Math General

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>>8761147
first fro ct

http://www.freebookcentre.net/SpecialCat/Free-Mathematics-Books-Download.html

This is the best collection of free online texts I've seen. Has texts on pretty much every subject of mathematics except logic and a few specific sub fields.

general advice for an undergrad math major?

>>8761419
about mathematics itself or academics/careers?

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>>8761147
>what are you studying?
Renormalization techniques for TQFT.
One of the defining features of a TQFT is the functoriality [math]\tau(M) = k \tau(M_1)\circ f_{\#} \circ \tau(M_2)[/math] where [math]k\in K[/math] is an invertible element of the ground ring, and [math]M[/math] is a [math]\mathscr{B}[/math]-space glued together from two cobordisms [math]M_{1,2}[/math] along the [math]\mathscr{A}[/math]-homeomorphism [math]f: \partial_+ M_1 \rightarrow \partial_- M_2[/math]. A TQFT is said to be anomaly-free if [math]k = \operatorname{id}_K[/math].
Apparently the existence of a [math]G[/math]-valued 2-cocycle [math]g \in \mathscr{P} \otimes G[/math], where [math]\mathscr{P} = \{P = (M,N,f) \mid M, N \in \mathscr{B}, f: \partial_+M \rightarrow \partial_- N\}[/math] is the collection of gluing patterns [math]P[/math] between [math]\mathscr{B}[/math]-spaces, on the cobordism theory [math](\mathscr{B},\mathscr{A})[/math]is sufficient to guarantee that the TQFT [math](\mathscr{T},\tau)[/math] based on it (possibly with anomalies) can be made anomaly-free.
This is a generalization of the usual process of renormalization in QFT where the quantum anomalies are gauged away by gauge-fixing in gauge-space (say that three times fast). The [math]k[/math] can be thought of as an obstruction to the quantum Ward identities.

>>8761475
99.7% sure the majority of uses of renormalization are not cases where you can sharp ans sweet get rid of particularly well specified QFT anomalies

>>8761475
Your overly verbose posts are genuinely cringe-inducing. Especially since what you keep yammering on about is (non-deep) category theory and elementary topology thinly veiled in pretentious physics lingo.

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>>8761504
And those would correspond to cases where you can't find the 2-cocycle.
Remember that TQFTs only contains topological data. Normal QFTs also contains dynamical data that needs to be taken into account when renormalizing. This is part of the reason why non-renormalizability is rampant in QFTs with non-Abelian interactions or non-conformal geometry.

some resources for computer science math for beginner?

>>8761537
SICP

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Samurai > Wizard

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Well, /sci/?

>>8761537
http://4chan-science.wikia.com/wiki/Computer_Science_and_Engineering#Mathematics_Primer

especially recommend concrete mathematics

>>8761616
Do you're own homework

>>8761670
no your do you're own homework

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Im studding derivatives but im stuck on how the highlighted part becomes possible.

>>8761728
its literally just the last equality rearranged to put the cosines and sines on the same side

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>you are now manually thinking

>>8761475
What a useless subject.

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>>8761737
>you suddenly feel itchy
(but in an abstract kind of way)

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>>8761737

>>8761736
I see now, also could you please explain why 2x is infront of sin2y. i dont know where it came from

>>8761759
the 2 comes from when u use the chain rule on cos(2y)

the x is in front of cos(2y) already

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>>8761769
Thanks mate its all clear now.

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>>8761740
Say that to me irl not online see what happens I'll hook you in your gabber

>>8761808
Name one possible use.

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>>8761823
Are you asking how a topological quantum field theory can be used when a large chunk of the previous thread had been people talking about using it for topological superconductors?

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Why didn't you protect his smile /sci/?

>>8761147
>what are you studying?
Trying to teach myself some measure theory.
>any good problems?
Here's an easy problem with a cute solution: you have a jar with 20 blue balls and 10 red balls. You remove balls one at a time until only one color is left in the jar. What is the probability that only red balls are left in the jar at the end of this procedure?
>cool theorems?
This was a problem in the measure theory book I've been working through that was satisfying to prove: A sigma algebra cannot be countable.

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>>8761853
A sigma algebra of [math]\mathbb{R}[/math], perhaps? Given any finite set, all the sigma algebras would be countable.

>>8761873
Countable as in countably infinite. The cardinality cannot be [math]\aleph_0[/math].

>>8761147
hope im not entering an undergrad thread
>researching
electrochemical materials for Li and Mg batteries
>studying
organometallics and solid state chemistry as well as electrochemical engineering
>any good problems?
yeah, how do I avoid high order lithium polysulfides forming in a Lithium sulfur battery? How do I make a solid state Lithium battery with a conductivity high enough to match liquid electrolytes? how do I get a magnesium battery to work reliably?
>book recommendations
Hartwig organometallics, Handbook of batteries by Linden
>cool theorems
no

>>8761878
Doesn't sound like math to me.

>>8761878
>retard can't even read the subject of the thread

>>8761874
Well isn't that immediate? A sigma algebra is a subset of [math]\mathcal{P}(X)[/math] which is uncountable for countable [math]X[/math].

>>8761897
What if you have a countable subset of [math]\mathcal{P}(x)[/math]? Why can't that set be a sigma algebra?

>>8761901
Closure under arbitrary union

>>8761905
A sigma algebra is closed under countable, not arbitrary union.

>>8761878
>engineers literally cannot read
bravo brainlets

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>>8761909
Oh I was thinking of a topology

>>8761450
Both

>>8761919
Not to mention the fact that you can have countable topologies (see the cofinite topology on IN)

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>>8761308
:DDDDDD

>niggers making new generals before the other one even hits bump limit, let alone dies
why

>>8761901
How about {{},X}

>>8761878
300k startin for a 30 iq

>>8762118
That is a sigma algebra, when I said countable, I mean countably infinite.

any canadians?

