/mg/ math general

[Anonymous No.10012488]

Previous thread >>10002000

Trivial proof edition

[Anonymous No.10012520]

>ANON PLEASE TELL ME WHAT BOOK TO READ

[Anonymous No.10012524]

>>10012488
induction nigger.

[Anonymous No.10012537]

>>10012520
https://arxiv.org/abs/hep-th/0609022

[Anonymous No.10012544]

>>10012524
Where's is base case?

[Anonymous No.10012904]

>>10012488
/Sci/ I am need of some help. What are some good books/online resources/methods to study lower-->mid division undergraduate math courses such as Analysis 1/Algebra1. I slowly want to work up to understanding Topology. I keep seeing topology in posts talking about mathematical modelling of biology (with or without ML references), so I figure this will round out my math education.

I've done calc 1/2/Lin alg1, and am currently doing calc3/discrete structures in maths/medium level probability, and soon Lin alg 2/medium level stats.

[Anonymous No.10012938]

>>10012904
Visit the site of your university of choice and check out the syllabus for the course you're interested in, it usually comes with a list of recommended textbooks.

[Anonymous No.10012948]

Why would anyone say that guessing the solution to a diff equation is not valid? What the hell are they doing to mathfaggs these days?

[Anonymous No.10012954]

>>10012938
For sure. Is there anything else you'd recommend apart from that with regards to self learning? I'll of course read and do practice questions, and not skimp out on either option

[Anonymous No.10012962]

>>10012938
For example, if I do analysis 1+algebra 1, should I then proceed into analysis 2/algebra 2? Or complex analysis (which is where you learn about topologies?)

[Anonymous No.10013002]

Talks from IAS Voevodsky conference are up on youtube

[Anonymous No.10013013]

guys, is computational geometry and/or topology a CS topic or is it math?

There was a mathanon here that is studying this in his ph.d and I wanted him to tell me more about it.

[Anonymous No.10013026]

>>10013013
It's both but it leans more to the math side, just like theoretical computer science

[Anonymous No.10013034]

>>10012904
>I slowly want to work up to understanding Topology
There's not really prerequisites for it. If you have an intro to proofs course, take that first. But algebra and real analysis aren't prereqs

[Anonymous No.10013040]

>>10013026
can you apply it anywhere and get a job (graphics, maybe?) or can you only just research it?

[Anonymous No.10013115]

>>10013013
>is computational geometry and/or topology a CS topic or is it math?
You're cute foxes compel me to answer. More math, but then again theoretical comp sci really is also just applied math. Look up any paper on complexity and see what you get.
>>10013040
>can you apply it anywhere and get a job (graphics, maybe?) or can you only just research it?
You can indeed apply it and get a job, here are some links to intros and applications
https://www.cs.cmu.edu/~kmcrane/Projects/DGPDEC/
There's also other links there to a book, videos, a blog, and the various courses based off of the material at other unis, some of which have extra course materials, papers, and homework exercises. They even tell you how to program these things.
Another link for ya
https://www.maths.ed.ac.uk/~v1ranick/papers/edelhare.pdf
And finally, say you want to make 3D animation or video games
https://www.youtube.com/watch?v=mX0NB9IyYpU
Have fun anon.

[Anonymous No.10013118]

How do you effectively self-study material? The only thing I've found that works is reading through the text and taking notes on everything, but this feels very slow. Assume there aren't a fuckload of exercises to do or proofs left to the reader.

[Anonymous No.10013132]

>>10013115
>Have fun anon
thank you so much!!

[Anonymous No.10013160]

>>10013115
I'm looking at the links you shared, this looks incredibly interesting, I'm in love.

Thanks again here's more foxes!

[Anonymous No.10013174]

>>10013115

[Anonymous No.10013179]

>>10013115
and another one

[Anonymous No.10013187]

>>10013179
These foxes warm my heart.

When is that mochizuki Stix paper out???

[Anonymous No.10013189]

>>10013118
https://fr.coursera.org/learn/learning-how-to-learn

[Anonymous No.10013193]

>>10013189
I need someone to tell me if this is a meme or not before I waste time on it

[Anonymous No.10013201]

>tfw get stressed out by how much I don't know
It was nice at the beginning of undergrad where everything was fairly self-contained and felt "complete", like when you're doing an introductory algebra class you only need to take the set theory stuff on faith, everything else was developed. It seems like the more advanced you go the more stuff you need to just accept is true though, which makes me sad.

[Anonymous No.10013390]

>>10013132
>>10013160
>>10013174
>>10013179
Thanks for the foxes
>>10013193
I'm not >>10013189 so I don't know if it's a meme or not but maybe try to look up the papers and presentations by the course lecturer on youtube and the like to get a better feel for what she's presenting. I think her results would probably be condensed into some talk somewhere.
https://www.youtube.com/watch?v=vd2dtkMINIw
The way I study is by doing every problem and if they lay out a proof to a theorem first try to prove it myself before looking at the proof they presented. It's kind of tedious but you get faster as you start seeing the tricks of how to proceed. It also makes learning the later chapters easier since you don't have to keep looking back to remember past results, so in some sense, taking a long time to deeply and thoroughly understand the basics can save you time in the long run. Efficiency is good and all
but you should aim for understanding. Hope that helps a little.
>>10013201
Rather than "take on faith" it's more that there are prerequisite material that in the interest of time they aren't able to cover. That's kind of why you're supposed to cover things like set theory before taking abstract algebra, so nothing is taken on "faith". It is possible to start from the ground up to build the foundations of a subject from scratch, but this is usually kind of tedious and the added value is dubious at best. Take this example
http://www.geometry.org/tex/conc/dgchaps.html
which goes very in depth to cover all the prerequisite material, unfortunately that means you have to go through over 1400 pages until the DG. This is kind of why you have separate classes to cover material that then build on one another. Also you shouldn't consider any class "complete". Every field of mathematics is not only growing, but constantly intersecting with other fields of math, blurring the lines between fields. Every textbook and class you've encountered are mere slices of the grand picture.

[Anonymous No.10013569]

is this accurate: >>10013528 ?

[Anonymous No.10013594]

>>10013569
Yes
https://math.stackexchange.com/questions/190628/in-group-theory-proofs-what-is-meant-by-well-defined

[Anonymous No.10013757]

>>10013189
This is nice but you're better of reading the book.
Write some notes of the important facts and re-read them every now and then so they don't leave your mind soon.


By the way, how do I tackle problem books like "challenging problems in algebra", I guess I need to develop some sort of mathematical maturity but I don't know how to tackle that, and kinda pains me to know that there are kids who are able to do so without even thinking about it.

[Anonymous No.10013769]

>>10013118
Teach it to someone else or create a project with it.

Find a test from that course online (google "<topic> exam pdf" and you will find something) and see how well you do.

[Anonymous No.10013872]

How do I catch up on Calc 1?

[Anonymous No.10013913]

Where are some nice places to do computational algebraic number theory?
I have not taken algebraic number theory per se but I've taken Galois Theory, Commutative Algebra, Berkovich Spaces and Computational Algebraic Geometry.
I've looked and there is no one in my institution that does number theory and I want to apply to grad school next year so I don't know who should I ask

[Anonymous No.10013916]

>>10013872
I'm on the same boat, I started MIT OCWs, seems quite to the point and somewhat precise, though I feel anons will laff at me but whatever, it keeps me entertained. After I'm done with it, I'll do the other version that's more throughout and introduces me to proofs and stuff that I highly need (not really because I'm in the EE meme but I feel like I should know this).

[Anonymous No.10013941]

>>10013872
>>10013916
https://www.gutenberg.org/files/33283/33283-pdf.pdf

[Anonymous No.10013996]

>>10013569
To prove that a function is well defined you simple must prove that the thing is a function. A function is a set of ordered pairs such that there exists no pair with the same first element. Aka there exists no x such that f(x)!=f(x) (or written kinder, if f(x)=y and f(x)=z then y=z).

[Anonymous No.10014000]

>>10012488
>tfw the person that makes spikedmath comics was my calc and linear algebra professor

Shame what happened to him.

[Anonymous No.10014008]

>>10013941
I don't want to doubt you but is it a legit book or jut one of thousands /sci/'s meme books?

