces we were working with.

>What is that even supposed to mean? PDE theory can be interesting purely by itself, saying it is "monkey work" because engineers and physicists make use of it is kida dumb.
It's even worse than monkey work because PDE theory as taught to mathematicians deals with really simple uncoupled _smooth_ systems. We spend all this time abstracting the spaces of easy to solve systems no one cares about because they are very well understood and considered to be solved problems.

>There are things like set theory and foundations, but that pretty much misses the point.
These fields are mature and there is virtually no research being done any more. Still in my opinion they are more worthy fields than anything stemming from the fields mentioned in my previous posts.

>I think there are diverging answers to the question "what is the point of math", both mine and the historical view makes mathematics out as an abstract description of reality, it is inherently inseperable from the question it likes to answer.
This is physics. This is engineering. This is even economics. But it's not my math, and it shouldn't be your math either.

>And I know that this is probably something that is seen as quite controversial, but I honestly do not think that is the case, all the most basic notions in mathematics are born out of the way we perceive reality.
Nah fuck that. We should be better than our ancestors.

[Anonymous No.10872080]

>>10872015
>But it's not my math
But it is what math WAS until, I don't know 100? 150? years ago?

>This is physics. This is engineering. This is even economics.
No, there is a fundamental divide here, which seems obvious to me, but I guess not to you.
Physics isn't concerned about abstract models of reality, the entire history of physics is taking mathematics and trying to create a model of reality with it.
It isn't concerned about an abstract view of what "distance" could mean or how these concepts in an abstract domain relate to each other.
Engineering is even less suitable, as it is fundamentally about what works, not truth and for that it desperately needs mathematics.

Mathematics is the abstract world, physics and especially engineering are the concrete world.

>We should be better than our ancestors.
Sure, but does that mean we should abandon, quite literally, 2000 years of mathematical Tradition?
Read a book on the history of analysis to see what I mean, from Archimedes onwards every great analyst thought pretty much exactly that about mathematics.

To the point about how to justify pure mathematics, there is no point, it is worthless garbage, like all research, whether in physics or engineering or any other field until one day one small part of it becomes enormously important and changes the world.
But if you do not care about that, and just mathematics itself, yes it is pure mental masturbation, but in that it is anything but alone.

[Anonymous No.10872307]

Not looking for a meme book list but im totally confused as to what order i should learn math if i were to learn from scratch?

[Anonymous No.10872312]

>>10872307
For the basics I'd recommend baby rudin

[Anonymous No.10872314]

>>10872307
>Not looking for a meme book list but im totally confused as to what order i should learn math if i were to learn from scratch?

[Anonymous No.10872316]

>>10872312
>For the basics I'd recommend baby rudin
Rudin is a meme.

[Anonymous No.10872324]

>>10864176
>>10872314
>he modified it a little just so he could post it again
Disgusting.

[Anonymous No.10872339]

>>10864149
What is the best thing I can do with a math undergrad degree?

I am tossing around the following ideas:
Comp Sci Masters
Engineering Masters
Statistics Masters
Law School

Which of these are based or non based?

[Anonymous No.10872344]

>>10872324
>>he modified it a little just so he could post it again
I'm not a "he".

[Anonymous No.10872352]

>>10872339
>>>/adv/

[Anonymous No.10872354]

>>10870476
not the guy you're responding too but the condescending tone is because you're type of guy who likes to huff his own shit and calls it roses

kindly shut the fuck up

[Anonymous No.10872355]

>>10872352
Yeah, you're probably right, but none of the anons there know anything about math

[Anonymous No.10872361]

>>10872344
shut up tranny

[Anonymous No.10872377]

>>10872344

then give me a blowjob

[Anonymous No.10872389]

>>10872361
>tranny
Why the transphobia?

[Anonymous No.10872595]

>>10864462
Also pivotal in Enumerative Geometry and related mathematical physics, e.g. quantum cohomology. One needs compactification of spaces to ask sensible questions and get nice answers. For example, CP^2 is essentially compactifying C^3 so we can make sense of infinities for instance.

[Anonymous No.10872700]

>>10872377
why the objectification?

[Anonymous No.10872732]

I'm trying to show that a sequence an is monotonely increasing. the sequence is [math]a1:=1, an:=a2n+(an)/2+1/16[/math]. im pretty sure i have it right (see pic) but i think i've overthought it. in a proof by contradiction, does finding one specific counter example like i've done prove the general idea? obviously it shows that our assumption is not the case, and law of excluded middle blah blah, so it should be the case, but i cant help but feel like theres something wrong

[Anonymous No.10872751]

>>10872732
[math]an:=a^2_n+(a_n)/2+1/16 , a_n:=1[/math]
sorry

[Anonymous No.10872755]

>>10872732
>does finding one specific counter example like i've done prove the general idea?
No. You want to show that for all naturals n, an =< a(n+1). The negation of this is that there exists natural n such that a(n+1) < an. If you want to show that the sequence is monotone increasing by way of contradiction, you have to show that no such n exists, which you did not do.