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>>8762246
sup

ubc here

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>>8762246
Yes.
>>8762247
Wtf same what are you studying? I may have TA'd you before rofl

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>>8762250
i'm a grad student

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>>8762257
>he's a gorillaposter
Math?

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>>8762259
>Math?
of course

[too close for comfort]

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>>8762262
Ok good, I'm in physics.

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>>8762264
i definitely have no idea who you are then, i only know one person who went from physics to math

is the physics dept good here?

I have to give a presentation on that paper : https://arxiv.org/pdf/0906.5137.pdf

If anyone has an elementary proof that two quaternion algebras on a local field that have the same subfields are isomorphic I'd gladly take it.

I know there are only two (up to isomorphism) quaternion algebras on such fields, one that is split and one that is division.

I thought every quadratic extension would embed in the split one but I read somewhere that it was the case for the division one, and I'm a bit lost.

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>>8762272
>is the physics dept good here?
It's pretty good, there are a few world-renowned condensed matter theorists that I work with here and the high energy team is also pretty strong I've heard. It's very competitive for physics here, I imagine that being the same for math as well?

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>>8762296
idk how competitive it is (i got in lol) but there's some great algebraists/topologists/geometers/number theorists here at least, i don't know much about the applied people

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>>8762296
you going to the 'Supermassive Black Holes' talk on wednesday?

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>>8762312
That's cool. It'd be nice to talk to them about some of my categorical ideas but I don't have the time to do substantial research (and I don't want to waste their time). Also I'm heading off to McMaster for my PhD since it's much more chill there.
>>8762317
No I don't like astrology.

>>8761616
am i just high rn or is the centered display symmetric in ij?

i wanna skip from linear algebra to topology. what do

>>8761853
1/(30 choose 10) ?

>>8762341
>i wanna skip from linear algebra to topology. what do

Stop being a brainlet, they're unrelated and you can learn them both at the same time, and they're both important topics.

>>8761853
let S be a non-finite sigma algebra. suppose we have an enumeration of all sets in S in disjunctive normal form. we can use closure under complements to do something cantor diagonalization-esque.

>>8762341
treat the classes as a day job and learn whatever the hell you want to

look up prerequisite knowledge as you need it

>>8762264
Do you work with Ian Affleck?

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>>8762505
I-I'd rather not say

>>8762514
I am a mathematical physicist, I am not a leaf though, I just have seen your posts in these threads and I remember skimming some of his work.

>>8762572
Well grad student and more on the math side.

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>>8762572
That's cool. Yeah my posts here aren't at all representative of the work I do with Ian, he's very smart the more physical sense.

God damn error bounds of Composite Simpsons Rule. Our coursework gives [math]f(t) = \frac{W(t)Q(t)}{M(t)}, W(t) = 3000\left(1+\frac{t}{T}\right), Q(t) = \frac{500000}{256}\text{exp}\left(-\frac{t}{12T} - \left(\frac{t}{T}\right)^3 \right), M(t) = 500000 - \int^t_0Q(x)dx[\math] and wants us to find the maximum value of [math]f^{(4)}(t)[/math]

oh yeah. He also wants it done by hand.

Fuck this class

>>8762648
god damn it I got all the formatting right and fuck up on the /math

>>8761601
question mark is the drowned god.

>>8762348
Nope. This has more of an ah-ha solution than a brutal calculation.
>>8762360
I'm not really sure what you mean by disjunctive normal form, and google isn't too helpful.

>>8762247
>>8762250
Same UBC here too, I'm BIE (Econ) first year

>>8761147
Taking topology research. Basically baby's first research class. Not bad. Doing motion planning based off of Father's work

>>8762745
>Farber's
Fixed

How much math do I need to know if I want to understand the anime categorist's posts?

I'm done with calculus and diff eq and will be taking abstract algebra and real analysis next semester

>>8762750
category theory can be a standalone activity

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>>8762750
I'm a physicist, not a category theorist. My goal is to find a way to use and abuse category theory like a dogtoy as a tool for physics.
You can find some resource recs in the prevoous thread. You can follow the chain starting from here >>8748655.

>>8762246
I got into Waterloo for graduate pure math.

WTF Real analysis
WHY CANT I FUCKIN STUDY FOR A TEST 5 DAYS PRIOR AND ACE IT? WHY THE FUCK DO I HAVE TO PAY ATTENTION TO LECTURE AND DO HW AND NOT MASTER THE Material 5 days prior? MATH IS A SHIT MAJOR SHITTTT

>>8762246
ay yo UoA here

>>8762839
real analysis is about as bad as undergrad gets tho

>>8762768

No, it can't.

>>8762854
yes it can

>>8762854

What do you need to know?

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Not a shitpost:

Alright guys, I'm sure you've heard this a million times, but I need some help with the Monty Hall Problem. Before you skip the rest of this, I understand the basic idea that switching gives you 2/3 chance of winning. The issue I have is that people keep telling me that it only works if the host already knows which door is the right one, and then intentionally chooses to reveal an incorrect door. Why would this be true? The problem already ensures that Monty did end up revealing the door with the goat. At what point does the logic of "He reveals a goat. At this point if you switch you will get the prize you didn't initially choose. You had a 1/3 chance of choosing the car so switching gives you a 1/3 chance of getting the goat." rely on him knowing what he's going to reveal?

To put it another way, imagine you were running the Monty Hall problem yourself, with no host. You randomly pick a door. You reveal a second door. If it is a goat, proceed as the standard problem. If it is the car, your universe is invalid. In what way does this situation mathematically differ from the original problem (if at all)?

