/mg/ maths general: Shimura curve edition

How should I respond if someone asks me for my preferred axioms? I know that respecting a person's axioms is vitally important to creating inclusive environments for all mathematicians

I was hoping for a few ideas, expecting a flame war and what I got was this one reply with nothing but a link. But the discussion you linked was able to ease my mind. Thank you, based user.

google deloitte report on benefits of math research

how do i review linear algebra in preparation for projective geometry ? what should I focus on?

Skim through the lecture notes you took back then

Thanks to you, too. I think I no longer feel like a waste by doing math, or if I ever decide to apply for a PhD program.

>if I ever decide to apply for a PhD program.
Don't. It will ruin your life.

For a life to be ruined by doing something, it is required that it is not ruined before doing it. My life can not be ruined.

How can I get better at topology? I'm in the beggining of Munkres and it is being a terrible experience.

>it is being a terrible experience.
What do you mean exactly?

What matters more in Math? High Abstract Pattern Reasoning (Raven Matrices/IQ testing) or creativity(unorthodox insights into problems).

Both.

What field of math do you think requires more unorthodox insight? Would it be Combinatorics? Or?

>Combinatorics
You just lost your reproduction license.

Topology for example. Pretty much anything where you benefit from being able to visualize the objects, and then twist and turn them around in your mind.

Probably the worst part is the exercises. In most textbooks I've used in other subjects, they were no real problem and normally I could solve them. In Munkres' Topology, however, the same didn't apply. This probably reflects something deeper about my understandment of the text.

Point set topology exercises are usually garbage though. Much like the parts of it which aren't used in algebraic topology or any other superior fields.

Exercises in point-set topology are mostly definition-pushing. In most cases, it's just "write out all the definitions and do the only thing you can do". Are you struggling with remembering the definitions? Have you studied analysis before to give some motivation/intuition for the definitions?

When I started doing topology (also using Munkres) I thought each exercise was some super involved thing. But once you're familiar with it it all seems super trivial.

The same applies to Dugundji. It's good to have problems reinforce the definition in your mind, but it gets boring quite fast.

Explain? I'm really into Combinatorics right now because I like coming up with cool algorithms that can count things in polynomial time.

I assume low dimensional topology, right?

Are they? Can I still understand the text without being able to solve a part of them?

You used the example of algebraic topology. I'm really interested in this subject, and I've already a good knowledge of algebra- and even the most fundamental concepts of algebraic topology, like homotopy and homology. Isn't point set topology that necessary?

Maybe I'm struggling with some definitions. I can remember most of them easily. My real problem- I suppose- is with intuition. In fact, they sometimes don't look quite familiar- and that turns into a big problem when trying to solve the exercises.

It is fairly easy to do in ZFA (can't well order atoms), but showing that ZFA has the same consistency strength as ZF is nontrivial.

>Isn't point set topology that necessary?
In the beginning you should focus on learning about limits and colimits in the category of topological spaces. Also learn about compactness, connectedness, the compact-open topology and everything needed to define it. This should be enough to get started with algebraic topology.

What does it mean if I do better in real Analysis than abstract algebra? I can just read the proofs in real analysis and get a nice grasp of the material but abstract algebra just seems like a new bum fuck definition comes out of no where with no sense of meaning behind it. With real analysis I can see why someone would want to define the Bolzano Weierstrass Theorem and the cauchy sequence but why the heck would anybody care about cosets and all that stuff(yes I know it has something to do with quotient groups and the decomposition theorem).

What did I do wrong guys? Please don't tell me that I have an analyst brain or anything, I think that's bull shit and I like to learn both subjects. Thanks.

>define the Bolzano Weierstrass Theorem

>What does it mean if I do better in real Analysis than abstract algebra?
It means you're better at engineer garbage than mathematics, it's a pretty common condition around here.

Sorry my English isn't that good. What I mean, is that I can see how the theorem fits in with the rest of the material.

By what I've seen, connectedness sounds really more intuitive. Maybe it's the subject

Please no meme replies. Everyone knows that analysis is a respectable branch of Mathematics, anyone who thinks other wise is a retard or someone who did horrible in real analysis and thinks being good in Algebra is the only requirement one needs in order to be a Mathematician. The inverse is also true.

>implying analysis is closer to engineer garbage than to math

You have an analyst brain, use it to your advantage

Study harder in algebra, then you will feel the same intuition.

I find abstract algebra so sexy though, I don't want to pigeon hole myself into analysis. How true is this meme, I know your not being an ass hole but I don't like being told that I can only succeed at x being apparently I have x brain.
Let me ask this, how do I get good at Abstract Algebra with an analyst brain?

>the only requirement one needs in order to be a Mathematician.
Not the only one, but it's a pretty major requirement.
>"inverse" instead of "converse"
Definitely an engineer.
That's indeed the case.

>how do I get good at Abstract Algebra with an analyst brain?
You have to start by actually learning mathematics instead of playing around with analysis. You're pretty far from your goal if you only "think" cosets have "something to do" with quotient groups.

Are you saying I should stress definitioms and thorough reading more than problem solving? Im really trying to learn, user.

Unless you are saying that real analysis isnt math, then I dont really want advice from an idiot who most likely failed analysis but isnt mature enough to realize its importance.

>stress definitioms
What do you mean?
>problem solving
The only kind of acceptable "problem solving" at the beginner level is proving theorems. If that's what you mean, then go ahead.

>most likely failed analysis
How does one fail engineering courses without taking them?