[Anonymous No.10014012]

>>10014008
Being said that, I like the format. I'll see if someday I can own an L copy, looks like A5 size.

[Anonymous No.10014017]

>>10014008
It's so far the most readable calculus book I've ever seen. If I ever have to teach calc (which I soon will) this is the book I'm using.

[Anonymous No.10014018]

>>10014012
physical copy*

[Anonymous No.10014028]

>>10014000
he ded?

[Anonymous No.10014041]

http://4chan-science.wikia.com/wiki/Mathematics

Can I really trust the wikia link? How can I distinguish between legitimately good books and /sci/‘s meme books?

[Anonymous No.10014059]

>>10013913
Have you read any papers in the field you're interested in? Who're the authors of those papers and what institutions do they work at? Those are the ones you want to apply to. Maybe email those guys ahead of time and ask them, many profs seem to be receptive to students who show initiative. You may also want to ask them if they themselves will be taking grad students in the next two years, that way you can apply to those schools and work with those people. A quick google search to get you started, but the rest is on you
https://scholar.google.com/citations?user=D6ptFeMAAAAJ&hl=da
https://scholar.google.com/citations?user=skWkGYMAAAAJ&hl=da
https://people.mpim-bonn.mpg.de/zagier/
>>10014041
>How can I distinguish between legitimately good books and /sci/‘s meme books?
By reading them. But in all seriousness you may just want to find a topic you're interested in, look at the corresponding books, a use the preview button for google books to check a few pages out. Maybe then ask /mg/ about them

[Anonymous No.10014062]

>>10014041
Most of those books are pretty standard.

[Anonymous No.10014064]

>>10014041
LOL

[Anonymous No.10014069]

>>10014041
Define a meme book.

[Anonymous No.10014072]

>>10014069
Not well written

[Anonymous No.10014105]

>>10013569
"well defined" is a stupid term. Really what they mean when they say
>Prove that the [type] X is well defined.
is
>Prove that X is a [type].

I really wish people stopped saying that cause it's actually retarded.
>Is the fish, 'trout', well defined? If so provide a proof, otherwise provide a proof of its negation.
Nigga, stop calling it a fish if we don't even know it's a fish.

[Anonymous No.10014140]

>>10014041
I just fixed up the set theory and logic section. It's good.

[Anonymous No.10014151]

>>10014140
Name one cool fact about Set theory. Give me a good motivation to learn Set Theory beyond the scope Paul R. Halmos’s Naive Set Theory book.

[Anonymous No.10014187]

>>10014151
There are the classics like forcing, large cardinals, definability, etc.. There is also alot of current research in descriptive set theory. I work in the effective theory, the use of computability theory tools that relativize up to say things about uncountable Polish spaces. A hot research area right now is the complexity of naturally occuring equivalence relations such as isomorphism or biembeddility of countable structures like groups, graphs, linear orders. This is called Borel equivalence relation theory. An open question is the classification of the isomorphism relation of abelian groups in terms of Borel reducibility. The book for this is "Invariant Descriptive Set Theory" by Gao.

[Anonymous No.10014189]

>>10014140
Why did you delete "The Foundations of Mathematics" by Kunen and "Model Theory (Dover Books)" by C.C. Chang and H. Jerome Keisler?

[Anonymous No.10014216]

>>10014189
Kunen's book is not good, horribly typeset, superficially glosses over some important things and the last chapter on computability is laughably bad. The pairing of a logic book like Enderton with something like baby Jech is way better. C&K is old and dated, Marker's book really emphasizes the algebraic nature of modern model theory. If anything I should have added Hodges as well. But a problem these lists have is that there are too many options. Just put out a book or two that will cover what a student needs and thats it. Plus Marker will cite C&K if there is something in there that he doesn't cover, so I don't think anything is lost.

[Anonymous No.10014244]

>>10014189
>>10014216
>>10014140
Looked up a diff:
http://4chan-science.wikia.com/wiki/Mathematics?diff=prev&oldid=5347
I used different books for Axiomatic Set Theory than either of you so I won't say much about that (except that Halmos Naive Set Theory should be mentioned somewhere on the page). That said there's a lot more to "advanced" computability theory than recursive function/set theory. Personally I think that the best intro on the subject is:
https://www.amazon.com/Computability-Complexity-Languages-Second-Fundamentals/dp/0122063821

Also, remove the "advanced" and "recursion" from computability theory.

[Anonymous No.10014273]

Okay faggots so my roommate asked me to help him with his calc homework and the question was Lim x->2- [[5x]] and I told him it was 9 but the computer marked that as wrong. Can someone please tell me if I'm retarded or if the computer is.

[Anonymous No.10014280]

>>10014273
You are retarded.

[Anonymous No.10014284]

>>10014273
It's 10 bro

[Anonymous No.10014287]

>>10014244
You're free to make any edits you want. There are three intro set theory books up there already, why another? Also, the book you posted is more of a theory of computation book rather than a computability theory book.

[Anonymous No.10014289]

>>10014284
He had already tried 10 & 5 before asking me for help

[Anonymous No.10014294]

Why is standard induction so fucking full of boilerplate? Write don't base case, write don't k=n for no reason, write down the next step case and try to get it to look kind of like the other case but with +1s everywhere, it's tought in highschool in a way that completely hides the underlying principle. I didn't fully understand induction till I was already a man. Why not do write the base case(s) and then get the equation in the form of a recurrence relation? That explicitly shows you how India toon works without all the retarded boilerplate. Also I have never read a single paper or textbook (outside graph theory for some reason) that uses induction in the way it's tought, it's always closer to what I described, or just implied.

[Anonymous No.10014303]

>>10014280
>>10014284
As x approaches 2 from the left it's literally 9

[Anonymous No.10014307]

>>10014303
You said [[5x]] not [math]\left \lfloor {5x}\right \rfloor[/math], retard

[Anonymous No.10014309]

>>10014303
I don't know why you're friend would answer 5, but yeah, floor of 5x as x approaches 2 from the left should be 9

[Anonymous No.10014318]

>>10014307
It's just a different notation for a greatest integer function it means the same thing if I'm not mistaken

[Anonymous No.10014324]

>>10014309
I think he was treating it like 5[[x]] instead of [[5x]]

[Anonymous No.10014327]

>>10014287
The book I posted develops
>Recursive function theory (primitive and general recursion with material on quantifiers and recursively enumerable sets)
>Equivalence of several different models of computation including less commonly covered ones like post-turing machines and an assembly language style model of computation. Also stuff like post correspondence problem.
>Standard intro concepts including: encoding everything as an integer (i.e. pairing functions, tuples via fundamental theorem of arithmetic, etc..), universality, reduction, halting, oracles, arithmetic hierarchy, sets recursively enumerable relative to an oracle, etc..
>Standard theorems including: Parameter Theorem, Rice's Theorem, Recursion Theorem, Posts Theorem, etc..
The book also covers other topics including complexity, formal languages, formal logic, operational/denotational semantics, etc..

I think you must be confusing it with a different book.

[Anonymous No.10014385]

>>10014327
Lookig at the table of contents that is a theory of comp book. I'm talking about the mathematical logic discipline computability theory. It is much different from what is done in CS Depts. There is overlap of course, but calling that book a computability text is like calling dummit and Foote a group theory text. Again, you're free to edit the wiki and put the book you like up.

[Anonymous No.10014469]

>>10014273
>[[5x]]
>[[]]

is that ⌊5x⌋ or ⌊5x+0.5⌋ or just (5x)?

[Anonymous No.10014475]

>>10014244
>Personally I think that the best intro on the subject is:
>https://www.amazon.com/Computability-Complexity-Languages-Second-Fundamentals/dp/0122063821

It's already on the CS&E page.
https://4chan-science.wikia.com/wiki/Computer_Science_and_Engineering#Automata.2C_Computability_Theory.2C_and_Complexity_Theory

[Anonymous No.10015545]

>>10012488
>/mg/ on page 8 before hitting the bump limit
What happened?

[Anonymous No.10015618]

>>10015545
The french mathematicians are busy taking some subsaharan dick.

[Anonymous No.10015621]

Is it possible to study EE and then get into a master/phd for maths? What would be the suggested steps to do so? Or which classes should I take?

