/mg/ - math general

[Anonymous No.10828810]

Previously: >>10803629

[Anonymous No.10828895]

>why yes, I completely disregard algebraic geometry since I don't speak french, how could you tell?

[Anonymous No.10828917]

>>10828895
Learn french

[Anonymous No.10828923]

T(0) = 7.5sin(pi/12(0-10))+10.5

How do I solve this? The answer is 6.75 but I can't figure out how

[Anonymous No.10828944]

>>10828923
Fuck that equation just looks disgusting. Did you sit on your TI-84?

[Anonymous No.10828950]

>>10828895
You're not missing much

[Anonymous No.10828972]

>>10828944
no, it was a story problem

[Anonymous No.10828980]

>>10828810
why do those ovals have eyes

[Anonymous No.10829060]

>>10828923
solve what? put it in a calculator

[Anonymous No.10829070]

>>10828810
post pointless subfields of math. I'll start
>category theory
>logic

[Anonymous No.10829103]

>>10829060
it comes out to 10.1 when I do it

[Anonymous No.10829113]

>>10829103
check your order of operations
7.5sin(-10pi/12)+10.5 = 6.75 to me

[Anonymous No.10829119]

https://en.wikipedia.org/wiki/Wheel_theory
Anton Setzer - Wheels
http://www.cs.swan.ac.uk/~csetzer/articles/wheel.pdf
Jesper Carlstrom - Wheels: On Division by Zero
http://www2.math.su.se/reports/2001/11/2001-11.pdf

[Anonymous No.10829135]

>>10829103
>>10829113
I thought I had it set in radians mode

[Anonymous No.10829155]

>>10829070
complex analysis

[Anonymous No.10829174]

>>10829119
>http://www2.math.su.se/reports/2001/11/2001-11.pdf

[Anonymous No.10829211]

>>10829070
computard science

[Anonymous No.10829316]

>>10826889
"do you have autism" was rhetorical, and that you didn't recognize that speaks volumes.
>>10826447
analysis is the pure distillation of mathematical intuition. everything in analysis is intuitive.
>b-but muh smooth but not analytic!
>b-but continuous but nowhere differentiable!
if you assumed these implications would hold and took more than 15 minutes to think of a relevant counterexample to each, you're not cut out for analysis.

[Anonymous No.10829593]

Hi /mg/
Looking for differential geometry suggestions.
I've read the Riemannian Geometry chapters of books in pic related. The optimization book was mostly to learn an application, mathematically interesting subject.

[Anonymous No.10829600]

>>10829316
>>"do you have autism" was rhetorical, and that you didn't recognize that speaks volumes.
me answering it was tongue in cheek
it's YOU that is the autist

>>10829593
tu
pavel grinfeld's tensor analysis is fun

[Anonymous No.10829626]

>>10829600
looks very interesting. I just accessed the book through my university's library logins. I've mostly been reading books which describe all the geometry intrinsically (except the baby undergrad book), regarding Euclidean space as an example. I like that the book you suggested seems to build from a more elementary angle. Also it is pretty short. I'll give it a read.

[Anonymous No.10829965]

>>10829070
Algebraic geometry

[Anonymous No.10829976]

>>10829593
What are the applications on matrix manifolds? Does it refer to the domain or the overall space of the problem?

I always see extensions of geometry based optimisation techniques to manifold domains, but I've never actually seen an application on a non-euclidean domain with the possible exception of spherical coordinates for dron perception, but that was just using a spherical projection of the euclidean domain anyway.

[Anonymous No.10830145]

How true is this image?

[Anonymous No.10830220]

>>10830145

shut up

[Anonymous No.10830324]

>>10829070
Pointless topology

[Anonymous No.10830334]

>>10830220
No u.

[Anonymous No.10830361]

>>10829600
SHIT! you got me

[Anonymous No.10830366]

>>10830324
Excellent post.
>>10829965
Even BETTER post!

[Anonymous No.10830370]

The minkowski sum operation is overpowered. Use it before it gets nerfed in the next update.

[Anonymous No.10830407]

>>10829070
You are shitting on my master thesis. It hurts.

[Anonymous No.10830448]

Why do so many mathematicians end up in finance. It's so infuriating. Here's someone who came #1 in his class at Cambridge.

[Anonymous No.10830458]

>>10830448
>Why do so many mathematicians end up in finance.
Many love money and material goods more than they love mathematics.

[Anonymous No.10830466]

>>10830407
lol’ing at your life

[Anonymous No.10830701]

How should I tutor Linear Algebra to a freshman economics student?
In class all they study is systems of linear equations, matrix operations, determinants, cramer's rule and linear indepence.
No mention of Linear Maps, why the matrix product is the way it is, what the determinant actually is, etc etc.
Just memorizing stuff and doing computations mechanically.

Should I quickly teach Linear Maps first and then proceed to matrices?
I mean that's definitely the better way if you truly want to understand linear algebra, but economics monkeys are worse than shitgineers.

[Anonymous No.10830708]

>>10830701
>economics monkeys are worse than shitgineers
You take that back, cunt.

[Anonymous No.10830726]

>>10829070
Analysis, topology, algebra.

[Anonymous No.10830729]

>>10830701
make them watch 3blue1brown's playlist as a start before actually working with them. Video >>>> words when you're beginning a new topic, especially if your mathematical maturity is that of an econ major.

[Anonymous No.10830752]

>>10830708
econ PhDs >= engineering PhDs >>>> engineering majors >> econ majors.

[Anonymous No.10830757]

>>10829070
Every math subfield excluding the one I study

[Anonymous No.10830915]

>>10829070
Combinatorics

[Anonymous No.10830926]

>>10830726
wha!?

[Anonymous No.10830991]

>>10830757
/thread

[Anonymous No.10831081]

>>10829976
That book considers itself with solving numerical optimization (see Nocedal and Wright) where the function minimize maps from a smooth riemannian manifold to the reals and is at least once differentiable. Twice differentiable for newton-like optimization algorithms.

Matrix manifolds are taken as key examples, showing that various linear algebra problems (e.g. eigenvalue problems, operator norms, symmetric matrix double-cone optimization problems) can be solved in the context of differential geometry.
This is a cutting edge area in the optimization literature. Also an exciting blend of both pure and applied mathematics.

[Anonymous No.10831089]

>>10829119
but is this meaningful and useful in anyway whatsoever?

[Anonymous No.10831103]

>>10831089
Read the paper

[Anonymous No.10831132]

>>10831089
I also have this question
>>10831103
This is a horrible way to motivate people to read a subject. You need to provide motivation to people outside of your immediate interests.

[Anonymous No.10831209]

>>10828810
if x is even, x^2 is even, x^3 is even, x^4 is even.
if x is odd, x^2 is odd, x^3 is odd, x^4 is odd.

Does this pattern continue? If we have the general form x^n, if x is even, then is (2k)^n even for all n? and if x is odd, is (2k+1)^n odd for all n?

how would one go about proving this?

[Anonymous No.10831232]

>>10831209
induction.
if x is even then x is 2k for some k
base case x^1=2k.
now for n bigger or equal to n,
if we assume that x^n is even
then x^n=2l for some l
x^n+1= x^n * x = 2l * 2k= 2(2lk) so it is even
odd :
x is 2k+1 for some k
base case n=1: 2k +1 is odd
for n bigger or equal to 1:
if x^n is odd, then x^n= 2l + 1 for some l
x^n+1=x^n*x=(2l +1)*(2k+1)=4lk + 2l + 2k + 1= 2(2lk +l + k) + 1 which is odd.

[Anonymous No.10831235]

>>10831232
>now for n bigger or equal to n
or equal to 1, fuck

[Anonymous No.10831250]

>>10831232
>even case
Correct.
>odd case
Just invoke the algebraic definition of prime element of a ring.

[Anonymous No.10831268]

>>10828810
I'm looking at the Lorentz transformations and a general thing done is considering the homomorphism [math]\mathbb{R}^4 \rightarrow \mathbb{C}^{2 \times 2}[/math] such that
[eqn]T:\begin{pmatrix}x_0 \\ x_1 \\ x_2 \\ x_3\end{pmatrix} \rightarrow \begin{pmatrix}x_0+x_3 & x_1 - ix_2 \\ x_1 + i x_2 & x_0 - x_3 \end{pmatrix} = x[/eqn], with the standard Minkowski bilinear (+,-,-,-). As far as I know, metrics are not preserved in homomorphisms yet
[eqn]\text{det}(x) = x_0^2 - x_1^2-x_2^2-x_3^2[/eqn]. Is this just an intelligently chosen map such that the the determinant correspond to the inner product of this element? If I 'cheat' and define an element of the dual space with [math]x_0 \rightarrow -x_0[/math] the usual inner product [math]<A,B> = \frac{1}{2}\text{Tr}(A^\dagger B)[/math]checks out.

[Anonymous No.10831285]

>>10831209
Of course. Think about what even and odd mean. Even means has a factor of 2. So if x has a factor of 2, then x times anything also definitely has a factor of 2. (write x = 2k, then xy = 2(ky)). in particular, if x is even, then x^n = x*x^(n-1) which is then also even.
on the other hand, if you multiply two odd numbers then neither has a factor of 2. since 2 is prime, then neither will their product. so by induction any product of odd numbers is odd. in particular, x^n is when x is.

[Anonymous No.10831315]

>>10831268
>Is this just an intelligently chosen map
Yes.

[Anonymous No.10831357]

>>10830729
I thought of that actually. Just teach matrices and have 3blue1brown as homework, but that might seem a bit too innovative, especially when the video is in English since that's not his native language.
Maybe I'll say fuck it teach linear maps And give 3b1b homework as well.

[Anonymous No.10831365]

>>10829070
Measure theory

[Anonymous No.10831392]

why is the man forgotten?
https://en.wikipedia.org/wiki/Simon_Stevin

[Anonymous No.10831588]

>>10831315
But why does the determinant happen to be the inner product?

[Anonymous No.10831600]

>>10831588
Pure coincidence.

[Anonymous No.10831605]

>>10829070
physics

[Anonymous No.10831641]

>>10831588
By choosing the map very intelligently. The mapping was constructed by a person with a particular representation in mind.

[Anonymous No.10831815]

>>10830324
as soon as i saw the question, i was waiting for this. should've been first reply

[Anonymous No.10832112]

>>10831209
Yes, this is very simple to see via prime factorization.
When squaring a number each prime factor just occurs twice as often.
If 2 is a factor 2*2 will be a factor after exponentiation, if 2 isn't it still won't be after exponentiation.

[Anonymous No.10832279]

>>10831209
In my TA evaluations I sometimes got comments that I was rude. I know very well who I got them from, because of the way they were written. And I agree with them, I may have been rude. But questions like these kind of piss me off when the answer is obvious if you just think about it for a second. I don’t think I am being elitist or anything, since I do believe the level of the students is way above these type of questions. I think what angers me is that they want to be spoon fed the whole problem and don’t want to think about it. Am I being unreasonable in reacting this way? I can’t remember a specific example, but it was a question like this from someone seeing series and sequences.

[Anonymous No.10832305]

>>10832279
The only thing unreasonable is caring in the first place.TA'ing a crowd of little dumbasses is just an unfortunate reality of being a non-rich grad student, it's not one of your duties you should be putting actual effort into.