[Anonymous No.10872774]

>>10871800
good. algebra is for morons, everyone should be forced to learn only analysis, topology, and geometry. algebra is merely a tool to advance those fields.

[Anonymous No.10872777]

>>10871987
>blah blah blah im so smart and authoritative blah blah
you belong wherever you came from. maybe physics is more your speed?
>>10871992
>>10872015
>>10872080
good lord. take it to a thread of people who give a single shit you fucking morons.

[Anonymous No.10872781]

>>10872339
>based
math phd
>unbased
all the garbage you listed, especially law "school"

[Anonymous No.10872792]

>>10872755
I thought not, my other idea was to use the fact that [math]a_n^2 +a_n/2 + 1/16 = (a_n + 1/4)^2 > a_n^2 \geq a_n[/math], but this relies on the fact that [math]a_n\geq1[/math], which seems circular as, we could only know if this was the case if we had already proven it was increasing, right?

[Anonymous No.10872796]

>>10872354
>you're type of guy
Learn to write, kid. This is a board for smart people. This isn't /v/.
>sh*t
Please don't curse in our thread.
>f*ck
Do I really need to repeat myself?
>kindly shut the f*ck up
Doesn't sound as though you're being very kind, does it?
>huff his own sh*t and calls it roses
Firstly, you conjugated "to call" incorrectly. Secondly, the analogy makes absolutely no sense in these circumstances. Care to explain your intent in using this analogy?

[Anonymous No.10872797]

>>10872792
are you supposed to have an a_{n+1} somewhere? currently your recurrence is just an equation for a single term not in terms of the prior ones.

[Anonymous No.10872804]

>>10872797
yes, im an idiot, it should read [math]a_{n+1} =a_n^2 +a_n/2 + 1/16 = (a_n + 1/4)^2 \geq a_n^2 \geq a_n[/math]

[Anonymous No.10872808]

>>10872792
>>10872804
what? do it inductively.
here's your hypothesis: "the sequence a_n is increasing and is always greater than or equal to 1"
here's your base: "a_1 is 1"
here's your inductive argument: "say that a_n is greater than or equal to 1. then a_{n+1} > a_n by your argument, and so a_{n+1} is also greater than or equal to 1."
by induction, all the terms are greater than or equal to 1. the inductive argument also shows that the sequence is monotone.

[Anonymous No.10872815]

>>10872808
thanks la x

[Anonymous No.10872818]

>>10864149
How do I improve my pattern recognition?

[Anonymous No.10872826]

>>10872818
Do online exercises in pattern recognition.

[Anonymous No.10872942]

I'm taking a grad level algebra course in 7 weeks. It's been over 3 years since I took my undergrad algebra course. Can anybody with experience give me pointers on where to focus my attention as I'm re-familiarizing myself with the content? I will certainly be giving a lot of attention to rings and groups. What else? Thanks

[Anonymous No.10872956]

>>10872796
Kek

[Anonymous No.10872972]

>>10872942
For group theory, know the isomorphism theorems like the back of your hand, do some exercises on Sylow groups until you can classify them for small to medium order, and that's about it I think. Depends on your university though. Better universities usually have rep theory and Lie algebras too.

[Anonymous No.10872982]

What's the best way to find where your gaps in knowledge are? I feel like I have some gaps, and diagnosing all of them is a chore. I picked up some elementary math books to try and relearn everything from the beginning and leave no gaps this time around, but it's a little bit overwhelming. Most of the time, I'm reading stuff I already know too.

[Anonymous No.10872992]

>>10872982
I always feel that I have gaps, but when I review the material it's less than I remember. A typical pattern is that I enounter something that makes me think that I need to review LA, but then it turns out that the theorem wasn't covered in my freshman LA text to begin with. What I really needed was a second text on LA.

So in conclusion I think it's more effective to just keep exploring new fields and textbooks. Assume first that you don't need to review. Never actually read lower level textbooks, notes are usually enough.

[Anonymous No.10873020]

>>10872992
This seems like a good method. I'll try it out, Anon. Thanks.

[Anonymous No.10873022]

>its another math majors hate themselves thread

lol

[Anonymous No.10873026]

>>10872355
;anything below phd you're only getting a good job if you network properly (are handsome and well liked by affluent peers/mentors). comp-sci will make you want to kill yourself, law will make you want to kill yourself, stats is soul crushing, engineering seems comfy but is brainlet I would just go into engineering or physics desu

[Anonymous No.10873045]

>>10872777
>take it to a thread of people who give a single shit you fucking morons.
You first.