[Anonymous No.10015622]

>>10015545
you see the demons are all around us
our castles taken the high lords hanged, the band of the hawk has ceased function.

[Anonymous No.10015629]

>>10015621
>Is it possible to study EE and then get into a master/phd for maths
Possibly, to my understanding the math required in EE would mean you'd have learned Calc 1-3, linear algebra, diff eq, pde, complex analysis, and maybe some stuff on fourier and laplace transforms. To fill the gaps classes like real analysis, abstract algebra, and maybe some basic topology would bring you up to the level of someone ready for grad school. I say that because one thing required for most grad schools is the math gre, so those topics should roughly be considered as a bare minimum for entering grad school in math.
>>10015622
Then we're already doomed.

[Anonymous No.10015642]

>>10015629
Thanks for the quick reply, I'll check if my program covers this and if not, I'll see if I can learn these subjects either on my own or enroll in some other uni with a pure math program (or maybe just switch to math altogether, I'll see).

Thanks again.

[Anonymous No.10015652]

This is somewhat off-topic, but I have a newfound interest for theoretical physics yet as a pure math major (second year) I don't have any kind of physics background.
How do I "branch out" into physics at the graduate level, i.e. which fields of math that have applications in theoretical physics should I specifically look into?
I'm interested in HEP and QM mainly.

[Anonymous No.10015658]

>>10015652
http://theoreticalminimum.com

[Anonymous No.10015662]

Hey, are there more lists like this?

hbpms.blogspot.com

[Anonymous No.10015690]

x=2+t
y=4+t
z=-1-4t
And
x=-1+2t
y=-1+3t
z=-1+4t

Do these fuckers even Cross???

[Anonymous No.10015749]

>is differentiable everywhere
>derivative bounded everywhere
>derivative is not Riemann-integrable.
https://en.wikipedia.org/wiki/Volterra%27s_function
WHY IS THIS ALLOWED.

[Anonymous No.10015751]

>>10015662
Holy shit, thanks Anon!

[Anonymous No.10015753]

>>10015751
You're welcome, you're always giving good advice and helping out others so I'm glad I was useful too.

(well, if you are who I think you are ofc, if not, just enjoy it)

[Anonymous No.10015807]

>>10015749
Because Riemann (or retard as i call them) integrals are shit and should never be used outside calc1.

[Anonymous No.10015874]

My dudes, I made a linkedin profile. What the fuck do I write in the summary section? I was thinking
>I love math but I am not smart enough to pursue it full time and I need to eat, so I'll settle for making a rich asshole richer by writing AI routines for him
but then I stopped because I realised this is the equivalent of dumping radioactive waste on my profile...

[Anonymous No.10015888]

>>10015874
What's your skillset anon?

[Anonymous No.10015891]

>>10015874
>I am not smart enough to pursue it full time
Is grad level math really incredibly difficult?
t. naive freshman

[Anonymous No.10015894]

>>10015888
You mean other than all the math I know? Programming with C, Java, python, R, and I've dabbled with Clojure a little. I'm focusing on machine learning shit right now, since it seems to be lucrative.

>>10015891
Nothing is difficult if you're one of those martians with the phenotype that ashkenazi women like.

[Anonymous No.10015898]

>Nothing is difficult if you're one of those martians with the phenotype that ashkenazi women like.
Which I'm not, in case it wasn't obvious enough.

[Anonymous No.10015902]

>>10015894
My phenotype isn't that good. I'm just getting scared reading posts about how utterly incomprehensible higher level math allegedly is for non-geniuses.

[Anonymous No.10015907]

>>10015902
Understanding it isn't the problem. Finding new paths in the thicket is.

[Anonymous No.10015916]

>>10015907
Are applied and statistics the same, or are you exclusively talking about research in pure math?

[Anonymous No.10015987]

>>10015916
I am talking about research in pure math of course. Applied maths and statistics is kinda what I will be doing from now on, provided I get a fucking job (I am still wrecking my brains on that profile summary, one hour later).

[Anonymous No.10015989]

How is this for an intro my dudes:

"I like maths. A lot. Unfortunately, I am not a martian — I can't live inside my head. It's just not big enough. So I had to settle for the next best thing — doing things with mathematics."

[Anonymous No.10015992]

>>10015989
Wrong punctuation marks but I think you get the point. This
>I had to settle for the next best thing
is bugging the hell out of me. How do I rewrite it so it stops bugging the hell out of me? Or is the stupid martian joke the problem? Should I ditch that?

[Anonymous No.10016022]

>>10015987
Why don't you try stalking people from your uni or something like that and read what they wrote?

[Anonymous No.10016057]

>working through proofs in analysis class
>struggle to work proofs in front of several people
>cant fucking figure anything out
>get home
>open textbook
>everything is perfectly clear
>solve all problems almost immediately

WHY

[Anonymous No.10016066]

>>10016057
Maybe you have a mild form of social anxiety.

[Anonymous No.10016084]

>>10015753
who do you think i am?

[Anonymous No.10016087]

>>10016057
This >>10016066 or what we like to call autism.

[Anonymous No.10016315]

Riddle me this, /mg/
I got the idea from some discussions on /sci/ that if one graduated without making any publication, it'll be really hard to find a job.
I also got the idea, which isn't necessarily from /sci/ alone, that you can be "too old" to join some fields, like physics.
So my question is: will I be able to pursue a career in mathematics as a 22yo?

[Anonymous No.10016316]

>>10016084
A nice guy.

[Anonymous No.10016329]

I've got a homework due for tomorrow. Should I learn latex now and write the equations really fast or should I write it all by hand. Some guy told me the homework is a dozen pages of diagonalising matrices while detailing every step.

[Anonymous No.10016351]

>>10014069
Hartshorne.

[Anonymous No.10016359]

>>10016316
>A nice guy.
I'm not a "guy".

[Anonymous No.10016420]

>>10016359
Who are you and why are you pretending to be me?

[Anonymous No.10016441]

>>10016315
It depends on the job, if you want to go into an analytical position that other PhDs apply to, probably not, but since a lot of jobs are code monkeying, I see no problem.

As in being a professor and doing research? You probably have to be good for that, that doesn't seem guaranteed at all, the thing is, it's the same for everyone, just put in the effort if that's what you really want to do, if it doesn't work out you have to get another job just like everyone else, it's not you're gonna be homeless

[Anonymous No.10016444]

>>10016329
Write it by hand, you probably don't have time otherwise

[Anonymous No.10016451]

>>10016420
who are you and why are you pretending to be me?

[Anonymous No.10016453]

It's been like a month since I started my master's and it's simply too much work. I feel like I only have enough time to do the homework but I don't have time to actually study stuff that I don't see in class.
I knew that it was going to be hard, but this seems overkill.
Do you have any tips you could share?

[Anonymous No.10016460]

either i'm fucking tripping or this conversation just gave me a déjà vu

[Anonymous No.10016461]

>mrw calc 2 is taught by a number theorist
>refuses to write anything on the board that isn't first categorized as definition, remark, recall
>waste half the class doing this
>class on series
>first application he does is .999999...=1

[Anonymous No.10016466]

>>10016461
>when all the engies complain to the dept head

>>10016057
that's everything in my life. it's like my brain shuts off around people. someone could ask me for help on homework and i'll be clueless, go home and i solve their problem in 10minutes

[Sage No.10016467]

>>10016461
>filename
why are posts like this allowed?

[Anonymous No.10016469]

>>10016329
How does any professor let you guys use latex? You can cheat so easily. At least if it's handwritten, you still got exposure to it even if you cheat

[Anonymous No.10016479]

>>10015749
https://en.wikipedia.org/wiki/Conway_base_13_function
>>10016329
If you don't already know latex that'll be a bitch to type up.
>>10016315
>will I be able to pursue a career in mathematics as a 22yo?
Do you mean you're starting undergrad as a 22 year old? In which case my belief is yes. There are people who switch fields later on and are able to adapt fair quickly. I think the most important thing is maturity and discipline.
>>10015652
Depends on what you want to do. For QM and related subjects functional analysis is what you're looking for. In fact, Reed and Simon have a book on mathematical methods in physics just for this purpose. If you want to go into HEP then you want to beef up on your differential geometry as that's heavily used in GR and gauge theory. Group theory (specifically Lie groups) are used extensively in particle physics.
This should also be of assistance.
https://www.youtube.com/playlist?list=PL7aXC0jU4Qk7K778c5nmgQImd6VKKFMYu
>>10015662
Consult the BIG LIST(s)
http://math.stackexchange.com/questions/302023/best-sets-of-lecture-notes-and-articles?lq=1
math.stackexchange.com/questions/94827/books-that-every-student-needs-to-go-through
https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
>>10016453
>Do you have any tips you could share?
How are you managing your time? What takes up the biggest portions of your day?