[Anonymous No.10832314]

>>10831605
t. Seething math major

[Anonymous No.10832422]

How can I become math professor? It seems like a pretty comfy career path.

[Anonymous No.10832488]

>>10831600
>>10831641
So a physicist claimings [math]\text{det}(x) = -x_0^2 + x_1^2 + x_2^2 +x_3^2[/math] means anything beyond a coincidence is rubbish? I could imagine constructing a map [math]T:\mathbb{R}^4 \rightarrow \mathbb{R}^{2 \times 2}[/math] for which it doesn't hold for example.

[Anonymous No.10832494]

>>10832422
Just profess math

[Anonymous No.10832505]

>>10832422
Why does he have his eyes closed in such a pretentious way?

[Anonymous No.10832653]

>>10832505
Some people literally see math or code in their heads. Take this kid for example, he's suppose to be like Neo, sees and dreams in code.

[Anonymous No.10832666]

>>10832653
I see maths in my head too, but I don't need to close my eyes for that.

[Anonymous No.10832708]

>>10832666
But are you a Field's Medal winner?

[Anonymous No.10832728]

>>10832653
I wonder what makes this kid a prodigy at software. Does he have a unique problem solving ability?

[Anonymous No.10832731]

Can someone help me understand how the scattering rate reduces to such a simple term? Given are [latex]V = - J/2N \sum_{k1,k2}(S_+c^\dagger_{k1\downarrow}c_{k2\uparrow} +S_- c^\dagger_{k1\uparrow}c_{k2\downarrow} + S_z(c^\dagger_{k1\uparrow}c^\dagger_{k2\uparrow} - c^\dagger_{k1\downarrow}c^\dagger_{k2\downarrow})[/latex] The states are defined as [latex]|\vec{k}\uparrow\rangle= c^\dagger_{\vec{k}\uparrow}[/latex]

[Anonymous No.10832733]

>>10832731
>Can someone help me understand how the scattering rate reduces to such a simple term? Given are [latex]$V = - J/2N \sum_{k1,k2}(S_+c^\dagger_{k1\downarrow}c_{k2\uparrow} +S_- c^\dagger_{k1\uparrow}c_{k2\downarrow} + S_z(c^\dagger_{k1\uparrow}c^\dagger_{k2\uparrow} - c^\dagger_{k1\downarrow}c^\dagger_{k2\downarrow})$[/latex] The states are defined as [latex]$|\vec{k}\uparrow\rangle= c^\dagger_{\vec{k}\uparrow}$[/latex]

[Anonymous No.10832735]

>>10832728
Apparently able to 'see' problems and solutions like Neo. Kinda like hyperintuition. He's a AI PhD student now.

[Anonymous No.10832888]

>hyperbolic identities
Do I need to know this shit? It's fucking boring

[Anonymous No.10832903]

>>10832888
You should be able to prove them, but memorizing is a waste of time

[Anonymous No.10832904]

>>10832494
kek

[Anonymous No.10832956]

>>10832279
You're not unreasonable at all. At the same time, it's rare that taking disapproval of someone who doesn't try to think the first time around will lead them to try the second time. A lot of these people don't know how to start thinking about a problem yet. On the other hand, giving them an encouraging but not so direct push can make them feel like they figured it out (even if they didn't) which when reinforced leads them to trust their intuition more when they try to start solving a problem.
Think about how you built your own trust in your problem solving ability when you were in high school / early undergrad, and (most likely) how sometimes you'd ask a question and realize upon getting an answer that it was obvious. It happens to all of us. And if the person answering you just talks about how obvious it is the whole time, it probably made you less likely to want to think more about it in the future.
I think it's also important to keep in mind that the person who asks a question, no matter how stupid, is always more inquisitive than the person who just sits there confused (which I can guarantee some of your students do as in any class). Try not to direct your frustration toward them because then they'll shut up and just sit there confused as well.

[Anonymous No.10832959]

>>10832888
>not just having an intuition for any low level identity anyone could throw your way

[Anonymous No.10833063]

>>10832956
Yes, you are absolutely correct. Thanks for the advice, I don’t want my students to sit there confused if I can clarify their questions easily. I don’t even know why I get frustrated at those questions. I think I need to reevaluate why I feel that way.

[Anonymous No.10833120]

inb4 post this on facebook/twitter/reddit, but whatever.

I've just published my first paper and am about to publish my second. I know my first paper is absolutely useless, I enjoyed the research but I honestly doubt anyone will read it, let alone give a shit about the research. On one side, it feels nice to have published something, I feel like I just took money out of people's pockets, took 4 months out of my own time to do useless work. I learnt a lot, from how to write a paper, to how to work with professors and proof work, it was quite enjoyable work. But in the end itll sit somewhere in some database, never to be look at again. just two lines on my CV to say I've done shit but that's pretty much it.
Even the reviewers were like "yeah this is standard work and the writing is exactly the sort of thing we publish in our journal, but what's the point of this? why have you not tried to apply your methods on these problems instead?

[Anonymous No.10833146]

>>10833120
Congrats! I mean, as long as you had fun and were paid for it, all is fine, right? Everything else is extra. Sure it would be great if a lot of people read it and found it useful, but as long as you are having fun in your research and can live off it, it’s a lot more than a lot of people get. And nothing is ever truly useless. You learned something from it.

[Anonymous No.10833228]

What's the best Differential Geometry book?
Something recent and clean that heavily uses linear algebra?

[Anonymous No.10833242]

>>10833228
http://www.topology.org/tex/conc/differential_geometry_books.html

Huge list

[Anonymous No.10833281]

>>10828923
Simplify the input for sine:
7.5sin(-5/6 pi) + 10.5

Use the oddness of sine (not necessary if you know your unit circle):
-7.5sin(5/6 pi) + 10.5

Use the phase shift identity (not necessary if you know your unit circle):
-7.5sin(pi/2 + pi / 3) + 10.5
=-7.5cos(pi / 3) + 10.5

cos(pi/3) = 1/2, so simplifying we have
=-7.5 / 2 + 10.5
=6.75

[Anonymous No.10833320]

>>10833228
http://www.geometry.org/tex/conc/dgstats.php

[Anonymous No.10833368]

>>10833120

> why have you not tried to apply your methods on these problems instead?

Why didn't you?

[Anonymous No.10833395]

>>10833242
>>10833320
Is this guy a crank or the real deal?

>>10833120
>>10833368
> Why didn't you?
Good question, maybe a better one - why don't you?
Is your second paper related?

[Anonymous No.10833401]

>>10833242
does Diff Geo actually take 2-3 years to pick up? Thinking more for the purposes of physics and other sciences than for the pure math

[Anonymous No.10833451]

>>10833401
Pure math diff geo is analysis, linear algebra,topology, algebra usually last years /grad topic.

But for non-pure mathematics
Just calculus plus linear algebra proof based course.
A First Course in Geometric Topology and Differential Geometry

Introduction to Diff Geo
Introduction to Manifolds by Tu

[Anonymous No.10833530]

>>10833395
>crank or the real deal
Mostly crank, but the recs are still solid. Petersen is a really nice text.

[Anonymous No.10833596]

The set of all metrics that generate a given topology is closed under multiplication by positive reals, and sum. It trivially has no identity element, and negative metrics don't exist.
Is there a name for this sort of structure?

[Anonymous No.10833602]

>>10833242
Intro to Smooth Manifolds, John Lee

[Anonymous No.10833617]

>>10833596
So like a vector space except your abelian group is just a commutative semigroup? Sounds too niche to have its own name.

[Anonymous No.10833665]

>>10833617
That's what I thought, but it seems like something that'd show up naturally when you're studying semirings, I just know jack abouy those.

[Anonymous No.10833863]

>>10833063
Oh don't get me wrong, I don't know if you have to be less frustrated because it IS frustrating. I just think it can be helpful to your students if you practice concealing the frustration and showing (maybe feigning) empathy instead. I'll be honest, it's kind of fun. I have had very similar experiences to yours and biting my tongue can be really tough when it's the same person over and over, but the frustration melts away for me when I start explaining the 15th thing and for the first time they stop me and say "I get it now!" and do it themself. It's really really rewarding to know you gave someone the courage to start pushing forward on their own. Even if it takes a long time. And sometimes it never happens, but if I keep that in mind as my goal when I'm trying to help people, I can ignore the frustration.
I'm very muddled about this myself, but I really like exploring the ideas behind pedagogy because I truly believe that it is one of the key skills one uses when doing any sort of mathematical communication in academia. Even if >>10832305 doesn't feel that way.

[Anonymous No.10833890]

>>10833120
Did you discover something new? Was it the thing you wanted to discover? That's the value. Someone at some point will ask the same question, and they'll look it up. And they might not find your paper. But they also might, and then they'll see that you discovered it and they'll be happy to know the answer to their question.
We also know you discovered something, even if we don't know what, and I will say that I appreciate your work and it has value to me regardless if I will ever see it, because it represents the expansion of mathematical knowledge.
Think about how much money is wasted on people who never manage to figure out the thing they're searching for.

[Anonymous No.10833949]

>>10833596
a cone

[Anonymous No.10833976]

>>10833949
not that guy, but i was thinking "hmm that really seems like the set of positive elements in an ordered vector space"
and there it is. thanks.

[Anonymous No.10833997]

>>10833949
What the fuck I'm retarded.
Thanks, lad.

[Anonymous No.10834000]

>>10833976
Yup, that sort of structures actually comes up very often when you deal with convex sets, for example in geometry or nonlinear analysis

[Anonymous No.10834357]

>>10834000
and that's why I like them so much. convex things are great.

[Anonymous No.10834393]

Please explain the difference between arithmetics (like calculus) and actual math. I know its more about proofs and logical thinking but thats too abstract to get a real understanding of.

What do you do in actual math? Whats the theory like? It cant be just heres X solve Y with a certain function

[Anonymous No.10834486]

>>10830701
I've tutored econ majors before on that subject and I just follow Grossman or Strang. Eventually you realize they don't really want to "understand" it so you just help them trough the problems.

[Anonymous No.10834537]

>>10834393
>It cant be just heres X solve Y with a certain function
It's more like "Here's theorem X which proves corollary Y under certain conditions"

[Anonymous No.10834557]

>>10834393
>that's too abstract to get a real understanding of
that's the idea yeah
here's a kind of notion. you might have an intuitive sort of idea for why taylor's theorem might work from calculus, why you can expand some functions in polynomials with coefficients proportional to the derivatives, and why the factorials show up. but do you actually know 100% why it works? like, have you seen anyone walk through step by step how to PROVE taylor's theorem?
that's the difference between arithmetic and real math.
similarly, why is it that the integral of a derivative is the original function? like, yeah, the fundamental theorem of calculus says so. and it makes sense that if you take the rate of change of a function and allow it to accumulate, you get back the original function value.
but there is a proper proof which makes use of the difference quotient limit and riemann sums which you can work out to conclusively know it's true.
this sort of thing is what you prove in real analysis, one sort of math. other sorts of math include number theory - like for instance, why is it true that every integer has a unique prime factorization? i learned that in like 4th grade and always thought it was just obvious but the proper proof actually works. and you can ask much tougher problems, like how many primes are there below a certain number? or how about fermat's last theorem: it seems like when n > 2, the equation x^n + y^n = z^n for positive integers x, y, and z is never actually satisfied. keep in mind when n = 2 this is the pythagorean theorem and there are plenty of solutions, one is x = 3, y = 4, z = 5. so it's almost strange that it never works for n > 2. and it took hundreds of years for number theorists, algebraists, and arithmetic geometers - and i'm sure plenty of other types of mathematicians - to prove that there actually are no solutions to the equation.
it's a question you can understand from an arithmetic background which a mathematician would study.

