/sci/ - Science & Math

>>12750260
1st for mathfags are abstract fags

What comes after linear programming, non-linear programming and operation research if I want to specialize in optimization

>>12750260
What is that hideous thing

>>12750395
Thats an old person you ingrateful child

>>12750260
Whats the math behind yang mills interesting for?

Suppose we have [math]A,B [/math] which are [math] n \times n [/math] matrices. I want to compute the lie bracket [math] [X,Y] [/math] where [math] X(x) = Ax \ \& \ Y(x) = Bx[/math]. Where do I even begin here? Is this just a simple application of the commutator on a local coordinate patch? Or should I be looking to arrive at the commutator?

>>12751311
According to the hint, I should achieve [math] [X,Y] = -[A,B] = BA - AB [/math]
Surely this must be a local coordinate problem right?

>>12750260
What's the point of the Marriage condition on finite graphs? If I'm going to count the number of vertices reached by every subset anyways, couldn't I just brute force a mapping? Or is there a slicker method I'm not aware of?

>>12750260
That is a man.

>>12751311
>>12751319
yes, working in local coords should be fine.

>>12751342
You want the
https://en.wikipedia.org/wiki/Hungarian_algorithm

Am I crazy or is this graph non-planar?

Can someone explain multiplicities in a decomposition of a representation into its irreps? In the context of finite groups, if it matters. For example suppose I have [math]\rho = \rho_1 \oplus \rho_2 \oplus \rho_3[/math], where each [math]\rho_i[/math] is irreducible and their corresponding representation spaces are [math]V_i[/math]. If [math]\dim V_1 = \dim V_2[/math], does that mean that [math]\rho_1 \simeq \rho_2[/math] (and hence [math]\rho = \rho_1^{\oplus 2} \oplus \rho_3[/math]) even if their actual actions on the vector space look different?

>>12750395
Never seen an old person before, Leina?

>>12750472
You get $1million if you can figure it out (millenium problem)

>>12751953
try drawing all the points of one of the squares completely inside the other

>>12751953
you're crazy

>>12750271
Circle programming

>>12750271
convex analysis? optimal control? optimal transport?

POST MATH CHARTS

If I wanna show that spheres are cogroup objects in the pointed homotopy category of topological spaces, does it suffice to show [math] [S^{n},X] [/math] is a group?

I'm not totally sure that an object is a group objects iff morphisms into it form a group, but that may be so.

>>12752028
Kinda. The main idea is that for any set of vector spaces K = {v1, v2, v3, ... , v(n-1)} we can define another set S to be equal to the set of all linearly independent co products of the vector spaces who are elements of K. Obviously since K and S are not isomorphic and the kernel of their respective ring isomorphism are not rings we can apply Hodges lemma to easily show that within the category of Vector spaces any two elements A and B there exists a trisymetric mapping thus the dimension of B and the dimension of Φ(B) and A are not equal (where Φ represents Euler's Internalization Algorithm) this means that any scalar quantity alpha who is a member of B is also a member of its respective transition group representation, coincidentally the underlying set of B's transition group is B ⊕ A ⊕ Φ(A). The proof is as follows:

Let A be a subring of a field K and let x ∈ K and x!=0. Let φ:A->L be a homomorphism from A into an algebraicly closed field L. then φ has an extension to a homomorphism of A[x] or A[x^-1] into L. First ectend φ up to a homomorphism of the local ring A sub p where p is the kernel of φ thus without loss of generality we may assume that A is a local ring with maximal ideal m. suppose that mA[x^-1] = A[x^-1] then we can write
1 = a0 + a1x^-1 + ... anx^-n. with a being a member of m. multiplying each side by x^n we get (1-a0)x^n + bn-1x^n-1+...b0 = 0. with suitable elements bi in A. since a0 is in m it follows that 1-a0 is not in m hence 1-a0 is a unit in A because A is a assumed to be a local ring. dividing by 1-a0 we see that x is integral over A and hence that our homomorphism has an extension A[x]. If on the other hand we have mA[x^-1] !=A[x^-1] then mA[x^-1] is contained in some maximal ideal B of A[x^-1] and the intersection of B and A cointains M. Since m is maximal we must have that the intersection of B and A IS m. since φ and the canonical map A -> A/m have the same kernel

>>12752371
yes

>>12750260
Anons what are some youtubers that are good at explaining CS related math? That is, statistics, Discrete math, set theory, linear algebra etc.? I have ADHD I cant read books it's too much for me

>>12752390
Get your ADHD treated. YouTube videos are trash when compared to a good textbook.

Is the entire field of algebraic geometry boring to anybody else?

>>12752394
I take meds but they're not a miracle cure. I dont read books as much as I'd like to. At the very least, can you recommend easy to digest books? I checked out a bunch of the books in the wiki but they seemed daunting

>>12750472
https://www.claymath.org/sites/default/files/yangmills.pdf

I think the geometric pov is kinda obvious; Scott Sheffield has some weird stuff from a probabilistic pov.

>>12752284
>convex analysis? optimal control? optimal transport?
I think we don't have those as electives. Just multi-objective programming and integer programming. Something about networks, too

Is Real Analysis supposed to be so... sloppy?

>>12752656
reals are ill defined in classical logic

>>12752680
Elaborate

Do mathematicians trust each other? Is that why you guys get mad when someone says inaccurate stuff? Because it breaks trust?

>>12752445
>The answers are partial, for in most of these field theories one replaces theMinkowski space-timeM4by a lower-dimensional space-timeM2orM3, or by acompact approximation such as a torus. (Equivalently in the Euclidean formulationone replaces Euclidean space-timeR4byR2orR3.) Some results are known forYang–Mills theory on a 4-torusT4approximatingR4, and, while the constructionis not complete, there is ample indication that known methods could be extendedto construct Yang–Mills theory onT4.

Why is it a torus

>think I have a really cool original idea
>someone already did it decades ago

>>12752772
nothing can be infinite except for the natural numbers for some reason, blah blah blah something completed something something LEM *shits pants*

>>12752838
What was the idea

>>12752872
Baka

>>12752838
The world of mathematics has been going for centuries, you’ve only had a couple decades, the ideas you have are only a couple decades behind what mathematicians have already done.
At this rate you’ll have an original idea in no time

>>12752838
>>think I have a really cool original idea
Tell us :)

If the composition series isn’t unique, then what’s the point of the classification of finite simple groups? Is anyone looking for a classification of all finite groups in general? What about just all groups?

Every topology can serve as its own basis, correct?

>>12753353
Yes. If in doubt, use the result which says that a collection of open sets is a basis iff whenever two sets in the collection intersect non-vacuously, there is a set contained in the intersection. Choose the collection to be the whole topology and note that any finite intersection is an element of your collection.