>>8762930
For him to always reveal a goat he needs to know where the goats are. If he didn't then he would guess himself and sometimes he would reveal the car's location instead.

>>8762930
You have the chance of the random selection opening the door with the car or prize behind it. What the fuck is the point then if you know exactly which door to pick, given you literally and physically see the car behind one of the opened doors. Or are you then limited to choose between two remaining doors you know for a fact both contain goats. That would be absurd and the example would have no practical application.

>>8761853
>>8761853
this is interesting, what's the solution ?

>>8762947
>>8762951
Let me try to explain better:

You have two goats and a car. You put them behind doors and then they are randomly shuffled so you have no knowledge of any of them. You select a door but don't open it yet. You then select a second door and open that one.

By random chance it happens that the second door contains a goat. This always happens. It is preestablished in the rules of the scenario. If you did happen to reveal a car, throw out the whole scenario and start over. The question only takes place in universes where you happened to reveal a goat. You are now faced with the choice to switch or not.

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How would you do this?

>>8761853
1/3

>>8762960
If in this universe he always reveals the goat by chance, then it is the exact same as the other universe where he reveal the goat knowingly. What is in his mind does not affect the outcome of the game if it results in him taking the exact same actions as it would if something else was in his mind.

>>8762994
Thanks. That's what I assumed, since the original problem states that he did in fact reveal a goat.

>>8762965
Since the ray starts at the origin, it will not perfectly repeat since if it did, it would repeat infinitely in both directions, and every line passing through the origin will escape immediately in at least one direction. The only other case is convergence, but that is impossible with convex surfaces.

>>8763012
You sure?
>there is a unique trapped ray from any starting point, but it is not trapped in backward time unless it is on the shortest path between the bodies. One can find it by minimizing distance of a zig-zag path alternately touching the two bodies a finite number of times, then passing to a limit.

>>8761147
Is Georgi Polyas How to solve it worth buying, or should i just keep lending it from the local library?

What are some good introductory discrete math/combinatorics/graph theory books

>>8763222
Combinatorics: Topics, Techniques Algorithms

>>8763115
overrated imo
just do sum exercises

>>8761147
>what are you researching

nothing

>What are you studying

MATH + CS with STAT Minor

>Any good problems

projecteuler.net is pretty good

>Book recommendations

Introduction to Algorithms by CLRS

TOC by Sipser

Baby Rudin

Graph Theory by Murty and Bondy

Freedman's Statistics

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>>8762738
>>8762250
what's the best place to eat on campus boys?

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>>8763408
Once I ate at the cafeteria next to a roastie and her chad friends. She said to the table that she likes sex to much to be fucked by a virgin

>>8762971
Correct!
>>8762955
Imagine you put all the balls in a line as you removed them from the jar. Then you want to know what color the block at the end of the line is. This is determined by what color the last ball is, so there's a 1/3 probability it is red.

I'm giving a talk about Jacobian varieties of curves, mostly following some notes of Milne. Does anyone know of any arithmetic results they feel would be wrong to leave out of a one hour talk?

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>>8763408
McDicks

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>>8763966
>not going to the cheap asian food court two doors to the right

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>>8763968
But I could eat all the Chinese food I want at home

>>8762352
>>8762361
I downloaded Topoly by Munkres. I read chapter 1 up to relations and gave up. Are relations talked about in a set theory class?

Send help.

I suck at analysis. I do well in Algebra and Geometry/Topology, but Analysis is just moonrunes to me. How can I improve? I feel like I'm just not thinking about things in the right way.

- t. Undergrad taking first year grad sequence in Alg/Topology/Analysis

>>8764153
What book are you using? What is your background?

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>>8764088
I probably should have just assumed you were Chinese

Do you have any homies in math?

>>8764126
If you can't handle that, you probably don't have the mathematical maturity for the rest of the book. Either be patient and try to take it more slowly, or spend your time reading any easier introduction to proofs style book.

>>8764153
Here are some helpful tips: https://terrytao.wordpress.com/2010/10/21/245a-problem-solving-strategies/
Often in analysis most of the challenging part is thinking about things in the right way. Spend your time drawing lots of pictures, it's a very visual subject.

everybody learns math and shit and im here like an ape looking at rods and pistons

>>8764160
Last semster was Folland, this semester is Ahlfors. Complex is a lot more intuitive than real analysis, but still not as intuitive as algebra or topology/geometry.

Analysis background is a class in Rudin, then a class using a text by Capinski and Kopp, then a class using a text by James Brown.

>>8764167
Thanks. It's visualizing it I suppose and thinking about things in the proper way I struggle with. Often times in analysis, when figuring out the solution to a problem, it feels like it's relying on a sneaky little 'gotcha!' trick that you just need to uncover.

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>>8764161
[sboiler]No.[/sboiler] Maybe a few acquaintances.

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>>8764223
>Maybe a few acquaintances
i-is that you Justin?

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>>8764232
No.

>>8764126

relations are a concept from logic, not math, which is why they seem foreign and thus "hard". brush up on same baby propositional logic, work your way into predicate logic, and then realize that set theory is just predicate logic with some new "operations" (lol, if you can call them that) and voila, we've pulled the beard off the giant and relations are no longer scary. imho logic is actually a lot of hand waving and (and can often devolve into posturing (transfinite recursion)) much easier than math once you overcome your fear of speaking broadly about things and realize you can abuse pretty much anything with disjunctive elimination. logic is kind of a desk organizer that thinks very highly of itself. Useful, but only necessary if you're braindead. hopefully you were thinking logically before you "studied" logic so it should be more about learning standard notation and not concepts or techniques. you might notice that there are a lot of monkey-see-monkey-do grad student types on sci who can only regurgitate what they read in the Official Text (people who couldn't pass the turing test) who are also going to try and brow beat you with esoteric looking notation to compensate for their lack of insight into the subject, but don't let them get to you- Logic isn't that scary.

