/mg/ - Math General: where has it gone edition

[Anonymous No.14714498]

Ret's tark math.

Formerly: ???

[Anonymous No.14714501]

fuck maths

[Anonymous No.14714540]

>>14714501
Dumb nigga.

[Anonymous No.14714599]

why people simps rudin principles? mental illness?

an amazon review

OK... Deep breaths everybody...

It is not possible to overstate how good this book is. I tried to give it uncountably many stars but they only have five. Five is an insult. I'm sorry Dr. Rudin...

This book is a good reference but let me tell you what its really good for. You have taken all the lower division courses. You have taken that "transition to proof writing" class in number theory, or linear algebra, or logic, or discrete math, or whatever they do at your institution of higher learning. You can tell a contrapositive from a proof by contradiction. You can explain to your grandma why there are more real numbers than rationals. Now its time to get serious.

Get this book. Start at page one. Read until you come to the word Theorem. Do not read the proof. Prove it yourself. Or at least try. If you get stuck read a line or two until you see what to do.

Thrust, repeat.

[Anonymous No.14714607]

If you make it through the first six or seven chaptors like this then there shall be no power in the verse that can stop you. Enjoy graduate school. You half way there.

Now some people complain about this book being too hard. Don't listen to them. They are just trying to pull you down and keep you from your true destiny. They are the same people who try to sell you TV's and lobodemies.

"The material is not motivated." Not motivated? Judas just stick a dagger in my heart. This material needs no motivation. Just do it. Faith will come. He's teaching you analysis. Not selling you a used car. By the time you are ready to read this book you should not need motivation from the author as to why you need to know analysis. You should just feel a burning in you chest that can only be quenched by arguments involving an arbitrary sequence {x_n} that converges to x in X.

Finally, some people complain about the level of abstraction, which let me just say is not that high. If you want to see abstraction grab a copy of Spanier's 'Algebraic Topology' and stare at it for about an hour. Then open 'Baby Rudin' up again. I promise you the feeling you get when you sit in a hottub for like twenty minutes and then jump back in the pool. Invigorating.

No but really. Anyone who passes you an analysis book that does not say the words metric space, and have the chaptor on topology before the chaptor on limits is doing you no favors. You need to know what compactness is when you get out of an analysis course. And it's lunacy to start talking about differentiation without it. It's possible, sure, but it's a waste of time and energy. To say a continuous function is one where the inverse image of open sets is open is way cooler than that epsilon delta stuff. Then you prove the epsilon delta thing as a theorem. Hows that for motivation?

[Anonymous No.14714614]

Anyway, if this review comes off a combative that's because it is. It's unethical to use another text for an undergraduate real analysis class. It insults and short changes the students. Sure it was OK before Rudin wrote the thing, but now? Why spit on your luck? And if you'r a student and find the book too hard? Try harder. That's the point. If you did not crave intellectual work why are you sitting in an analysis course? Dig in. It will make you a better person. Trust me.

Or you could just change your major back to engineering. It's more money and the books always have lots of nice pictures.

In conclusion: Thank you Dr. Rudin for your wonderfull book on analysis. You made a man of me.

[Anonymous No.14714624]

>>14714599
>why people simps rudin principles? mental illness?
those ppl like it the same way redditors like avengers. it still is probably the best intro analysis book but nothing more

[Anonymous No.14714625]

>>14714599

I assume it's better to have little background, initiation to maths before going for the Principles and the Real and Complex. However, those books are really really good. But you clearly can't read them quickly, you'll need to read each chapter 10 times but it is perfectly rigorous and understandable.

>>14714498

This book is super super hard.

[Anonymous No.14714628]

>>14714624

There are no equivalent for differential geometry, or group theory, or stochastic process. You'll have to jump between several books which is very very annoying. This is a teaching masterpiece.

[Anonymous No.14714633]

>>14714628
fair enough but then again the "intro analysis" curriculum is narrow enough that you can do that

[Anonymous No.14714968]

>>14714498
Could you pass the Harvard University math qual?
https://www.math.harvard.edu/graduate/study-the-qualifying-exam/the-qualifying-exam-syllabus/

[Anonymous No.14714997]

>>14714968
>Rudin: Real and complex analysis is a general reference but the following books have more useful techniques
rudin bros how do we cope?

[Anonymous No.14715014]

>>14714968
>syllabus: read these dozen reference books
>exam: may not cover every topic on the syllabus
>exam: stuff you've already done dozens of times in undergrad

[Anonymous No.14715019]

>>14715014
These "elite" think that they are so smart because "omg guyze its an even function, I found the trick"

[Anonymous No.14715024]

>>14714625
If you aren't reading the chapter again after every problem, it's a shit book

[Anonymous No.14715034]

>>14715014
The difficulty is in having the basics of many disciplines at your command off the top of your head i.e. the problems aren't especially meant to be tricky
>>14715019
What

[Anonymous No.14715041]

>>14715034
You break the function into [math] \dfrac{n^2+1}{n^4+1} + \dfrac{n}{n^4+1}[/math] The first term is 0 as it's even. The problem is near impossible to solve in the time limit without knowing the trick, which is taught, thankfully.

[Anonymous No.14715051]

>>14715041
Or rather, the second function is odd, so it's 0*

[Anonymous No.14715194]

>>14714498
Anybody read this? I'm trying but I don't get it >,<

[Anonymous No.14715419]

>>14715014
>problem 4 just know cot(pi*z) offhand
anyone who wants to ask questions involving reciprocal trig should be mandated to do a graduate course in elliptic functions
>problem 6 and the weierstrass approximation theorem
i feel like this is one of those results that ends up biting you any time you try to invoke it

[Anonymous No.14715741]

>>14714599
It seems "good" now that I have 10 years of experience in mathematics behind my back.

Elaborating on how to interpret the product of two convergent series, which is what Rudin does in Principles, is still overkill, and nobody should be made to believe this stuff at that stage is important for your development.

I used Spivak to teach myself analysis and I did fine.

[Anonymous No.14715751]

>>14714599
Yes, mental illness. You have the same retards on this board who've never read another analysis book (but then again it's just analysis so it doesn't matter too much). Imo this anon made a pretty good case as to why Rudin isn't as good as people claim and why Zorich is better >>/sci/thread/S14684883#p14689318

[Anonymous No.14715756]

>>14715419
You should know the series for cot imo it's a standard method coming up all the time in evaluating sums especially via the residue theorem and in intro to modular forms

[Anonymous No.14715766]

>>14714968
Why is there to much emphasis on geometry and topology? Fine analysis and algebra are staple topics but what about number theory or combinatorics? Even the analysis there is too little, where is the functional analysis? That is far more important to know over algebraic geometry/topology for the average mathematician

[Anonymous No.14715773]

>>14715766
Probably because it's a huge thing at Harvard where you've got guys like Yau. It's important for the incoming PhD candidates to be well matched to the faculty.

[Anonymous No.14715781]

>>14715766
Combinatorics is usually in the applied math fac

[Anonymous No.14715840]

What should I review before Complex Analysis in the fall?

[Anonymous No.14715850]

>>14715840
Just watch Borcherds and do exercises from whicever book you've been assigned.
https://www.youtube.com/watch?v=qXWRL6NHlWc&list=PL8yHsr3EFj537_iYA5QrvwhvMlpkJ1yGN

[Anonymous No.14715857]

>>14714498
In scientism, truth and value are quite literally in numbers. "Many people believe X." "The consensus is X." "My colleagues agree." "There are a number of books on the subject." "I have received no complaints." "There is much support." Truth is by popular vote. The more Nature does it, the more right it is. It is the authority of DNA - the authority of the tradition of Nature itself. And whereas in ordinary religion the logical fallacy of choice is the appeal to the authority of some holy book, in scientism it is the appeal to the authority of the number (argumentum ad numerum). For the adherents of scientism, numbers represent the only real value, and these become the very substance of their life.

>People become numbers. The numbers become their horizon - their all. They are just copies.
- Kierkegaard

If you explain to these numerous fellows that they are constantly, in every waking moment, appealing to the fallacy of the number, you are wasting your breath, because they don't know anything except the number. They cannot hear you, because existence requires contrast. And for this same reason such people don't exist as individuals. They have no self, and no soul, since the soul is precisely the self, and is the genius in man.

Samuel Butler accurately describes this soulless culture - the culture of the number - in his novel Erewhon, when he visits the hallowed "Colleges of Unreason".


>"It is not our business," he said, "to help students to think for themselves. Surely this is the very last thing which one who wishes them well should encourage them to do. . . ." In some respects, however, he was thought to hold somewhat radical opinions, for he was President of the Society for the Suppression of Useless Knowledge, and for the Completer Obliteration of the Past.

[Anonymous No.14715878]

>>14715857
Sir, this is a math thread, not a science one.