Is there any shame in finishing my math degree at 27? Will I face prejudice when I try to get a job in academia or enter a PhD program? I calculated that I'll only be able to finish my degree at 27 at the earliest and this is making me depressed.

>>12753353
yes, trivially

>>12753396
You will probably face prejudice from humans but only God can judge us. Just be charismatic and act competent.

>>12753396
Just be happy you aren't doing physics.

>>12753396
There's no shame at any age. I had people join my PhD group in their mid 30's and one was even early 40's. Having a Math degree impresses everyone.

>>12753357
>the result which says that a collection of open sets is a basis iff whenever two sets in the collection intersect non-vacuously, there is a set contained in the intersection
What if your collection of open sets is just one subset of X though?

>>12753427
if that subset is X, then it generates the trivial topology
if that subset is not X, then it's not a base

>>12753427
Yes of course the union of all the sets has to be the whole space. Then it is a basis for some topology. Good point. If there is only one set in your wnb-basis, then it is the (basis of) the trivial topology iff that set is the whole space.

This general usually is full of shizo's and trannies

What are some good geometric/organizational applications of topology to daily life? When I was doing linear algebra, Id walk in the forest and imagine the trees as vectors. What kind of topologies will I see in the hills?

>>12752656
What gave you this impression?

>>12752397
Yes.

>>12752656
Sort of, but that's what makes it fun.
Unless you mean foundationally sloppy, in which case, no, it's all foundationally very secure. This guy >>12752680 is a moron.

Is it possible to go to college after fucking up high school so hard? I love math but I've always been a terrible student; When I was a sophomore in high school I self-taught calculus and got a 5 on the BC exam (only person in my shit ass school who passed too lmao) but that year I got 3 Fs and a D- in Algebra 2 (my teacher rounded up a 53 because she knew I already knew the material). I never stopped self-studying I probably have approximately equivalent knowledge to the average 4th year undergrad. If I ever decide that I want to stop wageslaving and get serious about math is there any way I can do that? If I apply to a college I'm certain to be rejected because of my high school grades and even if I got into one how am I gonna stay motivated relearning all the shit that I self-taught, I wasn't able to motivate myself to do any of the assignments in algebra 2.

god I fucking hate adhd

>>12753767
Why not use your math skills to make some programming algorithms and build a CV without college? Algorithms for data efficiency and stuff

>>12753788
Programming and computer science don't really interest me, I'm mostly interested in Algebra. Even then I don't want to get a job in some math adjacent field like programming or finance or whatever. I would rather keep doing my current job than any of those jobs. What I want is to be able to go into academia and actually make real contributions to mathematics.

you know if there's an exam due I will skip my latuda for maximum creativity

>>12753811
I used to take tests in HS stoned

>>12753807
Algorithms use a lot of algebra. Its just away to get your foot in their door

>>12752656
>sloppy
Try incoherent and yes, all concepts built on lies, will start to become incoherent after a while.

>>12753767
If you’re American just go to a community college and get your associates retard, then transfer to a decent school.

>>12753396
>Is there any shame in finishing my math degree at 27? Will I face prejudice when I try to get a job in academia or enter a PhD program?
not in the Uk

Hey frens, next semester I'm gonna do Differential Geometry (the classical one, we're using Do Carmo's book). Thing is, I completely forgot a lot of things about multivariable calculus and it looks like this is extremely important in DG. Should I use the two weeks of vacations I'll have to study all of multivariable calculus again or will I be fine just going directly into DG? Thanks.

>>12753459
>Id walk in the forest and imagine the trees as vectors
Kek, how and why exactly?
>What kind of topologies will I see in the hills?
That's more about differential geometry and Morse theory. Topology would be more relevant to angelology and demonology.

>>12753767
To me the idea that highschool grades should play any part in college enrollment is bizzare.
If it's that vital for you to go no a non shit-tier college, maybe try seeking a program abroad then?

>>12752656
No, avoiding sloppiness is one of the main reasons of its existence. In practice, especially among non math majors, it is sloppy.

>>12754112
A quick refresh on multivariable calculus is not going to hurt because you are right. It's a must when it comes to DG.

>>12754112
Just make sure you understand the inverse/implicit function theorems.

>>12753973
yes in japan

>>12754112
>Should I use the two weeks of vacations I'll have to study all of multivariable calculus again
yes, definitely

>>12754198
>>12754200
>>12754283
Thanks!

>>12754273
You're in Japan? Do you have a strong homotopy theoretic school there due to Toda? Are Japanese superior at the homotopy groups of spheres?

>>12753973
thats good to here

Is a cofibration an inclusion in the intuitive sense? Like if [math] A[/math] is just some space and [math] i: A\to X[/math] is a cofibration, is it necessarily the case that [math] A[/math] is a subspace of [math]X[/math]? I've looked at a bunch of resources and it's not really clear if it is or not.

>>12750395
That's a level 100 mage with more power in her
hand than you can fathom. Tread lightly, or be
sent down the devil's staircase.

Just found out I got into Dartmouth’s PhD mathematics program. Best day ever.

>>12753767
CC for two years then transfer to a decent school. It goes without saying that you need to do well there if you want a shot at transferring into a good uni.

>>12755541
Congrats Ben.

>>12755541
gj benon

Any recommendations for a first dip course into non-linear analysis, fellow cu/mg/uzzlers?

>>12755721
My college has a course called “intro to nonlinear dynamics” so that would be pretty ideal if your college offers it. We also studied it in mechanics. Taylor has a section about it.

>>12755799
ah well, don't really have the semester of time to prep for it with another class was just kinda dropped on me.

>>12750260
Let's say I wanted to write a program to show the values compare the values of [math]n^{3}+17n+4[/math] and
[math] n^{3}[/math] for increasingly large values of n. What is the best tool to do this? I have heard python has good math libraries, but I was wondering if maybe there's some better option.

>>12755989
its 17n+4 lmao

>>12755989
Python is good. Would only take a couple lines then matplotlib to graph the results.

>>12755989
learn haskell

>>12756008
kek, sorry. First one should be [math]n^{2}+17n+4[/math]
but yeah i just meant in general being able to easily write in arbitrary expressions.

>>12755989
Python for sure. It supports arbitrary length integers by default and there are libs like GMPY

>>12755989
if all you're looking for is how they differ at large values you need only concern yourself with the degree of the polynomial. you can get a feel for how they compare by taking the limit of their ratio.
unless you really want some hard data, then any language will do.

where can I find grad-level mathematicians who want undergrad engineer boypussy?

>>12756105
>you can get a feel for how they compare by taking the limit of their ratio
Thank you anon, that is very helpful to know.

>>12756111
I don't have a penis but I'd still like some if you're cute.

>>12756319
please be in florida

>>12756111
The analysis department, probably.