[Anonymous No.10834581]

>>10832731
Pls use [eqn][eqn]~~or~~[math][/eqn]

[Anonymous No.10834583]

>>10834393
>>10834557
i wanted to continue a bit more but ran out of space.
so on the theme of fermat's last theorem there is another problem which you could probably understand what's being asked if you spent some time staring at it, you have all the tools to do so. the abc conjecture. well, right now there's a dude named shinichi mochizucki who has released a proof that the abc conjecture is true. the proof is hundreds of pages long and is considered incomprehensible to all but the top mathematicians in the field. and a few of those mathematicians, most notably peter scholze, think that the proof has errors and is not valid. it's more convoluted than that but that's the essence. so math is not without passion, debate, and uncertainty.
of course we'd all prefer the proof to be more clear, but considering that he developed a whole theory of math (a foundational bunch of results) called Interuniveral Teichmuller Theory to prove the abc-conjecture, an innocuous enough problem, seems to indicate that we won't get a nice proof. not to say that the proof of fermat's last theorem is nice!
there are problems in between of course, not intractible but also not that easy.
some other sorts of math that you might have an idea about: dynamics and differential equations regard more physical, scientific systems like pendulums or populations or chemical reactions. algebra is the math of different structures, like the set of polynomials or the complex numbers. analysis and topology are the math of continuous things and continuous/differentiable/integrable functions between them. geometry is the study of shape and form, which can go hand in hand with topology. there are also mixed fields of math too, people who study algebraic topology use algebraic structures like groups to find out information about topological spaces - for instance, we can associate the sphere with a different "group" than we associate the torus to prove that the torus has a hole but not the sphere.

[Anonymous No.10834593]

>>10834393
>>10834583
i know this is long. to finish off, if you want a fun video series that should give you a really good idea for how mathematicians think about math, you should check out the channel 3Blue1Brown. specifically i'd recommend a few videos, but just pick one that's interesting to you. they're all great.
https://www.youtube.com/watch?v=VvCytJvd4H0
https://www.youtube.com/watch?v=cyW5z-M2yzw
https://www.youtube.com/watch?v=XFDM1ip5HdU
https://www.youtube.com/watch?v=sD0NjbwqlYw
and a series i'd HIGHLY recommend checking out if you really want to see how mathematicians think about something which is often taught in a very computational way:
https://www.youtube.com/watch?v=kjBOesZCoqc

[Anonymous No.10834645]

>>10834393
>>10834593
oh god i forgot about this video and it's just 5 minutes long. holy crap, watch it. it's so fucking ridiculous it's not even funny.
https://www.youtube.com/watch?v=HEfHFsfGXjs
that type of shit is why people study math

[Anonymous No.10834652]

>>10833146
Thanks I actually really appreciate your message
>>10833368
>>10833395

good question. I am still an undergrad, the prof gave me the problem to work on as a learning problem, I solved it in a fairly simple setting, my next paper isn't related because it's not with the same professor. I would enjoy working towards applying the solution on the other problems they suggested, if given enough time.

>>10833890
yeah, I did. the discovery of it wasn't hard, the proof of it I found quite difficult.

thanks everyone. I was in my down period for this second paper thinking "was is even the point? is it going to end up like my first paper?" but you guys are right. I appreciate this positive feedback to my attention-seeking post and will use this good feeling to do good work.

[Anonymous No.10834669]

>>10834652
okay let's all go back to being vitriolic and mean to one another now, thanks for the break from the constant burning anger
now go fuck yourself, back to /lit/, mathematicians use we, i'm not a "he", why the homophobia, and have sex

[Anonymous No.10834816]

>>10834669
>the mind of a schizo mathematician who haven't published in a decade

[Anonymous No.10834834]

If you're a highschooler, a math major or a grad student please for the love of God keep Shinichi Mochizuki's name out of your mouth.

[Anonymous No.10834905]

>>10834834
i was doing my best to illustrate the idea of modern math for a normie who doesn't know what a proof is
go fuck yourself, it's not like i'm giving it to him as recommended reading

[Anonymous No.10835049]

>>10831588
Because the map [math]T:\mathbb{R}^4\rightarrow \operatorname{Lie}U(2)[/math] given by [math]x \mapsto x_\mu \sigma_\mu[/math] is an isomorphism of vector spaces over [math]\mathbb{R}[/math]. Now by considering [math]\operatorname{Lie}U(2)[/math] as the tangent space of [math]U(2)[/math] at the identity, the determinant [math]\operatorname{det}:\operatorname{Lie}U(2)\rightarrow \mathbb{R}[/math] induces the determinant line bundle over [math]U(2)[/math] (or the connected component at the identity thereof) after descending down via [math]\exp: \operatorname{Lie}U(2)\rightarrow U(2)[/math]. Given the trace metric on [math]\operatorname{Lie}U(2)[/math], the identity [math]\operatorname{tr}\ln = \ln\operatorname{det}[/math] pushes this metric into a section of the determinant line bundle on [math]U(2)[/math], and by pulling back through the map [math]T[/math] defined above we map the trace metric into a bilinear form [math]T^*\operatorname{det}[/math] on [math]\mathbb{R}^4[/math], which by your calculation is the Minkowski metric.
Alternatively you can think about embedding [math]\operatorname{Lie}SU(2)[/math] into [math]\operatorname{Lie}U(2)[/math] by ignoring the identity matrix, and using the fact that [math]\operatorname{Lie}SU(2) \cong \operatorname{Lie}SO(3)[/math] to induce an isometry between it and [math]TSO(3)\cong T(S^2\times S^1) \cong \mathbb{R}^3[/math]. Pulling back the metric induced on [math]\mathbb{R}^3[/math] from the trace metric on [math]\operatorname{Lie}SU(2)[/math] by the embedding then leads to the Minkowski metric.

[Anonymous No.10835053]

>>10835049
NEEEEERRRRRRRRRRRRD!

Can I get your autograph?

[Anonymous No.10835136]

>>10832708
Do you need to constantly close your eyes when you become one? No wonder Perelman refused the medal.

[Anonymous No.10835147]

>>10835049
yukarifag is so precious

[Anonymous No.10835310]

>>10834593
>>10834557
Thanks a lot anon

[Anonymous No.10835387]

Can someone tell me what the total order on the cardinals looks like? Or show me a list of cardinals, I didnt find one online.
For example aleph one > aleph naught, so by the continuum hypothesis aleph one should be 2^N or > 2^N?
Also the continuum hypothesis makes it look like the order is similar to N, i.e. discrete.

[Anonymous No.10835454]

>>10835387
It is a "well-order" (by which I mean that any set of cardinals is well-ordered) so yes, it looks like the order of N, but much longer.
Here is a visualization of it: http://www.madore.org/~david/images/omega-2.svg
(this is a picture of the ordinals, but you can imagine that each of them corresponds to an infinite cardinal)

The (generalized) continuum hypothesis has no incidence on the shape of that order, it just tells you "quantitatively" how cardinals relate to one another.

[Anonymous No.10835492]

>>10834593
Thanks for recommending this guy. I had long seen some vids from him but not his linear algebra stuff.

[Anonymous No.10835530]

Is there an introductory Differential Geometry textbook where this shit doesn't happen?
Wtf is this atrocius notation.

[Anonymous No.10835598]

>>10835530
This thread just blows my mind, how the fuck do people understand or ball this stuff in their head. I mean best I can solve is some shitty differential equations

[Anonymous No.10835678]

>>10835598

Stop watching anime you weebbrain

[Anonymous No.10835685]

>>10835678
I dont though

[Anonymous No.10835720]

I am a fucking retard, Google failed my googling attempts.

How do I calculate the rate of change between two win rates? Say, from 50% win rate to 55%? What's the winrate I need for that 5% increase?

Does my question even make sense lmao

[Anonymous No.10835728]

>>10835720
Is that a vidya question? If yes, it depends on the number of games you've played, and how many you have yet to play (or within how many games you want to achieve 55%).

[Anonymous No.10835729]

>>10835530
what book is this

[Anonymous No.10835747]

>>10835720

No, that doesn't make sense.

[Anonymous No.10835767]

>>10835530
that’s pretty disgusting desu
>>10835729
lol

[Anonymous No.10835768]

>>10835454
but where is 2^N here? doesnt the CH imply that nothing can be between N and 2^N?

[Anonymous No.10835772]

What is geometry as a field actually like?
I listened to an introductory geometry and topology class but we only did topology.
So all I can imagine is that geometry is a mix of analysis and topology?
What objects does geometry study? Metric spaces? what are some fundamental theorems of geometry and definitions?
When I google this I only get pages about highschool geometry

[Anonymous No.10835779]

>>10835772

"Geometry" isn't bearded guys sitting around playing with rulers and compasses wearing togas.

There's algebraic geometry, differential geometry, algebraic topology, etc.

They study sets of points defined in various ways

[Anonymous No.10835784]

>>10835768
That picture just shows ordinals, the only cardinal there is [math]\omega[/math] which is the same set as [math]\aleph_0[/math]. Yes CH implies [math]2^{\aleph_0}=\aleph_1[/math]. Whenever you are working in a model of set theory that satisfies choice then cardinals are well-ordered.

[Anonymous No.10835822]

>>10835530
Try the one by Wolfgang Kühnel

[Anonymous No.10835848]

>>10835779
>They study sets of points defined in various ways
this has to be the worst explanation of modern geometry I have ever seen

[Anonymous No.10835855]

>>10835772
Geometry is "rigid" when compared to topology.
So you'll have things like conformal geometry, which is concerned with maps that preserve angles, metric geometry, which works over isometries, etc.

[Anonymous No.10836222]

>>10835598
You know what, that stuff really isn't too advanced. It's just the retarded notation, which I am fairly certain it could be heavily simplified by using more linear algebra.
That's why I am asking for a different book.

>>10835729
It's Ted Shifrin's book.

>>10835822
Thanks, I'll check it out.

[Anonymous No.10836264]

>>10835822
>>10836222
Currently reading it and it seems to be Exactly what I was looking for. Really impressed. Thanks again.

[Anonymous No.10836279]

>>10829155
Arent concepts from complex analysis applied in fluid dynamics, electrical engineering, astrophysics, and a shitload of other applied math/physics fields?

[Anonymous No.10836283]

>>10829155
are you for real (no pun intended) ? complex analysis is super useful

[Anonymous No.10836298]

>>10829593
I liked the Dover book you posted. Most people suggest Do Carmo. I came from more of an algebraic background, so actually liked Shahshahani the most. I found Shahshahani to be the best as far as being explicit in setting up the algebra, giving you abstract computations first locally, then globally. I also really like his sections on de Rham cohomology, integration, and Stokes-Cartan. I then went back to the first few sections of Do Carmo for concrete examples and computations.