[Anonymous No.10873193]

>>10872796
HEY FUCK FACE. GIVE ME AN ANSWER>>10870962
>>10870962
>>10870962
>>10870962
>>10870962
OR YOUR FUCKING LIAR

[Anonymous No.10873207]

>>10873193
r u mad?

[Anonymous No.10873209]

>>10873207
nah the dude's bullshittin. If he really knows as much math as he says, he can answer the question.

[Anonymous No.10873215]

Why can't I get into a top PhD program for Math? Surely the competition isn't THAT fierce right? Nowadays I can't imagine many people want to become mathematicians... goddamn it.

[Anonymous No.10873220]

>math major
>take my lower div math
>take my core math
>take my math semi electives
>all that's left for me are math electives
>none of them have upper division prerequisites
>PDEs and ODEs are literal formula memorization classes, just an extension of calculus and some linear algebra. The "proofs" are laughably easy
>number theory and combinatorics are taught as if I haven't taken abstract algebra yet
>numerical analysis makes me want to claw my eyes out
>there's nothing that will really expand upon my core knowledge
>except second course in anal, second course in AA

[Anonymous No.10873245]

>>10873215
The competition is extremely fierce and funding is limited. Most top schools have thousands of applications and only take the top 10 or so students that apply per year.

[Anonymous No.10873258]

>>10873245
I would've thought something like computer science or electrical engineering would be like that but math? Wow...

[Anonymous No.10873275]

>>10873258
pure math is a stupid decision you will regret if you aren’t genius iq

[Anonymous No.10873277]

>>10873209
I don’t care about your quarrel with the turbo sperg I just think that whining about elitism in a fucking math general is funny desu

[Anonymous No.10873283]

>>10873277
DOES THIS LOOK LIKE IM WHINING, BITCH?

[Anonymous No.10873309]

Applied Math/Physics is better.

[Anonymous No.10873356]

>>10864149
Guys, how do I hold myself accountable? I never finish the textbooks I want to read even though they aren't challenging. I don't want to waste another summer.

[Anonymous No.10873371]

>>10873356
have iq
>>10873309
this desu

[Anonymous No.10873395]

Why am I unemployed with a BS in Math?

[Sage No.10873417]

>>10873395
You were an autist that didn’t network in undergrad and didn’t do any internships.

[Anonymous No.10873422]

>>10873371
Are you saying that I should just be cleaning toilets?

[Anonymous No.10873430]

>>10873356
Trust me, you don't want to. Just take the summer classes at your college, or just have fun, or whatever. You don't want to experience the agony that comes along with not being lazy
>decide I want to study for the math classes that I'll be taking next semester
>buy the textbook
>take hours on a trivial problem
>read and reread the definitions over and over again, trying to make sense of it all
>the internet is 0 help
>always make it to about halfway into the book
>can literally feel the neurons in my brain tying a knot with themselves, and then the blank "does not compute" npc feeling wash over me
>try to think harder/faster/smarter
>it doesn't work
>give up
>spend the rest of the summer getting drunk smoking weed and fucking bitches
>I do this every. fucking. summer. with a different textbook each time. I always fail.
>go into the semester hoping that I atleast prepared myself decently
>I'm a B student
god, I'm such a depressed brainlet I should kill myself

[Anonymous No.10873441]

>>10873193
>>10873209
I obviously can't do that you troglodyte. You are trying to bait me into saying something incorrect. It is an elementary result of Galois theory that such a formula cannot be found (well, using common tools... of course one can be if you take a function that spits out the roots of a few quintics).

[Anonymous No.10873445]

>>10873220
You were supposed to mix in electives like everyone else. Aren't there grad courses you can take instead?

[Anonymous No.10873447]

>>10873430
Yeah sorry, I definitely get why in your situation that would suck but there's a good chance that the person your responding to is not a complete idiot like you are.

[Anonymous No.10873475]

>>10872354
this

[Anonymous No.10873479]

>>10873475
Very dumb post, likely written by one of /mg/'s worst posters. No worries, I'll pick up the slack. As usual.

[Anonymous No.10873624]

>>10873430
>spend the rest of the summer getting drunk smoking weed and fucking bitches

pretty based minus the weed part

[Anonymous No.10873637]

I'll get my math degree in about 4 months. After that, I will apply for a masters degree in math. I have a handful of optionsbut I am now almost completely sold on one that focuses almost exclusively on analysis (what I want to do my Ph.D. in), with topics in Algebra and Topology only covered as far as required for analysis (so we'll see the topology of metric spaces and such). However, a professor of mine adviced me that regardless of what I want to specialize in, for a Ph.D. I should master not only analysis but also algebra and topology. Clearly in my masters I will not learn anything about algebra/topology beyond what I already know from my undergrad. Are there any particular books that would level me up on algebra and topology for Ph.D. level studies (assuming I know the basics) that I could just study on my own?