>>12756345
New York, sorry.

stop trying to make please be in london be a meme. please be in london is never going to be a meme

>>12756319
post tits
please?

>>12756443
Post boypussy first.

YOURE NOT REAL YOURE NOT REAL GET OUT OF MY HEAD

>>12756470
Im not that anon
I just want to see boobies because Ive never seen them outside of porn

tips for doing maths in bed? programming is super comfy cuz i can just set the laptop on my thighs and sit up slightly. however, writing is fucking pain while even remotely horizontal.

can you do math with a keyboard instead of pen and paper?

>>12756628
Aside from this being a blue board, ¿wouldn't it still be porn to you if I post my tits?

>>12756668
I’m actually going to be going to be a grad math Chad in New York this fall. Want to be my housewife?

>>12756668
I don't know I've never made it this far before... I feel like it'd be different because getting some after asking nicely makes it a bit more special and personal.

>>12756697
I only like cutesy guys and girls, sorry.

>>12756706
I don't wanna get banned, plus there are no girls on the internet. Go fap to your trap legs in stockings /mg/.

>>12756728
:( I don't like traps but okay, it was worth a try.

>>12755721
bumping up my question anons I'm going to a library tomorrow and it's quite a long way there so literally any books you'd think applicable and worthwhile would be cool

holy SHIT you guys are pathetic

>>12756776
shut the fuck up

>iwn fall asleep with my head resting on a math girls tummy slowly moving up and down as she plays with my hair
why live, /mg/?

>>12756847
see>>12756776

>>12756744
Fuck that bitch bro. You become the gf and I’ll be your math Chad bf.

Which mathematical field should I specialize if I wanna learn about the nature of time itself?

>>12755799
nonlinear analysis schechter

I'm transferring to uni fall, next term I'm only taking Electricity and Magnetism then just waiting until fall. I've taken the calc series (including vector), applied/intro lin alg, and applied/intro diff eq.

I feel I didn't really understand a lot of the linear alg and diff eq, but understanding isn't really stressed in applied classes either IME. that being said, what should i study over summer to prep?

>>12756983
Geometry

>>12757044
can you recommend a specific text? sounds like a good opportunity to do this desu

>>12757044
oops, sorry i thought you were talking to me (sparkling sloth guy)

>>12757044
Which geometry? There are dozens of them these days

>>12757084
Algebraic.

>>12757041
samefag, decided I’m gonna take the opportunity to hammer down on a classical mechanics text (SICM). I’d like to continue self studying physics

>>12750271
Control theory ,micro local analysis

>>12757383
Symplectic is better,so is finsler

https://youtube.com/watch?v=4GYPem-bAO0
https://youtube.com/watch?v=9O237FJNipg
Why read textbooks when the yukkuri blobs can teach me everything?

>>12757704
It’s painful to listen to

What to read in order to understand calabi-yau manifolds?

>>12755489
>Is a cofibration an inclusion in the intuitive sense?
I dont think so. Cofibrations are the dual of firbations and fibrations are just a tool to transport, by pullbaks, things over a space to another space

https://ncatlab.org/nlab/show/cofibration

>>12754157
I talk to a lot of demons and angels. What kind of topology should I look for next time?

Any good suggestions for showing to fields are not isomorphic?

>>12758443
Look at what polynomials have roots in them, look at cardinality, look at transcendence degrees, etc.

anons i thought calc III would be hard but its actually comfy

>>12758641
Nothing is truly hard if someone else has discovered it, you can just adapt their elgorithms. Tha hard thing is finding radically new systems, and to a lesser extent, deciding whether/which old system might fit a new appearance.

Anons today I am going to the woods to find a good stick to try and make a bow and arrow to protect myself from Mountain Lions when I go camping. Somehow I will use topology, to compare sticks by their intersections in the foresdtal boreal topolog. The boreal topology.

https://www.youtube.com/watch?v=wE0BxYnba7s

Are complex geometers superior to other geometers in the differential sphere?

>>12759263
No.
If anything they're inferior due to excessive interaction with algebraic geometry.

>>12756668
>>12756706
>>12756728
Post it on a red board, crosspost it here
Probably would get off with a warning if mods cared

Sorry for asking this but if a, b, c and d are natural numbers and a/b = c/d, does a have to be equal to c and b to d?

Please note that I'm a huge brainlet.

>>12759444
Almost. c=na, d=nb where |n|>0

any idea how hard is it to get into a phd program in the usa, europe or east asia? I'm brazilian and i know some people doing physics and engineering phd in the usa, singapore, europe etc but i've never heard of math.

I am really bad at writing greek letters. I have bad writing in general but when I write lambda, theta, or omega for example it's even worse. I am going to try to improve my handwriting, many times my notes are barely even decipherable. Perhaps I need a desk or a work table of sorts...

>>12759444
no, 1/2 = 2/4

>>12759588
lambda and gamma are my favorite symbols to write

>>12759525
most of the grad students in the physics department at my university are latin American so, presumably, not that difficult

When I go out, I do combinatorics on the contents of my bag and pockets, to make sure I dont lose anything. I was sitting there, reading about bases, stoned in the sun, and I realized... I could perform combinatorics on the symbolic-conceptual elements involved in a proof. How many components and steps.

And then he started talking about the Real Line and I was like wtf is this boring shit gimme my sets and sets back

Uhm... How does modern mathematical training differ from ancient teaching methods? Nowadays, textbooks serve as proof-food to train the general known methods of proof, but back when proofs were sparser, how did they train? It was mostly just integers back then wasnt it....

>>12760535
ancients used to move beads, chase heretics and fear corn
you have a lot to learn

>>12760549
How do heretics and corn have to do with that? When did they start fearing corn? At the beginning wasnt agriculture seen as a blessing? When did they start chasing heretics? When did the concept of heretic originate?

I got rejected from the one grad school I can go to.

>>12760555
you have a lot to learn

>>12760580
¿How can you go to it if you got rejected?

Anyone know of a good book on manifolds that isn't too bad for self study? I'm pretty retarded so the simpler the better.

>>12760580
Why cant you go to other ones?

>>12760588
Elaborate, if only for my 5trips and 5conceptcount

>>12760618
meant "could", been drinking
>>12760628
family obligations, only go to local one

>>12760627
Tu Introduction to Manifolds is goat.

>>12753417
Why?

>>12760627
Do pic related (ironically)(unironically).
>>12760740
Also good.

>>12757645
>micro local analysis
That sounds kino, I'll check it out, thanks.

>>12760686
Its a real shame anon. Why did they reject you?

Does anyone study percent algebras?

So we have cotangent spaces. Anybody ever heard of sine or cosine spaces?

Why isn't this limit equal to one?