What is a good introductory text for category theory?
No memes please.

To be fair, you have to have a very high IQ to understand modern algebra. The proofs are extremely subtle, and without a solid grasp of real mathematical reasoning most of the theorems will go over a typical viewer’s head. There’s also quotient groups, which are deftly woven into cosets- its deep meaning draws heavily from Lagrange's Theorem, for instance. The algebraists understand this stuff; they have the intellectual capacity to truly appreciate the depths of these groups, to realise that they’re not just interesting- they say something deep about POLYNOMIALS. As a consequence people who don't understand algebra ARE brainlets- of course they wouldn’t appreciate, for instance, the Isomorphism Theorems, which itself are a cryptic reference to category theory. I’m smirking right now just imagining one of those addlepated simpletons scratching their heads in confusion as Galois' genius wit unfolds itself on their textbooks pages. What fools.. how I pity them.

And yes, by the way, i DO have a Cayley Diagram tattoo. And no, you cannot see it. It’s for the ladies’ eyes only- and even then they have to demonstrate that they’re within 5 IQ points of my own (preferably lower) beforehand. Nothin personnel kid

Come here for help. All I get is meme replies = /. Can someone with a more mature view on Mathematics please help a nigga out? I may be stupid but I'm not enough enough to think an entire branch of Mathematics is engineering.

Thanks.

>All I get is meme replies
How exactly is a "meme reply"?

Leinster - Basic Category Theory

...

>not enough enough to think an entire branch of Mathematics is engineering
A branch of mathematics can't be engineering, this is correct. But real analysis isn't a branch of mathematics.

this and Steve Awodey - Category Theory. You can read both while skipping certain sections of Awodey depending on your needs.

mac lane - categories for the working mathematician

math.stackexchange.com/questions/355418/should-i-be-worried-that-i-am-doing-well-in-analysis-and-not-well-in-algebra

Thanks senpaitachi

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>What is a good introductory text for category theory?
why bother? it's irrelevant to most of mathematics anyway

>most of engineering
ftfy

That's true too, but I'm no sure what it has to do with my post.

> I'm an elitist ass hole who thinks studying pure math at a third rate university makes me special.

How does it feel being so brown?

>> I'm an elitist ass hole who thinks studying pure math at a third rate university makes me special.
Who are you quoting?

Did that hit too close to home?

You are daydreaming.

The only one day dreaming are people who major in pure math and act overtly elitist in order to make up for intellectual short comings.

This. Leave the category theory to physicists, kids.

Arithmetic Gauge Theory: A Brief Introduction
Minhyong Kim
arxiv.org/pdf/1712.07602.pdf

>Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular, the geometry of moduli spaces of principal bundles appears to be closely related to an effective version of Faltings's theorem on finiteness of rational points on curves of genus at least 2. The study of arithmetic principal bundles includes the study of {\em Galois representations}, the structures linking motives to automorphic forms according to the Langlands programme. In this article, we give a brief introduction to the arithmetic geometry of principal bundles with emphasis on some elementary analogies between arithmetic moduli spaces and the constructions of quantum field theory. For the most part, it can be read as an attempt to explain standard constructions of arithmetic geometry using the language of physics, albeit employed in an amateurish and ad hoc manner.

They told me I could learn physics with just calc diff equations and linear algebra :(

>They told me I could learn physics with just calc diff equations and linear algebra :(
Oh sweetie...
arxiv.org/abs/1111.5056

>pure math
There is no other kind.

This is me (except the last part).
Graduated with pure math three years ago but went straight into industry. Hate everyone here.
Would I do it again? Yeah I loved the major. People are autist so if you weren’t one you were already better. Def lots of lost potential tho.

>There is no other kind.
What do you mean?

...

Applied Math? Combinatorics?

Being overtly elitist is retarded and only serves to hamper your world view.

>uh?

>Applied Math? Combinatorics?
Neither of those are math.
>elitist
I didn't say anything negative about them. They simply aren't math in the same way history isn't.

I guarantee you would hate a life of being a research professor. The math purism view is just some kind of shitty Stockholm syndrome pushed by retards, people like perelmeme already BTFO academia faggots, so if you want to do pure math why not just do it without the illusions of grandiose that entails being a research professor?

> I didn't say anything negative about them. They simply aren't math in the same way history isn't.

I don't get how someone could have their head so far up their ass. It's quite funny to be honest, and sad at the same time.

>enough enough
the worst kind of enough

Brainlet undergrad sophomore here. What exactly is the difference between geometry and topology?

>What exactly is the difference between geometry and topology?
Nothing

You might be retarded. As in medically.

topology is a subfield of geometry

Get mad fag. Take your pseudointellectual elitism some where else.

define "math"

>fag
Why the homophobia?

Do you deny your nature?

see

No. I just think you are a faggot; as in, you are being an elitist cuck just for the sake of showing off your epeen.

Geometry is local while topology is global. Though this doesn't mean that they're mutually exclusive.
arxiv.org/list/math.GT/recent
Pretty based field actually.
arxiv.org/abs/1709.04306

see

>No.
Props for your honesty. At least you realize your own retardation, too bad that doesn't help you understand that combinatorics is not mathematics.
>you are being an elitist cuck just for the sake of showing off your epeen.
Everyone with a brain begs to differ.

>Do you deny your nature?
en.wikipedia.org/wiki/Homosexual_behavior_in_animals

...

Geometry = Topology + additional structure

"additional structure" varies, generally a sheaf encoding some algebraic or analytic structure