[Anonymous No.10016487]

>>10015652
>>10016479
I almost forgot, Fredric Schuller is good for this sort of thing

[Anonymous No.10016533]

>>10016479
>Do you mean you're starting undergrad as a 22 year old? In which case my belief is yes. There are people who switch fields later on and are able to adapt fair quickly. I think the most important thing is maturity and discipline
Yes, that's what I meant. Thanks, anon, you gave me hope.
>>10016441
I'll try to go as far as I can, I just don't want to be a burden to my family.

[Anonymous No.10016566]

>>10016533
>I just don't want to be a burden to my family.
Weak

[Anonymous No.10016567]

https://www.twitter.com/Quasilocal/status/1042359040305704960

Michael Atiyah present proof Riemann hypothesis

[Anonymous No.10016573]

>>10016566
Why?

[Anonymous No.10016591]

>>10016567
Is Riemann Hypothesis's reign of terror finally going to end? I'm so fucking hype right now.

[Anonymous No.10016599]

>>10016591
I don’t believe it but it’s fucking Michael Atiyah maybe some new approach line

[Anonymous No.10016641]

Why is number theory such a god damn fuck?
I have no idea what is going on.

[Anonymous No.10016673]

At what point in your life you should give up on solving the Goldbach Conjecture?

[Anonymous No.10016711]

>>10016567
The twitter post is like a day old, how long do we have to wait?

[Anonymous No.10016796]

>>10016567
>>10016591
I think Atiyah really does have a radical new line of thought, but I don't think it's a proof. There's likely a subtle error somewhere. I mean, it would be really weird for there to be a "simple" proof to the Riemann hypothesis, given how many people have bashed their heads at it. One thing to check is to see if the proof works for the Weil's conjectures as well. If it does that means there's more credence to the claim that his method works.

[Anonymous No.10016897]

>>10016567
Oh look, another old fart going senile and thinking he unlocked the mysteries of the universe.

[Anonymous No.10016900]

>>10016453
Stick to a schedule, eat healthy, and sleep a full 8 to 9 hours every night.

[Anonymous No.10016906]

>>10013013
>>10013040
>>10013132
>>10013160
>>10013174
>>10013179
This be the latest fad around here? Foxes?

[Anonymous No.10016910]

>thinking anyone gives a shit what your major is in the year of our lord 2018
lol all you dumb faggots are going to be cleaning toilets

[Anonymous No.10016930]

>>10016910
What are you referring to?

[Anonymous No.10016969]

>>10016711
>how long do we have to wait?
Until next Monday: https://www.heidelberg-laureate-forum.org/event_2018/

[Anonymous No.10016982]

>>10015690
[2, 4, -1] + t[1, - 1, -4] = [-1, -1, -1] + v[2, 3, 4]

Solve the system. 3 equations, 2 unknowns.

[Anonymous No.10017021]

>>10016969
lmao

[Anonymous No.10017035]

>>10017021
That has to be a coincidence. There is no way Atiyah posts here.

[Anonymous No.10017059]

>>10017021
>>10000161

[Anonymous No.10017093]

Show by definition that [math] f: R^2 -> R^3 f(x,y)=x, y, x+y is continuous. [/math]

[Anonymous No.10017161]

>>10017093
This is trivial, come on.

[Anonymous No.10017164]

>>10017035
Why not? Senile old people do all sorts of weird shit.

[Anonymous No.10017178]

>>10016359
I see, I thought you were >>10016479
anyways, have a nice day.

[Anonymous No.10017181]

>>10017164
Like fucking your sister?

[Anonymous No.10017217]

>>10017164
>tfw all those posts recommending Atiyah textbooks is just Atiyah shilling for his own books

[Anonymous No.10017227]

>>10016567
Atiyah has been providing false proofs to things in the past few years. It'll be nonsense again.

[Anonymous No.10017242]

Lets say you're a dude taking the basic math for engineering but you also have an interest in everything math olympiad related.
How do you begin nurturing your brain to reach some mathematical maturity, and learn topics that might no be given during HS/first years of college, to start doing hard/uncommon math problems just for the joy of it?

I've read Evan Chen's blog but it seem it's aimed to people who were part of this competitions already.

[Anonymous No.10017453]

>>10017242
Storm through Khan Academy's stuff then read the recommended books here
http://4chan-science.wikia.com/wiki/Mathematics..

[Anonymous No.10017542]

Baby here. Just started learning about permutations as a precursor to groups. I'm just wondering what kind of behavior with respect to permutations/cycles happens with infinite groups?

[Anonymous No.10017556]

>>10017242
post your attempt at a proofhere and get ridiculed until you get it right

[Anonymous No.10017575]

>>10016906
As someone who frequents /an/ I kind of like it
>>10017242
They have a college equivalent for the math Olympiad, it's call the putnam exam. Basically to get better at problem solving you have to learn the heuristics and do problems. Books like Polya how to solve it, Polya's two volume set, Fomin's mathematical circles, any book by Titu, Putnam and beyond, Challenging mathematical problems with elementary solutions, Larsen Problem solving through problems, and Engel Problem solving strategies are all books that can help you with both. Also, and this may interest you in the future, is that the AMS publishes two relevant journals, the american mathematics monthly and the college mathematics journal. Both journals publish hard problems which readers can then solve and submit. If you solve it your solution may then be featured in a subsequent issue. Here's an example
https://maa.tandfonline.com/doi/full/10.1080/00029890.2018.1424478
Have fun.
>>10017542
Well things can get a bit wonky. Consider this, a bijection between a finite set and itself can be thought of as a permutation, right? Well this is not true for infinite sets. Consider a function from the integers to itself f(x)=2x. This is a bijection but dosen't line up with what you would consider a permutation.
>>10017178
I'm >>10016479 >>10015629 >>10014059 >>10013390 >>10013115 and no prob anon.

[Anonymous No.10017581]

>>10012488
>enter college calc class
>everybody is retarded

welp looks like I get to keep self studying

[Anonymous No.10017613]

>>10017575
Heh, figured. I thought you were that other anon that's also kind though he uses animu avatars sometimes.

polite sage.

Also, thanks for the heads up on the putnam competition and those books, I'll research it.

[Anonymous No.10017626]

>>10017575
>This is a bijection
No

>>10017542
It works exactly the same as in the finite case, the only difference being that you can now have "infinite cycles" (ie. things like the bijection n -> n+1 from Z to itself)

[Anonymous No.10017658]

>>10017626
Do infinite cycles have any interesting properties that finite ones do not?

[Anonymous No.10017661]

>>10017626
Whoops, you're right, sorry, fucked up. I should've said that a function that's one-to-one. My point was that the finite and infinite cases are just slightly different, but not too much.
>>10017613
>Also, thanks for the heads up on the putnam competition and those books, I'll research it.
The putnam also publishes their problems and solutions if you want to see the past exams.

[Anonymous No.10017690]

I'm having real trouble figuring out any sort of intuition about local rings in the context of algebraic geometry and the proofs with them I understand but really painfully. Am I a brainlet or is this some far-fetched stuff that requires more getting used to.

[Anonymous No.10017724]

This is now a math feels thread

>be in love with math
>no money for a degree
>parents agree to pay for my degree if they get to choose it
>tell them I want a math degree
>tell me no, there's no jobs
>argue for weeks
>finally agree on actuary degree
i guess that's as good as I'm going to get :'( at least they have real analysis in their actuary program here

[Anonymous No.10017727]

>>10017724
Well, at least when you get money after graduating you can always enroll in a math program, or study by yourself and take the GRE or something like that.