[Anonymous No.14715904]

>>14715850
creepy pedo

[Anonymous No.14716064]

>>14714498
No, I want more schizo posts from /pol/

t. math major

[Anonymous No.14716490]

I'm a bit stumped by this and can't really pinpoint where the proof goes wrong. Could anyone please help?

[Anonymous No.14716503]

Calculating the area of a circle by making smaller and smaller portions until they're so thin they form a rectangle is.... retarded, no?

I obviously don't have a better way but Math has been so precise, exact it feels strange that this is our best method.

Even the language is dumb, less "bumpy"?
Is this really our best option?

[Anonymous No.14716743]

Alright, post the hardest textbook out there. I want to get fucked.

[Anonymous No.14716790]

Have seen anything like this https://www.youtube.com/watch?v=H46ON2FB30U
Can write formulas and draw diagrams the page fast. Some guys on /g/ said can use most of the latex command but its a WYSIWYG editor. Looks perfect for college.

[Anonymous No.14716958]

>>14715756
yea i took another look right after and realized i did know it, i guess its boundedness makes it come up in complex analysis way more
i think it's the fact that any change effectively doubles the number of trig functions makes me shut down with the less common ones

[Anonymous No.14716979]

>>14716958
>i guess its boundedness makes it come up in complex analysis way more
no it's the fact that [math]\pi\cot\pi z[/math] has poles at the integers with residue 1, this means you can easily convert a series into a contour integral where your general term [math]a_n[/math] is now a function integrated against cotangent, or cosec if the general term is alternating in sign
also cosec (and cot) is to the circular functions as the sigma function (basically a theta function) is to elliptic functions

[Anonymous No.14717210]

>>14716979
yea that
i used spiegel's book so i'm retarded

[Anonymous No.14717377]

Do you know any functional analysis books accessible to someone who hasn't taken any analysis class but has taken all calculus classes? Could you share?

[Anonymous No.14717435]

>>14716743
This one will stump you, good luck getting past the first page.
>>14717377
Why? Have you had any upper level classes yet?

[Anonymous No.14717494]

>>14717435
Basically, I live in Brazil and want to get out. My target is Germany, since I have descendancy from there. There is a prof in my uni that has strong ties with Germany, and to maximize my chances of getting out I want to do an undergrad research (about functional analysis, more specifically operator algebra) with him. I don't want this just because of the opportunity, I am doing a math degree exactly because of my interest in analysis and topology, even though I have no formal experience with it.
As for the classes that I had, I have done all the calculi like I said, all linear algebra classes, one abstract algebra class (and will do another next semester) and I will do an "analysis on the real line" class next semester.

[Anonymous No.14717532]

>>14717494
You can try these:
Analysis Now, Pedersen
Problems and Theorems in Functional Analysis, Kirillov & Gvishiani

[Anonymous No.14717548]

What’s wrong with the other /mg/ that’s up

[Anonymous No.14717550]

>>14717532
Vielen dank!

[Anonymous No.14717585]

>>14717550
cringe

[Anonymous No.14717601]

>>14715194
What maths prerequisistes do you have? It's heavily using category theory

[Anonymous No.14717617]

>>14717548
Is there one? Couldn't find it in catalog.

[Anonymous No.14717624]

>>14715751
He doesn't make a case at all.

[Anonymous No.14718175]

>>14714498
Why are Japanese people so good at writing math textbooks? Also, I wonder what it's like to be at Oberwolfach, especially what it was like back in the day...

[Anonymous No.14718317]

Does anyone have a book on geometric proofs to try on your own? I've been out of school and doing math for a long time and want to get my feet wet again, but some other books I've tried have been intimidating to say the least.

[Anonymous No.14718349]

>>14718317
this or gelfand's geometry

[Anonymous No.14718374]

>>14718349
Will check these out, thanks!

[Anonymous No.14718431]

>>14714599
People who dislike Rudin are brainlets.

[Anonymous No.14718462]

>>14717494
Amann Escher is a very self contained and general Analysis, which is available in German. It can get you into research fast since it starts with very modern topics like Banach spaces.

[Anonymous No.14718511]

>>14717624
no need to deny

[Anonymous No.14718936]

>>14715773
it's still retarded
mathematicians should know functional analysis before algebraic geometry/topology any day of the week

[Anonymous No.14719668]

[Anonymous No.14719704]

>>14719668
(c)

[Anonymous No.14719726]

>>14718462
It's available in English too.

[Anonymous No.14719728]

>>14719704
No way you're screwing them both in

[Anonymous No.14719737]

>>14719728
You're not screwing anything, the bolts themselves don't rotate.
Assume the upper bolt stays still and we rotate the lower bolt around it. The rate at which the groove of the upper bolt moves leftward is exactly matched by the grooves at the contact point on the lower bolt moving leftward as well.

[Anonymous No.14719749]

>>14715857
>appeal to the authority of some holy book
>every one of those men was a fervant zealot

Heaven and Hell is 1 and 0. 1 (side length 1 (Infinity/Infinitely divisable)) and 0 (being approaching Plank, Infinitely divided (not nil, thats modern interpretation of 0)).

If you desire to know the subject youre talking about dimensions deeper than you already do...ask.

My credentials exceed your citations, my son. I dont care who you quote, I will destroy him.

[Anonymous No.14719769]

>>14715857
On second thought...np, it is YOU that is this "creature of the number". It is you that has little concept of math of perception of reality and constantly appeals to authority (name dropping).

Mirror mirror...

[Anonymous No.14719776]

>>14719668
The peaks and troughs at the contact point will both move right at the same speed, therefore the bolts do not change position relative to each other.

[Anonymous No.14719830]

>>14714498
Whats the kind of math where you find out the amount between something like 360 and 240 where the answer would be something like a 20% difference between the two

[Anonymous No.14719842]

>>14719830
measure theory

[Anonymous No.14719868]

>>14719749
something something synagogue of satan

[Anonymous No.14719884]

>>14719868
The correlation of pentagon and hexagon, best expressed in the bent pyramid in Egypt, used to express macrocosm and microcosm.

One must be a genuis to understand, smart to recognize it and a moron lambasts it because he knows he is neither.

[Anonymous No.14719892]

>>14719884
low iq post

[Anonymous No.14719901]

>>14719892
Im the most intelligent person you have ever met. Ive been to every corner of the world for research purposes.

You have nothing but shitposts.

>Atomic harmonics at the macro scale.
I havnt finished reading Kepler's Harmonics...I should get on that.

[Anonymous No.14719905]

>>14719901
>look le geometric patterns
Do you have aspergers?

[Anonymous No.14719938]

>>14719905
Yes. This is why I know how the universe works and a subatomic (Quantum mechanical/standard model) and celestial levels (general relativity, space/time). I had to invente my own mathematics (similar to guage theory) because I needed ways to calculate gravity and time in novel ways.

This is your one chance to learn something you wont find in any book in the world...I would know...I looked.

[Anonymous No.14719945]

>>14719938
Put it all in one [math]\LaTeX[/math] document like Tooker did.

[Anonymous No.14719956]

>>14719945
What part of "Invemted my own mathematics" do you not understand. I dont use your symbols numb nuts.

Guage theory is some basic bitch shit. Prove youre not retarded;
>>14719892

Youre fucking dumb and deserve a beating because youre father didnt teach you how to realize when real steps before you.

[Anonymous No.14719959]

>>14719956
>I dont use your symbols
low IQ

[Anonymous No.14719967]

>>14719959
>lmao what a retard le "magic shape"

Youre midwit as they come.

[Anonymous No.14719968]

>>14719967
>>14719956
I HAVE WON

[Anonymous No.14719983]

>>14719968
Why are you even on a science and mathematics board? You visiting for lulz or just a fool wanting to not feel stupid?

[Anonymous No.14719992]

>>14719983
see >>14719968
I told the monkey to dance and he did. Truly low IQ.

[Anonymous No.14720003]

>>14719992
You are what you post, memes and low IQ shitpost. Thats who you are, shit.

[Anonymous No.14720004]

>>14720003
>he keeps on doing it

[Anonymous No.14720006]

>class did well on Calc II over summer
>professor wants to cover more advanced topics that wont be on the final, and still grade us for it

fellas, is it okay to cover vector functions in calculus II? Last week was a quick look at dot/cross product and 3d planes. I want to learn it, don't get me wrong, but I feel as if spending time on this now will affect my grade in the course.

[Anonymous No.14720030]

>>14720004
God I wish I was in the same room as you and your friends and family so I could rip you in half in front of them.

Beatings. The only cure for your insolance is physical beatings.

[Anonymous No.14720033]

>>14720030
aahahahhaha. So little effort is required to get this schizo monkey dancing

[Anonymous No.14720046]

>>14720033
You dont get it. I "danced" against the greatest minds in human history and defeated half of them. Einstien, Feynman, all your heroes.

Dancing made me one of the greatest mathemticians in human history.