[Anonymous No.10873643]

Do you believe the Königs lemma should be considered true?

[Anonymous No.10873668]

https://en.wikipedia.org/wiki/Partition_of_sums_of_squares#Partitioning_the_sum_of_squares_in_linear_regression

Why is [math]\sum_{i=1}^n \hat{\varepsilon_i} = 0[/math] if the model has a constant?
In particular I do not get the next to last line of the proof where
[math]\sum_{i=1}^n\hat{\varepsilon_i}x_{ij} = 0[/math] for each of the terms [math]j[/math]

The sum of the residuals being 0 seems to me to imply that RSS is 0 which makes no sense

[Anonymous No.10873776]

>>10873624
Based, all other vices are okay but potheads are disgusting.

[Anonymous No.10873778]

>>10873637
Your professor is a moron. Algebra is worthless to analysts. Of course you should know topology.

[Anonymous No.10873791]

>>10873778
Yeah, probably. But he did mention that I will need it to pass entrance exams and such. Though I see many programs that don't even require that, you take exams after you pass the first couple of classes.

[Anonymous No.10873803]

>>10873778
algebra isn't worthless to analysts. singularity theory deals with smooth maps and their deformations using algebraic toolkit - it studies the ring of smooth function and its ideals and modules.

[Anonymous No.10874320]

How long should it take to finish a calculus book such as Apostol?

[Anonymous No.10874355]

>>10873441
DID I SAY USE COMMON TOOLS, YOU BITCHASS? THERE IS A FUCKING FORMULA FOR THE GENERAL QUINTIC JUST NOT IN RADICALS. UNLESS OF COURSE YOU CAN PROVE ME WRONG, BITCH.

[Anonymous No.10874358]

>>10873447
I still have a math degree from a top math school in USA. Laziness is a form of stupidity, so I doubt it.>>10873624
>>10873776
bitches love weed though. I wouldn't have gotten laid in high school without it.

[Anonymous No.10874372]

>>10874320
>How long should it take to finish a calculus book such as Apostol?
Why don't you try it and find out?

[Anonymous No.10874401]

>>10874320
usually 4-6 years

[Anonymous No.10874421]

Any good introductory books on linear programming?

[Anonymous No.10874434]

>>10873803
Well, I am willing to edge on the notion that algebra and topology are important just because there's not much you can do anywhere without at least a basic understanding of groups and fields. As I asked in >>10873637, do you have any book recommendations? Maybe some sort of "algebra for analysts" kind of thing?

[Anonymous No.10874442]

>>10873422
No, try harder. Learn to lean into the psychological torture of self propelled study outside the academic pressure cooker. If you can’t then accept it and understand you’re neither as strong nor as smart as you thought you were. Its very wise to learn one’s limits while the stakes are still low. Iq is a limiting factor only at the extremes but otherwise you have no excuse.
>>10874421
>>>/g/
>>>/lgbt/
>>>/out/
>>>/trash/
>>>/r/eddit
>>>/b/
not in this general, no
>>10874320
1-3 months depending on how hard you work

[Anonymous No.10874471]

>>10874434
what do you want to do for your phd ?

[Anonymous No.10874481]

>>10874471
Well, one area of research that particularly interests me is stochastic analysis. I could easily see myself going that route for a Ph.D., and there would be many options. But for now I am being more open and just thinking that my Ph.D. will be something in analysis, as that's what I like and will likely benefit me regarding the lifestyle I want.

[Anonymous No.10874507]

>>10874434
Basic Algebra and Topology are just absolute standard knowledge, not knowing them is like an English major not knowing how to read. Just pick the standard books, like Foote or Aluffi or Lang or whatever

[Anonymous No.10874524]

>>10874507
Well, I have one point-set topology course and 3 algebra courses under my belt. However, the professor who I mentioned before (who taught me that 3rd and final algebra course) told me to my face that even though I got an A in his course (and all other algebra courses) I am not at all ready for a Ph.D. and will likely get murdered if I go to somewhere like Germany.

That's why I want to level up. I don't want to get murdered in Germany.

[Anonymous No.10874550]

>>10874442
>not in this general, no
>convex analysis and optimization are now not maths

[Anonymous No.10874579]

>>10874421
>good books in anything programming
Basically don't exist.

[Anonymous No.10874637]

>>10874524
Have you had analysis on manifolds or differential topology? These could be relevant for someone interested in Analysis.

And what where these three Algebra courses? If you already took a proper course on abstract Algebra, you should be fine imo

[Anonymous No.10874655]

>>10874637
>Have you had analysis on manifolds or differential topology?
The closest thing I've had is differential geometry. My university (and all other universities in my country for that matter) are not as sophisticated as places like Germany. A friend of mine went to Germany and he showed me that it is basically another world. But I still want to be a mathematician, it will just be an uphill battle.