>>12761088
I dont know, I thought it was 1 too

>>12761088
Fix an integer k > 0, then n! > k^{n-k+1} and thus the liminf of your sequence is >= k.

Not gonna make it into a grad school worth going to. Wtf do I do. I graduate May '22

>>12761240
Try to do a funded masters at a decent place, then apply to the schools of your dreams.

>>12761204
Howd u do that

In the previous 1-3 threads one anon said that 4 last months of phd funding is too late to prepare a plan B outside of academia to another anon who was sick of the mainstream attitude of academics.

I'm just starting my phd and at first I like the idea of preparing for a good plan B, but it doesn't seem that much worth to invest like 1h/day average to learn coding or whatever while I have the opportunity to make my main plan work. I can't say I'm as enthusiastic for a plan B as I am for math, and all the time I can get either improving for it or rewinding is important. Plus I'm on pure mathematics, not even close to probability which could be useful for going into the private sector or something.
It seems to me that an all in is better, and if I decide to not get into academia I'll just pay the price and start a plan B from scratch.

>>12761240
Industry like everyone else. Independent research if you have the tenacity for it.

>>12761088
It appears that the rate of relative difference between the numerator and denominator grows faster than the exponent in the denominator can close it.

>>12760627
Differential Topology by Guillemin and Pollack is really focused on intuition and visualization.

>>12750260
How do I into calculus? I don’t want to be a retard anymore.

>>12761279
there is no math that you are doing that wouldn't benefit at least somewhat from a working knowledge of programming. it is used all of the time in every discipline.

>>12761462
what precisely is difficult to you about calculus?

>>12751953
If you cant visualize that in your head you are low IQ and should give up on math

>>12761471
It doesn't seem to matter how many times I revise the basics (arithmetic, algebra & precalc) and how many rules and definitions I memorize and try to understand. Logarithmic functions and exponential functions with base e always sucker punch me in the worst possible way.

>>12759525
brazil and france used to have ties in maths, grothendieck went to brazil to eat only bananas and milk

if you are good you should tap this link

https://www.fondation-hadamard.fr/fr/bresil/reseau-franco-bresilien-en-mathematiques

http://www.rfbm.fr/

https://impa.br/en_US/eventos-do-impa/eventos-2019/1st-joint-meeting-brazil-france-in-mathematics/
contact those people to know what is possible in terms of funding

>>12760627
isham book

https://www.youtube.com/watch?v=T9-a1tiT66E

thoughts?

Redpill me on Tucker decomposition and tensor factorizations in general. What is the intuition behind them?

>>12761782
>mother and stepfather

>>12761536
Elaborate on your difficulties with logarithms and exponentials.

>>12761088
n!/(n!)^(1-1/n) = (n!)^(1-1+1/n) = (n!)^(1/n)
= 1^(1/n) * 2^(1/n) * ... * n^(1/n)
all of those k^(1/n) are bigger than one

>>12762154
That doesnt prove its boundless yet, just that its greater than 1

>>12761088
[math]\frac{n!}{n!^{1-\frac{1}{n}}}[/math]
[math]n!(n!)^{\frac{1}{n}-1}[/math]
[math]n!^{\frac{1}{n}}[/math]

>>12762236
yeah thats what op asked, why it isnt one

is there a different way of calculating inverse matrixes other than with the adjugate matrix?
>t. highschool

>>12762464
Yes, Gaussian Elimination.

>>12762092
The concepts are too abstract. When I'm solving functions I have no real notion of what I am doing and I make stupid mistakes.

>>12752788
No idea what physishits are doing but I guess they use the metric $$ds^2 = du^2 +dv^2$$, and that is the metric of a Torus (if you consider, say a rectangular strip). That is probably what they mean by compact approximation.

>>12763027
Sounds to me like your teacher(s) have done a bad job at explaining the concepts. I struggled a lot more with trig and trig identities than I ever did with e and ln.

I'm currently self studying Linear Algebra. Are there any resources that have tests and exams that I can use to gauge my progress?

>>12763138
Yes.

>>12763205
Okay thank you for the help.

>>12753396
I will tell you that you won't get a good job on academia, if you are getting back into undergrad. it's too late.

you should be able to get a phd and a job though.

>>12752680
so equivalence classes of cauchy sequences is I'll defined?

there are so many ways to prove this result, through topology, algebra, etc.

>>12752788
The torus is, by far, the simplest compact smooth manifold, and it has most of the structures you want. Flat metric? You got it. Kahler structure? In all even dimensions. Parallelizable? Yup.

>>12750260
I looked at some stuff with Karen Uhlenbeck.

I wasn't very impressed.

>>12750468
>>12752085
What is that hideous thing

What are your "must-read" mathematical articles? I'd like to exclude surveys and metamathematical articles.

>>12753396
I'm a /mg/ tourist for fun and I'd be impressed by anyone with a maths degree, no matter when they graduated. From my understanding of maths, physics and history it's not who's the smartest which matters the most, it's a collection of luck, availability of information and interest which determines who and why things are discovered, not necessarily degree of education

>>12755989
Why would you ever want to compare that..? They're the same.

//Compsci

Physicsfag here. Is there a Clebsh-Gordan theory for arbitrary compact Lie groups?

How to get good at math? I got some govt IQ tests and I'm pretty high up but I eat shit really hard at math. For refence, I never was able to move past semester one of freshman algebra in highschool. I could only graduate by dropping out and then getting my GED via tests I practiced for, because the math classes were mandatory for graduating.

can anyone recommend me a good series on measure theory and lebesgue integrals?
Don't need to be that fancy, I just need to be up to speed for a course on functional analysis

>>12764451
Folland

>>12764451
and by series I mean a series of youtube videos or video lectures possibly
>>12764457
thanks I'll give it a look

>>12763138
You can use the exams / homeworks on MIT Open Course Ware (you should probably also use their lectures if it's your first time doing linear algebra and you haven't done much with proofs, they're great lecture videos).

Did anyone here manage to get 300k starting with a maths PhD?
Were most of you at least fantasizing about 300k starting when you decided to do maths?
Places like Jane Street has 300k starting and I think some pay even more.
t. dropped out but still want to imagine what could have been if I didn't suck

Discuss.

http://steve-patterson.com/pi-rational-finite-number/

>>12763363
4chan needs "like" buttons.

>>12764164
Use permutations. Just calculate all kinds of permutations of things.

What are my frens studying?

>>12765558
Grammar tonite.. I need to fuckn get off 4chan..

>>12764451
Stein and Shakarachi is easier than Folland I think. The latter won’t make for quick reading from what i hear

Any anon here who knows how to compute the number of cusps [math]\varepsilon_\infty[/math] of the modular cure [math]X_0(4)[/math]?
I keep getting that their ramification indexes are all equal to 1 and then I get [math]\varepsilon_\infty = 6[/math], but the answer should be 3. No idea wtf is wrong.
I need this as soon as possible. Fuck my life.