For diffgeo, my personal preference was to start very general, then learn the specifics of, say, Riemannian surfaces. It wouldn't hurt to have an algebraic topology book around as well and google some of the big relationships (Poincare Duality and de Rham's theorem in particular). The Dover Algebraic Topology book is good too, though has some obvious typos and idiosyncratic notation throughout.

[Anonymous No.10836323]

>>10836298
do you have a recommendation for a material on Riemannian surfaces? Algebraic topology and differential geometry is not a problem, I'm short on complex analysis and algebraic geometry though.

[Anonymous No.10836353]

>>10836323
I am not great at complex analysis. Lee and Do Carmo are standards for more rigid diffgeo.

Not sure how AG will help you (usually people think intuition in diffgeo helps with AG, not the other way around). But, Vakil's notes are literally the best text on AG around imo. Pair with Hartshorne and The Geometry of Schemes.

[Anonymous No.10836356]

>>10836353
I was asking about Riemannian surfaces

[Anonymous No.10836375]

>>10835779
well that's exactly why I asked.
algebraic geometry is algebra
algebraic topology is topology
idk differential geometry.
I was wondering if geometry stands as a field on its own, with it's own methods, but i guess not and it's just sth you can do with other mathematics

[Anonymous No.10836380]

>>10832314
Physics major. I study physics because is useless

[Anonymous No.10836381]

>>10836375
>idk differential geometry.
>I was wondering if geometry stands as a field on its own, with it's own methods, but i guess not and it's just sth you can do with other mathematics
well why don't you learn a bit of differential geometry before making guesses like this

[Anonymous No.10836445]

>>10836375
differential geometry is one of the biggest fields of mathematics. it's geometry in the sense that it studies volumes, symmetries etc. (among other things), but the methods used are completely different from the "high school geometry" which you're probably talking about.

[Anonymous No.10836507]

>>10836445
ah yes then that's what I was looking for

[Anonymous No.10836588]

>>10835779
>>10836445
Why do I have The feeling that you have never actually formally studied any geometry outside of high school?

[Anonymous No.10836595]

>>10836588
We're not the same person (I'm the second) and I have no idea. I have a master's in geometry.

[Anonymous No.10836689]

>>10836356
Donaldson works, but I haven't read that many books on the subject.

[Anonymous No.10836698]

>>10836588

you'd be wrong about that

[Anonymous No.10836707]

>>10836588
Probably because you're a synthetic geometry boomer.

[Anonymous No.10836724]

>>10833401
https://www.youtube.com/watch?v=V49i_LM8B0E&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

https://www.youtube.com/watch?v=7G4SqIboeig&list=PLFeEvEPtX_0S6vxxiiNPrJbLu9aK1UVC_

The dude explains stuff better than any of the books recommended here.

[Anonymous No.10836735]

>>10835049
based mathematical physicist

[Anonymous No.10836773]

>>10836222
how can you be certain if you don’t know the subject?

[Anonymous No.10836873]

I scored top 99.9% on the SAT and have 152 IQ.

[Anonymous No.10836891]

I'm stuck, /mg/. I I have transcribed Cardano's fomula to Python, but one of the test cases inputs bonusFindCubicRoots(5, 1, 3, 2)..

My problem is that this polynomial (5x^3 + x^2 + 3x + 2) does NOT have integer roots! I don't get it, the question states it will. I've been stuck for hours now with no meaningful progress, just checking for transcription errors and reading other sources, testing on other calculators, etc..

[Anonymous No.10836911]

>>10836891
Here's my code:

def bonusFindIntRootsOfCubic(a, b, c, d):
p = -b/(3*a)
q = p**3 + (b*c-3*a*d)/(6*(a**2))
r = c/(3*a)
root1 = (q + (q**2 + (r-p**2)**3)**(1/2))**(1/3)
+ (q - (q**2 + (r-p**2)**3)**(1/2))**(1/3) + p
root1 = root1.real
print(root1)
return None


[Anonymous No.10836915]

>>10836911
formatted better over here: >>72042844

[Anonymous No.10836924]

Can someone explain to me the Implicit Function Theorem intuitively?

I intuitively understand the Inverse Function Theorem this way: the derivative of a function f at a point p is the best linear approximation of f around p i.e. [math] f(p+h) \approx f(p) + D_p h + o(\lVert h \rVert) [/math], therefore if the derivative is invertible it means that f is invertible as well for small enough neighborhoods of p.

Is there a similar explanation for the Implicit Function theorem?

[Anonymous No.10836947]

For the love of sweet christ, help me out here.
I need to memorize around 200 theorems from real analysis with proof verbatim within the next month. Due to my prof's autism, muh "just understand it lmao" is kinda useless as a guide. Sure, I understand the logic behind it, I can explain it to a layman with notes available, that doesn't mean I can pull three lengthy definitions, theorem and its proof and lemmas word for word out of my ass exactly as my prof wrote them.
It's stressing me the fuck out as it's literally the only thing holding me back from going forward with my degree. Any of you encountered this? Like I'm not even remotely interested in the content anymore, I just have to pass this autistic cunt.

[Anonymous No.10836981]

>>10836947
>Any of you encountered this?
Yeah, memory's the only thing holding me back nowadays.
Still, how lengthy are his tests? If you have enough time, you can just memorize the outlines and fill the formalisms in on the spot.
Make sure to get a bunch of textbooks to attempt to bullshit him into believing you used a definition from somewhere else in case he marks you as wrong.

[Anonymous No.10836984]

>>10836891
>>10836911
it's from this website, btw: http://www.kosbie.net/cmu/spring-17/15-112/notes/hw1.html

[Anonymous No.10837014]

>>10836981
>Yeah, memory's the only thing holding me back nowadays.
can you expand on this? I've never found it that important, how is it holding you back?

[Anonymous No.10837017]

Is everyone studying math here in school? Are most of you guys grad students? Anyone here who's studying on their own free time?

[Anonymous No.10837030]

>>10837017
>anyone here who's studying on their own free time?
I was, but I'm going back to school now (undergrad). Shit's comfy, and classes should be a perma breeze until grad school, if i decide to go

[Anonymous No.10837032]

How do I make this formula undefined after x>2

y= -2*|x|

[Anonymous No.10837045]

>>10836924
how is someone supposed to intuitively explain something you have no intuition for?

[Anonymous No.10837068]

>>10837032

make it piecewise you highschooler

[Anonymous No.10837093]

>>10837014
I understand faster than I can memorize.
It's a really disgusting situation where I don't take time to grasp the definitions, so I can't remember them later.
>>10837032
>undefined after x>2
Restrict the domain?

[Anonymous No.10837097]

Can anyone please recommend me good math book(s?) for self learning?

I would like to cover everything from basic arithmatic on through high school level math.

In short I floated by in school math classes and am comfortable up to algebra but nothing after that, and I would like to expand my knowledge/skills to further my career. python is involved in network automation, i want to go further and get good at python, i know i need more/better math. Yes I am serious.

Please and Thank You.

[Anonymous No.10837101]

>>10837093
if you understand, why can't you derive? After deriving enough, things usually become built in intuition for me, personally. Unless you're forgetting notational things, I still don't understand.

Not tryna be a butthole, just want to know - I should probably start taking my memory more seriously anyway, I've always let it take the backseat.

[Anonymous No.10837102]

>>10837097
Also I know about free things like khan academy, but i prefer a hard cover book in front of me when i learn.

[Anonymous No.10837108]

>>10837097
do'nt waste time on arithemetic, stretch your skills and backfill as needed. Grab a book on trigonemetry or calculus and just look up what you don't know. Axler's Precalculus might be a good start, or Jame's Stewart's Calculus

[Anonymous No.10837112]

>>10837068
It was on an ALEKS placement test. y=f(x) was graphed and they wanted you to graph y=1/2f(x)

-2*|x| was basically what got the values needed for f(x), but I couldn't think of how to make the formula undefined after x>2.

[Anonymous No.10837118]

>>10837101
>why can't you derive
Because I don't remember the intuition, either.

[Anonymous No.10837126]

>>10837097
>basic arithmatic
Top kek. Are there really people who consciously study arithmetic? For what purpose, adding numbers in your head faster? Is this a brainlet cope mechanism, like the handwriting thing?

[Anonymous No.10837130]

>>10836924
The most intuitive case is that of a plane curve C defined by one smooth equation f(x,y) = 0.
The theorem tells you that if C does not have a vertical tangent line at some point (x0,y0), then locally around that point, the curve can be parameterized using x alone, ie. y is locally a function of x (which should be clear from a drawing).
Now the handwavy argument similar to what you gave is that, locally around (x0,y0), we have:
[math]f(x,y) = \partial_1 f(x_0,y_0)(x-x_0) + \partial_2 f(x_0,y_0)(y-y_0) + o(|x-x_0|+|y-y_0|)[/math].
If [math]\partial_2f(x_0,y_0) \ne 0[/math] (ie. the curve does not have a vertical tangent line), then a point (x,y) is on C if [math] \partial_1 f(x_0,y_0)(x-x_0) + \partial_2 f(x_0,y_0)(y-y_0) + o(|x-x_0|+|y-y_0|) = 0[/math], which, if (x,y) is sufficiently close to (x0,y0), allows you to express y in terms of x (the proper argument of course uses the inverse function theorem)

[Anonymous No.10837132]

>>10837126
>adding numbers in your head faster
precisely.

[Anonymous No.10837213]

>>10836947
Try memorizing 7 or more proofs a day

[Anonymous No.10837223]

>>10837213
Theorems

[Anonymous No.10837244]

>>10837118
it sounds like you should focus on developng intuition, not scapegoating with your memory. poor fella dindu nuthin wrong

[Anonymous No.10837261]

>>10836924
Eureka!
Consider [math] F: \mathbb{R}^k \times \mathbb{R}^m \to \mathbb{R}^m [/math]

The derivative of F at [math] (\mathbf{a},\mathbf{b}) [/math] is the linear map [math] (\mathbf{u},\mathbf{v}) \mapsto D_{(\mathbf{a},\mathbf{b})} F (\mathbf{u},\mathbf{v})[/math]
(bolded letters denote vectors)

We denote by [math]\frac{dF}{d\mathbf{x_j}}[/math] the j-th column of the map's matrix and write [math]\mathbf{u}=(u_1,\ldots,u_k),\ \mathbf{v}=(v_1,\ldots,v_m) [/math] we get:

[math]D_{(\mathbf{a},\mathbf{b})}F(\mathbf{u},\mathbf{v})=\frac{dF}{dx_1}u_1+\ldots\frac{dF}{dx_k}u_k+\frac{dF}{dx_1}v_1+\ldots \frac{dF}{dy_m}v_m=\frac{dF}{d\mathbf{x}}\mathbf{u}+\frac{dF}{d\mathbf{y}} \mathbf{v} [/math]
where [math]\frac{dF}{d\mathbf{x}}[/math] denotes the first k columns of the matrix and [math]\frac{dF}{d\mathbf{y}}[/math] the rest m ones.