What has shitposting gotten you? A slumping grade in school? Memes? "hahahaha"'s? You have to force a fake narrative to make yourself not feeling retarded.

So sad...its fascinating how retarded humans are.

[Anonymous No.14720048]

>>14720046
>I "danced"
I accept your concession.

[Anonymous No.14720067]

I posted it in other thread, but it seems to be dead

https://www.researchgate.net/publication/346967755_The_TRUE_Mathematics_of_Infinity_for_Scientists_and_Engineers#pf4

you think this schizo posts here?

[Anonymous No.14720073]

>>14720048
Dancing, like boxing, is patterns (a type of combinatronics proble), and as such, mathematical.

This is a mathematics thread, keep on topic, retard.

[Anonymous No.14720080]

>>14720073
>patterns = mathematics
low iq

[Anonymous No.14720091]

>>14720067
I read a bit of it and it looks pretty entry level to me. I'll pass on it. Id rather flex on peanuts.

[Anonymous No.14720098]

>>14720080
Fibonacoi *cough-retard* ah jeez....fucking nuts in here...

Organic mathematics, derived from life, and by proxy matter, itself.

See....youre fucking retarded and you keep posting so I need to keep reminding you.

[Anonymous No.14720100]

>>14720098
read Bourbaki

[Anonymous No.14720131]

>>14720100
Thanks. I will. Thats my jam right here, really into those topics.

[Anonymous No.14720248]

>>14720098
are you a bot

[Anonymous No.14720280]

>>14720248
If one can compute high enough even life itself is purly a biomolecular reaction emitting electromagnetic pulses.

You are a drone to me. AIs, no matter how advanced, are limitied by fundemental computer archetecture, limiting their ability to process reality in way even children can, and binary mathematics, limiting it further.

Bot...pfft...to you they are advanced...but biological computers, now that is something advanced and powerful.

[Anonymous No.14720520]

>>14718175

Same for stochastic calculus. Nips are really smart but no one goes for maths studies in Nipland. All of them go for "Economics" ou bs like that. Their maths classrooms are empty like a desert.

[Anonymous No.14720577]

>>14714498
>romanian geometry

[Anonymous No.14720603]

>>14719842
Thanks

[Anonymous No.14720683]

>>14714498
>Hey guys I'm le epic /x/ schizo! I invented my own hecking mathematics! Saturn CUBE, right? Shadilay!

[Anonymous No.14720700]

>>14720280
https://archive.macleans.ca/article/2005/5/30/the-star-trek-connection
>THE STAR TREK CONNECTION
>A surprising number of child sex abusers appear to be Trekkies. Trying to figure out what that means, however, shows how little we really know about pedophiles

[Anonymous No.14720901]

>>14717377
There is Erwin Kreysig's functional analysis with applications. Check it out and see if that's what you are looking for

[Anonymous No.14721021]

>>14720683
>>14720700

Go back to /b/ you no IQ degenerate pieces of shit.

Kill yourselves.

[Anonymous No.14721073]

>>14721021
You're not interesting never post again

[Anonymous No.14721082]

>>14721073
>soi-faced meme lord faggots
You have absolutely norhing in your life worth sharing with anyone.
You have zero merit in any field of study.
You have failed life.

Kill yourself.

[Anonymous No.14721127]

>>14720520
What stochastic calculus book are you talking about?
I'm taking it this semester

[Anonymous No.14721209]

Did we ever get closure on whether Satoshi Nakamoto proved the poincare conjecture or not?

[Anonymous No.14721211]

>>14721082
>>14721021
You're not interesting or funny in the slightest. All you do is read random mathematical papers and use the language in them to come up with nonsensical poetry.
Man, it must suck to be too low IQ for symbolic notation.

[Anonymous No.14721221]

>>14721211
POST MATH YOU STUPID FAGGOT!
>wont, pretend to be competent
You are so threatened its fucking pathetic!
>CNN tier false narrative to feel like a victim
KILL YOURSELF.

[Anonymous No.14721234]

>>14721221
low iq post

[Anonymous No.14721247]

>>14721234
I am better than you by every metric of reality.

t.Mathematical Physicist to dunk on professors for lulz

[Anonymous No.14721256]

>>14721247
>>14721234
why are homosexuals so mean to each other

[Anonymous No.14721257]

>>14721247
maybe go to bed you degenerate fucking retard

[Anonymous No.14721261]

>>14719749
just wait till you find out what the chemical structure of your favorite drug really looks like, stoner

[Anonymous No.14721266]

>>14721247
you have a tiny jaw and drooping farmer-bug abdominals, small lats, garbage pec insertions.

[Anonymous No.14721267]

>>14721247
you look 60 lmao

[Anonymous No.14721277]

lmao THE BODY GOTTEM!

I AM THE KING OF THIS BOARD.

YOU ARE ALL ANTS.

[Anonymous No.14721495]

Question for all the professors who post here. On a scale from chemically content with life to keeping a revolver in your desk, how suicidal are you?

>>14721247
Built for looks, not practicality. You look like you would crumple if an emaciated homeless guy punched you.

[Anonymous No.14721525]

>>14721495
>Built for looks, not practicality

You need help...but not by your peers, theyre retarded like you.

Ask, my son...and I can open temporal door you had no notion that existed for;
Ye Are Blind for Ye Are Pride.

[Anonymous No.14721530]

>>14721525
don't shoot up a fucking school you massive schizo

[Anonymous No.14721547]

>>14720006
If you plan on taking cal 3, vector functions is what you'll start with. It shouldn't be that bad of a topic to learn at this point, especially if you've already had linear algebra, but if you're not sure about it, be frank with your professor and voice your concerns. Sounds like he's just trying to get you well prepared for cal 3.

[Anonymous No.14721627]

>>14721209
The inventor of Bitcoin? I wasn't aware he made an attempt.

[Anonymous No.14723201]

If an article had cost me 10% less, the gain would have been 12% more: what was the gain per cent?

[Anonymous No.14723214]

>>14723201
Before attempting calculus, try this problem, if you can't just give up on math.

[Anonymous No.14723229]

>>14723201
>>14723214
You should learn English first.

[Anonymous No.14723265]

>>14723229
>Pajeet can't into arithmetic.
SAD, many SUCH CASES.

[Anonymous No.14723323]

>>14714607
You've inspired me to keep working at the topological groups textbook I picked up, anon. Based encouragement

[Anonymous No.14723372]

>>14720006
My school does that as a standard, although it's partly because they had room after cutting a bunch of the sequences/series stuff. Shouldn't be too hard, anyways; you should've done the basic 3D surfaces stuff in Calc I or precalc, so this is just basics to prime you for Calc III. Just remember the dot product measures "angle between two vectors" but is scaled by their lengths (actual identity: a dot b = len(a) len(b) cos(angle) -- this can actually be derived from the law of cosines in Euclidean space) while cross product is mostly used for finding a perpendicular vector to two other vectors

[Anonymous No.14724359]

>>14723201
Didn't realize /mg/ would get filtered by this, just goes to show how far schools have fallen.

[Anonymous No.14724482]

>>14724359
not a homework thread

[Anonymous No.14724496]

>>14720006
wait this calc 2 that Americans speak of, you haven't even learned about planes? Or about the dot product? This is literal high school material

[Anonymous No.14724518]

Best (free) math software?

[Anonymous No.14724521]

>>14724496
American education. In Europe, we immediately start with Analysis in university.

[Anonymous No.14724551]

>>14724496
every calculus book has that material

[Anonymous No.14724842]

>>14724482
>not a math thread
Keep wanking off with your category theory bullshit.

[Anonymous No.14724998]

>>14724518
To do what?

>>14724551
Yeah for the dumb fucks who happen to stumble upon it

[Anonymous No.14725004]

>>14724842
Again, go to /wsr/ you underage retard.
>cat theory is le bad
Nobody gives a shit about what a high schooler still solving for x thinks. You're just as obnoxious as undergrad cat theorists feigning superiority.

[Anonymous No.14725027]

>>14725004
>category theory can't even solve a simple problem of percentages
I though categories were supposed to be the foundations of all of math.

[Anonymous No.14725205]

>>14714599
I don't think Rudin is good as a textbook for a first-time learner (although it's not as bad as some claim), however it's a fantastic reference for basic real analysis (except measure theoretic stuff). whenever i forget anything i first look in Rudin, it usually suffices

[Anonymous No.14725352]

What prerequisites do I need to know before learning differentiation?

[Anonymous No.14725562]

Studying Zorich and it's almost unbearable. For almost every exercise I have to google someone's solution. Sometimes I move in the right direction but that's not enough for a complete proof. I've only got to the chapter about real numbers and I've skipped a lot of exercises. I know that this is bad but I can't do them and I don't find exercises about functions or set theory interesting. The thing is, they are probably more or less needed for understanding further chapters. I couldn't even prove this without help.
Feel very stupid and filtered, but don't wanna quit. Don't want to change the textbook either. Does it get easier? Should I go back and try to do almost all exercises?