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>mfw I walk into my office with a girl inside

So I am trying to solve fundamental set of solutions for a problem. y1 = cos log(x). I can easily find the first derivative but any tips on finding the second derivative? I could break it down into -(1/x)sin log(x) but can you use the product rule on 1/x and sin log(x) while ignoring log(x)?

I am really shit at integrating and finding derivatives.

>>8765147
nevermind, I figured it out. I need to use the quotient rule.

>>8764860
Lol thanks

>>8764250
zheng shi ?

bumpity

>>8761832
>>8761808
>>8761475
Take your pedophile cartoons back to >>>/a/

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>>8766098
ur 1st day on 4chan?

>>8766105
I think most people just have a problem with the avatar-fagging. Just a tip.

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>>8766173
ur 1st day on 4chan?

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>>8766173
Posting with pics of different anime characters attached is not avatarfagging. Just a tip.

>>8766174
No, but I am providing insight into why people tend to be not so amicable with you.

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>>8766179
>No, but I am providing insight into why people tend to be not so amicable with you.
speak for yourself, i find most responses to be amicable

>>8766178
>http://www.urbandictionary.com/define.php?term=Avatarfag
>A person using a genre/character/show/topic specific picture, an "avatar", accompanying each post on 4chan, typically with the reaction image of the "avatar" relevant to the tone of the post.
>genre [...] topic

Welp. Gotta go fast!

>>8765449

yw buddy. Just remember when things get spooky and estoteric looking, there are two options that will demystify it most of the time:

1. reading the history. were there any earlier versions of this concept? is it actually original or just restated in modern jargon? is the original easier to understand?

This usually takes care of a lot of "hard" concepts. If you trace topology back to its origins with leibniz and then work your way forward into algebraic topology, category theory stops looking like "advanced math" and starts looking like more like clerical property checking (transitivity, associativity, commutativity) for transformations on big hairy "systems".

2. Madlibs and drawing. This should really take care of anything that 1. couldn't finish. By rearranging the nouns and verbs you are essentially playing a medieval syllogism game with the definitions. This won't necessarily shed light on the concepts, but it will at least allow you to abuse substitution rules for predicates and start writing true statements. If you're still not "seeing it," just make a drawing. Seriously. It amazes me how few people make drawings when they're trying to understand something (and then when they do, they go, "Ooooohh why did you say so!" Lesson: skip semantics and get right to the "Ooooh!" with a picture. It seems to be a mixture of pride and something else, maybe people think making drawing is "cheating." Bizarre. I wouldn't be surprised if most of it was a hangover from millennia of observing the second commandment. You're not going to executed for depicting g-d's image, so don't worry. Do what works so you can understand the concept.

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>>8766190

> @8766186

Get back to >>>/r/eddit

>>8766497
>this new

I want to start studying modular forms. Here's a syllabus I made for myself. I am using Apostol's book and Serre's Arithmetic:

Elliptic functions: lattices, Weierstrass p-function, Eisenstein series, the discriminant, the j-function. The modular group: fundamental domain, modular functions/forms, zeros/poles of modular functions, rational functions of j. General facts about Fourier series, Fourier expansions of these functions.

The Hecke theory: A brief review of Dirichlet series. Spaces of modular forms, Hecke operators. Eigenfunctions of Hecke operators, product expansions of Dirichlet series. More about Eisenstein series and the discriminant.

Is there anything I'm leaving out? What should I know about Ramanujan's tau function and the Dedekind eta function? What's something cool to study after all this?

>>8766581
>Is there anything I'm leaving out?
might as well study the L-function associated to a modular form, L-functions show up everywhere and are pretty interesting

> What's something cool to study after all this?
automorphic forms, automorphic representations, modular forms of half-integral weight, the list goes on... knowing modular forms opens tons of doors

Anyone want to do a grad level reading group? We could maybe do an irc channel? What interests do you all have at the grad level?

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>>8767292
Geometric quantization.

>>8767320
Quantum geometry

>>8767320
What book would we read for that?

>>8767292
This might be a silly question, but you're at the grad level and don't know anyone in real life you could read with?

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>>8767338
Guillemin & Sternberg for an introduction from physics and Woodhouse for a general overview.

>>8767343
Everyone else is either too busy, or master in stats.

>>8767358
I was thinking a more pure math topic rather than physics. Are there any purer books than Woodhouse?

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>>8767365
Why don't you take a look yourself and find out? It being inspired from physics doesn't mean it's physics.

>>8767368
It is more physics-centric than math centric. I do symplectic geometry, so I do get my fair share of physics-inspired mathematics. In my brief search on google I could not find anything apart from half a dozen of more pure research papers that would not be suitable for a group reading.

>>8766098
i missed this meme. welcome back friendo!

>Parallel shit bitch don't get lined up
>Ugh, ugh
>Sosa in his prime huh

pump

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Finishing up geometry
On my through trigonometry
Then precalculas
Then calculus

I get so excited thinking about doing calculus and all the problems I can now solve . I am already seeing how powerful trigonometry is in solving simple geometry problems. Just imagining what Calculus can do is so intense to think about .

Here the quick rundown on my daily routine

1) study algebra and geometry for 15-30 minutes

2) Practice 3 algebra and 3 geometry problems

2)Study Trigonometry 15-30 mins

3) do at minimum 15 trigonometry problems but usually average 30 trigonometry problems and occasionally max out at 50 trigonometry problems

>>8768128
nigga u taking rest days? dont wanna overtrain breh

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are these based?