>And what where these three Algebra courses? If you already took a proper course on abstract Algebra, you should be fine imo

They were just continuations of each other but very roughly they corresponded to group theory, ring theory and finally field theory. As you can notice, nothing was said on modules or algebras which is something that my professor also stressed will have me killed in Germany.

[Anonymous No.10874656]

>>10874550
>maths
Not maths.

[Anonymous No.10874664]

>>10874358
a "math degree" is worthless
Cs get degrees

[Anonymous No.10874665]

>>10873803
wow, no one gives a single shit. and no self respecting analyst uses such "tools"

[Anonymous No.10874669]

>>10874550
Correct. In fact, they have never been "maths." Who are you quoting?

[Anonymous No.10874672]

>>10874655
i think you're severely overestimating the preparation you need to have. like sure, a bit more algebra and topology can't hurt, but you don't need to be a fucking expert. almost any advice anyone gives you will be tainted by a sense of pride by the person who has already done it, and they'll do their best to make it seem hard so that they can feel good about themselves.
if you know how rings work and how vector spaces work, most module theory is very analogous and you'll learn it quickly. and who the fuck uses algebras.

[Anonymous No.10874856]

>>10873220
>numerical analysis makes me want to claw my eyes out
The worst course

[Anonymous No.10874978]

>>10874664
Post your degree, nudes of your woman, and pay stub then, you jaded prick.

[Anonymous No.10875096]

>>10874978
oh, i have a math degree. one with a 4.0 gpa at a top school backing it.
i'm saying just about anyone can get a math degree by merely passing.
and i'm not interested in women. why the heteronormativity?

[Anonymous No.10875103]

Is it feasible to learn basic statistics in a week? It's a prereq for a class I want to take that is only offered once every two years, so my only option is to grind it for a week and test out of it.

[Anonymous No.10875110]

>friend asks me what I'm reading
>tell him it's manifold calculus
>"Oh, Rudin?"
>"Yeah"
>mfw I'm reading Goodwillie-Weiss

[Anonymous No.10875113]

>>10875103
of course it is.
>>10875110
you don't have many other friends, do you?

[Anonymous No.10875128]

>>10875113
he doesn't have any friends besides his circle of undergrads that he wants to worship him
what would you expect out of a dead field in a dead shithole and a dumb discordfag?

[Anonymous No.10875135]

>>10864149

Imagine playing a Final Fantasy game and having these two guys in your party

[Anonymous No.10875139]

>>10875128
i didn't know about the discord stuff or the shithole. wow, yukari"bro" really is disgusting

[Anonymous No.10875305]

>>10874665
just because you've never heard of that doesn't mean nobody gives a shit anon

[Anonymous No.10875378]

>>10875110
why did you lie to your friend?

[Anonymous No.10875389]

>>10869994
me
how is it a meme?
did you get a kuru toga?

you might find that you actually rotate the pencil yourself. stop doing that

[Anonymous No.10875409]

>>10875128
>>10875139
imagine being this jealous of a sperg avatarfag

[Anonymous No.10875488]

>>10875409
your confidence really is made up
no wonder your entire department mocks you to your face

[Anonymous No.10875501]

>>10873778
>what is geometric group theory
>what are Banach and operator algebras
>what are differential algebras and Picard–Vessiot theory
>what is abstract harmonic analysis
>what is Thom's catastrophe theory
>what are Riemann surfaces

[Anonymous No.10875512]

>>10875501
> Banach and operator algebras
don't need too much algebra desu.
>abstract harmonic analysis
this shit, in my opinion, is one of the most forced meme branches of analysis.

[Anonymous No.10875513]

>>10875096
I literally said I'm a B student with a math degree from a top school. Now following your reasoning, there's no difference between our intellect, and you called me a brainlet. Except I took graduate classes for my degree.
>im not into women
fag
>why the [big word]
>>>/lit/

[Anonymous No.10875531]

>>10875513
>fag
Why the homophobia?

[Anonymous No.10875611]

>>10875512
>>abstract harmonic analysis
>this shit, in my opinion, is one of the most forced meme branches of analysis.
why ?

[Anonymous No.10875628]

>>10875531
why are you a faggot lover?

[Anonymous No.10875631]

>>10875628
>faggot
Why the homophobia?

[Anonymous No.10875634]

>>10875631
why are you a faggot lover?

[Anonymous No.10875909]

What is the name for a finite subset family whose elements are closed with respect to intersection?