When [math](\mathbf{u},\mathbf{v})\approx (\mathbf{0},\mathbf{0}) [/math] we have that
[math]F((\mathbf{a},\mathbf{b})+(\mathbf{u},\mathbf{v}))\approx F(\mathbf{a},\mathbf{b})+\frac{dF}{d\mathbf{x}}\mathbf{u}+\frac{dF}{d\mathbf{y}}\mathbf{v} [/math]

Now consider the equation [math] F(\mathbf{x},\mathbf{y})=\mathbf{0} [/math] and the assumptions [math] F(\mathbf{a},\mathbf{b}) = 0 [/math] and [math] \frac{dF}{d\mathbf{y}}[/math] invertible.
We can always write [math] (\mathbf{x},\mathbf{y})=(\mathbf{a},\mathbf{b})+(\mathbf{u},\mathbf{v})[/math] and consider only the case where (u,v) is small, i.e. (x,y) is in a small region around (a,b)

[math] F(\mathbf{x},\mathbf{y})=\mathbf{0}\\F((\mathbf{a},\mathbf{b})+(\mathbf{u},\mathbf{v}))=\mathbf{0}\\F(\mathbf{a},\mathbf{b})+\frac{dF}{d\mathbf{x}}\mathbf{u}+\frac{dF}{d\mathbf{y}}\mathbf{v}=\mathbf{0}\\\frac{dF}{d\mathbf{x}} \mathbf{u}+\frac{dF}{d\mathbf{y}} \mathbf{v}=\mathbf{0}\\(\frac{dF}{d\mathbf{y}})^{-1}\frac{dF}{d\mathbf{x}} \mathbf{u}+ \mathbf{v}=\mathbf{0}\\\mathbf{y}=\mathbf{a}-(\frac{dF}{d\mathbf{y}})^{-1}\frac{dF}{d\mathbf{x}} (\mathbf{x}-\mathbf{b})
[/math]

[Anonymous No.10837271]

>>10837261
We denote by [math] \frac{dF}{d\mathbf{x_j}}[/math] the j-th column of the map's matrix and write [math]\mathbf{u}=(u_1,\ldots,u_k),\ \mathbf{v}=(v_1,\ldots,v_m)[/math].

[Anonymous No.10837274]

>>10835530
Nakahara. Proofs there are coordinate-free.

[Anonymous No.10837282]

>>10836891
> My problem is that this polynomial (5x^3 + x^2 + 3x + 2) does NOT have integer roots! I
But you're never asked to find the roots of that polynomial.

The arguments to testFindIntRootsOfCubicCase() are the scale factor and the roots. From these, it calculates the coefficients, calls your function, and checks that the roots returned by your function match the original values.

For testFindIntRootsOfCubicCase(5,1,3,2), the polynomial is 5*(x-1)*(x-3)*(x-2) = 5x^3-30x^2+55x-30, so it calls bonusFindIntRootsOfCubic(5,-30,55,30) and checks that it returns [1,2,3]

[Anonymous No.10837285]

>>10837274
>>10837261
Not them, but thank you.

[Anonymous No.10837297]

>>10831209
even means factor of 2^n where n>0 and an integer

if x is even ur just multiplying twos

if its odd u have no twos as factors

[Anonymous No.10837302]

>>10837282
I've gotten that since the first post, but my code is still not returning an integer when fed the input of (5, -30, 55, 30). It returns "0.5000000000000002" after converting to a real from a complex, and I'm pulling my hair out trying to figure out why I'm essentially getting 0.5, not an integer.

[Anonymous No.10837344]

>If P(D) = 0.7, P(D U E) = 0.8, and P(E) = 0.4, the value of P(D n E) is:

The answer is 0.28 right?

[Anonymous No.10837347]

>>10837302
> my code is still not returning an integer when fed the input of (5, -30, 55, 30).
Did you miss a minus sign there?
> It returns "0.5000000000000002"

Are you using Python 2.x or 3.x? That code won't work with 2.x as a) (1/3)=0 (integer division) and b) ** applied to real arguments returns a real or raises an exception (for a negative value to a fractional exponent).

With 3.6.5, the code in >>10836911 works fine (it returns 3.0000000000000004, which is one of the roots to within rounding error (it's close enough for the almostEqual() function used by the test harness). So check that you're getting the first root correct then check the code which factors out that root and solves the quadratic.

[Anonymous No.10837357]

>>10837347
>Did you miss a minus sign there?
yes
>Python 2.x or 3.x?
3.7.3
>With 3.6.5, the code in >>10836911 (You) works fine (it returns 3.0000000000000004
wtf? i don't understand, I'm getting 0.50..004 with the same code, see pic. Copied and pasted the code straight outta this thread to be sure.

[Anonymous No.10837360]

>>10837357
>pic
wrong one, here.. maybe it's some 3.7 change, I guess I'll look into that momentarily..

[Anonymous No.10837402]

>>10837360
Delete the newline in the middle of the assignment to root1. That should all be one statement.

[Anonymous No.10837433]

>>10837402
holy shit anon thank you. how stupid..

..I didn't realize I had to wrap equations in parens in Python for it to evaluate properly. The built in testers would get mad if line length exceeded 80 chars, so I just indented for readability like I would elsehwere.

fuck. well i won't forget that. thanks. this was my second time doing this problem, and I remembered the first time it was super easy, so i was getting frustrated to be hung up on it - I see now it was easy all along :^)

[Anonymous No.10837446]

>>10837223
But then why are we assuming F(a,b)=0? We could still solve for y without that assumption.

[Anonymous No.10837692]

just polling; what do you guys do for work?

[Anonymous No.10837713]

>>10837692
self-employed and today I earned cos90

[Anonymous No.10837777]

>>10837692
retail at a sports store

[Anonymous No.10837779]

>>10837777
>I earned cos90
90 wat

[Anonymous No.10837832]

>>10837692

> work

[Anonymous No.10837898]

>>10831081
Fascinating, I didn't know this was considered a cutting edge area, but I was aware that some LA problems can restated as problems on a non-euclidean manifold. I recent developed a global optimisation method which works on purely topological arguments to minimize maps from any p-normed space domain to a real scalar or vector range, the method also doesn't require the mapping function to be differentiable or even smooth (it was originally developed to solve a problem in the usual real space, but with a super weird function geometry).

I've been looking for applications or collaborators on this project, but no one seems to able to suggest viable test problems. Potential applications pop up in computation physics and chemistry all the time, but researchers just use smooth approximations instead of solving the true model and they don't seem to care about doing better.

[Anonymous No.10837900]

>>10837692
I work in in engineering science research earning 1/5th of what real engineers do :)

[Anonymous No.10837908]

>>10835530
>introductory

https://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf

Chapter 3 has some really good (but zero rigour) limited notes if you want to build some initial intuition for key concepts. After that Carmo is very accessible but limited to surfaces and a bit too coordinate heavy for my taste.

Finally grab a real book like Lee's

[Anonymous No.10838020]

to take the applied stats pill or no?

i may want to go to grad school afterward, but I dont want to be stuck studying applied/stats postgrad, I have more interest in pure stuff. BUT, applied/stats means instant job if I don’t wanna do grad school.

part of me thinks it’s wise to keep pure math a hobby and pursue applied, the rest thinks yolo just do what i like and pray it works out

halp

[Anonymous No.10838090]

>>10837692
I TA computer science courses.

[Anonymous No.10838128]

>>10837692
I work in IT/Infosec.

I studied math in undergard but I still study it for fun on the side.

[Anonymous No.10838218]

>>10836947
>>10836981
Why don't you try using Anki?

[Anonymous No.10838231]

>>10837118
>"""remember the intuition"""
This might be the most retarded thing ever posted in these threads.

[Anonymous No.10838239]

>>10838231
Your intuition is learned. You didn't come out of the womb with an instinct for open coverings.

[Anonymous No.10838245]

>>10836981
>Still, how lengthy are his tests? If you have enough time, you can just memorize the outlines and fill the formalisms in on the spot.
Two hours, three topical questions. Say, Darboux sums, full marks would be writing down everything he wrote on the blackboard. He's also very anal about usage of commas, notation and shit if he feels it changes the meaning even a little. I've seen people fail because they fucked up a subscript once in four pages of text because it's technically wrong, even though it was obvious from context. It's basically pass/fail.
>Make sure to get a bunch of textbooks to attempt to bullshit him into believing you used a definition from somewhere else in case he marks you as wrong.
No textbooks, course is self contained. Bad idea.

>>10838218
I have no idea how to apply anki to this, I need to write down basically the entire chapter down, it's not like I have questions like "prove intermediate value theorem". Half the time I forget a whole theorem because I though it's in the next or previous chapter.

Maybe I'm just retarded.

[Anonymous No.10838260]

>>10838239
I don't see how that's relevant to """"""remembering"""""" your intuition. Did you reply to the correct post?

[Anonymous No.10838306]

>>10838260
When one has many things to learn (in this case lots of intuition) remembering it becomes harder.
Is this clear enough for you or do I need to step it out in more detail?

[Anonymous No.10838308]

>>10830915
Alright guy stand still

[Anonymous No.10838311]

How the hell is this equality true?

[Anonymous No.10838319]

>>10838311
L is a linear and invertible transformation, right?
Just consider that the infimum on the right is achieved by L(v), where v achieves the supremum on the right.
>>10838245
>three questions
Extremely doable, relax.

[Anonymous No.10838321]

>>10838319
*where v achieves the supremum on the left.

[Anonymous No.10838423]

is it too late to get a degree in math at 30yo? brain is past its peak/getting old? you guys know or heard of any good mathematician late bloomer?
I really love math

[Anonymous No.10838593]

>>10838423
An undergrad degree is fine. I hope you're not seeking tenure.

[Anonymous No.10838731]

>>10838306
that's not what intuition is

[Anonymous No.10838736]

>>10838593
what's the upper limit on difficulty finding tenure due to age? If I finish my undergrad by 27, will i be ruined?

[Anonymous No.10838813]

>>10838306
I see, I'll repost when I remember my intuition for making sentences in English.

[Anonymous No.10838833]

Are all those posts "You should be able to solve this" someone's homework? Or are they brain teasers?

[Anonymous No.10838838]

>>10838736
Stop being stupid, just do the thing

[Anonymous No.10838846]

>>10838838
i know i only realized after posting

back to doing thing

[Anonymous No.10838885]

>>10838833
It's probably mixed, I put my homework in there once.

[Anonymous No.10838907]

>>10837126
>Basic arithmetic
>adding numbers in your head
Names (like factor, quotient, remainder). Properties (commutative, associative, etc) and geometrical interpretations of basic operations. Word problems. Prime factorization, MCM, MCD, divisibility tests, number systems and units (money, meausurements, geometry of lenghts, areas, volume). Fractions, decimals and operations with fractions and decimals, percentages, ratios, rates, proportionality. Mixed number. Amplification and simplification. Rounding. Conversion of units. Rule of three, power, roots, logs, grouping signs, hierarchy of operations. Modular arithmetic (clocks). Formulas (area, volume, interest). Algebraic irrational (this is, for example, multiples of square roots of non-square numbers) and its manipulation, rationalization. The number line. Scientific notation. Basic statistics of one variable.

Is not just adding numbers in your head, is basic problem solving skills, first mathematically motivated definitions and basically all that is prealgebra of numbers. That is basic arithmetic. On the other hand, the Arithmetic, is pure mathematics, related to logic (see Peano, Gödel), axiomatization of numbers and number theory.

[Anonymous No.10838958]

If I major in pure math, will I, hypothetically, be able to hop right into some statistics / probability courses in grad school? I don't want to spend my undergrad studying stats/probability because I'd miss out on the canonical subjects (analysis, algebra, etc), but I want my options open postgrad.