>>8768309
I torrented these and flipped through them for a bit after I read the maa review. They're cool looking books but they're fucking weird. Something like 2/3 of the first volume is linear algebra. Groups get deferred until page 300-ish, which is usually page 30 of an algebra book. There's no real field stuff at all until volume 2.

I can't imagine who the hell the audience was supposed to be but they're neat things anyway.

>>8768128
is that a new mass effect pepe a-anon?

what are good unis for algebraic geometry

Calc 2 is so fucking SHIT

>>8768482
Paris VI (also good if you like "pure" algebra: representation theory, Lie algebras etc.), Paris VII (also good for the interactions with model theory), Paris XI, ENS Paris, Lyon I (again, also good for pure algebra), ENS Lyon (if you're more into arithmetic algebraic geometry and number theory)

>>8768508
>it's all french
damn it, won't be able to avoid learning french I guess
thanks anyway!

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>>8768508
Are those good for algebraic topology?

>>8768482
Like...undergrad? What a bizarre question if so.

>>8768592
no for grad school ofc

>>8768634
Okay, kind of a weird way to phrase it but here it goes. It partially depends on what kind of AG you like, e.g. birational or complex geometry differ wildly from derived AG or arithmetic AG. So there are obvious ones like Harvard, Princeton, Columbia, Berkeley but also schools like Michigan, Utah, UIC, Wisc with strong groups.

>>8768646
as for it is right now a tendency towards complex geometry, I should have been more specific.
I just have no idea how to find out which uni is good on what area (I mean yeah they can write stuff on their website, but I dont know how good that actually might be)

>>8768652
Ask professors at your school. They will be well aware of where good things are happening.

>>8768675
also did that
just want to get as many opinions as possible

>>8768652
What kind of complex geometry?

>>8768701
Kaehler-Manifolds, cohomology of differential forms
maybe also higher dimensional varietes

>>8768710
>Kaehler-Manifolds,

Kahler Geometry is generally a more analytic subject. Well you do have a theorem like "every compact kahler mfld with rational kahler class is equivalent to a smooth projective variety". But Kahler mflds are characterized by their metrics, so it isn't really something you can forget and still study the thing properly.

>>8768732
well it is more of a differential geometry approach and I can see vector bundles maybe being a helpful subject in these studies, so you might do a bit AG stuff there. I thought of it maybe rather as an example of my interests

>>8766173
I don't have a problem with this guy. I see him a lot on /sci/. I kinda like the anime-math mix tbhq; it takes a serious subject and puts it together with immature little girls and its delightfully absurd

>>8768515
I think the Paris area is basically the biggst french hub for all kinds of math so the parisian ones are probably good. I also have a friend doing his PhD in knot theory at UFJ Grenoble and I hear they do great work in algebraic topology over there (there are also good complex geometers and algebraists there)

Here i am barely grasping limit functions even though the theorems and definitions sound ez, i cannot do one by myself. and my test is tomorrow

On top of that, my proffesor and peers grin or laugh whenever i mention something that was not obvious to me but it was to them, and when i ask them to explain it, they dont want to.

When do i know when to quit pursuing a math career?

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I hate categories and I want to die

what level of math do i have to be at to use that fancy circle with a cross symbol

>>8769049
most likely linear algebra
>inb4 cross product

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>>8769049
[math]\otimes[/math] denotes the tensor product, https://en.wikipedia.org/wiki/Tensor_product. Just read some group theory and commutative algebra.

>>8768875
Thanks for the answer, I'll see what they have to offer.

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>>8769070
w-why would you recommend group theory for tensor products?

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>>8769076
To give a strong understanding of what modules, and rings, are. Just abelian groups with extra structure, and knowing groups also helps knowing ideals, or the submodules of a unitary ring thought of as a module over itself. There is also (because they are modules over the integers) tensor product of abelian groups. Note the word 'some', too.

if x - > a and x -> b then x > a and b?

why isnt this used in cont. functions instead of making two different theorems?? (i.e. boundness and min max theorem?) they literally have the same hypothesis

I think integration is funner than differentiation. Anyone else agree?

How can I check if a function is positive, continuous, and decreasing?

>>8769111
Is it above the x axis? If yes it's positive

Does it contain a continuous line with no breaks or values that are not included (open intervals)? If yes it's continuous

Is the slope at the given interval negative? It's decreasing

>>8769118
How would you find all that out with just a function?

>>8769118
f(x_n)< f(x_(n+1)) for all n that belong in N

and so on

do u kno induction?

>>8769122
Well of the output f(x) contains only positive values then the function is positive.

If the a of x-->a is in the domain of f, and the limit of the function exists and a is = to the limit then the function is continuous. Polynomial, root, trig and power functions are always continuous.

If the values of the output f(x) decrease as x approaches a then the function is decreasing.

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>>8767380
>It is more physics-centric than math centric.
Wrong, but I wouldn't expect you to know that since you're a reactionary towards anything that isn't borne out of abstract gibberish.

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>>8769172
You're on here a lot, do you shitpost from Hennings?

>>8768128
>dience was supposed to be but they're neat things anyway.
what book of trigonometry you use?

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>>what are you researching?
nothing
>>what are you studying?
System engineer
>>any good problems?
I learn analysis with poor base in geometry and trigonometry and i hate trigonometry any way to learn only base of trigonometry
>>book recommendations?
An introduction to Kolmogorov complexity and its applications and topology by munkres
>>cool theorems?
https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem

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>>8769174
I'm actually posting from the gym right now.

>>8769172
>"i don't understand how people can do mathematics with no applications"
the post

>>8769243
>not automatically disliking mathematics inspired from other disciplines means that you don't understand why people do pure math
Fucking retard.