I feel like it's a lattice or simplical complex or matroid, but I don't remember these definitions very well

[Anonymous No.10875930]

>>10875909
Gaussian functionals converge to the dirac delta in a distribution sense. What about in a measure theoretic sense? Are there integrable functions whose integral with respect to a sequence of gaussian measures doesn't coverge to f(0), or whatever?

[Anonymous No.10875932]

>>10875930
Didn't mean to quote >>10875909

[Anonymous No.10875945]

>>10875909
Meet semilattice.

[Anonymous No.10876023]

I have done Calc 1-4 during the first semester and in a engineering major thats kinda it for now. I guess Im asking what would be the natural continuation from this, maybe set theory?

[Anonymous No.10876035]

Hi /mg/, which mathematics books should I purchase in order to impress people and maybe skim them a little? Difficulty may be arbitrarily high but preferably well written

[Anonymous No.10876049]

>>10876035
Just read famous proofs and thesis's. If you tell someone you've read Andrew Wiles proof of Fermat, most people will seem impressed

[Anonymous No.10876086]

>>10875139
Redpill me please.

[Anonymous No.10876129]

>>10876023
Linear Algebra Peter Peterson
Mathematical Analysis Apostol
Topology Munkres
Algebra Artin

[Anonymous No.10876207]

>>10876129
All of these are brainlet books

[Anonymous No.10876260]

how many comments before the next /mg/?

[Anonymous No.10876264]

>>10876207
http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf

http://www.ams.org/publications/authors/books/postpub/simon

[Anonymous No.10876269]

>>10876207
why

[Anonymous No.10876316]

I have completed a degree in physics mostly focusing on experimental but I realise my passion is more for mathematics. I have a good basis in mathematics from my course and plan to work on the curricula I've seen in these threads but what would be my best pathway to get into a field in mathematics? Are there graduate mathematics course designed to flesh out the mathematics for brainlets like myself?

[Anonymous No.10876321]

>>10876316
Check this
http://www.math.harvard.edu/quals/index.html

[Anonymous No.10876355]

>>10876321
thanks friend

[Anonymous No.10876358]

Greeting /mg/ I was looking to explore a bit of math and I decided to try following Harvard’s Math 55a. Have any anons tried to do that? It’s not exactly a book but the lecture notes are useful and you’re following Axler. There are no videos so it’s not like I’m trying to be lazy and avoid reading the book. I was basically trying to find a reasonable curriculum to follow.

Maybe I’m crazy but my goal was to get a bit of exposure to abstract algebra, analysis, complex analysis and topology. Are there good books to follow that touch on all these at an undergraduate level?

So far the problems have been pretty hard. Pic related.

For some reason it seems like they’re suggesting there is an identity for convolution in the ring they provide. But I thought convolution didn’t have an identity in general. Any thoughts?

[Anonymous No.10876392]

>>10876358
Pic related doesn't contain a problem but okay. It's introducing formal series. The first term in the sequence corresponds to the 0th exponential term, the second to the 1st, etc. So (-2,0,1,...) corresponds to x^2-2. Think of the convolution operation as multiplying polynomials.

If you've having trouble with rings/algebras I suggest looking at groups first to get more comfortable with the abstract setting. If you've already covered groups, then look for another book on rings (on the libgen website) until you find one that you like.

[Anonymous No.10876484]

>>10876392
The problem continues across the divide of the page in the pdf. The actual question starts at 8. The first part is just for context. I actually got it. The identity element should be sequences where the first element is one and the rest are zero. I don’t know why I couldn’t see until after posting.

[Anonymous No.10877072]

>>10876035
stay current on the annals and you're good

[Anonymous No.10877189]

>>10876035
Higher Topos Theory by Jacob Lurie
Disquisitiones Arithmeticae by that one german guy
EGA and SGA

[Anonymous No.10877372]

>>10876035
Griffiths and Harris - Algebraic Geometry
Gromov - Differential Relations
that one measure theory book

[Anonymous No.10877392]

>>10871492
When pure math gets applied, it tends to be really specialized and technical stuff you can black box, like the stuff people are working on in fully nonlinear pde. The real reason why pure math isn't applied is that cs / engineer / non-theoretical physics people are incompetent at geometry. Find anyone outside the math and physics department who can explain the index theorem.

Nowadays people study geometry, yeah it has roots in algebra but ever since Lefschetz that hasn't been the right way of thinking about it. The major achievements since 1950 have been through a structured paradigm that doesn't "describe sets" but rather "finds and extracts invariants" in geometry, whether that's via the Weil conjectures in finite field point counting questions or via relating the inverse scattering problem for the Schrodinger equation and KdV to Hamiltonian flows on the Jacobian of the spectral curve. Most grad students, sadly, don't read enough to get even that far and are pushed into fields whose true motivation is above their heads. Many who fail conclude that mathematics is a dead end.