>>12765757
Nevermind, I've found the mistake.

should i take homological algebra? i can't tell if such a class would be interesting or extremely boring abstract nonsense

>>12753732
>>12752680
>>12763288
Laff at those undergrads. Learn what it is the weak countable choice.

>>12750271
cum analysis

So there is [math]sin(x), \; sin^{2}(x), \; sin^{-1}(x)[/math]. Does this go for any rational composition of trigonometric functions?

>>12766216
Yes

>>12753396
No. You will acutually be surprised how people will go "Wow, you're only 28 and doing your PhD already", at least that's what happened to me

Consider the set [math]A = \{ (x, y) \in \mathbb{R} : x, y > 0 \}[\math]. Define a binary relation [math]R[\math] so that [math](x_{a}, y_{a}) R (x_{b}, y_{b})[\math] if and only if [math]x_{a}y_{b} < y_{a}x_{b}[\math]. Is [math]R[\math] transitive for all [math]i \in A[\math]?

>>12766398
Consider the set [math]A = \{ (x, y) \in \mathbb{R} : x, y > 0 \}[/math]. Define a binary relation [math]R[/math] so that [math](x_{a}, y_{a}) R (x_{b}, y_{b})[/math] if and only if [math]x_{a}y_{b} < y_{a}x_{b}[/math]. Is [math]R[/math] transitive for all [math]i \in A[/math]?

>>12766408
Suppose [math](a, b)R(c, d), (c, d)R(e, f)[/math]. Then [math]af = \frac{ad}{d} \cdot f < \frac{bc}{d}\cdot f = b \cdot \frac{cf}{d} < b \cdot \frac{de}{d} = be[/math].

>>12766030
ALGEBRA TRANNY ANSWER THIS QUESTION

>>12765558
Problems in Algebraic Number Theory, it's a based book

>>12752399
for linear algebra, try Hefferon's "Linear Algebra", it's free, has full solutions, and he even put up a complete video class on YouTube. I worked through it a few weeks ago and I highly recommend it.
I don't have any good blanket recommendations for the rest, but what worked for me was, whenever I didn't get a certain thing working from the textbook/lecture notes, I'd search YouTube for a good explanation of that one thing.
You might also want to check out Coursera, edX, and MIT OpenCourseWare or however it's written for video lectures, sometimes you'll find a good course exactly for your topic (rare, but possible - or you'll find one video from the course that explains whatever you're working on right now).
Other than that, maybe spend more time reading math books and getting familiar with them, you'll get better as you do it more and the other anon is correct, no YT video can replace a good textbook. Godspeed.

>>12766561
> Hefferson
> Not H&K or Halmos or Lax or LADW or Axler
NGMI

>>12766030
>>12766454
I was gonna answer your question, but now that I know that you actually just want a (You) from the anime tranny I might as well not bother.

I got the spirit lose the feeling let it out somehow

Absence versus thin air show down of the century

>>12763354

Serre's FAC is still a very good read along with Grothendieck's Tohoku paper.

Atiyah's papers on Vector Bundles over an Elliptic Curve and his paper on the Moment and Equivariant Cohomology are also incredibly readable.

>>12766760
>he even put up a complete video class on YouTube
which is what the other guy asked for, a youtube video.

What's the most applied field in maths that will certainly land me a job?

>>12766907
Statistics

>>12766907
Diff eq

>>12763354
>What are your "must-read" mathematical articles?
any article by COQuand

>>12750271
Differential programming.

>>12766918
>>12766921
Any rigorous resource for these two, without them being treated like a bourb*kist trash?

>>12766907
Excel

What the fuck does: "Let A be an n × n matrix and λ a real number. If rank(λI − A) > 0, then λ is an
eigenvalue for A" mean?
I only know that A has to have n number of eigenvalues for it to be diagonalizable.

>>12767300
Start with V.Arnold - ODEs

>>12767527
it's false, the rank needs to be lesser than the dimension of the matrix, not >0

>>12753192
Look up the Jordan-Hölder Theorem

>>12767527
Maybe think about it for a moment.
What does rank mean?
What is the connection of λI − A to Eigenvalues?

>>12767533
>>12767541
Thanks for the replies, but I am still confused. Rank is the leading number of 1s in the matrix right? So, according to >>12767533
the condition here is that rank should not be equal to n. If n = r then we would only have 1 unique solution but I don't see how that links to eigenvalues.

>>12767300
Just look up binomial distribution

Right now I'm going through Linear Algebra Done Right and its my first introduction to proof based math and GOD DAMN these problems are hard. How many of the problems in each section should I do and how long should I spend on each one.

I understand all the material just fine but these exercises are kicking my ass

>>12767568
x is a solution to

(λI − A)x = 0

if and only if

Ax = λx

which means exactly that x is an eigenvector corresponding to λ (and hence that λ is an eigenvalue)

>>12767597
I still don't get it but thanks anyways.

>>12767590
Linear Algebra is where math starts IMO. Calculus is hand wavy shit and that's why bad teachers get away with memeijg it to engineers. Linear algebra, there is no way to make that course easy. This is where math starts for a typical undergrad. You have to do proofs, and deal with abstract objects. Go m8

>>12767300
Bain & Englehardt is the entirety of undergrad mathematical statistics

>>12766773
Can you please answer the question? I’m not >>12766454 and I don’t know who algebra tranny is, I don’t normally browse this board

>>12767300
Michael Jordan’s book list has good lists for probability, stats, and optimization.

>>12766773
yes if you want to learn algebraic topology or algebraic geometry at some point in the future. otherwise no.

>>12750260
Anyone can help me with computing the homology of compact surfaceses?
I just dont get it. Most important is do it for orientable surfaceses?
Or at least the solution?

>>12767732
Dumb frogposter

>>12767704
Alright, alright, I was really just taking the piss.
Homological algebra is extremely boring. Absolute pain in the ass abstract nonsense.
But if you're studying algebra, algebraic geometry, algebraic topology or homotopy theory it's very much obligatory.
>>12767732
Pants decomposition.

>>12767841
>Pants decomposition.
Ok so i use the classification theorem and say because they are homeomorphic to only 3 struktures they only have the homology of these 3 structures? Homeomorphic surfaces have the same homology right? Then i cumpute of the sphere. For the other i decomposite them into tori (or real projective planes) and then i compute the homology of a torus (projective plane)?
Is that the right way? Thanks
>>12767837
:(

>>12767990
>Homeomorphic surfaces have the same homology right?
Never mind, this isn't gonna work, drop out of the class.

>>12768012
I hate topology but ill make it.
So what i was thinking that 2 surfaces that are homeomorphic to eachother have the same homology. Is that wrong?