[Anonymous No.10017729]

>>10017724
Don't worry actuary is high pay and job security even could jump to stats,physics or Math for master.

[Anonymous No.10017760]

>>10017658
Besides being infinite, not really. What is perhaps counter-intuitive is that you may have infinitely many of these infinite cycles.
The thing is that we understand permutations of finite sets, but infinite sets are really big (you can divide N into infinitely many copies of itself), so you have to be careful not to apply intuition of finite sets. There are many more than we can picture.

[Anonymous No.10017785]

>>10012520
Patchouli likes watersports.

[Anonymous No.10017811]

>>10016057
I hate this shit, but my inability to perform in front of others has recently gone away because of some medication I am on. I just get so focused that I zone everything out. My social anxiety in lectures is pretty much gone since I am so focused on the material.
But honestly who cares as long as you understand the material and can work with a handful of people when necessary you should be fine, right?

[Anonymous No.10017835]

If I have a sub-matrix which consists of all dependent columns, will the matrix it's embedded in also have all dependent columns? It seems like it should.

[Anonymous No.10017925]

I've been stuck on the first part of this (a) for literal hours spread over the past two days.
How do I know what the regions are?

[Anonymous No.10017939]

>>10017925
So far I'm getting one region. Would I integrate it from 4 to 2 or from 4 to t-1 or what?

[Anonymous No.10017953]

>>10017835
What do you mean embedded? This doesn't sound true to me.

[Anonymous No.10018009]

Scholze-Stix paper on IUTT: http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf
Mochizuki Strikes back: http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html
The return of Fesenko: https://www.maths.nottingham.ac.uk/plp/pmzibf/rapm.pdf

IUTTitans clash: https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/
tl;dr - the worst outcome happened

[Anonymous No.10018013]

Is there any chance of me getting a professor to let me piggy back on their research if I only know up multivariable calculus and linear algebra? I am looking to buy an intro to proofs book I haven't decided on one yet. I have really good relationship with two of my professors and I plan on asking them the same question within the coming week.

[Anonymous No.10018026]

>>10017953
Let [math]\displaystyle A = \begin{bmatrix}

a_{11} & a_{12} & a_{13} & a_{14} \\
a_{21} & a_{22} & a_{23} & a_{24} \\
a_{31} & a_{32} & a_{33} & a_{34} \\
a_{41} & a_{42} & a_{43} & a_{44} \\

\end{bmatrix} [/math] and let [math]\displaystyle B = \begin{bmatrix}

a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33} \\


\end{bmatrix} [/math] be a submatrix of [math]A[/math] such that the columns of [math]B[/math] are linearly dependent. So my question is will the columns of [math]A[/math] be linearly dependent?

[Anonymous No.10018027]

>>10018013
How much boring grunt work are you willing to do?

[Anonymous No.10018034]

>>10018027
All of it, I just want to do something outside of classes. Anything will do for now until I build a stronger base.

[Anonymous No.10018039]

>>10018013
>I am looking to buy an intro to proofs book
You are not even going to be competent enough to be a liability if you haven't taken an intro proof course yet.

Unless the stuff your professors are doing is very applied, then they might have some ultra-grunt level computations you could do for them.

By all means start talking to faculty about it if you have an interest in research mathematics, they'll probably be happy to guide you along as you go, but you're jumping minimum a couple years ahead of yourself by asking to do research with literally zero exposure to any kind of abstract math.

[Anonymous No.10018041]

>>10018013
How good are you at making coffee and printing paper?

[Anonymous No.10018045]

>>10018009
Do all arithmetic geometers write all their shit in such an infuriatingly vague fashion or is it just a Mochi-ism?
If you gave me a dime for every occurrence of the phrase
>a certain
with reference to IUTT I could retire right now.

[Anonymous No.10018047]

>>10018039
>>10018041
I had a feeling this was the case, thanks. I'll just ask them for advice.

[Anonymous No.10018078]

>>10018026
If it can be any submatrix then consider the counterexample.

[math]\displaystyle A = \begin{bmatrix}

1 & 1 \\
0 & 1 \\

\end{bmatrix} [/math]
and
[math]\displaystyle B = \begin{bmatrix}

1 & 1 \\


\end{bmatrix} [/math]

I'm not immediately sure if it's exactly those dimensions.

[Anonymous No.10018089]

>>10018026
Counterexample (according to my calculator):
Let [math]\displaystyle A = \begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 1 & 0 \\
0 & 0 & 0 & 1 \\
0 & 1 & 0 & 1 \\

\end{bmatrix} [/math] and let [math]\displaystyle B = \begin{bmatrix}

1 & 0 & 0 \\
0 & 1 & 1 \\
0 & 0 & 0 \\

\end{bmatrix} [/math]

[Anonymous No.10018101]

>>10017925
first step is to write the convolution integral. If you can write it down, then you can integrate piecewise

[Anonymous No.10018103]

>>10018026
No, it depends on the rank of B. In this particular case, if B has rank 2, you can always make A invertible (exercise)

[Anonymous No.10018110]

>>10018078
>>10018089
Might I add some other conditions, as I just realized that isn't precisely what I needed.
Let [math] \displaystyle A = \begin{bmatrix}
a_{11} & a_{12} & a_{13} & \dots & a_{1n} \\
a_{21} & a_{22} & a_{23} & \dots & a_{2n} \\
a_{31} & a_{32} & a_{33} & \dots & \vdots \\
\vdots & \vdots & \vdots & \dots & \vdots \\
a_{m1} & a_{m2} & \dots & \dots & a_{mn}
\end{bmatrix}[/math] by an [math]m \times n[/math] matrix with [math]m<n [/math] and [math]\displaystyle B = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \\ \end{bmatrix}[/math] be a submatrix with its columns linearly independent. As an added stipulation, [math]a_{ij}\neq 0[/math] . This is more accurate to my original intention. So now, what can be said of the columns of [math]A[/math]?

[Anonymous No.10018115]

>>10018110
fuck sakes, this still isn't what I need. The submatrix itself is of size [math]m-1 \times n-1 [/math]. Too lazy to re-TeX it.

[Anonymous No.10018119]

>>10018115
with [math]m-1 < n-1[/math] *

[Anonymous No.10018124]

>>10018110
I don't think whether or not zeros are allowed makes a difference. As (>>10018103
) said it depends on the rank of the matrix. If m<n then any submatrix will have linearly dependent columns as any matrix with less rows than columns does.

[Anonymous No.10018127]

>>10018124
any m-1 by n-1 submatrix that is

[Anonymous No.10018228]

http://www.kurims.kyoto-u.ac.jp/~motizuki/Cmt2018-08.pdf
>I can only say that it is a very challenging task to document the depth of my astonishment when I first read this Remark! This Remark may be described as a breath-takingly (melo?)dramatic self-declaration , on the part of SS, of their profound ignorance of the elementary theory of heights , at the advanced undergraduate/beginning graduate level.

[Anonymous No.10018234]

>>10017729
>>10017727
Thanks guys, there is a research course for undergraduates so hoping to put some theory to actuarial math

[Anonymous No.10018236]

>>10018228
Mochizuki is REEEEEing throughout. I am still on his side though.

[Anonymous No.10018237]

>>10018228
LOL

[Anonymous No.10018283]

any takers?
>>10018270

[Anonymous No.10018286]

>>10017093
Whats your definition of continuous? Depending on what it is it should more or less be plug and chug.

[Anonymous No.10018293]

>>10018283
do you need to prove it by induction?

Instead:

Let [math]f(x)=(x-1)^n[/math]. By the binomial formula, [math]f(x)=\sum_{k=0}^n {n\choose k}(-1)^kx^{n-k}[/math]. Now compute [math]f(1)[/math]

[Anonymous No.10018294]

>>10018293
Unfortunately yes. I've seen the other proofs using that method you posted.

[Anonymous No.10018361]

"five is greater than or equal to four."
how? five isn't equal to four so why does it have the ≤ instead of > ?

[Anonymous No.10018365]

>>10018361
"or" in mathematics typically means the inclusive "or", i.e. "five is greater than or equal to four." is true since at least one of the statements
1) 5 is greater than four
2) 5 is equal to four
is true.