[Anonymous No.10839017]

Anyone have any hints for proving that if a linear map is injective, its dual map is surjective? Kind of stumped.

[Anonymous No.10839033]

>>10839017
this is not true in infinite dimension, so just do it using matrices

[Anonymous No.10839036]

>>10839033
nevermind, I changed the question in my head while thinking about it

[Anonymous No.10839038]

>>10828810
[spoiler] test [spoiler]

[Anonymous No.10839057]

>>10838311
The infimum in the left can be changed as you to run over v of norm 1 is equivalent to inf|w| over such vectors that satisy |L^(-1)(w)| =1 From this its easy to show that the the right hand side is a lower bound on such vectors. Then do the opposite and you get two inequalities.

[Anonymous No.10839064]

There is an optimization task - minimize the above sum with given constraints, where c is nonnegative real.
I am stuck here - all I know is that this is non linear programming, but it seems that answer must be kinda analytical, not using any sort of numerical methods.
Which method should I use for that?

[Anonymous No.10839073]

>>10839017
need to think more carefully about the definitions you're using this is a fairly simple problem.

[Anonymous No.10839083]

would it be better to take a class called "models and methods of applied mathematics" or to take partial and ordinary diff eq? I want to keep options for mathematical finance open and they both sound good

[Anonymous No.10839114]

>>10839083
ok, turns out I'd have to take 3 differential equation related classes to really flesh it out.
>systems of diff eq
>partial diff eq
>ordinary diff eq

I thought diff eq was basically a requirement for undergrads? I amjust trying to fill my 'applied' requirement. should I take these, or say fuck it and just take the 'methods and modeling' course? There's a huge time cost to taking 3 classes (and real cost!) so I think I already know the answer.. I just feel not having diff eq sort of nueters my degree

[Anonymous No.10839115]

>>10838958
"Hypothetically," you would be able to go into a masters program in stats with a pure math major and no probability/stats courses, but it would definitely put you at a disadvantage compared to other applicants with at least one or two courses in stats/probability theory.

I would advise taking the pure math that you want and then also doing at least a course on probability theory and ideally another course on mathematical statistics (or, if possible at your school, just one class in mathematical statistics - at my school prob theory is a prerequisite for math stats). Even if you don't go to grad school in stats, it's useful to know this stuff. I'd even argue that stats is a "canonical subject" in math.

Take this advice with a grain of salt though, I'm a math undergrad.

[Anonymous No.10839122]

>>10839114
so i guess a better question is, should I take systems of diff eq or methods and modeling? I'm inclined to do the former to at least cover my fundementals..

[Anonymous No.10839125]

1/10 of a population is black, and 6/10 is white. If 6/10 violent crimes are committed by blacks, then 'blacks commit violent crime at x times the rate of whites'. Solve for x.

[Anonymous No.10839128]

>>10839122
Do you have any more info on the syllabi/exactly what's covered in these classes?

I'm a math undergrad and I just took Ordinary Differential Equations. I feel like that's a pretty standard class to have in a math major (not a requirement at my school, but it is at some).

I would think mathematical modeling would involve a taste of diff eq's but also contain things like statistics, graph theory, etc. Easy class that doesn't go too in depth (at least that's the case at my school). A regular old ODE class seems like it would be the most foundational though.

[Anonymous No.10839130]

>>10839115
thansk for the advice, sincerely. I will tack on a stats class before graduating, I also feel it's essential. Actually, I am scheduled to take a "Machine Learning" course, do you think that counts, or should I still take a stats course?

Anyway, here is my (planned) upper division course list. Anythin missing or looking funky?

-WIC: MATHEMATICAL MODELING (323)
-COMP: NUMERICAL ANALYSIS (440)
B&D (a, b, c):
- [X] (a) depth requirement: A pair of classes from one of the 6 areas is required. Some exceptions are noted.
- [X] (b) breadth requirement: One course each from 3 of the 5 remaining areas.
- [X] (c) elective - choose 2 more.
- Algebra:
- ABSTRACT LINEAR ALGEBRA (443)
- Analysis:
- REAL ANALYSIS (441)
- Applied:
- SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS (480)
- Geo & Top:
- METRIC SPACES AND TOPOLOGY (430)
- INTRODUCTION TO DIFFERENTIAL GEOMETRY (434)
- Numerical Analysis:
- Probability:
- PROBABILITY I (463)
- PROBABILITY II (464)


I will be minoring in CS too, so I'm also taking, in addition to the standard required classes:
- Operating Systems I
- Analysis of Algorithms
- Machine Learning and Data Mining
- Graph Theory w/ CS Applications

[Anonymous No.10839132]

>>10839130
sorry the indentation got a little fucked up..

>>10839128
it's right here: https://catalog.oregonstate.edu/search/?P=MTH%20480

i forgot that i also have to take a writing course, and I can do the modeling there so I'm definately going to be taking diff eq. I'll learn PDEs on my own time, I need to for some projects anyway

[Anonymous No.10839135]

>>10839017
>dual map
T*, with F as the base field?

[Anonymous No.10839137]

>>10837898
I think a main reason why it is considered cutting edge is because most people in geometry and topology don't know computational methods and most people in computation don't know any topology.
Your work sounds really intriguing. Do you have a way I could contact you? I think I have an application in mind. I have a goal of writing an ODE solver for a particular class of ODEs with stupidly large Lipshitz constant. Part of developing an algorithm to solve these would require either a robust minimzation algorithm or a sophisticated modifaction of Newton's rootfinding algorithm adjusted to Riemannian manifolds. The optimization problems I would want to solve are smooth, but computing the gradient-based search direction is a massive overhead which is blocking progress. An algorithm which does not rely on gradients would possibly be the key.

>p-normed space
does it have to be finite-dimensional? there is a formulation of my problem which can be re-posed as a sequence of optimizations on function spaces.

[Anonymous No.10839143]

>>10839064
It's convex so you can use the KKT conditions for the analytical solution

[Anonymous No.10839148]

>>10839135
Yeah. Actually this commutative diagrams kind of helped desu. I'm just having a hard time developing intuition for dual spaces in general.

[Anonymous No.10839149]

>>10839130
Looks good.
One thing you might want to consider adding is a class on Abstract Algebra (not abstract linear algebra -- more like group theory, ring theory, Galois theory, etc).

Machine learning probably counts for stats. Just make sure general stats isn't a prerequisite or something. I'd think some stats theory would be covered in probability I/II.

And just make sure ODE's isn't a prereq to systems of ODE's. They do it differently at every school so I'm not sure.

[Anonymous No.10839153]

>>10839132
>https://catalog.oregonstate.edu/search/?P=MTH%20480
Just saw this too. Personally I'd take MATH481, I don't know though.

[Anonymous No.10839157]

>>10839148
That one is almost never surjective, tho.
Riesz immediately gives that dim Hom(R, R)=1, and dim Hom(R^2, R)=2, while the inclusion of R into R^2 is injective.

[Anonymous No.10839159]

>>10839157
Oh shit, I completely forgot the dual went backwards. The actual insanity.
Just use the first isomorphism theorem.

[Anonymous No.10839162]

>>10839017
This is simple, because of >>10839033. Just show that rank of [math]A[/math] and [math]A^*[/math] are the same via elementary row operations and elementary column operations respectively.

[Anonymous No.10839173]

>>10839017
Might be using big tools for something trivial, but the dimension of the dual space A* of a sub-vector space A is equal to [math]n - dim(A)[/math], the dual space of the Kernel is the Image of the dual map, since it's it's injective, dim(kernel) = 0 so dim(image) = n and here you go

[Anonymous No.10839178]

>>10839148
In a Hilbert space, orthogonality is a very good way to see it.

[Anonymous No.10839183]

>>10839173
>>10839178
these are both what you want to use

[Anonymous No.10839188]

>>10839149
unfortunately, they don't offer it until grad school. what they offer at the undergrad level is called modern algebra here, but's a sub 400 level class so it wouldn't work for upper division course work. They do offer Abstract Algebra, but it's a postgrad class I think (with Abstract Linear Algebra as a prereq). Maybe I'll complete abstract linear algebra and try to also complete abstract algebra before walking. If I do end up adding a stats class, I could just take them together to mitigate the extra time cost..

>just make sure general stats isn't a prerequisite or something.
yeah, the only prereq is analysis of algos, oddly. I may still take stats though, i imagine it helps a ton with resume polishing and getting in the door.

>And just make sure ODE's isn't a prereq to systems of ODE's. They do it differently at every school so I'm not sure.
just checked and it's not, thanks for the tip though.

thanks for the replies

[Anonymous No.10839189]

>>10839148
>having a hard time developing intuition for dual spaces in general
in finite dimensional spaces, they're literally row vectors.
[math]\text{Hom}(V,{\mathbb F})[/math] is naturally isomorphic to [math]\mathbb{F}^{1\times n}[/math] where [math]n=\text{dim}(V)[/math].
Can be proven by computing the formula for [math]v^*\in\text{Hom}(V,{\mathbb F})[/math]
with respect to a given basis [math]{\cal B}[/math] for [math]V [/math].

As far as I'm aware, th infinite dimensional case is core topic
for an intro class to functional analysis, so you probably don't need to
understand that right now.

[Anonymous No.10839190]

>>10839153
why 481 over 480? just for the applied nature of the course or what?

[Anonymous No.10839233]

>>10839188
Yeah, modern algebra would be the class, but if it doesn't fulfill your requirements, then don't worry about it. Abstract linear is pretty cool too.

>>10839190
Just looked at the courses again. Have you taken math 256? That looks like the typical diff eq's foundational course and it's a prerequisite for 480 and 481. I'd try to take that first. If you already have then either 480 or 481 would be good to take.

[Anonymous No.10839265]

>>10839233
>256
oh shit, duh. I'm supposed to take that this term or next. I thnk I'll just cross off any upper division ODE course then if that's reasonable.. I've heard ODEs come in handy for diff geo and I'm looking forward to nosediving into that so idk

[Anonymous No.10839274]

>>10839233
>>10839190
And sorry to stalk your school, but make sure you do these requirements if you're in fact a math major
https://catalog.oregonstate.edu/college-departments/science/mathematics/mathematics-bs-hbs/#requirementstext
The reason I mention it is because it looks like the foundational course in applied diff eq's is already a lower division requirement

[Anonymous No.10839280]

>>10839265
Ok yeah just saw this post. Ya personally i don't think you need an upper division ode class if you have 256, unless you KNOW you want to do applied math grad school or something

[Anonymous No.10839301]

>>10839274
>And sorry to stalk your school
no, thanks a ton for doing it! I've been referencing that link all day, I'm getting ready to transfer from community college and all of those stupid prereqs are done except for the applied diff eq. Also, I still need to take intro biology or chem (lol).

>>10839280
I think as an update to >>10839130, I will drop systems of ODEs (480). But, due to the breadth requirement I still have to take one of the following:
>NUMERICAL LINEAR ALGEBRA
>NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
>NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS
>MODELS AND METHODS OF APPLIED MATHEMATICS
>INTRODUCTION TO MATHEMATICAL BIOLOGY
>STOCHASTIC ELEMENTS IN MATHEMATICAL BIOLOGY
>SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS 3
>APPLIED ORDINARY DIFFERENTIAL EQUATIONS 3
>APPLIED PARTIAL DIFFERENTIAL EQUATIONS

and I'm not sure which would be best. None of them sound particulartly interesting.