>>12766907
BIG DATA

>>12767732
one way is >>12767841 you can write any surface as connected sum of tori and projective planes. so you need to compute H(torus), H(projective space) and the effect of the connected sum on the homology (probably by Mayer-Vietoris), then you know everything.
other way is the cellular decomposition. there are very easy models for both orientable and non-orientable surfaces. these give you nice chain complexes from which you can compute the homology explicitly.

>>12767590
ngl, if you can't do the exercises that means you don't understand it.

>>12768063
>other way is the cellular decomposition. there are very easy models for both orientable and non-orientable surfaces. these give you nice chain complexes from which you can compute the homology explicitly.
Thanks you look into these, maybe not today but thanks

>>12768012
But this was just troll am i right?
Because my statement was true!?

>>12763354
Artin: Algebraic approximation of algebraic structures over complete local fields
Baily, Borel: Compactifications of arithmetic quotients of bounded symmetric domains
Schlessinger: Functors on Artin rings
Tits: Classification of algebraic semisimple groups
Tits: Reductive groups over local fields

going to graduate school soon. Should I focus on finite group theory or algebraic topology for the next few months?

>>12768400
Algebraic topology you absolute baka

>>12768400
aren't those like both dead/dying fields

>>12768439
>>12768413
i mean, as long as there are still open problems in those fields, it's good isn't it? what does it mean for a field to not be dying?

>>12768439
certainly not algebraic topology, there's lots of new stuff being done and plenty of open questions. Finite group theory is probably a bad idea tho

>>12765558
trying to learn which one is which of sine, cosine and tangent

For a right pyramid with a regular base you're given the apex angle of the triangular sides and the number of sides of the base. How do you find the volume?

Is Abbott's Analysis the best Analysis book for brainlets? I tried Rudin and it filtered me so now I'm looking into books that are more suitable for my level of intelligence.

Any maths teachers at high school/secondary school here? Thinking of going into teaching maths after graduation (EE degree) as not exactly motivated to go into the field. I enjoy the subject but I don't think I'd enjoy wageslaving over it.

>>12768300
yeah a continuous map f induces a map [math]f_*[/math] on homology, so if f is a homeomorphism you get an isomorphism on homology groups because you have an inverse map [math](f^{-1})_*[/math]. basically this follows from the fact that homology is a functor

>>12768654
Ah great thanks now i even remember.

>>12768618
Rudin is fine you just need to study harder.

>>12768551
are torsion groups active?
i like my orders finite

>>12768464
No Im saying you should do alg topo

What can one do with clifford algebras?

Does anyone else feel their self esteem effected by math? In daily life, I almost never fail to find a solution to a problem, but math is one of the rare things that constantly stumps me. It makes me doubt in my competence, and thus doubt in my ability to survive, causing great anxiety at times. How do you guys cope?

>>12769443
That's what makes it fun to me. I like being able to be stumped by something.

>>12769443
Which is why I enjoy it. Many other parts of my life comes very easily but math I have to really work at and when I solve a particularly difficult problem or truly understand some new theory that gives me a real feeling of accomplishment.

>>12769526
So in clifford algebras, in R2, its supposed to mimic complex numbers. The scalar term is real and the multivector is imaginary, algebraically. But I dont get it geometrically, where is the area and scalar coming from, representing?

Trying to get back into complex analysis after undergrad, my class used the Brown & Churchill book. You guys have any better recommendations, or is this is the state of the art out there?

>>12769669
Try Stein and Shakarchi

Can someone tell me why I should care about Algebraic Geometry?
It seems to have this prestige within mathematics, and Grothendieck is considered such a legend, but whenever I start reading a textbook on the topic I just think "really, people are interested in this shit?"
Like an introduction might mention Bezout's Theorem about how many points at which two plane curves intersect and I just can't imagine giving a fuck. Like who cares? I really just don't care about gay little fucking curves in the plane.
Do I just not have a soul? Can I not understand how much SOUL there is in studying a big steaming pile of polynomials?

>>12769443

This is something I think about often; people like Dyson got gud because they put in incredible amounts of work to get where they got: think 16 hour days of grinding through book after book.

It's a bit like endurance sports, in that there are freaks of nature who will sprint laps around you no matter what you're doing. In some cases, they've been training longer and harder or have cross-trained in sports you've never even heard of.

But can you beat your time from last year?

>>12769810
Once you get to the modern stuff, algebraic geometry is about studying schemes - locally, this reduces to commutative algebra so algebraic geometry gives you lots of geometric understanding of how commutative algebra works.

In this way, you can sort of think of it as just studying a more rigid version of something like complex manifolds - instead of asking that our space looks locally like C^n, we ask that it looks like the spectrum of some algebra over C. There's actually strong connections between these too - the category of compact Riemann surfaces is equivalent to the category of smooth projective curves over C, so you can study Riemann surfaces using the extra structure provided by algebraic geometry or vice versa (this principle is called GAGA - good example is Chow's theorem). It's pretty neat to look at differences/similarities between varieties and less rigid objects like manifolds and it can often help you understand one or the other better.

Hope this gives a better sense of why people might study AG. Personally, I just think the theory is really clean and elegant once you get deeper into it. It also has lots of connections to things like number theory (Weil conjectures, Shimura varieties, Honda-Tate theory), representation theory (representation theory of finite groups of lie type is hopeless without embedding in an algebraic group) and lots more.

>>12764164

>>12769696
>Stein and Shakarchi
Damn they go in a completely different sequence of exposition than brown & churchill.

any cool /sci/ sites? thread: >>12770243

>>12769413
talk about the local structure of SO and Spin groups

>>12769413
they give you a tangible model of spin groups which you can actually use for computations

>>12768618
I'm in the same boat (brainlet who got filtered by Rudin) and I'm working through it right now. It couldn't be more brainlet-appropriate, so yeah give it a shot, it's great. Solution manual is also somewhere on the internet, grab that pdf as well and you'll be all set to understand analysis.

>>12770506
>>12770538
Can you share any resources that start from intro level? Havent done much algebra

>>12769842
I think the cross training metaphor is really important, if only because life is so much more than textbooks. I find it useful to try and apply mathematical thinking everywhere in life, both to make life easier and also to constantly passively train

I dont get the intuition for this. Why should the area of a parallelogram correspond to the imaginary value, and whats the geometry for the scalar component of the clifford?

>>12770926
Wait a sec. A clifford multiplication is literally just dot product plus cross product. Wtff!!

What is the most important undergrad math course?