[Anonymous No.14725596]

>>14725352
You need to know what functions and limits are.

[Anonymous No.14725622]

>>14725562
Finding an injective function from (0,1) to [0,1] should be trivial. For the other direction you just have to fit in two extra points.
[eqn]f:[0,1] \to (0,1) \\
f(x) = \begin{cases} \frac{1}{2} & \text{for }x=0\\
\frac{1}{3} & \text{for }x=1\\
\frac{1}{n+2} & \text{for }x=\frac{1}{n} \text{with }n\in \mathbb{N} \text{ and } n \geq 2 \\
x & \text{else}
\end{cases}
[/eqn]
The function is bijective too so there is nothing extra to do.

[Anonymous No.14725639]

>>14725562
I'm in the same boat here. I've thought about going through a mathematical logic book first or so but then came to the conclusion it would probably be better if I just studied the solutions to Zorich's exercises. It seems like you only learn math by struggling, though I wish Zorich included solutions. You need some sort of feedback on what you did to learn.

[Anonymous No.14725654]

>>14714624
>the best intro analysis book
Sorry, but the best intro to real calculus is Differential and Integral Calculus by G. M. Fichtenholz. (Too bad it was never released in English.)

[Anonymous No.14725672]

>>14725654
And it's cheap as fuck too. Thank you very, very much. How glad I am to be able to speak German. So much soviet shit has only ever been translated to German.

[Anonymous No.14725755]

>>14725672
fuck why can't I find volume 1 anywhere?

[Anonymous No.14725776]

>>14725622
That's neat, thanks. I've figured out how to prove it using the theorem with a hint from google, but I was completely stuck on finding a suitable bijection.
>>14725639
The struggle is real. And not having a feedback certainly doesn't help. It should probably get easier with practice. Maybe I will try to post my solutions here and ask for help when I'm completely stuck. I hope that after building some mathematical intuition I will not feel like a complete retard.

[Anonymous No.14726000]

Is there a more elegant way to prove
[math] f: \mathbb{N} \to \mathbb{Q}, n \to \frac{3n}{2n^2+1}
\\ lim_{n \to \infty}f = 0[/math]


Can't think of anything other than

[math]lim \frac{3n}{2n^2+1} \\ =lim \frac{3}{2n+1/n} \\ = \frac{3}{lim(2n) + lim(1/n)} \\ \forall \varepsilon \in \mathbb{R^{+}} \ \exists n_0,n_1 \in \mathbb{N}: (n_0>\frac{\varepsilon}{2} \implies 2n_0>\varepsilon) \land (n_1> \frac{1}{\varepsilon} \implies \frac{1}{n_1}<\varepsilon) \\ \implies \forall n \geq max\{n_0,n_1\}: f \to \frac{1}{\infty + 0} = 0 [/math]

which feels really sloppy, furthermore does the step in which I break up the limit in to two parts require additional theorems/lemmas to use or does it follow trivially from the definition of a limit?

[Anonymous No.14726012]

>>14723201
Is it my English or there is some strange thing about this question? I cannot understand what you mean by gain. Is it there is some profit you are selling for?

[Anonymous No.14726787]

>>14726000
cringe pseud

[Anonymous No.14726814]

>>14726787
>intro to undergrad analysis question
Maybe you're just retarded?

[Anonymous No.14726833]

>>14726814
or maybe its cringe pseud shit to obsess over trivially simple and very obvious facts. you dont need an elegant way to prove such things
I really shouldnt bother coming here during summer

[Anonymous No.14726835]

>>14726000
If n is at least 1 then
[math]3n / (2n^2 + 1) \leq 3n / (2n^2) = {(3/2) \over n}[/math].

The latter clearly tends to 0 (Archimedian property of real numbers)

[Anonymous No.14726865]

>>14726000
Just use l'Hopital's rule

[Anonymous No.14726991]

What if we set pi equal to 1?

[Anonymous No.14727105]

>>14726833
Anon, no one cares. Please stop being such a fat faggot. Thanks.

[Anonymous No.14727113]

>>14726991
time travel is possible

[Anonymous No.14727147]

>>14727105
>fat faggot
How have you measured his weight from his post

[Anonymous No.14727157]

>>14717617
here
>>14699453

[Anonymous No.14727168]

>>14727147
The same way i figured out your mother is a swollen fat whore. Trade secret, can't give it away, lest other autists start stealing my juicy fat whores out of spite.

[Anonymous No.14727529]

New NJW dropd:
https://www.youtube.com/watch?v=F8eO2z13BLI

[Anonymous No.14727952]

How do I solve exercises like pic related? The way I solved it seems to be too specific to this sequence, and I don't see how I could apply it to other sequences.

What I did was suppose that exists some [math] f\in\mathcal{R} [/math] whose [math] k [/math]-th Fourier coefficient is given by [math]a_k [/math], and then arrive at contradiction. Since [math] a_0=0 [/math], then [math] f[/math] must vanish everywhere on [math] [0,2\pi] [/math] except on a set of measure zero. So it would follow that [math] |f|^2[/math] would also vanish everywhere except on a set of measure zero, and its integral would also vanish. But this would contradict Parseval's identity: [math] ||f||^2=\frac{1}{2\pi}\int_0^{2\pi}|f(x)|^2\,dx=\sum_{n=-\infty}^{\infty}|a_n|^2=\frac{\pi^2}{6}\neq0 [/math]. So [math] f [/math] doesn't exist.

[Anonymous No.14727967]

>>14727168
Are you literally 14 years old?

[Anonymous No.14727980]

>>14727952
>then f must vanish everywhere on [0,2π] except on a set of measure zero.
You've instantly lost me with your proof.

[Anonymous No.14728087]

>>14727952
>Since a0=0, then f must vanish everywhere on [0,2π] except on a set of measure zero
Doesnt follow

[Jeo No.14728093]

Math is bad and a lie.

[Anonymous No.14728094]

>>14728087
This is a Riemann integral
[math] a_0=\frac{1}{2\pi}\int_0^{2\pi}f(x)\,dx=0 [/math]

[Anonymous No.14728099]

>>14728094
Yes. It doesn't follow that f is zero almost everywhere.

[Anonymous No.14728104]

>>14728099
You're right, I'm retard. That is only true if f is non-negative

[Anonymous No.14728188]

>>14726000
squeeze theorem
1/n and 10/n

[Anonymous No.14728236]

>>14727952
How did you define the Fourier coefficents. Is it
[eqn]a_k = \frac{1}{2 \pi}\int_0^{2 \pi} f(x) e^{i k x} dx[/eqn]
or something else?

These things are differently defined in different books.

[Anonymous No.14728249]

>>14728236
Like this [math]a_k = \frac{1}{2 \pi}\int_0^{2 \pi} f(x) e^{-i k x} dx[/math]

[Anonymous No.14728256]

>>14715773
Who’s Yau and why would people base their curriculums over what he personally researches

[Anonymous No.14728263]

>>14726000
what are you, stupid? [math]\frac{3n}{2n^2+1}=\frac{\frac{3}{n}}{2+\frac{1}{n^2}}\to\frac{0}{2+0}[/math]

[Anonymous No.14728383]

What are wavelets good for?

[Anonymous No.14728412]

>>14728383
Wavelets are a Hilbert basis, just like the sines and cosines of Fourier transform. The applications overlap with the latter, in particular in fast computational compression of images or spatial data.

[Anonymous No.14728419]

Henlo frens, how/where do you start learning math? I'm a complete brainlet with too much free time, may as well use it in a productive manner.
I kinda forgot half the stuff they taught me in high school.

[Anonymous No.14728452]

>>14728419
You open some introductory textbook and read the first chapter. Then you do all the exercises and once you're sure you have understood everything correctly you move on to the next chapter.

[Anonymous No.14728535]

>>14726012
Yes, expanding: If my supplier have sold this article to me for 10%; the gain I would have had from selling the article would have been 12% more.

[Anonymous No.14728540]

>>14726000
Perhaps learn algebra before learning calculus?

[Anonymous No.14728554]

>>14714498
I want to show that if [math]\Sigma[/math] is a sigma algebra on some set [math]U[/math] and [math]E \subseteq U[/math] then the set given by [math]\Sigma_E = \{S \cap E: S \in \Sigma\}[/math] is also a sigma algebra.
Im stuck in trying to show that [math]\tau \in \Sigma_E \implies \tau^c \in \Sigma_E[/math] any hints?

[Anonymous No.14728623]

>>14728554
The issue here is that you have two different types of complements in [math]\Sigma[/math] the complement of a set [math]A [/math] is [math] U \setminus A[/math] while in [math]\Sigma_E[/math] the complement of a set [math]B [/math] is [math] E \setminus B[/math].