Can you do pure maths while being a physicist, or are the two so different ?

>>8769272
Depends what you mean by "do" pure maths.

>>8769272
Edward Witten

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http://archive.is/g4Q1T
> Abel Prize 2017: Yves Meyer wins 'maths Nobel' for work on wavelets

>>8769278
I mean researching stuff in pure maths alongside doing physics.

>>8769282
He didn't do his phD in physics tho. And I'm probably not as smart as him.

>>8769286
>2^11-2^5+2^0
>not researching on wavelets

fucking brainlets

>>8769299
thats 2018 brainlet

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>>8769307
>not doing your 2018 research in 2017
brainlet

>>8769307
Wrong.

>>8769297
>He didn't do his phD in physics tho
Yes he did. Witten has a PhD in physics from Princeton

>>8769172
>>8769265
>``stop liking things I don't like!!!''

Any geometry students apply to this?
http://www3.nd.edu/~cmnd/programs/cmnd2017/

>>8769357
>University of Notre Dame
Burgers, why are your city names so uncreative

Also, how much does this kind of things cost ? Is it useful to do just 1 week ?

>what are you studying?
Laplace Transforms

How do I prove [math]L\{x^nf(x)\}=(-1)^n\frac{d^n}{ds^n}[F(s)][/math]?

>>8769388
Can't you do it by induction ?

>>8769395
I thought so, and I am trying to achieve it through integration by parts, but I can't seem to figure out the second term [math]-\int_0^\infty\int[e^{-sx}f(x)dx]\cdot nx^{n-1}dx[/math].

For power series it's simple, due to linearity.

>>8769434
So the outside integral becomes a power series and the inside integral [math]\int e^{-sx}f(x)dx[/math] becomes [math]\frac{d^k}{ds^k}[F(s)][/math] for some arbitary [math]k\in \mathbb{Z}[/math]?

>>8769092

give an example of a module that isn't a vector or has anything to do with vectors and i'll let you keep posting

>>8769181

learn about chords if you want to enjoy trig. ancient texts explain trig (and geometry) better than modern ones which are almost entirely written in predicates which you only need if you're automating very large proofs, not if you're proving something by hand on a single sheet of paper.

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>>8769700
>has anything to do with vectors
What did you mean by this? Anyway, the first condition is easily satisfied:

[math]\mathbb{Z}[/math] as a module over [math]\mathbb{Z}[/math] is not a vector space.

This follows from the two facts that
>unitary rings are modules over themselves
>[math]\mathbb{Z}[/math] isn't a field

>>8769297
>I mean researching stuff in pure maths alongside doing physics.
>stuff
what the fuck is "stuff"?

If you're doing research level theoretical physics you're probably doing research level math in the process. Just don't expect to be a simultaneous expert in something that has very weak/no ties to physics. You won't be an additive number theorist.

>>8769758
> additive number theorist.
Yeah that's reserved for the experimentalists

bumpity

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can one of you niggers tell me how to define a canonical Ord functor B-->Set

???

>>8770485

what book on ct is that

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>>8761737

>>8770501
basic CT
Leinster

really could use some help

>>8761147
Can someone give me some intuition behind the residue theorem, principal parts, etc

I have a pretty strong background (in terms of undergrad) in differential manifolds, so Cauchy's Integral Theorem was an obvious special case of stokes to me, etc.

The residue theorem also has a shadow of intuition, in that the integral should be zero if all points are analytic, and then since the set of singularities is countable, we can account for the contribution to the integral from each of those points in a summand

but what the fuck is a residue it doesn't help that my complex analysis class doesn't talk about Laurent series at all and every description I read is "it's the first term of a laurent series" well this doesn't make intuitive sense to me either since we are accounting for the contribution to the integral how can we discard all terms past the first

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>>8770619
Look into hHolonomy

>>8770646
Is this just jargon to look smart?

>>8770646
Oh boy, I can tell that this is a reasonable suggestion but it is way beyond my background

>>8770485
>a canonical Ord functor B-->Set
well the objects of B are already sets
the arrows of B are already arrows of SET

>>8770485
>Ord functor
so you need to tell what is a ord functor

>>8770646
what else would they be classified by?

>>8770651
go away

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>>8770701
There's a one-to-one correspondence between isomorphism classes of TQFTs and quantum invariants. This is proven in chapter 3 of Turaev.
Tbh that just felt artificial to me, since the "quantum invariant" he defined there already looks vaguely like how the modular functor of a TQFT would look like.
Not sure if there are other invariants that can classify TQFTs. Certainly not one that could be inspired from physics.

>>8770619
Geometric intuition should be in any decent Complex Geometry book.


In fact I think the idea of residues extend to general algebraic geometry (See Hartshorne).

>>8770485
>canonical Ord functor B-->Set
take obj X in B to ord(X)
take a bijection X->Y in B to ord(X)->ord(Y)

there is no diffiuclty in this, but I do not see a universal property to define the functor

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I need an introduction to proofs for brainlets like me

>>8770971
How to prove it

>>8770993
i thought that was a meme. i got like 25% in and it's just common sense stuff

>>8771004
my mistake, i was erroneously referring to how to solve it by poloya

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Is there any way to integrate this with a u subsitution or something similar? I can't see how it can be done.

How would you make a symbolic algebra program?

say it is limited to only basic arithmetic (+-*/) and it only deals with diophantine equations ()I guess that means no trig, logarithms)

For a start, you would tell it to solve for X and then it would be able to do it or tell you if it is impossible

I've already created a lexer that looks kind of like Lisp not sure were to go from here

>>8771081

the first step would be to substitute for 1-3x.