[Anonymous No.10018383]

>>10018365
whats the difference between greater than or equal than just greater than?

[Anonymous No.10018390]

>>10018383
>whats the difference between greater than or equal than just greater than?
5 >= 4 if 5>4 or 5=4
5 > 4 if 5 > 4

[Anonymous No.10018402]

>>10018390
i don't understand why would 5 equals 4 is my main issue

[Anonymous No.10018403]

>>10012488
This bullshit really makes me hate mathematicians

[Anonymous No.10018416]

>>10018402
x>= y, if either x>y or x=y
So 5>=4, 5>4, 5=5, 5>=5, but not 5>5

[Anonymous No.10018449]

[Anonymous No.10018453]

>>10018449
Is this correct?

[Anonymous No.10018554]

>>10018228
based peter

[Anonymous No.10018578]

/our guy/ Mochizuki strikes back against fuccboi Scholze, and Atiyah claims to have found a short proof of the Riemann Hypothesis (not short enough to be contained in the abstract, but enough to be developed in a single talk), yet /mg/ has barely reacted.
Is this general officially dead?

[Anonymous No.10018580]

>>10016906
At least it's better than ponies, Trump, Hitler, Bane, Touhou and all the other insufferable memes this site has produced.

[Anonymous No.10018797]

>>10018578
Mochizuki and Atiyah are both hacks.

[Anonymous No.10018799]

>>10018578
To clarify,
>Is this general officially dead?
The only thing dead in here is Mochizuki's proof of the abc conjecture.

[Anonymous No.10018858]

>>10018228
Why can't Mochizuki just admit he's wrong? This reads like a 4chan fight.

>you're a brainlet
>no YOU are a ___brainlet___

[Anonymous No.10019063]

>>10018228
>http://www.kurims.kyoto-u.ac.jp/~motizuki/Cmt2018-08.pdf
Is this real life? I few threads ago I was touting it all as a mature exchange and part of the natural academic process.

This shit is fucking 4chan tier childish. They might as well be shitposting on /mg/.

[Anonymous No.10019074]

>>10019063
>he doesn't know

[Anonymous No.10019088]

>>10019074
Ah, good, it's a troll.

For a second there I thought real, prize winning academics were actually calling each other undergrads as an insult.

Good to know everything is still good.

[Anonymous No.10019104]

>>10019088
>all this naivety
So cute.

[Anonymous No.10019121]

>>10019088
>it's a troll.
what did he/she mean by this?

[Anonymous No.10019130]

>>10019121
Did you just assume *zher gender could only be male/female?

[Anonymous No.10019166]

>>10019121
I'm pretty sure it's not a troll.
Taken from Mochizuki's website:
http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html

http://www.math.columbia.edu/~woit/wordpress/?p=10560

[Anonymous No.10019177]

>>10013118
>How do you effectively self-study material?

Do a fuckload of exercises

[Anonymous No.10019179]

>>10014105
Yes but with functions they really mean
>Prove that relation f is a function.
And most people are unfamiliar with relations so they invented a new term for it.

[Anonymous No.10019184]

>>10014294
Induction is used for more things than recurrence relations / equations.

[Anonymous No.10019190]

>>10016469
It's actually harder to cheat because then you can copy-paste and search for the text

[Anonymous No.10019196]

>>10018009
better than remaining in limbo indefinitely

[Anonymous No.10019203]

>>10018580
Bane?

[Anonymous No.10019250]

>>10019203
congratulations you've got yourself caught.

[Anonymous No.10019255]

>>10019177
>exercises
Not him but I rarely do exercises. Is it a good idea to read through a book first and do a problem book afterwards?

[Anonymous No.10019264]

>>10019255
No. Do the exercises as you are reading. Reading math is not really learning math.

"I hear and I forget, I see and I remember, I do and I understand"

[Anonymous No.10019274]

>>10019255
from my experience, exercises are where the idea actually comes together strongly, and i suspect its almost every writers intention for this to happen.
being guided by the writer as he explained can make certain subject feels easy, exactly because he's holding your hand.

but when ur all alone trying to solve the problem, you really have to put together the material yourself

[Anonymous No.10019280]

>>10018580
delete this

[Anonymous No.10019281]

>>10019255
You should only go to the next chapter when you finish at least 80% of the previous chapter's exercises.

[Anonymous No.10019295]

>>10019264
>>10019274
>>10019281
...ok, thanks

[Anonymous No.10019301]

>>10019255
are you asking us or telling us?
it would seem either both or neither
what are you hiding?

[Anonymous No.10019315]

>>10019104
>>10019121
>>10019166
Stop disrupting my COPE please.

[Anonymous No.10019366]

im trying to construct a short exact sequence (if it even exists)

[eqn]?\to k[x,y]/(f)\to k[x,y]/(I^2,f)[/eqn]
Where [math]f[/math] is a polynomial with no constant term and [math]I=(x,y)[/math], and [math]k[/math] is an algebraically closed field. Any ideas fellas?

[Anonymous No.10019374]

Guys, guys is complex number taught in high school or even elementary school? I've seen some videos about it and the concept isn't completely alien to me, in fact, is quite natural and makes sense. I just don't remember if we're taught this early in life, it's been so long since those days.

[Anonymous No.10019389]

>>10012524
isn't true for n = 1. So its not really induction.

[Anonymous No.10019393]

>>10013118
Usually if you learn some other topic which requires your topic as a pre-requisite, that will force you to learn the prerequisite properly. So the trick is to look up some advanced topics and try reading. Usually you'll get fucked in the start and realise the importance of the prereq.

[Anonymous No.10019395]

>>10013187
mochizuki got BTFO by based Peter
>>1001786

[Anonymous No.10019518]

I've seen anons here shill whiteboards for personal use, but does anyone use a chalkboard? I vastly prefer them, but I worry about the effect of using one in a confined space that's not cleaned regularly.

[Anonymous No.10019549]

absolute retard here
(2^2)^2 can be written as (2*2)*(2*2)
how do you write out (2^2)^1/2 in the same format (2*2)*(something)?

[Anonymous No.10019564]

>>10019549
[math]\sqrt{2*2}[/math]

[Anonymous No.10019568]

>>10019518
This post gave me cancer. I refuse to believe there exists someone in this world with such horrible fucking taste.

[Anonymous No.10019588]

>>10019568
>t. mathlet

[Anonymous No.10019655]

Are there any specific fields I should go into if I want to have at least a minuscule chance of making a major discovery? Where are most new and exciting results coming from?

[Anonymous No.10019741]

>>10019374
I learned it in high school but 1) it was a relatively advanced program and 2) it was just basic things like deMoivre's theorem. They also come naturally out of the quadratic equation so that's where you might first see them.

[Anonymous No.10019756]

>>10012488
>>10012488
What book did you find this bullshit in?

[Anonymous No.10019758]

Just a friendly reminder that zero is not a number, and is in fact neutral infinity.

[Anonymous No.10019766]

What is intuitively a topology? I know what it is formally, but not intuitively. I can say informally what a vector space, metric space, poset is, but I don't have any intuitions behind topology

[Anonymous No.10019782]

>>10019655
just make shit up and obfuscate it so much that people wont know the difference.

[Anonymous No.10019783]

>>10019766
It's a coffee cup but it's made of rubber
No really it's a way of describing how "close" or "connected" points are without actually using a metric

[Anonymous No.10019791]

Who's in the right in this thread?

>>>/a/178384187

Would you try to solve this problem in a test? Or write that it's unsolvable?

[Anonymous No.10019803]

>>10019791
I'd probably assume it was a right angle because it would be dumb if it was not. Mathematics is not about trick questions.