[math]\tau = S \cap E [/math] for some [math]S \in \Sigma[/math]. Since [math]\Sigma[/math] is a sigma algebra we have that it's complement [math]U \setminus S \in \Sigma[/math].
[math] \tau^c = E \setminus \tau = E \setminus S = E \cap (U \setminus S) \in \Sigma_E[/math].

[Anonymous No.14728625]

>>14728623
>The issue here is that you have two different types of complements in ΣΣ the complement of a set AA is U∖AU∖A while in ΣEΣE the complement of a set BB is E∖BE∖B.
Ah shit indeed. Thanks!

[Anonymous No.14728627]

>ywn prove [eqn] e^{i\pi}+1=0 [/eqn] why even live
why even live?

[Anonymous No.14728644]

how does one find the curve over an area?

[Anonymous No.14728757]

>>14728263
>>14728540
Absolute state of /sci/?

[Anonymous No.14728851]

>>14728757
are you implying what i wrote is wrong?

[Anonymous No.14728882]

>>14726000
Fix $\epsilon > 0$
Let $N \in \mathbb{N}$ be such that $N > \frac{3}{2\epsilon} $
Then $ \forall n > N$ it holds that
$ \frac{3n}{2n^{2} + 1} < \frac{3n}{2n^{2}} = \frac{3}{2n} < \frac{3}{2N} < \frac{3}{2\frac{3}{2\epsilon}} = \epsilon $
Thus satisfying the definition of
$ \lim_{n \leftarrow \infty} \frac{3n}{2n^{2} + 1} = 0 $

[Anonymous No.14728888]

>>14726000
>>14728882
Fix [math]\epsilon > 0[/math]
Let [math]N \in \mathbb{N}[/math] be such that [math]N > \frac{3}{2\epsilon} [/math]
Then [math] \forall n > N[/math] it holds that
[math] \frac{3n}{2n^{2} + 1} < \frac{3n}{2n^{2}} = \frac{3}{2n} < \frac{3}{2N} < \frac{3}{2\frac{3}{2\epsilon}} = \epsilon [/math]
Thus satisfying the definition of
[math] \lim_{n \leftarrow \infty} \frac{3n}{2n^{2} + 1} = 0 [/math]

[Anonymous No.14728896]

>>14728888
Wasted

[Anonymous No.14728915]

>>14728888
not wasted
good proof except that retarded arrow that is pointing at the wrong direction

[Anonymous No.14728933]

>>14728627
You can prove that with basic calculus

[Anonymous No.14729033]

>>14727157
Weird

[Anonymous No.14729044]

>>14728851
yes, outstanding proof retard

[Anonymous No.14729058]

>>14729044
are you an imbecile?

[Anonymous No.14729075]

>>14729058
>>14729044
dont fight pls

[Anonymous No.14729119]

>big defense contractor
>coworker talking about their job, I state my job
>they tell me it sounds easy once you memorize all the formulas
>Tell him there is no such thing as there isn't a formula for any of our work and that isn't how it works
>"yeah but once you find the formula you just plug it in"

I just told him he's right and I use a cheap casio calculator to plug in the formulas since I didn't know if he was just yanking my chain. He was one of the machinists I think.
Should have just told him "if its so easy why don't you just learn it and do it to double your pay real quick".

[Anonymous No.14729122]

>>14729075
awwww

[Anonymous No.14729317]

>>14729119
>Should have just told him "if its so easy why don't you just learn it and do it to double your pay real quick".
I haven't had anyone tell me my job is easy, however there are a lot of people I know who are good at reasoning but work menial jobs, I ask them why they don't learn to code and quadruple their salary and they always tell me they're scared to code. It's sad because there's a continent worth of people who have no business coding that do anyway, yet I likewise know a ton of people that could easily shave decades off their work life and/or far increase their salary but there's just a mental block that won't let them accept that they should be doing something with computers.

[Anonymous No.14729478]

>>14729317
programming is gay

[[e-mail] No.14729511]

[[e-mail] No.14729515]

[Anonymous No.14729697]

>>14729478
how is getting paid six figures to do half an hour of work a week from home "gay"? if anything it lets me support a family which is the opposite of gay

[Anonymous No.14729792]

>>14729511
>>14729515
nah

[Anonymous No.14730532]

How much math do I need to set up some machine learning algorithm for predicting future sales based on historical data?

On the programming and data wrangling side I think I'd be fine, but I wonder if I need to upgrade my HS level math knowledge to really fully use this kinda stuff

[Anonymous No.14731211]

>>14730532
ML =/= writing a simple program, which is more than enough to start automated trading.

A common trading algorithm is:
Buy when the 5 day moving average crosses above the 20 day moving average.
Then sell if there's either a 5% decrease or a 10% increase.

Before putting real money in it you probably want to test this on historical data, just sample random spans of time in a historical dataset and see how this strategy would have performed.

[Anonymous No.14731367]

>>14731211
I meant sales as in making a forecast for the company I work at, like let's say Japan sells 2000 in August, the model would spit out things like that based on past data. It's not what they hired me for and it's not something that I know to be 100% meaningful or feasible, but I'd like to take a crack at it one day. I know there's many factors that the finance people use and they consider general market situation and so on, but I'm still curious about how accurate a number one could get from an algorithm that deals purely with the past numbers.

still, the trading stuff you mentioned is interesting too, so thanks for sharing.

[Anonymous No.14731442]

When you randomly see homotopy used in a video game video.
>C) A trajectory is a shortcut if it is not homotopic to a trajectory on the road

[Anonymous No.14731541]

what is wrong with reddit mods?

[Anonymous No.14731544]

>>14731442
kek, but i don't see the point, what if the road is curved and you take a straight path that's homotopic to the road, wouldn't that count as a shortcut?

[Anonymous No.14731554]

>>14731541
What did you do?

[Anonymous No.14731581]

>>14731554
made some off-hand innocuous comment related to (((gender)))

[Anonymous No.14731618]

>>14731581
>(((gender)))
The way you talk about it isn't even "innocuous", so who are you trying to fool?

[Anonymous No.14731676]

>>14731618
>The way you talk about it isn't even "innocuous", so who are you trying to fool?
that's because i'm here and am free of pretension, there it was relatively innocuous, if slightly snarky. certainly not a bannable offence in my mind

[Anonymous No.14731764]

This sounds like a stupid question and I feel like I should know how to answer it but I don't have the required background.
Let S1 and S2 be two squares of unit length in R^2, one centered at (0,0) and the other at (5,5).
Let C be a circle of radius 2 centered at (0,0). (Basically S1 is completely inside of C).
Is there a simple theorem or a clean way to say that there is no continuous affine map from S1 to S2 in R^2 \ C?
Is this a straightforward result of Jordan curve theorem?

[Anonymous No.14731809]

>>14731581
> innocuous comment
riiiiiiight. no one believes that, not even you

[Anonymous No.14731863]

>>14731809
>>14731618
>trannies seething
kek

[Anonymous No.14731915]

>>14731764
No need to use Jordan's curve theorem here.
Suppose there is a continuous affine map [math]f:[0,1] \to \mathbb{R}^2 \setminus C[/math] with [math]f(0) \in S1[/math] and [math]f(1) \in S2[/math]. Then consider the function [math]g:[0,1] \to \mathbb{R}[/math] defined by [math]g(t) = \| f(t) \|_2[/math].
Clearly [math]g(0) < 2 [/math] and [math] g(1) > 2 [/math] so by the immediate value theorem there is a [math]s[/math] with [math]g(s) = 2[/math] but this would imply that [math]f(s) \in C[/math].

[Anonymous No.14732196]

>>14731915
That's really clear and intuitive. Thank you so much.

[Anonymous No.14732262]

What is normed, complete, yellow and curved?

A Bananach space.

[Anonymous No.14732375]

>>14729033
Weird

[Anonymous No.14732404]

>>14721209
The proof can only be understood by people whose native language is not an Indo-European language.

[Anonymous No.14732438]

>>14715781
Why did you post the Queen of the Night from Mozart's Magic Flute

[Anonymous No.14732445]

>>14728256
A fields medallist at HARVARD
https://en.wikipedia.org/wiki/Shing-Tung_Yau

[Anonymous No.14732462]

>>14732262
I prefer pic related as a smoother way to tell the
same joke.

[Anonymous No.14733024]

>>14728627
>>14728933
You don't need calculus to prove [math]e^{i\pi} + 1 = 0[/math]

Just use the definition of [math]e^x = \lim_{n \rightarrow \infty} (1 + \frac{x}{n} )^{n}[/math] to get a basic complex number multiplication problem, namely:
[math]e^{i\pi} = \lim_{n \rightarrow \infty} (1 + \frac{i \pi}{n} )^{n}[/math]

[Anonymous No.14733548]

>>14733024
You know limits is calculus, right?

[Anonymous No.14733852]

Why are mathematical journals and mathematics in general so poorly archived?