>>12768400
definitely not group theory

>>12769571
for clifford algebras, i made a bibliography


https://boards.fireden.net/sci/thread/11975242/#11986310

>>12769810
>Like an introduction might mention Bezout's Theorem about how many points at which two plane curves intersect and I just can't imagine giving a fuck. Like who cares? I really just don't care about gay little fucking curves in the plane.
>>12769810
same

>>12770709
>>12771067

>>12771067
>>12771089
Danks anon gonna look rn

>>12771067
Alder_2009_Geometric Algebra An Introduction to Clifford Algebras.pdf

I wanna cehck this one but its buried in a sea of other pdfs when I just enter into search bar, am I suppsoed to use a e library or somethnig

>>12771303
>Geometric Algebra An Introduction to Clifford Algebras.
I have put it there
Alder_2009_Geometric Algebra An Introduction to Clifford Algebras.pdf
https://www23.zippyshare.com/v/KuNILXfX/file.html

>>12771303
you jdownloader portable to get all this

zippyshare deletes all the content after 30 days from the last download

Ablamowicz et al._2003_Idempotents of Clifford Algebras.pdf
https://www85.zippyshare.com/v/4iFP8842/file.html
Ablamowicz, Fauser_2005_Clifford and Graßmann Hopf algebras via the package for Maple.pdf
https://www85.zippyshare.com/v/tikoCQC7/file.html
Ablamowicz, Fauser_2005_Mathematics of Clifford - a Maple package for Clifford and Graßmann algebras.pdf
https://www85.zippyshare.com/v/20hxn4o4/file.html
Ablamowicz, Fauser_2010_On the transposition anti-involution in real Clifford algebras I The transposition map.pdf
https://www85.zippyshare.com/v/MEzTkYVh/file.html
Ablamowicz_1982_Clifford algebra approach to twistors.pdf
https://www85.zippyshare.com/v/3hXm2HYZ/file.html
Alder_2009_Geometric Algebra An Introduction to Clifford Algebras.pdf
https://www85.zippyshare.com/v/9vJ2WVa7/file.html
Anyaegbunam_2010_Geometric algebra via sheaf theory A view towards symplectic geometry.pdf
https://www85.zippyshare.com/v/KlmasMXQ/file.html
Arcaute, Lasenby, Doran_2008_Twistors in Geometric Algebra.pdf
https://www85.zippyshare.com/v/oUkqbFEq/file.html
Arthan_2006_A Minimalist Construction of the Geometric Algebra.pdf
https://www85.zippyshare.com/v/Y7AAJiv4/file.html
Bales_2011_The Clifford Twist.pdf
https://www85.zippyshare.com/v/zc9154YC/file.html
Bohm, Hiley_1984_Generalisation of the twistor to Clifford algebras as a basis for geometry.pdf
https://www85.zippyshare.com/v/ht48RyHP/file.html
Boi_2009_Clifford Geometric Algebras, Spin Manifolds, and Group Actions in Mathematics and Physics.pdf

>>12771396

https://www85.zippyshare.com/v/nl8Ny2Dg/file.html
Bouma, Dorst, Pijls_2001_Geometric Algebra for Subspace Operations.pdf
https://www85.zippyshare.com/v/l7Wex4GJ/file.html
Brannen_2005_Particle Symmetry Breaking in Density Matrix Formalism with Geometric Algebra.pdf
https://www85.zippyshare.com/v/7BWOGcla/file.html
Castro, Pavšič_2003_Clifford Algebra of Spacetime and the Conformal Group.pdf
https://www85.zippyshare.com/v/gW4CJF1I/file.html
Castro_2010_Generalized Gravity in Clifford Spaces , Vacuum Energy and Grand Unification.pdf
https://www85.zippyshare.com/v/HThajlhc/file.html
Chappell et al._2012_An explanation for galaxy rotation curves using a Clifford multivector spacetime framework.pdf
https://www85.zippyshare.com/v/R0asfGY4/file.html
Chappell, Iqbal, Abbott_2011_Geometric Algebra A natural representation of three-space.pdf
https://www85.zippyshare.com/v/6e11tSYt/file.html
Clifford_1878_Applications of Grassmann's extensive algebra.pdf
https://www85.zippyshare.com/v/rU9osG42/file.html
Conte_2010_A Reformulation of von Neumann’s Postulates on Quantum Measurement by Using Two Theorems in Clifford Algebra.pdf
https://www85.zippyshare.com/v/KC5FV16i/file.html
Conte_2011_An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra.pdf
https://www85.zippyshare.com/v/VWDMhFCD/file.html
Cortzen_2010_Direct Construction of Grassmann, Clifford and Geometric Algebras.pdf
https://www85.zippyshare.com/v/ajUzUqf6/file.html
da Rocha, Vaz_2004_Revisiting Clifford algebras and spinors II Weyl spinors in Cl(3,0) and Cl(0,3) and the Dirac equation.pdf
https://www85.zippyshare.com/v/pMBXjJOm/file.html
da Rocha, Vaz_2004_Revisiting Clifford algebras and spinors III conformal structures and twistors in the paravector model of spacetime.pdf
https://www85.zippyshare.com/v/GrsacWha/file.html

da Rocha, Vaz_2006_On Clifford Subalgebras, Spacetime Splittings and Applications.pdf
https://www85.zippyshare.com/v/7JQnfCF9/file.html
Dixon_1978_Super Clifford algebra.pdf
https://www85.zippyshare.com/v/JBwlM5Xb/file.html
Fauser_1996_Vertex normal ordering as a consequence of nonsymmetric bilinear forms in Clifford algebras.pdf
https://www85.zippyshare.com/v/b1OXHOv0/file.html
Fauser_1998_On an easy transition from operator dynamics to generating functionals by Clifford algebras.pdf
https://www85.zippyshare.com/v/qL5btQAk/file.html
Fauser_1999_Hecke algebra representations within Clifford geometric algebras of multivectors.pdf
https://www85.zippyshare.com/v/wtD7FU97/file.html
Fauser_2000_On the relation of Manin's quantum plane and quantum Clifford algebras.pdf
https://www85.zippyshare.com/v/IVa0X1hX/file.html
Fauser_2001_Clifford geometric parameterization of inequivalent vacua.pdf
https://www85.zippyshare.com/v/fCr1KAjQ/file.html
Fauser_2003_Quantum Clifford Hopf gebra for quantum field theory.pdf
https://www85.zippyshare.com/v/TDHahdh8/file.html
Francis, Kosowsky_2005_The construction of spinors in geometric algebra.pdf
https://www85.zippyshare.com/v/nKDouiJk/file.html
Gallier_2009_Clifford Algebras, Clifford Groups, and a Generalization of the Quaternions The Pin and Spin Groups.pdf
https://www85.zippyshare.com/v/9IaHaWjB/file.html