[Anonymous No.10877487]

measure theory should be required for any mathematician

[Anonymous No.10877518]

>>10877392
>>10877487
this, desu

[Anonymous No.10877642]

>>10874421
These lecture notes cover most of the fundamentals
https://www.win.tue.nl/~rudi/opt.pdf

[Anonymous No.10877710]

>>10875501
No worries, I was just doing the "algebra and analysis are forever opposed" joke. The thing I had in mind was Lie Algebras but I forgot about Banach & Operator Algebras and that stuff is fucking beautiful. Best type of math hands down.

[Anonymous No.10877714]

>>10875513
I took plenty of graduate courses as well, usually with extra coursework cause there was too much I wanted to take. I mean it's not a competition or anything but A student is better than B student...

[Anonymous No.10877722]

>>10876358
Good lord, what a horrific, unmotivated way to introduce convolution. Can anyone imagine a class so awful that these rings S_A and S_A^0 are introduced as sequences and not as power series / polynomial rings? Christ.

[Anonymous No.10877724]

>>10877189
>that one german guy
gauss, HIS NAME WAS GAUSS!!! WHAT THE FUCK?!!

[Anonymous No.10877735]

>>10877722
It is an exercise, the goal is not to introduce power series rings (but they are referred to in the comment), but only to write simple proofs and test your knowledge of ring axioms

[Anonymous No.10877750]

>>10877735
It didn't seem much like an exercise. In any case, exercises like that are braindead, so simple a child could do them. Math 55 is a meme.

[Anonymous No.10877772]

>>10876035
Horrible reason for buying books but you can try:
. Anything in the Springer Monographs in Mathematics series
. Fuchs-Fomenko
. SGA, but anything by Grothendieck will do
. Demazure and Gabriel’s thicc book on algebraic groups
. Any book with the word topos in the title
. Federer’s Geometric Measure Theory
. Hörmander’s linear PDE 4-volume behemoth
. Any multi-volume book, really
. Anything by Milnor
. Anything by Neukirch (even better if you read them in the original german versions)
. Villani’s book on optimal transport
. Anything older than 1900 (to establish yourself as a person of culture)
. Complete works of a mathematician (for good writers, I suggest Milnor, Serre, Atiyah, Tits). This can be combined with the former by buying complete works of historical mathematicians, eg. Cauchy, Galois, Riemann, Hilbert, etc.

[Anonymous No.10877795]

>>10877772
Kino post. Absolutely excellent post.

[Anonymous No.10877800]

>>10877772

Yeah really bad reason for buying a math book.

Honestly though, if you don't know what's in the book, any calc book will probably be impressive to the people you hang out with.

[Anonymous No.10877896]

>>10877772
>Any book with the word topos in the title
Top kek
Also immediately made me think of Peter Johnstone's Elephant

[Anonymous No.10877951]

>>10877896
Ah yes, "The Elephant in the Room: How Topos theory is killing pure mathematics", a truly great work, presenting the many ways in which Topoi appear in and debase maths.

[Anonymous No.10877961]

I am trying to self-learn mathematics, I read Calculus Made Easy by Thompson and I really liked it, sadly in my country we don't learn Calculus in High School, so I was ignorant on the topic before reading the book. After finishing it I went to 4chan's wiki on mathematics, downloaded Challenging Problems in Geometry and got stuck in the first problem.

I am a brainlet. HELP. What is the next book that I should read to get better at Mathematics?

[Anonymous No.10877992]

>>10877951
>presenting the many ways in which Topoi appear in and debase maths
I'm glad toposes don't do that. It would suck balls if there was a mathematical construction doing such nasty things.

[Anonymous No.10878007]

>>10877951
sounds like my kinda book. heh.

[Anonymous No.10878019]

>>10877961
Well, if you'd like to continue more into the theory direction, I'd highly recommend Gilbert Strang's Linear Algebra lecture videos, available for free on the MIT OpenCourseWare website. Class number is 18.06SC I think? Strang is a really wonderful lecturer and linear algebra is important to learn. It's also a great way to start getting used to proofs and problem solving.
Another option might be Fraleigh's A First Course in Abstract Algebra, which is very gentle and helpful for developing a problem solving mindset. But honestly I'd recommend linear algebra over general algebra first, cause linear algebra (the study of vector spaces) motivates other parts of algebra like group theory, ring theory, and field theory enormously.
Alternatively, if you really liked your calculus stuff a lot more than high school algebra, you could pick up Tao's Analysis 1 and 2, which will show you why all the things in Thompson are actually true (and will before that take a very gradual approach to building up your theoretical understanding of math).
Many geometry problems are predicated on being tricky and clever, which are skills you build as you solve more problems which force you outside your comfort zone. I would recommend learning some more math and finding something that really grabs your enthusiasm before you start going after these intense problem solving books (for me, this ended up being Polya and Szego's Problems and Theorems in Analysis which is a wonderful but very tricky book).