[Anonymous No.10839314]

>>10839301
actually, nvm. I don't have to pick from either applied or numerical, I am able to do neither and place my electives elsewhere. In that case, maybe I can count an elective towards that stats class, or abstract algebra.

[Anonymous No.10839324]

>>10839301
ah gotcha. personally i'd just take models and methods because it sounds pretty general. If you're also in CS some of the numerical classes could be good i guess. It's really up to you. Might want to see what some other anons think as well as I've never really taken the upper level type numerical analysis classes

[Anonymous No.10839333]

>>10839314
ah ok just saw this
yeah that sounds like a better idea those classes look a little boring desu
It looks like you'll also already have intro to modern algebra though so i wouldn't say a grad class in abstract algebra is strictly necessary but it could be cool

[Anonymous No.10839343]

0,7%, 0,7%, 1% chances for 3 things.
What's the chance for all of them happen at least once if you got 170 tries. Also please leave me basic (just the way to do it) info how you made it because either im retard or 50-60h with ~4-5h sleep killed me (prolly both)

[Anonymous No.10839345]

>>10839324
I think I'm able to take abstract algebra as my final elective if I complete abstract linear. that, in conjunction with "Machine Learning and Data Mining" would cover the last bits I felt I was missing (abstract alg and some stats), while costing me no additional classes.

regardless, I still may tack on an "intro to mathematical statistics" just to round it out a little bit with a single extra class.

That puts the final list as:

Math Major:
-WIC: MATHEMATICAL MODELING (323)
-COMP: NUMERICAL ANALYSIS (440) (I would like to take computational number theory instead, but feel it's less employable.... any suggestions here?)
B&D (a, b, c):
- [X] (a) depth requirement: A pair of classes from one of the 6 areas is required. Some exceptions are noted.
- [X] (b) breadth requirement: One course each from 3 of the 5 remaining areas.
- [X] (c) elective - choose 2 more.
Algebra(b - 1/3):
>ABSTRACT LINEAR ALGEBRA (443)
>(e)ABSTRACT ALGEBRA (hopefully)
Analysis(b - 2/3):
>REAL ANALYSIS (441)
Applied: N/A
Geo & Top (b - 3/3):
>METRIC SPACES AND TOPOLOGY (430)
>(e)INTRODUCTION TO DIFFERENTIAL GEOMETRY (434)
Numerical Analysis: N/A
Probability(a):
>PROBABILITY I (463)
>PROBABILITY II (464)

MAYBE?:
-INTRODUCTION TO MATHEMATICAL STATISTICS (421)


CS Minor:
>Operating Systems I
>Analysis of Algorithms
>Machine Learning and Data Mining
>Graph Theory w/ CS Applications

[Anonymous No.10839349]

>>10838319
Dude, those any random three questions are basically chapters, more than 10 pages long total, almost always pass/fail. I've failed a fair share of times, it's probably the hardest course to pass within the first two years of my degree. People have dropped out because of this single course. I might be one of them, it's not really relaxing.

[Anonymous No.10839360]

>>10838311
2 norm, yes? The answer is https://en.wikipedia.org/wiki/Min-max_theorem .
Apply the method of lagrange multipliers to the infinmization on left side of equality and supremalization on the right side.

[Anonymous No.10839361]

>>10839349
damn sorry to hear that anon. I try to avoid any courses without textbooks as I fear having a crazy teacher with no external structure I can reference. My favorite classes tend to be directly built on top of a books existing strucutre.

[Anonymous No.10839374]

daily putnam problems are kill aren't they?

[Anonymous No.10839376]

>>10839345
Looks good. Take numerical analysis over comp number theory I'd say.

Isn't intro to modern algebra a core req for the major though? Cause if so, you could replace that grad abstract algebra class with something else if you wanted. You could also replace probability ii with something else too - it's all up to you though. I'm not sure how much of the math stats class would overlap with probability because I see it's offered through the stat department so you would have to check on that. I can tell you though that what you have there looks to be well rounded and solid.

You should definitely see if you can connect with an advisor from your school though, or even just email someone on the math faculty, maybe the undergrad director, to see if they can put you in touch with a faculty advisor to confirm all this.

[Anonymous No.10839393]

>>10839376
This is math 343 I'm talking about for intro to modern algebra btw

[Anonymous No.10839394]

>>10839376
that’s the first thing they should have done

[Anonymous No.10839395]

>>10839376
yikes! I don't know how I missed that. I guess I just scanned for abstract alg and didn't see it. You're right, Modern Algebra is required (thankfully).

Ok, so Prob II and Abstract Algebra DROPPED, now I have two slots opened up for electives and can place them whereever I want. I will probably drop one in Diff Geo because I think I'll really enjoy that, and ideally I'd be able to drop another in Complex Analysis after taking Real Analysis but it doesn't look like it's offered without an override.

there is MTH483 Complex Variables and 419 MultiVariable Adv Calc, but neither one seem canonical to a standard math degree (why not just offer complex analysis?). I might add Prob II back if nothing better is available. Or maybe I can make that CS Graph Theory class count doubly..?

thanks anon I'm liking my prospective schedule more and more.

At any rate, once I solidify this plan I am going to email the advisors.

[Anonymous No.10839404]

>>10839394
I don't even have my list finalized yet or my research done. I'm going to talk to them once I've at least done my portion of the homework.

updated list:
>https://catalog.oregonstate.edu/college-departments/science/mathematics/mathematics-bs-hbs/#requirementstext
Math Major:
-WIC: MATHEMATICAL MODELING (323)
-COMP: NUMERICAL ANALYSIS (351)
B&D (a, b, c):
- [X] (a) depth requirement: A pair of classes from one of the 6 areas is required. Some exceptions are noted.
- [X] (b) breadth requirement: One course each from 3 of the 5 remaining areas.
- [X] (c) elective - choose 2 more.
- Algebra(b 1/3):
- ABSTRACT LINEAR ALGEBRA (443)
- Analysis(b 2/3:
- REAL ANALYSIS (441)
- Applied:
- Geo & Top(a):
- METRIC SPACES AND TOPOLOGY (430)
- INTRODUCTION TO DIFFERENTIAL GEOMETRY (434)
- DIFFERENTIAL GEOMETRY (435)
- Numerical Analysis:
- Probability(b 3/3):
- PROBABILITY I (463)


I get one more class, so make it count anons

[Anonymous No.10839418]

>>10839404
There's also this list:
>https://catalog.oregonstate.edu/courses/mth/

[Anonymous No.10839424]

I'm probably going to go wtih Complex Variables, fwiw.

[Anonymous No.10839437]

>>10839424
The class called "complex variables" at my school is basically introductory complex analysis. So you'll get analysis in that class.

Yes, definitely get in touch with the advisors.
And yeah, if you really really like diff geo, you could prob take that instead of probability ii. But also the probability sequence would be really employable, as would perhaps another applied math class.

Basically you're good and really aren't missing any major area as far as i can tell.

[Anonymous No.10839458]

>>10839437
Originally I wanted to take stats and probability for employability, so maybe I should peel back a bit and do that.

Def gonna take Complex Variables in that case then, because I'd feel like a phony not taking anything resembling Complex Analysis in undergrad.

I'll consider adding an applied class, but I feel like the class list is already pretty lean and there's not a lot of room to take stuff out without leaving gaps in fundementals. I may add a stats class on top what I'm already taking though, so perhaps it wouldn't hurt to add an additional class for employability sake. Would you recommend anything in particular? The classes under "applied" all seem kind of lame and not really job-worthy, but I could maybe add Applied or Numerical ODEs/PDE (not sure what the difference would be between Applied ODE/PDEs and Numerical ODE/PDEs though), Numerical LA, or perhaps even just tack on Prob III. Any opinions here would be most welcome..

[Anonymous No.10839469]

>>10839458
I think you should get a complex vars class in for well roundedness sake. That's what I'm doing at least

I can't really recommend any of those classes in particular in the applied/computation category, that's not really my area of expertise haha.

I think this looks good...

Math Major:
-WIC: MATHEMATICAL MODELING (323)
-COMP: NUMERICAL ANALYSIS (351)
B&D (a, b, c):
- [X] (a) depth requirement: A pair of classes from one of the 6 areas is required. Some exceptions are noted.
- [X] (b) breadth requirement: One course each from 3 of the 5 remaining areas.
- [X] (c) elective - choose 2 more.
- Algebra(b 1/3):
- [ ABSTRACT LINEAR ALGEBRA (443) ] ? or comp. number theory? whatever interests you more and talk to your advisor - abstract lin isn't strictly necessary but could be fun/interesting - it's good for kids who want to go into representation theory i think
- Analysis(b 2/3:
- REAL ANALYSIS (441)
- COMPLEX VARS
- Applied:
- Geo & Top(a):
- METRIC SPACES AND TOPOLOGY (430)
- INTRODUCTION TO DIFFERENTIAL GEOMETRY (434)
- [ DIFFERENTIAL GEOMETRY (435) ] ? could replace down the line, or keep if you really like it - talk to an advisor
- Numerical Analysis:
- Probability(b 3/3):
- PROBABILITY I (463)
- [ PROBABILITY II ] - could also swap out if you wanted but good for employability, again, talk to an advisor

Like i said before I'm only an undergrad myself and I haven't taken several of these classes, ha

But what you have is definitely solid still

[Anonymous No.10839474]

>>10839437
>>10839458
Ok, so the applied / employable options see to be:
>Applied or Numerical ODEs/PDE
>Numerical LA
>Probability III
>Intro to Mathematical Stats

I'm pretty sold on Intro to Math Stats esp w/ the CS minor containing Machine Learning, but should I add anything else? Probability III might be nice just to push it over the top a bit... But at this point, I'm getting into taking classes that aren't strictly required.

Just as a reminder, this is my current draft class list for upper div stuff (the only part I get a choice over):
-MATHEMATICAL MODELING (323)
-NUMERICAL ANALYSIS (351)
-ABSTRACT LINEAR ALGEBRA (443)
-REAL ANALYSIS (441)
-COMPLEX VARIABLES (483)
- METRIC SPACES AND TOPOLOGY (430)
- INTRODUCTION TO DIFFERENTIAL GEOMETRY (434)
- PROBABILITY I (463)
- PROBABILITY II (464)

And the above is a complete minimum, no further upper div classes are required. But I think Stats would pay for itself, or at least be a nice safety net..

[Anonymous No.10839475]

>>10837032
pls answer how I do this without domain restriction.

[Anonymous No.10839477]

What do I learn after linear algebra? Abstract?

[Anonymous No.10839480]

>>10839469
thanks, i think swapping abstract LA for Comp Number Theory is a great idea. I didn't really wanna take LA again and would rather just do abstract alg later. So consider Abstract LA swapped with Comp Number Theory (really happy to be able to fit in some number theory).

And thanks for the help! I think the template looks solid, now I just have to decide whether I should hang around in uni a little longer / pay a little extra to walk out with a couple more employable classes under my belt like Stats, Numerical ODEs, etc.. As I said before, I will probably take the Stats at the very least, as there is not a sprinkle of stats anywhere else in my cirriculum other than that Machine Learning elective for CS.