[Anonymous No.10019814]

>>10019655
i paraphrase what some categoryfaggot in this board once spewed, with certain accuracy in what he meant. If you want your name somewhere, then you want to study pure category theory for the chance of naming some faggotyass functor that might be useful somewhere

[Anonymous No.10019823]

>>10019814
I don't really care about the fame as much as feeling like I did something useful. My (albeit limited) research experience feels fairly depressing in the sense that any "progress" we make is really just marginally advancing a hyper-specific area. I understand that is simply the reality of a lot of modern mathematics, but given the chance I'd at least like to try something grander desu

[Anonymous No.10019826]

>>10019823
try applied math instead then

[Anonymous No.10020383]

>>10017785
do you know me

[Anonymous No.10020389]

>>10012488

Why you mathfags are so annoying about proving this? Bitch if I were wrong the bridge would fall and its still there

[Anonymous No.10020445]

>>10020389
Say that to Tacoma narrows, small mind

[Anonymous No.10020949]

I'm curious about Type Theory (as an alternative to Set Theory) and in particular the hot new meme of Homotopy Type Theory

What is a good place for me to get started with this? I'm studying axiomatic set theory currently

[Anonymous No.10021068]

>>10020949
https://ncatlab.org/nlab/show/type+theory
Set theory replacement tried use topos on category theories to avoid choice Axiom and exclusion on middle, using topoi as logical base.

[Anonymous No.10021489]

>>10020949
Try Martin-Lof's original paper/lecture and then the HoTT book.

[Anonymous No.10021710]

>>10021679
What did anon mean by this?

[Anonymous No.10021713]

>>10021710
Stop linking your own posts, Atiyah. No one cares.

[Anonymous No.10021716]

>>10021489
in particular these lecture notes:

https://intuitionistic.files.wordpress.com/2010/07/martin-lof-tt.pdf

There is a nicer typeset version somewhere but you'll have find it.

[Anonymous No.10021723]

>>10020949
https://leanprover.github.io/
Try learn this. It makes the differences between the two systems very apparent when you work on such a low level.

[Anonymous No.10021729]

>>10021716
Found it:

https://archive-pml.github.io/martin-lof/pdfs/Bibliopolis-Book-retypeset-1984.pdf

It explains very clearly the meaning behind type theory and its constructions.

In the same spirit, can anyone else recommend any particularly lucid papers that explain things in a simple, intuitive way?

[Anonymous No.10021763]

>>10021713
EH? I'm not Atiyah.

[Anonymous No.10021805]

>>10020949
First, you should know a few things.
>1. There are a lot of different type theories.
>2. The original type theories developed in the early days (alongside set theory) aren't really studied anymore. The big ones are:
>>2a. Russel's Theories of Type: After developing Russell's paradox, Russell developed many type theories that adhered to the "vicious-circle principle" (i.e. wouldn't be subject to such paradoxes) and ultimately settled on his Ramified Theory of Types (built on principles like avoiding impredicative definitions, using "typical ambiguity", having a hierarchy of types, etc..). Unfortunately the vicious-circle principle was nullified when one added the axiom of reducibility to the theory (necessary for induction). It is similar to set theory in some ways.
>>2b. Simple Type Theories: At some point other researchers refactored the Ramified Theory of Types into a simplified version called Simple Type Theory. This version lacks the axiom of reducibility and collapses the hierarchies. It is more like a higher order logic. Nowadays there are many variants of simple type theory, here is an intro paper to a very simple variant: http://www.cas.mcmaster.ca/sqrl/papers/SQRLreport18_rev2.pdf

(cont.)

[Anonymous No.10021808]

Had to fix formatting.

>>10020949
First, you should know a few things.
>1. There are a lot of different type theories.
>2. The original type theories developed in the early days (alongside set theory) aren't really studied anymore. The big ones are:
>2a. Russel's Theories of Type: After developing Russell's paradox, Russell developed many type theories that adhered to the "vicious-circle principle" (i.e. wouldn't be subject to such paradoxes) and ultimately settled on his Ramified Theory of Types (built on principles like avoiding impredicative definitions, using "typical ambiguity", having a hierarchy of types, etc..). Unfortunately the vicious-circle principle was nullified when one added the axiom of reducibility to the theory (necessary for induction). It is similar to set theory in some ways.
>2b. Simple Type Theories: At some point other researchers refactored the Ramified Theory of Types into a simplified version called Simple Type Theory. This version lacks the axiom of reducibility and collapses the hierarchies. It is more like a higher order logic. Nowadays there are many variants of simple type theory, here is an intro paper to a very simple variant: http://www.cas.mcmaster.ca/sqrl/papers/SQRLreport18_rev2.pdf

(cont.)

[Anonymous No.10021810]

>>10021808
(cont.)

>3. The major theories developed shortly after that are required reading:
>3a. Simply Typed Lambda Calculus: Church developed his own take on Simple Type Theory and many variants were developed. The Simply Typed Lambda Calculus is very popular and gives a good introduction to the general concepts, syntax, and results present in related type theories (including the Curry-Howard isomorphism). Here are some great intro lecture notes: https://www.irif.fr/~mellies/mpri/mpri-ens/biblio/Selinger-Lambda-Calculus-Notes.pdf
>3b. Martin Lof's Intuitionistic Type Theory: A modern style type theory that can be interpreted as a logic, an alternative to set theory, a programming language, etc.. It includes a good introduction to dependent types and the general concepts common to modern type theories. Here are his lecture notes, they're very approachable (don't be scared away by the preface): https://archive-pml.github.io/martin-lof/pdfs/Bibliopolis-Book-retypeset-1984.pdf

(cont.)

[Anonymous No.10021813]

>>10021810
(cont.)

>4. There are many modern type theories developed mainly by computer scientists working in programming language theory. A common theme is that they abuse a generalization of the curry-howard isomorphism (that gives a correspondence between logics, type theories, and categories) to develop type theories (for programming languages) that can be interpreted as certain (often non-classical) logics and certain categories with interesting properties.
>4a. Homotopy Type Theory (HoTT): A type theory for Homotopy Theory with features from Martin Lof's Intuitionistic Type Theory. It has two active branches of study, HoTT for the sake of HoTT and HoTT for the sake of mathematics; and is one of the largest and most well funded research projects these days. The standard resource is the HoTT book.
>4b. Theorem Provers/Proof Assistants: These are actually programming languages built on type theories powerful enough to encode mathematics (via the curry-howard isomorphism). The big ones are Coq, Agda, Idris, and others.
>4c. Research type theories: Computer Scientists working in programming language theory develop countless of these for research purposes. Some get implemented as programming languages but it's all for research purposes. A modern trend is a move towards Domain Specific [Programming] Languages (DSL), these are languages geared for a specific application like visualization or concurrent programming.

A good general resource if you've got a strong comp sci or math background is to attend the Oregon Programming Language Summer Camp.(or watch the lectures online for free). The talks include crash courses on category theory, proof theory, and typically a type theory but you would benefit from studying the Simply Typed Lambda Calculus ahead of time at a minimum.

[Anonymous No.10021872]

Atiyah claims to have a simple proof of the Riemann Hypothesis.

Crossposting from the Atiyah thread for all the mathheads who only browse /mg/ to avoid brainlets:
https://twitter.com/HLForum/status/1042670700652318720 (embed)
https://twitter.com/Quasilocal/status/1042359040305704960 (embed)
tl;dr: Atiyah is presenting at the Heidelberg Laureate Forum on Monday, Sept. 24. A video of the talk will be available online afterwards. Only people attending may view the abstract but a partial screenshot has been leaked by an attendee that says:
>The Riemann Hypothesis is a famous unsolved problem dating from 1859. I will present a simple proof using a radically new approach. It

[Anonymous No.10021880]

>>10021872
Is this a prank? What's he REALLY going to do, what's the endgame?

[Anonymous No.10021897]

>>10021880
I kind of suspect it might be a joke "proof" (like it may only hold under some ridiculous conditions or for certain values or something) that he just put together for a fun talk. If so it would explain why the person who posted a screenshot decided not to post the relevant part of the abstract and why the only reason people know about it is because of some rando's facebook post. That said, it's just my own gut feeling. To be honest I have no idea what the situation is and I haven't seen any commentary by other mathematicians.

[Anonymous No.10021902]

>>10021897
>>10021872
I fail at twitter, there's a bit more to the abstract in the screenshot. Is it possible that this is the entire abstract???