[Anonymous No.10878024]

>>10877961
>>10878019
I should mention, Strang's course has a book and the OCW website has problem sets and exams as well. There's a lot there.

[Roy Aldik No.10878050]

>>10877961
Words will hardly help you. Draw shapes & number edges. Play with numbers if you want number skills not words. The amount of bullshit people write around mathematics is dumbfounding....& it helps if you have a problem worth solving then the solution is easier to invent.

[Anonymous No.10878199]

>>10878019
Thanks for the advices, anon. I appreciate it.

[Anonymous No.10878344]

>>10876321
That is clearly biased towards algebra. Galois theory is already something that is taken as an elective. Why would you have fucking algebraic geometry there too?

[Anonymous No.10878419]

>>10873283
yes

[Anonymous No.10878422]

>>10878344
>muh algebra vs analysis
Grow up, retard

[Anonymous No.10878494]

>>10878422
>Reading comprehension
The quals are retarded. Not the subjects.

[Anonymous No.10878524]

>>10876321h
>http://www.math.harvard.edu/quals/index.html
Are those qualifiers for the PhD program or the masters one?
>>10878344
>Galois theory as an elective
Your university is dogshit.

[Anonymous No.10878530]

>>10878524
>http://www.math.harvard.edu/quals/index.html

I didn't know Harvard had masters, but if I had to guess, I think it'd be right hand side since the algebra problems (I can only do algebra) are quite simple. Left hand algebra problems seem more involved.

[Anonymous No.10878545]

>>10878530
All the problems are easy, and quite a few are basic results you can find in textbooks. It says in the page it's an exam to check for knowledge.
Quite a few are an absolute huge fucking pain, tho. Specially some algebra ones.

[Anonymous No.10878553]

>>10878344
It's because Harvard is a fucking meme and anyone who has attended the school is a talentless hack. Name a single prominent analyst or geometer from Harvard, I'll fucking wait.

[Anonymous No.10878689]

what would solving the prime numbers entail for civilization?

[Anonymous No.10878776]

>>10878689

It would cause mathematics as we know it to conclude. Many professors and grad students would resort to becoming full time giggalos and the rest will join the French foreign legion.

[Anonymous No.10878880]

The canonical norm on the product of two Hilbert spaces is the pythagorean norm, is that also the case for arbitrary normed vector spaces or do you just sum the norms?

[Anonymous No.10878888]

>>10878880
Many such methods work to combine norms of Banach spaces

[Anonymous No.10878889]

>>10878888
Yeah, but what's the standard?

[Anonymous No.10878932]

https://youtu.be/Ox0tD58DTG0

Made a clip elaborating on computably enumerable sets (and also sketching the halting problem with some implementation support)

[Anonymous No.10878962]

<TT*u, v> = <T*u, T*v> = <u, TT*v>.
Such a shitty result, such a shitty proof.
Beautiful.

[Anonymous No.10879218]

>>10878889
there is no standard. depending on the situation people either max or sum, whichever looks nicer / makes your calculations nicer. they're equivalent norms, of course, so the topologies are the same.

[Anonymous No.10879221]

>>10878962
yep, you sure are right about it being shitty!

[Anonymous No.10879292]

>>10878050
No

[Anonymous No.10879349]

>>10875378
To boost his confidence.

[Anonymous No.10879356]

>>10878524
My uni didn't even offer Galois theory.

[Anonymous No.10879456]

>>10878019
I second Strang's lectures. Only thing is that he doesn't emphasize Jordan Canonical form, which personally I think is important. I would look into it somewhere else.

[Anonymous No.10879554]

>>10878553
Umm Mirzakhani ? Also, Abhyankar, Mumford, Quillen, Voevodsky...

[Anonymous No.10879582]

>>10875611
I don't know it just feels like it. I know you have the haar measure, so you have a natural way of defining an integral over a group. You also have the Gelfand transform, so that is nice, but the thing that you don't have are the nice decomposition and covering theorem, or more fundamentally it's hard to define and apply the maximal operator (I mean I don't even see the point of that). Aside that, and all the other things, the main question is" what's the point? Can you get to know something qualitatively new and different then in the case of n-dimensional torus or R^n or is it just generalization for the sake of generalization?

[Anonymous No.10879855]

>>10878422
everybody knows geometers are superior

[Anonymous No.10879942]

>>10873430
>the agony that comes along with not being lazy
Boomer nonsense

[Anonymous No.10879999]

>>10879456
I agree, but you really need to do hoffman and kunze or axler or something after doing strang's lectures so you'll get that there.

[Anonymous No.10880001]

>>10879855
uhhh lemme get a BASED

[need marketing homework help No.10880001,1]

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