For the rest, my post above remains accurate.

[Anonymous No.10839481]

>>10839477
yes, or ODEs or analysis

[Anonymous No.10839490]

>>10839474
That looks good.
The only thing to be careful of, and this is where you would want to check with an advisor, is making sure that the material in the probability sequence doesn't overlap too much with the material in the intro to math stats class, since they're offered in different departments. If there is an overlap then maybe he/she can suggest a different collection of courses for your applied/numerical/employable bit.

I'll give you a little advice, try to hone in on what you want to do for grad school sooner rather than later. You want a well rounded education for the sake of knowledge but also don't try to spread yourself too thin, I guess.

You're already on the right track having stats and computer science in addition to math. That's a powerful combo.

[Anonymous No.10839498]

>>10839480
Yeah if it comes down to finances I'd say prioritize stats and cs.

[Anonymous No.10839559]

>>10839490
>try to hone in on what you want to do for grad school sooner rather than later
I'm trying - it's just hard, and I'm also trying to design my cirriculum to reflect that and keep things open. I really enjoy studying math, so I think I'd be super thrilled to be a real researcher, but I need credentials that can support looking for a regular job too, incase that backfires. I also need to explore different math fields before deciding what I'd want to study further. So I'm trying to keep things open with the stats/data/cs bent, but also trying to cover my math fundementals. I enjoy programming, so worst case I'll just get a dev job.

Also, GREAT idea about emailing to make sure the overlap isn't too significant. And yeah, when I do that I'll also ask about the applied/numerical/employable recommendations. I'm inclined to think they don't overlap too much, because the school offers a statistics focused option for math majors here: https://catalog.oregonstate.edu/college-departments/science/mathematics/mathematics-bs-hbs/statistics-option/#requirementstext, and they have these students take ProbI-III and Intro Math Stats I-II. But I'll email regardless.

Thanks for all the help.

[Anonymous No.10839574]

>>10837692
neet. live off of investments.

[Anonymous No.10839583]

>>10839574
did u invest in ur parents?

[Anonymous No.10839588]

>>10837692
mcdonalds

[Anonymous No.10839602]

>>10837777
checked and good luck to you

[Anonymous No.10839603]

>>10839583
I got lucky, if that's what you mean.

[Anonymous No.10839614]

>>10839603
i was trying to imply that you're actually broke and live with your parents

I had a good run like that on a smaller scale, it was really nice. I lived for about year before having to return to being a wagie in a cagie. best year of my life so far. what'd you invest in?

>inb4 buttcorn

[Anonymous No.10839650]

>>10839559
No prob. Good luck

[Anonymous No.10839857]

>>10837692
Math PhD student. Earn $24k per year from research stipend. Doesn't feel like working. I just read whatever I want and write down my ideas. Finishing up a paper now.

[Anonymous No.10839888]

how many hours / week should I allow for upper division coursework as a full time pure maths student? Just trying to figure out how many hours a week I'll have to work to pay for rent, how much time I'll have for other hobbies, etc..

>>10839857
C O M F Y
O
M
F
Y

is this typical phd student life? how many hours do you spend / week "working"? don't undersell the time commitment pls

[Anonymous No.10840122]

>>10839857
how did you manage to get this?

[Anonymous No.10841090]

[Anonymous No.10841095]

>>10837692
Physics student, will do my thesis next year.

>>10839888
For having done an internship in a lab and talked with professors a fair bit, it really depends on the subject matter and the advisor. Solid State Physics phd students are slaves that don't count their hours, but they usually have a wide variety of things to do, from theory to experiment, so if you're tired with something you can do something that fits you better.

Unfortunately, most PhDs expect results at some point or another, so you will have to work like a madman to produce posters, articles, book an expensive piece of equipment to run an experiment while everyone else is having lunch...

Math PhDs are really comfy, I hope I could have done it, but engineering and then physics felt a lot safer.

[Anonymous No.10841098]

>>10839137
>I think a main reason why it is considered cutting edge is because most people in geometry and topology don't know computational methods and most people in computation don't know any topology.
Ha! This is very true based on how long the review process for my first journal article in this area took to complete.

>Your work sounds really intriguing. Do you have a way I could contact you? I think I have an application in mind. I have a goal of writing an ODE solver for a particular class of ODEs with stupidly large Lipshitz constant.
Absolutely, this sounds like a perfect application and something I've actually wanted to work on myself for the longest time (essentially this algorithm can find all the fixed points in a vector field with both normal and weird geometries very quickly), but we ran out of funding for pure work projects so my job has dragged me away to more applied projects. So essentially the algorithm works very well on the kind of problem you're describing, it was actually developed for handling very large jumps in the gradient to the order of [math]\times 10^{50}[/math] (and it even converges when the space is non-continuous and has singularities etc.), it also uses some tricks to avoid the usual issues with floating point errors.

[cont.]

[Anonymous No.10841099]

>>10841098
>>10839137

The big caveat to this is that if the ODE system is a coupled "black-box" it is limited to few dimensions in terms of the number of optimisation variables (~10-20). The caveat to this caveat is that if you have any information at all about the structure of your equations (such as symmetry of variables, global bounds on the Lipschitz constant, Jacobians etc) you can push this to hundreds or thousands of variables. Also if the ODEs are uncoupled then the system can be treated in parallel as 1D sub-problems very efficiently. The most I have done on a home computer is on energy surfaces with 180 variables (which retrieved millions of local minima in a few minutes). I recently completed parallelization so in practice tractable problems are basically related to the number of processor nodes you have available.

There's one guy in Germany I have e-mail correspondence with who has been very happy with the performance of using it to find fixed points on smooth vector fields for his PhD project, but no one has been ambitious enough to test it on the types of problems you have in mind. This might be fate. My throwaway e-mail address is [e-mail], if you send me a blank email with /mg/ Anon in the subject field I will send you my real details (I've collaborated with people I met from 4chan before so I don't mind sending this even if you want to stay Anon).

[cont.]

[Anonymous No.10841104]

>>10839137
>>10841098
>>10841099

>Part of developing an algorithm to solve these would require either a robust minimzation algorithm or a sophisticated modifaction of Newton's rootfinding algorithm adjusted to Riemannian manifolds.
A central theorem of my work involves using a fixed point theorem from old school combinatorial topology (good old Brouwer's theorem/Sperner's lemma, but generalised to allow for non-linear constraints, Lipschitz spaces, exotic homologies etc.). Currently the global optimisation method can find the approximate sub-domains of fixed points in p-normed spaces quickly (and has some convergence guarantees that it will find all of them), however, as you said there aren't any robust local minimisation algorithms that can take it from there. I've experimented with using a few for non-smooth spaces and they tend to be garbage. So my usual strategy has been to keeping refining the global optimisation until the sub-domains bounds are very small and then use a local minimisation algorithm to find these fixed points exactly. I'm currently doing some work in my spare time on a local solver using the same topology based theorems for faster local optimisation.

>The optimization problems I would want to solve are smooth, but computing the gradient-based search direction is a massive overhead which is blocking progress. An algorithm which does not rely on gradients would possibly be the key.
I've been working on exactly this (a solver that solves this problem in convex sub-domains, as I mentioned these locally convex domains can be computed in non-convex spaces quickly using the global optimisation algorithm), the algorithm currently involves maintaining data constructs that only vary linearly ([math]O(n)[/math]) with the problem dimension. The biggest so far is that each iteration still involves an expensive matrix inversion computation which bottlenecks the complexity to [math]O(n^2)[/math], but there could be a workaround to this.

[Anonymous No.10841107]

>>10839137
>>10841104

The results have been a promising algorithm that converges even quicker than Newton's algorithm (even on parabolic smooth functions), but does not require the construction of a gradient (not even an approximation). I was shocked that it works so well, I think it's because it uses a lot more information about the geometry of the problem than gradient/Taylor approximations at a single point on the function. However, this work is far from done and largely untested on non-toy problems.

>does it have to be finite-dimensional? there is a formulation of my problem which can be re-posed as a sequence of optimizations on function spaces.
Computationally speaking it has to be finite or finite approximations of course, however, someone smarter than me can probably use the mechanisms of the method to understand how to generalise it to infinite dimensions.

I will be travelling next week so I might miss a post if you reply here, but if you think this is something that could potentially work for you please don't hesitate to contact me.

[Anonymous No.10841113]

Did you ever get some weird or spooky mental imagery from math?
When I read a proof on the maximum principle in Complex Analysis, in which the fact that the function is constant on a non-empty open set, no matter how small, implies that the function is constant everywhere, I had the vivid imagery in my mind of "the constant area" just rapidly spreading all over the plane like a tumor

[Anonymous No.10841135]

Any amphetamines you guys recommend? What will happen long term by taking these? It shouldn't be so different from daily coffees, right? Should I just make meth and take miniscule amounts?

thanks /mg/

[Anonymous No.10841139]

@10841113
>R14kkDj.png
Don't know about math, but just now I got some spooky mental imagery of your brain getting taken over by tumors.

[Anonymous No.10841145]

>>10841139
What a good contribution to the thread

[Anonymous No.10841148]

>>10841135
Nah dude, it totally doesn't do anything to you. Use it and be sure to start early too so you get the max benefits even while you're doing your undergrad. Don't listen to the naysayers here.

[Anonymous No.10841151]

>>10841145
What a good contribution to the thread

[Anonymous No.10841188]

>>10841148
Paul Erdos was a proud user

[Anonymous No.10841258]

It's a fucked up world we live in. Y''all ever think that? Primes ramify, proofs in alg topo are all just applied functorality. It's a mess. We all live. Fuck. FUCK. Where did it go so wrong. >????
Footy. Sorru. Sorry. Ideals. Zariski. La Femme. WDTMBT? Sorry. Mstodds. ?
Gender stamdards. Why do we conform?
FUVK. PAIN. Thanks guys. Whats it all folr?
The reals probably don't exist. The axiom of choice was a mistake. The axiom of infinity is suspicious and so is the axiom of powerset. Type theory will take over. Differentiate this!!
Hilbert.
Should've construced it.
No
What's it all for? I give up

[Anonymous No.10841264]

>>10841188
Pretty sure he was asking for mathematicians.

[Anonymous No.10841274]

>>10841264
>Pretty sure he was asking for mathematicians.
I'm not a "he".

[Anonymous No.10841279]

>>10841274
Mathematicians use "we", not "I".

[Anonymous No.10841288]

>>10841113
I can’t say that I have.

[Anonymous No.10841292]

>>10841279
cuz we wuz kangs n shit?

[Anonymous No.10841293]

>>10841264
Erdos was a boss you stupid nigger

[Anonymous No.10841446]

when I'm stuck on a problem I just rewrite it neatly in a bigger font then get really angry

[Anonymous No.10841469]

What exactly do I need to do to prove this theorem? Does the following argument work?

A neighborhood is an open set, so taking the coordinate ring of a neighborhood is taking the coordinate ring of its closure

the neighborhoods of points in an irreducible variety are dense in the variety, hence K[U] = K[X]?

[Anonymous No.10841480]

> Tfw I had a few "math chad" moments last year, but still got ultimately got Cs in all 3 math classes I took

[Anonymous No.10841634]

>>10841293
Many people in this world are bosses, and almost none of them are mathematicians.

[Anonymous No.10842669]

>>10841292

dude epic