[Anonymous No.10021909]

>>10021902
Note, it does NOT explicitly say that the "simple proof" will be a proof of the Riemann

[Anonymous No.10021917]

>>10021902
>this is the entire abstract???
yes

[Anonymous No.10021920]

>>10021902
>>10021909
>the riemann hypothesis is a famous unsolved problem
>i will present a simple proof
He's going to prove that it's still unsolved, kek

[Anonymous No.10021922]

>>10021920
I have no hope that the RH will be proven, so I really hope he makes a good joke like that instead of disappointing everybody with a failed solution

[Anonymous No.10021950]

>>10021920
>He's going to prove that it's still unsolved, kek
lmao

[Anonymous No.10022018]

>"FACT: there exists disjoint sets, A, B, such that [math]m^{*}(A\cup B) < m^{*}(A) + m^{*}(B)[/math]"
why is the axiom of choice still allowed to exist

[Anonymous No.10022019]

What is the algebraic interpretation of Heisenberg’s uncertainty principle?

It resonated with me that it could be thought of as a result of attempting to enclose a wave over a certain interval would necessarily introduce uncertainty amongst the wave’s components, however in working through Griffith’s quantum mechanics, it’s mentioned that the principle is a result of non-commuting observables.

I guess a better way to word my question is what is the algebraic basis for non-commuting observables introducing uncertainty?

I mean I suppose I can wrap my head around the fact that without commuting observables, the eigenvalues corresponding to the respective operators don’t completely describe the system, but why does that produce a specific inequality rather than just being a general statement?

[Anonymous No.10022055]

>>10022019
have you read the name of the thread, bucko

[Anonymous No.10022073]

>>10021920
>He's going to prove that it's still unsolved, kek
kek I hope the madman does it

[Anonymous No.10022099]

>>10022055
I’m asking a question mainly about algebra, just in context of physics.

“Observables” are just hermitian operators whose eigenvalues correspond the the possible states of said operator.

Commuting operators depict the entire state, while non-commuting operators obviously make the commutator non-zero. My question is what is the algebraic basis for that commutator to have a specific bound.

[Anonymous No.10022102]

>>10022099
there's a complete statistical proof as to why the inequality is necessarily a consequence of quantum assumptions. But again, this is neither /pg/ nor /stat/, so see ya later

[Anonymous No.10022107]

>>10022102
Again, not what I’m asking.

If there is no algebraic basis for the value of the inequality, that would answer my question, not telling me that the value can be proven elsewhere. I understand that. I just want to know if there is a specific algebraic process by which you may put bounds on the value of the commutator of non-commuting operators.

[Anonymous No.10022122]

>>10022107
well what would i know? I've never gone to university

[Anonymous No.10022140]

>zero divided by zero
what's the right answer?
undefined is a cop-out

[Anonymous No.10022143]

>>10022140
Any division by zero is undefined in a standard algebraic structure. 0/0 is even worse because there's not even a clear way to extend the number system to accommodate it. It's not a "cop out" it's just a fact.

[Anonymous No.10022157]

this should prove to be entertaining regardless

[Anonymous No.10022182]

>>10022140
“Undefined” is defined as the right answer.

[Anonymous No.10022183]

>>10022140
work over a wheel algebra if you want division by zero.

[Anonymous No.10022185]

>>10016567
Has his proof of the non-existence of a complex structure on the 6-sphere even been confirmed yet?
Wtf are you doing Atiyah

[Anonymous No.10022188]

>>10022019
>what is the algebraic basis for non-commuting observables introducing uncertainty?
https://en.wikipedia.org/wiki/Heisenberg_group
The framework can be generalized to locally compact abelian groups as well, so you can actually establish uncertainty like inequalities in a much more general context.

[Anonymous No.10022193]

>>10022185
I'm actually a little concerned for Atiyah. If it were me, and I had already had a major proof of mine thrashed by the mathematical community, the only reason I'd submit a proof of the biggest conjecture in all of mathematics is if I was gonna die soon and it didn't matter what my reputation was like next year.

[Anonymous No.10022202]

>>10022193
The mathematical community is retarded. There really are no complex structures on the 6-sphere.

[Anonymous No.10022207]

>>10022019
It's the Cauchy-Schwarz inequality for the representation of the generators of the Heisenberg algebra on the Banach space of unitary linear bounded operators on a Hilbert space.
Simple, really.

[Anonymous No.10022230]

>>10022202
>>>/toy/ physicist

[Anonymous No.10022245]

>>10022230
I'm not a physicist. Give me a proof that complex structures on the 6-sphere exist.

[Anonymous No.10022259]

>>10022185
actually i agree with you but go to >>>/toy/ regardless

[Anonymous No.10022262]

>>10022259
i made an Ouchie
meant for >>10022245
but likely samefag

[Anonymous No.10022314]

>>10022259
>>10022262
What would I be doing on /toy/ faggot? I hate you.

[Anonymous No.10022336]

>>10022314
>took my panties

[Anonymous No.10022342]

why are groupoid so cute?

[Anonymous No.10022348]

>>10022342
why are english so hard?

[Anonymous No.10022452]

>>10022202
Just because something is true, it doesn't mean that a) it's provable, or b) any particular "proof" is correct.

Fermat's conjecture is true, and it's now been proven. But that doesn't mean that the hundreds (thousands?) of rejected proofs over the years weren't invalid.

[Anonymous No.10022459]

>>10022452
lol bro what are you smoking

[Anonymous No.10022638]

>>10022140
Everything.

Everything satisfies 0x = 0.

[Anonymous No.10022929]

good book for differential algebra?

[Anonymous No.10022936]

How do I find da or dv when solving 2D or 3D integrals? Especially when in spherical or cylindrical coordinates.

[Anonymous No.10022940]

what the fuck

[Anonymous No.10022960]

Need your help /sci/
I'm working on optimization problems, I can easily formulate problems from text and similar, do not have any problem with underlying math in general. I'm studying graph theory on the side and I understand most of the proofs presented. However, everytime I try to do a proof, even for the easiest motherfucking problem, I struggle.
Any recommendation to become better at doing proofs?

[Anonymous No.10022978]

>>10022936
Any orthogonal coordinate transformation [math]x \rightarrow y[/math] on [math]M[/math] is a diffeomorphic endomorphism [math]f:M\rightarrow M[/math] for which [math]\operatorname{det}\left|\frac{\partial y_i}{\partial x^j}\right| = 1[/math] locally on the patch [math]U = \operatorname{Span}\{x_i\}_i[/math] and [math]f(U) = \operatorname{Span}\{y_j\}_j[/math], hence you can find the volume form [math]f^*d\nu[/math] by pulling back [math]f[/math], hence [eqn]\int_{f(U)} d\nu = \int_U f^*d\nu[/eqn].
If you have a surface [math]S[/math] that's embedded in [math]M[/math], you need to find the embedding [math]\iota: S \righthookarrow M[/math] then pull back the volume form by the composite [math]f\circ \iota: S\rightarrow f(S)[/math].
Hope this helps.

[Anonymous No.10022982]

>>10022978
idiot autist. they're clearly in baby's first vector calculus and don't understand any of that shite.

[Anonymous No.10022988]

>>10022978
What category (clearly define your objects and morphisms)?

[Anonymous No.10022992]

>>10022988
>he couldn't figure this out himself
You retarded or something?
[math]{\bf Man}[/math] with manifolds as objects and diffeomorphisms as morphisms.

[Anonymous No.10022993]

>>10022978
based
>>10022982
cringe

[Anonymous No.10023002]

>>10022992
Are you sure it's not [math]{\bf Diff}[/math]? The category with differentiable/smooth manifolds as objects and differentiable/smooth functions as morphisms?

[Anonymous No.10023031]

>>10023002
LOL

[Anonymous No.10023085]

>>10022988
blue pill & cringe
>>10022993
blue pill & cringe
>>10023002
blue pill & cringe
>>10023031
blue pill & cringe

[Anonymous No.10023091]

>>10022978
you're way too recognizable. your roleplay sickens me

[Anonymous No.10023109]

>>10023091
This.

[Anonymous No.10023143]

Just hit some frobenius endomorphism and I'm down for some "group action" with some freshmen in the quad if you know what i mean ,':^/ get the strap

[Anonymous No.10023206]

>>10013013
Math skills to solve but would be used to solve computer science domain problems, eg networks and traveling salesmen

[Anonymous No.10023297]

>>10022978
10/10