Then it probably wants you to use the identity

[math]\int{udv} = uv-\int{vdu}[/math]

but instead of writing it like this

[math]4\int{u^3e^{2u^2}du}[/math]

you write it like this

[math]4\int{(u^2)(u)e^{2u^2}du}[/math]

so that you can integrate dv, which is this

[math]u*e^{2u^2}[/math]

through substitution

>>8761853
>Measure theory

Just use a ruler

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Does anyone understand this question? Would someone be able to kick me in the right direction? I simply do not get how to translate (b) into a linear congruence

>>8771238
>Does anyone understand this question?
Basically MC (Melborune cup) happens the first tuesday in November and USE (US presidential elections) the day after the first monday in November.

If the USE would happen every year, those events would coincide always UNLESS the first day of November was Tuesday. In that case the USE would have happened the weed after the MC.

In 2000 both acts coincide, the first question is when was the previous time when they coincided and the second tone ask you the next time they will coincide.

>>8769700
but what book of trigonometry

>>8769700
>ancient texts explain trig (and geometry) better than modern ones
Also some of them they explain the relationship between trigonometric and hyperbolic functions. And I don't mean the usual cos(I*x)=Cosh(x), I mean the relation between the circular and the hyperbolic angle.

>>8771658
you can't say that kind of shit without actually giving soome names>>8769700

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>>8769092
Modules are literally just vector spaces on rings.

>>8769092
Studying group theory is not going to help you understand a tensor product of abelian groups any better, dude.

>>8762312
that harambe is [math]thicc[/math]

Hi, I haven't taken a math class for a year and I'm going to take Introduction to Ordinary Differential Equations this summer. What stuff should I brush up on before I go?

I think Power/Taylor Series, basic integration, and line integrals. What else? Thanks

>>8771194
stack

>>8771875
Skill with integration is probably the most important thing. If you're rusty on (very) basic linear algebra that's probably a good thing to review too.

Honestly don't worry about it much, ODEs is a piss-easy course. You'll learn maybe a dozen tricks to solve certain forms of equations, and probably some babby application problems.

>>87706
Well I'm not sure how "intuitive" it is but one thing to keep in mind is that [math]\frac{1}{2\pi i}\int_{C(0,r)} \frac{dz}{z^k} = \delta_{k,1} [/math] for each integer k and r > 0.
It tells you that, for a meromorphic function f with Laurent series expansion [math]f(z) = \sum_{k = 1}^{n} \frac{a_k}{z^k} + g(z)[/math] on D(0,r), with g holomorphic, we have [math]\frac{1}{2\pi i} \int_{C(0,r)} f(z)dz = a_{-1}[/math].
To get from here to the residue theorem, you need only note that, if [math]\gamma[/math] is the boundary of a domain where f has finitely many poles [math]z_1, \dots, z_n[/math], then the Cauchy formula tells you that, for a sufficiently small r > 0 (such that z_k is the only pole of f in D(z_k, r) for each k), the integral of f along [math]\gamma[/math] is the sum of the integrals along the [math]C(z_k,r)[/math], ie. 2pi i times the sum of the residues because of the above remark.

>>8771959
was answering to >>8770619

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>>8770675
It's quite intuitive actually. Fix a Lie group [math]G[/math] and we define the set of maps [math]S^1 \rightarrow G[/math] as the loop group [math]LG[/math] on [math]G[/math]. For a semisimple [math]G[/math], we can find a Lie algebra-valued 2-cocycle [math]\omega \in \Omega^1(LG_\mathbb{C}) \otimes \hat{L\mathfrak{g}} [/math] that induces a Hermitian line bundle [math]L \rightarrow LG_{\mathbb{C}}[/math], where the subscript [math]\mathbb{C}[/math] denotes the complexification and the hat denotes the central extension. Now fix a smooth section [math]s:U_\alpha \rightarrow L[/math] with the connection [math]\nabla = d+i \theta_\alpha[/math], where [math]\bigcup_\alpha U_\alpha = LG_{\mathbb{C}}[/math] is a coordinate patch and [math]\theta_\alpha[/math] is the connection 1-form [math]d\theta_\alpha = \omega[/math]. Define the first Chern class [math]c_1(\nabla)[/math] as the equivalence class of [math]\theta_\alpha[/math]. For the identity [math]e∈LG_\mathbb{C}[/math], set [math]u∈s(e)[/math]. The parallel transport of [math]u[/math] around a loop [math]\gamma⊂L[/math] is given by [eqn]v = u\exp\left(2\pi i\int_D c_1(\nabla)\right)[/eqn], where [math] \partial D = \gamma[/math]. This is the holonomy of [math]\nabla[/math] around [math]\gamma[/math].

>>8772030
Your posts are very masturbatory.

>>8772030
This has nothing to do with residues.

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>>8772045
By Stokes's theorem [eqn]v = u \exp\left(\oint_\gamma \theta\right).[/eqn] Under appropriate constraints the residue is the integral.

>>8772049
Meant [math]2\pi i\oint_\gamma [/math] in the exponential.

>>8772030
This is so overengineered it's almost comical

please stop shitting up these threads with your desperate attempts to look smart to strangers

>>8772043
>>8772061
>no one understands sarcasm and irony

>>8772066
>when you spend 20 minutes typing out a wall of LaTex, delete and re-try the whole thing when you fuck up and then try to pass it off as "just ironic"

>>8772049
>>8772054
Maybe by the Residue Theorem, but that doesn't tell you what a residue is. Just how they are related to contour integrals.

>>8772070
I try to make sure that I'm accurate even when I make jokes.
>try to
>the post starts out as "it's intuitive actually" followed by an extremely convoluted and unintuitive construction
>not irony
>I actually have to explain this to fully grown adult
This is actually sad as fuck.