Gonzato_2005_Algèbres de Clifford.pdf
https://www85.zippyshare.com/v/O5gydymh/file.html
Havel, Doran_2000_Geometric Algebra in Quantum Information Processing.pdf
https://www85.zippyshare.com/v/KSW3G1Ue/file.html
Havel, Doran_2004_A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space.pdf
https://www85.zippyshare.com/v/wVIbU47g/file.html
Hestenes, Holt_2007_Crystallographic space groups in geometric algebra.pdf
https://www85.zippyshare.com/v/nZbvc2As/file.html
Hestenes, Ziegler_1991_Projective geometry with Clifford algebra.pdf
https://www85.zippyshare.com/v/AHO5P9x4/file.html
Hestenes_1986_Clifford Algebra and the interpretation of quantum mechanics.pdf
https://www85.zippyshare.com/v/txzS5wC4/file.html
Hestenes_2003_Spacetime physics with geometric algebra.pdf
https://www85.zippyshare.com/v/ST92HYLR/file.html
Hiley, Callaghan_2010_The Clifford Algebra approach to Quantum Mechanics A The Schroedinger and Pauli Particles.pdf
https://www85.zippyshare.com/v/vW7a3OaD/file.html
Hiley, Callaghan_2010_The Clifford Algebra Approach to Quantum Mechanics B The Dirac Particle and its relation to the Bohm Approach.pdf
https://www85.zippyshare.com/v/NjlYU5j4/file.html
Hiley, Callaghan_2011_Clifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation.pdf
https://www85.zippyshare.com/v/FI2fB8o3/file.html
Hiley_2011_Process, Distinction, Groupoids and Clifford Algebras an Alternative View of the Quantum Formalism.pdf
https://www85.zippyshare.com/v/28QnDdwP/file.html
Hitzer_2003_Axioms of Geometric Algebra.pdf
https://www85.zippyshare.com/v/gMrEzugw/file.html
Horn_2006_Quaternions and Geometric Algebra.pdf
https://www85.zippyshare.com/v/JkPskW2l/file.html
Jagannathan_2010_On generalized Clifford algebras and their physical applications.pdf
https://www85.zippyshare.com/v/oBlHvIOL/file.html
Kock_2010_Geometric algebra of projective lines.pdf
https://www85.zippyshare.com/v/NRsiHym7/file.html

Kwaśniewski, Bajguz, Jaroszewski_1998_On quantum mechanics and generalized Clifford algebras.pdf
https://www85.zippyshare.com/v/90iFIJy2/file.html
Lachièze-Rey_2009_Spin and Clifford Algebras, an Introduction.pdf
https://www85.zippyshare.com/v/ObvwWdu2/file.html
Lasenby, Doran, Gull_1998_Gravity, gauge theories and geometric algebra.pdf
https://www85.zippyshare.com/v/3xlQJveD/file.html
Lasenby, Doran, Gull_2004_Gravity, Gauge Theories and Geometric Algebra.pdf
https://www85.zippyshare.com/v/8wGRxhHi/file.html
Lounesto_1996_Counter-examples in Clifford algebras.pdf
https://www85.zippyshare.com/v/XwclQp33/file.html
Lu_2010_Yang-Mills Interactions and Gravity in Terms of Clifford Algebra.pdf
https://www85.zippyshare.com/v/52KSLAwF/file.html
Lundholm, Svensson_2009_Clifford algebra, geometric algebra, and applications.pdf
https://www85.zippyshare.com/v/f1DgeFWK/file.html
Macdonald, College_2009_A Survey of Geometric Algebra and Geometric Calculus.pdf
https://www85.zippyshare.com/v/e2iLghhn/file.html
Macdonald_2002_An elementary construction of the geometric algebra.pdf
https://www85.zippyshare.com/v/faDKCIBU/file.html
Makkab_2005_Idempotents et Representations de Certaines Algebres de Clifford.pdf
https://www85.zippyshare.com/v/nbUD4hHD/file.html
Pappas_2001_The geometric algebraCl 3 as a model for a projective plane.pdf
https://www85.zippyshare.com/v/FUxZA4bx/file.html
Pavšič_2003_Clifford Space as the Arena for Physics.pdf
https://www85.zippyshare.com/v/gwTdRnYc/file.html

Pavšič_2005_Clifford Space as a Generalization of Spacetime Prospects for QFT of Point Particles and Strings.pdf
https://www85.zippyshare.com/v/yjwOStyG/file.html
Plotkin, Aladova, Plotkin_2011_Algebraic logic and logically-geometric types in varieties of algebras.pdf
https://www85.zippyshare.com/v/1tLs333d/file.html
Pozo, Sobczyk_2002_Geometric algebra in linear algebra and geometry.pdf
https://www85.zippyshare.com/v/pRlrlLcA/file.html
Salingaros, Dresden_1983_Physical algebras in four dimensions. I. The Clifford algebra in Minkowski spacetime.pdf
https://www85.zippyshare.com/v/Inaqmn3t/file.html
Sobczyk_2010_Unitary Geometric Algebra.pdf
https://www85.zippyshare.com/v/V4mdQ4nS/file.html
Toen, Vezzosi_2004_Homotopical Algebraic Geometry II geometric stacks and applications.pdf
https://www85.zippyshare.com/v/yNUi9kJI/file.html
Traubenberg_2009_Clifford Algebras in Physics.pdf
https://www85.zippyshare.com/v/6PTrBOkz/file.html
Ulrych_2006_Gravitoelectromagnetism in a complex Clifford algebra.pdf
https://www85.zippyshare.com/v/UEaybyiV/file.html
Wene_1989_The Clifford algebra of an infinite-dimensional space.pdf
https://www85.zippyshare.com/v/W54kftWE/file.html

>>12771043
Probably (Functional-) Analysis.
Can't really count linear algebra, and its pretty trivial anyways.

do any of you PhDfags or PhDfags in the making regret your decisions? How is the pay? Is it as cucked as alot of anons complain? I need answers now!

>>12765558
Some of the basics of derived categories

>>12765558
Algebraic Number Theory. Apostel is kicking my ass. What an awful book but the course is based around it.

>>12772535
>awful book
Dumbass...

>>12772700
Quite possibly but while it may be a great reference book it's shit for explaining / learning.

>>12768439
Algebraic topology will be done only after all the homotopy groups of spheres are known.

>>12769669
I have been enjoying Lang

>>12761302
What's funny is that if you subtract the linear term (which is n/e idk why) you have miniscule logarithmic term which doesn't converge either. Can't figure out the scaling of the log term, seems close to log(n)/e^2.
>>12761088
>>12761103
Fun troll function

Are there any courses on good universities open to the general public or students from other institutions?
Mine allows me to get credits through online courses from other institutions, so I need to know what opportunities are out there.
I'm particularly interested on courses about Algebraic Geometry, Algebraic Curves, Arithmetic Geometry and Commutative Algebra. Nothing too advanced though, I'm still starting on those areas.