[Anonymous No.14733972]

>>14733548
R slash whoosh

[Anonymous No.14733979]

>>14733852
libgen, arxiv, sci-hub, google.
Dude we have papers of Newton and Euler, what are you talking about?

[Anonymous No.14733985]

>>14733548
limits is pre-calc

[Anonymous No.14733990]

>>14733979
>papers
Yes, journals are separated by each article. And all of that is illegal.

[Anonymous No.14734000]

>>14732445
Yau's work is largely reliant on functional analysis and PDEs, if you weren't aware, so he's actually a very weird example to hold up for why Harvard requires little analysis.

[Anonymous No.14734163]

It's summer,,,the cicadas are singing... and I'm so bored. Is there a mathematics discord server full of anons who I can have autistic discussions with?

[Anonymous No.14734179]

>>14734163
##math on libera

[Anonymous No.14734212]

>>14733852
>journals poorly archived
What do you mean? They maintain a big list of all the articles in them, and then they compile the issues into giant volumes to send to libraries. The newer ones are online, for a price. So what do you mean by archived?

[Anonymous No.14734424]

>>14733024

[Anonymous No.14734597]

>>14734179
IRC is the sane choice but we know no one use it.

[Anonymous No.14734616]

>>14734179
>>14734597
I'd like a more active option if you guys don't mind, the less sane the better

[Anonymous No.14734718]

I'm looking for a kindle copy of 'Complex variables and applications brown Churchill, 9th edition' anyone know where I can find it? I can only find pdf versions online...

[Anonymous No.14734744]

>>14734616
#math on efnet

[Anonymous No.14734790]

>>14734718
You do know that the Kindle can read pdf's right?

[Anonymous No.14734824]

>>14734790
Yes, I am just asking if anyone has an epub/mobi version that I can zoom properly, I know it exists because you can buy it on Amazon for £50

[Anonymous No.14734890]

What's the best precalc book for self-study?

[Anonymous No.14734902]

>>14734163
There's the discord with the "anon" who shall not be named

[Anonymous No.14734904]

>>14734744
>>14734179
not op but i've been on both of these (##math on freenode not libera though) and they are super slow and inactive

[Anonymous No.14734919]

Yo /mg/ i seem to recall a big book of integration methods / tricks but I don't remember what it's called, anyone know what I mean?

>>14734718
just buy the indian version of the book it's like 15 bux. better yet read a better complex analysis book

[Anonymous No.14734987]

Which mathematician is made the most fun of? My vote goes to this jobber

[Anonymous No.14735168]

>>14734902
that sounds insteresting, is this some deep lore of /mg/ I don't know about? do you have the link?

[Anonymous No.14735188]

Is calculus1 - full college course by freeCodeCamp.org on YouTube a good place to learn calculus in general? about 3:40 minutes in it said (x+4)(x-4) equals (x^2+16).

[Anonymous No.14735670]

How can I verify the answers at the back of the book of Calculus Stewart are correct?
I've been grinding my integrals axe for the past month and it's seriously nervously and somatically severe to my CNS. I am wracked mentally, and my body needs rest from this overtaxing strain in hours issued on Calc II. And I often get wrong answers. I realized I needed a cheat sheet.
However, with a cheat sheet I am now realizing that some of the answers in the back Just Can't Be Correct, are misprinted, hijacked, or whatever. I feel like a wizard calculating rigorously visualized integrals and also a clown in circus with Stewart over trivial things he does explain in one sentence, or a stoop to be precise: du = dx. He never explains balancing correctly, he just imagines that you will visualize the differential in it's integrated measure on your own. It seems like he has obfuscated the visualization of trig functions too, in the integrals. There are methods, all of them are fully being concentrated and devoted to wholly in effort of will at maximum force, yet they do not simply appear correct persistently; See that, I review, they are right here, now, At Once; now, later they are wrong. There is no reason. No reason is in this book captured efficiently. It is a lack of logic and insight in explanation from a guru. The guru expects grinding on cheat sheets that appear to be faulty in full effect of error of calculation. At my rate of calculation, it should be done in a month, if the rest questions are of the same fortitude. The fortitude, I find myself persisting on a problem, is generally down to half a page, a whole page, or less if I'm thinking clearly and keeping up with my orchestration of the calculus. It seems the book likes to argue with sound principles, in general, in favor of argumentation and reason and transcendental debate or discussion amongst the intellectual; really, is it really prefabished nonsense in order to make you squirm as larvae into a monstrous xenomorph?

[Anonymous No.14735675]

>>14734919
It’s called Impossible integrals and it’s the most based math book I’ve ever skimmed

[Anonymous No.14735677]

>>14734824
Have you checked library genesis? They usually have multiple formats

[Anonymous No.14735678]

>>14734163
I wish the main math discord weren't so awful

[Anonymous No.14735694]

>Grading undergrad proofs be like.

[Anonymous No.14735727]

>>14735694
>Prove that f is injective
>Suppose a = b. By definition of a function, we must have f(a) = f(b)

[Anonymous No.14735775]

[Anonymous No.14735794]

>>14735677
...yes, otherwise I wouldn't ask

[Anonymous No.14735881]

I know how to write correct induction/recursive proofs for state machines, but I honestly have no clue why it works or what's going on... anyone have some suggested readings? This feels like a hurdle, it always feels like magic.

>t. CS brainlet specializing in theory.

[Anonymous No.14736024]

[Anonymous No.14736174]

>>14736024
looks like russian disinformation

[Anonymous No.14736205]

>>14720006
Calc III is easier than calc II in my opinion, vector functions aren’t too scary. It’ll be easier than you think, just pace yourself.

[Anonymous No.14736213]

>>14716490
Uh when n=0, you can't go from
>By assumption all i<n are greater than 0
to
>and n>i, so n>0
because there is no such i. Does that help?

[Anonymous No.14736324]

>>14735678
I joined a while back and while there were some knowledgeable people there it was completely dominated by 1 or 2 high school conversations all the time

[Anonymous No.14736375]

>>14734987
You mean this ladies’ man?

[Anonymous No.14736492]

>>14735678
>>14736324
Is there like an "advanced" section?

[Anonymous No.14736498]

>>14736492
They actually did make one because of issues with too many people getting driven away I think, but i didn't rejoin so idk
There are a few discord which are good, there is a combinatorics one and an algebra one and I think a topology one

[Anonymous No.14736945]

>>14735678
>>14736324
>>14736492
>>14736498
i joined just a couple of weeks ago to ask some algebra question, the channels are grouped into beginner (calculus, linalg, etc) and an advanced sections (algebra, topology, analysis, number theory, etc). i've only browsed the server a couple of times (the advanced section), but it looked pretty civil and on the level, people asking and answering serious mathematical questions, none of that "ermahgerd, e^ipi+1=0 and 1+2+3+...=-1/12" shit

[Anonymous No.14737009]

>>14735881
Can you give a resource for the induction/recursive proofs for state machines that you are studying? I would like to check that out

[[e-mail] No.14737011]

[Anonymous No.14737373]

does calculus use units and unit conversion
t. dropped out of high school and trying to relearn algebra from scratch for calc 1

[Anonymous No.14737414]

>>14737373
>does calculus use units and unit conversion
>t. dropped out of high school and trying to relearn algebra from scratch for calc 1
Not necessarily, it's extra if you want. I have a PhD in Math specialized in this (think calc 1 - calc 15) and I never had to use unit conversion though I could if I wanted to. It's only really necessary if you plan to do physics or maybe chemistry later.

[Anonymous No.14737533]

>>14737373
Math isn't physics. There aren't any units involved.

[Anonymous No.14737666]

>>14737533
>There aren't any units involved.
Not even unit vectors?

[Anonymous No.14737844]

>>14737533
Someone has never done unit analysis with measures.

[Anonymous No.14737883]

>>14724496
Could I see the curriculum for your calculus II course? If you're in Germany, it should be your Analysis II course.
High school in USA is not standardized.

[Anonymous No.14737933]

>>14737844
>analysis
That ugly part of math? Who even wants to go there?

[Anonymous No.14738146]

>>14737414
cheers
I'm currently getting my ass beat by high school level algebra with unit conversion
have a long ways to go before I can touch calc 1 but at least I can skip this unit conversion shit

[Anonymous No.14738250]

Enjoying probability and statistics, a little bit too much actually. I'm scared that my fellow math majors will call me a brainlet faggot if I take any more probability courses.....
Brothers, will I stop being a math chad like you guys if I finish my BSc in math, but go to grad school for statistics?

[Anonymous No.14738254]

>>14738146
Good luck and stick with it, for someone starting from scratch I think high school type algebra is a bigger hurdle than calculus. Of course you need to know that stuff to do calculus, but once you are comfortable with variables and graphing equations with variables (like a parabola for example) then calculus is straightforward after that.