>>8772074
I mean it tells you that the residue is the parallel transport of a loop in [math]\mathbb{C}[/math] along a conformal transform. If you have geometric intuition then should tell you something.

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what's a great, yet relatively quick read for an intro to elementary number theory?

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>>8771839
Yes, indeed vector spaces are literally just modules over fields.

>>8772112
Read the problem book by Andreescu/Feng

There's an intro in like 70 pages that covers most of the standard topics and then a big section of hard (sometimes pretty cool) problems to go with them

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>>8772170
Listen here you little shit

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>>8772185

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>>8772193

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>>8772194

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>>8772198
Put the fucking gun down

>>8772170
>>8772185
>>8772193
>>8772194
>>8772198
>>8772222
wtf is wrong with you faggots

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>>8772222
Checked.

>>8772229
I'm proving my claim using violence.

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>>8772112
>what's a great, yet relatively quick read for an intro to elementary number theory?

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Can /sci/ solve geometry's hardest easy question?
>pic related

I'm having a bit of trouble with the concept of "basis of open sets" in Topology. I need examples.

For N, the natural numbers, all natural numbers form a basis of open sets, right ? ({0}, {1}, {2}, ...) And since this basis is countable, the set N is countable as well.
From that point on, what would be a basis of, say, R ? A infinite collection of subsets whole union is R but whose intersection is always [math]\emptyset[/math] ?
Now with density. From what I've understood, a set A is "dense" in E if any open subset of E cross at least one point of A.

This would mean that the subset of even integers is not dense into the subset of integers. But the subset of rationals with an even numerator is dense in the rationals.

Did I understood this correctly ?

>>8772359
>but whose intersection is always O
No

>>8772428
So two open subsets can overlap ?

>>8772445
The requirement is that the overlap must also contain a basis element.

>>8771891

Thanks for the helpful suggestion, I'll write it down under "special needs"

>>8771194

I thought about it some more.

I'm going to treat an equation like folders on a computer, except a folder is a parentheses

>>8771194
>only deals with diophantine equations ()I guess that means no trig, logarithms)
>For a start, you would tell it to solve for X and then it would be able to do it or tell you if it is impossible
https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem

>>8772548

that's actually very helpful thank you

Find first five please

Please ;_;

>>8773008

>>8772268
>>8772182
you guys rock, thank you

>>8761147
Who is the guy on bottom? I've been looking for him

>>8773272
>>8761601

>>8773272
KKK grand wizard

>>8770651
Yes. But this jargon is necessary.

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I took a look this
http://www.christophertownsend.org/Documents/townsendphd.pdf
and section 1.1 already got me interesting. It seems that one can have the Tychonoff theorem for locales constructively. That's pretty cool.

>>8761419
>>8761450
>>8761936
Curious too

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>>8773896

BUMPeD AND SAVED.

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Post-shit bump.

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>>8761147
What exactly is a determinant and can I find one of an "infinite", bijective linear transform?

My go-to example for infinite vector space is the ring of polynomials.
Clearly the set of bijective transforms is not empty.
I think of the Id function, which I feel should have a determinant of 1, but struggle to explain it without using an infinite process.

tl;dr Is there a determinant defined for a transforms of a general vector space?

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If I am going to spend $500 on lottery tickets this year do I have a better chance of winning big if I spread it out evenly each week or just do it all at once?

>>8777625
>What exactly is a determinant
for a linear transformation on a finite dimensional (say n dimensional) linear space, the determinant can be thought of as the n-volume of the unit n-cube after being transformed

>can I find one of an "infinite", bijective linear transform?
sometimes:
https://en.wikipedia.org/wiki/Determinant#Infinite_matrices

>>8777625
To really understand the determinant, you look in exterior algebra.

>>8777635
As a brainlet who has forgotten everything he learned in school about probability, I would also like to know this. Intuitively it feels like buying many tickets for one draw is slightly better, but I'm not sure how to calculate it.

>>8777992
What leads you to suspect that buying tickets for the same draw would benefit you?

>>8777992
>>8777635
It's better to buy them all at once.

Say you're going to buy 100 tickets and there's a 1/1000 chance of winning for each ticket.

It's clear if you buy them all at once the chance of winning is 100/1000 = 10%.

On the other hand, the chance of winning if you buy them one at a time is equal to one minus the probability of losing each time, which is 1 - (999/1000)^10 = 9.52%.

>>8778046
Addendum: You could do a more sophisticated calculation which accounts for the fact that the probability changes depending on how many people are playing. If you bought a lot of tickets at once, you'd be changing the size of the pool, and this would affect the probability.

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>>8777635
One per drawing because you're lucky and will probably win multiple times.

>>8778046
The expected value is the same, because if you spread out your purchases, you can win multiple times. Mathematically this will account exactly for the difference in percentages

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I'm looking for a PDF of pic related.
Title of the book is An introduction to the modern theory of dynamical systems by A.Katok and B.Hasselblatt
I would greatly appreciate it if someone knows where I can find it.

>>8778156
>An introduction to the modern theory of dynamical systems
http://gen.lib.rus.ec/

>>8778176
Thank you very much Anon.

How do I start learning the stuff people are doing in topology, physics, TQFT, etc.?

I'm out of school right now, in undergrad i had QFT at the level of Peskin and geometry/topology at the level of Nakahara for whatever that's worth.

>>8778281
Look in the previous thread. >>8762771

How can i concentrate when i'm trying to study? My neighbors and family make a lot of noise, i usually wear headpones with rainymood or white noise, but somethings this distracts me too, any suggestions? I'm not american, moving out at 18 is impossible here