[Anonymous No.14738260]

>>14738250
>Enjoying probability and statistics, a little bit too much actually. I'm scared that my fellow math majors will call me a brainlet faggot if I take any more probability courses.....
>Brothers, will I stop being a math chad like you guys if I finish my BSc in math,
Up until this point you were fine. Probability is a respectable mathematical field, as is mathematical statistics.

>but go to grad school for statistics?
Hold up there chief... the answer depends on your ultimate goal. Statistics PhDs impress business people with money who can offer you a job, but rarely to they impress math bros unless you're going to a really good reputable program. I knew some Statistics PhD students at Carnegie Mellon and I would say they were legit doing some math there so I respect. But I've met a lot of "Statistics PhDs" who turned out to be more like "Professional Studies" PhDs rather than "Statistical Theory" PhDs. If you care what math bros thing, do math. If you care what Business people think, do statistics. If you just want to do something interesting, I strongly suggest a probabilistic math phd, for example doing something with stochastic calculus.

[Anonymous No.14738274]

>>14738260
I see, well I've been living semester to semester and putting off plans for the future, but I know I want to continue into graduate school. Stochastic calculus I believe would fall under an applied math umbrella rather than "Statistics", as the former in a sampling of American universities just now does seem to be filled with useless courses.

Thanks for the info.

[Anonymous No.14738530]

How to quickly review all math up until Calc 1

[Anonymous No.14738746]

Do I need to review everything I've learned before going up to the next cumulative lesson?

[Anonymous No.14738863]

what is the expected number of letters that match between two random strings of length k generated from an alphabet of length m that are independent of order?
i have a bunch of strings that appear to be substrings of pi plus some noise, the first two match to over 70%, some over 90%, but i want to determine with confidence

[Anonymous No.14738909]

>>14737883
Ok sure https://courseoutline.auckland.ac.nz/dco/course/MATHS/250/1215

[Anonymous No.14738972]

>>14738863
If I understand correctly an example of your problem would be:
>abcca matches acaac on 4 letter because both have 2 as and 2 cs
If this is right then your answer is just the sum
>(expected number of shared as) + (.. bs) + …
which equals
>m times (expected number of shared as)
which you should be able to solve

[I feel peaceful and empty in bali at the same time No.14738984]

Pls help calculation to produce the same worth of pic https://www.pixiv.net/en/artworks/26339586 like the same pageviews and traffic but not the same just equivalent

[Anonymous No.14739010]

>A fine sheaf over X is one with "partitions of unity"; more precisely for any open cover of the space X we can find a family of homomorphisms from the sheaf to itself with sum 1 such that each homomorphism is 0 outside some element of the open cover.
Why a family of homomorphisms from the sheaf to itself? Why not just a family of sheaves?

[Anonymous No.14739041]

>>14738972
yes, but the string length k is very close to the size of the alphabet m
i thought there was some kind of elaborate combinatoric pigeonholing going on
also some strings don't correlate with portions of pi at all, maybe there's other constants used

[Anonymous No.14739207]

>>14716503
>>14716503
Thats not how areas are calculated

[Anonymous No.14739227]

>>14738909
>Auckland
AHAHAHAHAHAHAHAHAHAHA
have fun at clown school nigger, I hope tom ter elst rapes your asshole in analysis

[Anonymous No.14739275]

>>14738909
Imagine talking about literally any other country when you're from fucking New Zealand, possibly the least relevant country to anything ever.

[Anonymous No.14739434]

>>14739227
Unlike you and most of the hair-brained retards that populate this department I'm not mentally handicapped.

>>14739275
America gets a lot of things right, but the difficulty of their regular schooling is not one of them.

[Anonymous No.14739464]

>>14739434
Irrelevant country, didn't read

[Fun to watch folks losing their minds here over numbers No.14739500]

>>14739434
Unironically the easiest things to do is also some of the most profittable and easily occupied market and thats why everyone gets their ass filled with water and goes nuts

[Anonymous No.14739690]

>>14739434
>I'm not mentally handicapped
you go to Auckland of course you're a retard, just like everyone else in this shithole country

[niggerland No.14739700]

>>14739275
>NZ least relevant country in existence

next to USA

[Anonymous No.14739779]

>>14739700
your country worships America
I don't even have to know where you're from to know that's true since it's true for all countries which aren't America

[Anonymous No.14739814]

>>14739779
Least self-centered American.

[Anonymous No.14739881]

>>14735694
whats wrong with pic related? I mean why is a block of manipulations so bad?

[Anonymous No.14739885]

>>14739814
>t. citizen of completely irrelevant country

[Anonymous No.14739886]

>>14739881
normalfaggots can't into symbols and want 10 pages of funny text "explaining" it with an analogy instead.

[Anonymous No.14739900]

>>14739886
A lot of times when proving identities I end up multiplying by 1 (i.e. a/a) a lot and/or splitting terms into even and odd parts or combining parts of different remainders mod something. I really dont want to break up the flow of what im doing by explaining such obvious things though.

[Anonymous No.14739920]

>>14739779
>your country worships America
>I don't even have to know where you're from to know that's true since it's true for all countries which aren't America
The elites worship America. The people worship God.

[Anonymous No.14739925]

>>14739881
it's frequently messy as fuck, poorly organised, overly long when a concise argument would work better, and stupid steps are commonly made
you're also going to be the 10th person to write this sort of stuff so the patience for these things vanishes very quickly

[Anonymous No.14739929]

>>14739920
Sorry, I can't hear you over the sound of American media playing all throughout your country

[Anonymous No.14739937]

>>14739929
>instead of studying, the undergrad retard wastes his time arguing about America on the internet
You will never be a mathematician, by the way.

[Anonymous No.14739968]

>>14739925
ok i can see that for undergrads but for people who know what theyre doing i dont see the problem? Im not thinking of stuff exactly like your pic but more like my pic but longer.

[Anonymous No.14739975]

>>14739937
This

[Anonymous No.14739990]

>>14739885
>yeah I'll keep proving his point, that'll show him

[Anonymous No.14740058]

>>14739968
that's absolutely not what the picture is getting at

[Anonymous No.14740069]

>>14714498
we don't have code tags here?

[Anonymous No.14740307]

is it okay to assume that f(x + dx) = f(x) + dx when doing a proof with "nice functions" assumption ? If not, any ideas how to get rid of f(dx)?

[Anonymous No.14740314]

>>14740307
No because it's f(x + dx) = f(x) + f'(x)dx

[Anonymous No.14740346]

>>14738909
>vector spaces
>least squares
>series, sequences, power series
>multivariate functions
>taylor series

Anon, this is practically no different than the curriculum in America. Albeit slightly out of order and some topics from Calc I and Calc II there, but the Calculus series should be seen as a whole.
As for your criticisms of American curriculum, you should know that they are all accredited and standardized to meet an unofficial international standard. That is still just calculus II. You graduating from Auckland, or anon graduating from X State university, would be viewed the same when applying for a graduate program.
I do not understand the obsession with people from Europe and elsewhere, being so critical of US degree programs. Its the same thing, and the fact you don't understand that speaks volumes.
I can assure you that you are not learning some secret calculus that American students are not being taught or tested on.
also,
>30% of grade from group work and homework.
Yikes.

[Anonymous No.14740351]

AMS notices are such garbage filled with non-mathematical content presented as mathematics. This month, types of "art" as math. Too much crap in the "pure" math world and I want nothing of it. Very glad to have shifted my focus to applied mathematics and PDE's, I want nothing of that childish nonsense, non-serious world that pure math circles are becoming.
I'll keep my subscription to the AMS bulletin for now at least.

[Anonymous No.14740369]

>>14740314
i keep getting a term like this, if it's wrong is there something close? what should it be instead?

[Anonymous No.14740373]

>>14740314
this is the term i keep getting, i posted out of order

[Anonymous No.14740378]

>>14740351
PDEs are based

[Anonymous No.14740400]

I've been thinking about trees of various depths with the condition that each node can have [math]0, 1, ..., m[/math] children. pic is for [math]m = 2,[/math] this number grows much more rapidly than I'd expected, but I suppose it makes sense that there's approximately a squaring of the previous number of trees for every new depth.

[Anonymous No.14740461]

>>14740400
If you start with 0, you should rather say 0,1,...,m-1 children, otherwise your language will always be 1 off and that's annoying. (I'd actually start at 1.)

Anyway, always check oeis
https://oeis.org/search?q=1%2C2%2C10%2C170&language=english&go=Search

[Anonymous No.14740504]

>>14740369
>>14740373
niqqa I don't know

[Anonymous No.14740697]

>>14740346
The guy said he didnt learn about planes or dot products until calc 2, and even that was extension material. Goes to show why I can graduate in 3 years with the same degree as he gets in 4.

[Anonymous No.14740779]

>>14740461
Yeah that's the same sequence. I asked about something like this here a few days ago but I didn't get any yous and didn't know what to search for.

[Anonymous No.14740992]

>>14738909
>>14739227
>>14739434
>>14739690

Topkek

[Anonymous No.14741595]

Anyone got a problem set for Pugh's Real Analysis?

[Anonymous No.14741689]

>>14741595
You can use the problems from literal any other introductionary real analysis book. It's all the same stuff in all books/classes. There might be a few order differences. Some will do Real Analysis purely in R^1 before generalizing it later while others start introducing metric spaces right away before considering the special case of R^1 but you can just do exercises in a different order if you want.

[Anonymous No.14741805]

kiwiniggers are a fucking disgrace. You're more embarrassing than Swedistan at this point.

[Anonymous No.14741978]

Any good text on multi-linear algebra? I'm looking to supplement Munkres' Analysis on Manifolds.

[Anonymous No.14742323]

>>14739434
>America gets a lot of things right, but the difficulty of their regular schooling is not one of them.
Imagine criticising any other country's education when we've absolutely tanked in both literacy and numeracy over the past 10 to 15 years, this shithole is one of the worst educated first world countries in existence.
Just in case the fact we are now going to start teaching Maori creationism again didn't clue you in.
Oh and go look at how many science books they got rid of in the university library to make room for the Maori section, kek. Shelves of maths books tossed out to make room for our new woke brown overlords.

[Anonymous No.14742386]

Just read the Springer, Dover Books, Universitext catalogue guys. Adios!

[Anonymous No.14743403]

>started uni during covid lockdowns
>lived with parents, packed every semester to the most I could handle, even summer semesters
>This coming fall is my last semester
>tfw I used symbolab, google, open notes, take home exams, the entire time. Still have trouble doing basic integrals

I cheated in pretty much every single course and every single class. The only course where I legitimately didn't look up answers and google during exams was abstract algebra and combinatorics, but I got A's in both of those courses.
I don't think I could solve even the simplest differential equation without symbolab.

Anyone else here an ACTUAL fraud? I'm at a public ivy, and I'm sure I will get into a great graduate programs where I will be exposed and ridiculed.

[Anonymous No.14743446]

Other anon here bumping for this question
>>14728419

I am in exact same position. I have tried reading sticky but it didn't really helped. Is "Road to Reality" by Penrose a good choice?

[Anonymous No.14743457]

>>14743446
No, start reading Lang's Basic Mathematics

[Anonymous No.14743470]

>>14742323
I'm too young to know what it was really like in the before times. I had the pleasure of not having to deal with NCEA, so I suppose you're right that I shouldn't talk for the country as a whole. I have been wondering how the entire math collection fits on three bookshelves while there's entire rooms and corridors of books in a language no one spoke until it became politically convenient.

[Anonymous No.14743684]

What are the odds of making it into academia with a pure math phd in hodge theory from a tier 2 uni ?
Should I take courses to get some more down to earth math ( probabilities and stats mostly ) to secure an opening to the industry as a quant ?

[Anonymous No.14743768]

Any recommendations on where to learn about computational complexity?

[Anonymous No.14743796]

>>14743768
Introduction to algorithms, fourth edition.
Chapter 2 and 3

Currently reading that textbook, I'm on chapter 3 myself

[Anonymous No.14743804]

>>14743768
YouTube.

[Anonymous No.14743808]

imagine you're in a forest where the trees grow in such a way that each node has an equal chance of having 0, 1 or 2 children. what is the average height of trees?

[Anonymous No.14743812]

>>14743808
The question doesn't even make sense.

[Anonymous No.14743826]

>>14743808
Don't you need two nodes with 0 children for each node with 2 children or the tree will never end?
The average height seems to be clearly infinite.

[Anonymous No.14743831]

>>14743812
generate trees by starting at the root node and flipping a three sided dice to determine if the current node gets 0, 1 or 2 children. at the start you have 1/3 chance of not getting any further. there's an 1/9 chance of having a tree with two nodes, and a 1/27 chance of having a tree with 3 nodes, where the root has 2 children, etc.

what is the expected value of the depth.

[Anonymous No.14743836]

>>14743826
yeah it's clearly infinite. as you collect more trees the ways for the trees to reach greater depths increases much faster than the number of trees you collect.

[Anonymous No.14743843]

>>14714498
With everyone discussing textbooks, I have a question.

Had to review calc 1 and 2 material bit ran low on time so I've been just speed reading the chapters of Spivak's calc w/o doing the problems as a refresher, but I want to actually go in depth this fall when I have time.

My plan is to do Stewart's calc as a baby companion while I work mainly through Apostol's. Should I do that or should I just redo Spivaks and take it slow and do the problems?

[Anonymous No.14743871]

>>14743831
>>14743808
>>14743836
Let's simplify the question, and make it 0 or 1 child.
Probability 1/2 of getting 0 height.
Probability 1/4 of getting 1 height.
Probability 1/8 of getting 2 height.
In general: Probability 1/2^(n+1) of getting n height.
Expected value is then the infinite sum of n/2^(n+1).
Playing around with the power series of 1/(1-x)^2, you get the answer is 1.

Let's do it a different way: 1/2 Probability of height 0, 1/2 probability of getting a node with a tree with an average height. So if with call the average height A, A = 0*1/2 + (1+A)*1/2. So 2A = 1+A, and A = 1. Checks out.

Do this in the case of 3 options: 1/3 chance of 0, 1/3 chance of average tree, 1/3 chance of 2 average trees. But note: The two average trees will both have average height. So A = 0*1/3 + (1+A)*1/3 + (1+A)*1/3, giving 3A = 2(1+A), hence A = 2.

[Anonymous No.14743878]

>>14743843
Depends on what you want to do. Stewart is going to be a ton of computation and will take a considerable amount of time to work through. When you get to the calc II portion and begin integrals, you will spend close to an hour per problem, or computing proofs for trig integrals.
Around the same amount of time will be spent on problems involving volumes of revolution and applications for physics.

[Anonymous No.14743941]

I think I have a mistake here >>14743871, but don't know how to fix it.
I don't think the approach works with 2 children because the height would use the MAXIMUM of the heights of the two children. The approach worked fine with the simpler example because we didn't have to use the max function.

I think the correct approach may have to use order statistics: https://en.wikipedia.org/wiki/Order_statistic

[Anonymous No.14743942]

>>14743871
I don't think so. try generating some yourself.
https://www.wolframalpha.com/input?i=random%281%2C+3%29

it's very easy to get way past two levels of depth. in particular what do you mean by
>probability of getting a node with a tree with an average height
>But note: The two average trees will both have average height
is this true?

[Anonymous No.14743954]

>>14743941
true, you can try generating some yourself
https://www.wolframalpha.com/input?i=random%280%2C+2%29

very easy to get pretty deep in just a few trees.
2 seems way too low. I'm pretty sure the expected value of depth has to be infinity.

[Anonymous No.14743979]

>>14715766
Harvard is a leftist shithole so you will find trannies who don't like analysis because it actually makes sense and is useful

[Anonymous No.14743986]

>>14743808
Consider the slightly related Markov chain [math](X_n)[/math] with
[eqn]X_0 = 1[/eqn]
[eqn]P(X_{n+1} = k-1 | X_n = k) = \frac{1}{3} \\
P(X_{n+1} = k |X_n = k) = \frac{1}{3} \\
P(X_{n+1} = k+2 | X_n = k) = \frac{1}{3}
[/eqn]
Basically [math](X_n)[/math] counts the amount of nodes you haven't looked at yet and at each step you check one node. The probability that this chain ever hits the state 0 (that is that the tree is finite) is [math]\frac{\sqrt{5}}{2} - \frac{1}{2}[/math]. Conversely there is a chance of [math]\frac{3}{2} - \frac{\sqrt{5}}{2}[/math] that the tree is infinite. A non-zero chance for an infinite tree automatically leads to an infinite expectation.

[Anonymous No.14744015]

>>14743986
Shouldn't that third one be a +1 instead of a +2?

[Anonymous No.14744034]

>>14744015
You're right. Then the rest of the arguement doesn't work.

[Anonymous No.14744123]

>>14744034
I think it's still doable.
Think of it as a random walk in 1D, where a third of the time you step forward, a third you step back, and a third you wait. The wait is irrelevant and can be ignored. So think of it as half the time you step forward, half you step back.

The expected number of steps to reach any given number (in particular 0) is infinite. The expected number of steps represents the number of nodes in the tree minus the "wait" nodes (nodes with 1 child). So the height is also unbounded.

[Anonymous No.14744418]

>>14744148
>>14744148
>>14744148
>>14744148

[Anonymous No.14744533]

>>14743470
>I have been wondering how the entire math collection fits on three bookshelves
We used to have nearly 20

[Anonymous No.14744923]

>>14741595
https://www-users.cse.umn.edu/~rmoeckel/course/syllabus.5615.alt.f08.html
https://math.berkeley.edu/~brent/105.html
Should cover your needs.