/mg/ maths general: back to mochi edition

[Anonymous No.11575679]

talk maths, formerly >>11572312

https://www.math.columbia.edu/~woit/wordpress/?p=11709

[Anonymous No.11575684]

>>11575679
0.999... = 1

[Anonymous No.11575720]

imagine being so desperate to force your little meme back into the OP you make a new general while the other one's on page 2

[Anonymous No.11575743]

>>11575720
>what is a bump limit

[Anonymous No.11575758]

>>11575679
he forked math with no survivors

[Anonymous No.11575774]

>>11575743
Yes, I am aware that there is a bump limit on 4chan. I am also aware than /sci/ is slower than my 93-year-old grandma and the other general will be up for at least another full day.

[Anonymous No.11575776]

>>11575743
Why does bump limit matter? Does it affect discussion?
Are you an attention whore who wants /mg/ on the front page all the time? ARE YOU?

[Anonymous No.11575799]

>>11575679
>back to mochi edition
You are embarrassing

[Anonymous No.11575861]

Let [math]\{a_n\}_n[/math] be a sequence of non-negative numbers such that [math]\sum_{i=0}^\infty a_n < \infty[/math] and [math]\sum_{i=0}^\infty a^2_n < \infty[/math].

Fix some positive constant [math]c[/math]. What is [math] \sum_{i=0}^\infty a_n c^n[/math]?

I know that the series converges since [math]\sum_{i=0}^\infty c^n = 1/(1-c) < \infty[/math], but I can't evaluate the limit for an arbitrary [math]a_n[/math].

[Anonymous No.11575868]

What are /mg/'s users hobbies outside of STEM?

Mine:
>Violin
>Drawing
>Reading
>Writing

[Anonymous No.11575873]

>>11575684
brainlet here, are you "allowed" to represent x as "0.999...." in formal logic?

[Anonymous No.11575876]

>>11575868
I like history and wasting time. I'm really good at the latter, not so much the former. What do you write?

[Anonymous No.11575883]

>>11575861
If this can't be computed in general, how can I at least lower bound [math]\sum_{i=0}^\infty a_n c^n[/math]?

[Anonymous No.11575884]

>>11575868
>video games
>shooting
>lifting
>binge reading wikipedia articles about history, econoics and religion

[Anonymous No.11575886]

>>11575868
Cheese making, using those green ties you normally use to tie your grocery bags to make figures and dragons and cars and shit, dancing if that counts, the cello is my instrument of choice, and I am learning how to draw (I totally suck at the moment).

[Anonymous No.11575892]

>>11575679

[Anonymous No.11575894]

>>11575886
How do you manage your time? You practice your instrument and drawing everyday?

[Anonymous No.11575898]

>>11575679
What is the minimum IQ required to understand Inter-universal Teichmüller theory?

[Anonymous No.11575908]

>>11575894
I played the cello for 7 years from middle school to high school, so less about actively practicing and more about just having fun with it/ As for drawing, I only dedicate maybe 30 minutes to an hour per day on average.

[Anonymous No.11575909]

>>11575898
>120IQ to understand calculus
Kek, yeah, right you don't know what IQ means

[Anonymous No.11575915]

>>11575868
Doing psychedelic drugs

[Anonymous No.11575916]

>>11575908
I started violin at high school, wish I had started earlier, but I'm at an OK level nowadays

[Anonymous No.11575919]

>>11575868
>reading
>shitposting
>walking
I would like to start HEMA, but I'm too weak and feel guilty for doing stuff that's not maths.

>>11575898
Cannot be understood by a human being restricted to just one universe.

>>11575909
And 150 to discover you can use Wolfram Alpha.

[Anonymous No.11575922]

>>11575915
Which do you recommend? I planned on taking them with a friend, but can't go back due to quarantine, and I heard that they might help with deppression.

[Anonymous No.11575927]

>>11575919
Oh and singing too. It's fun.

[Anonymous No.11575928]

>>11575916
I get that, there was this one guy who started playing violin in elementary school and by the time I started playing the cello he completely blew everyone out of the water in terms of skill. Was kind of a dick about it too. A friend of mine started working out in middle school and by the time he got to college the dude was massive. I doubt I could ever catch up to his level of fitness. If I ever have kids (long shot, I know) I want to try pushing them towards trying things out new things early on, just so they never feel regret.

[Anonymous No.11575935]

>>11575922
ALD-52, 1P-LSD, 4-HO-MET, and 4-HO-MiPT are all good. 4-AcO-DMT might be useful if you're looking for something with potentially therapeutic value.

[Anonymous No.11575936]

>>11575922
This best psychedelic drug is p-adic analysis. But seriously if you even do psychedelics, start painting or drawing or something. Fomenko isn't making art anymore and I need new pretty math pictures. But actually Fomenko is why I'm learning to draw.

[Anonymous No.11575942]

How much money would I be making if I PhD in pure math but fail in academia?
$0? $40k? $100k?
(no 300k starting meme please)

[Anonymous No.11575944]

>>11575928
How old are you right now?

[Anonymous No.11575945]

>>11575936
I don't know how to draw, and I'm scared of doing it like shit. I doubt I'd like it anyway, and have nothing I'd want to draw.
>>11575935
The thing I don't like about DMT is that the duration is really short. I don't know how relevant this is in practical terms, but I imagine it's a bit lacking compared to Ayahuasca. What can you tell me?
>>11575942
Depends on a lot of factors.

[Anonymous No.11575946]

>>11575942
$0. The only place for Mathematicians in the academia, you idiot, or are you naive enough to believe the market will hire you?

[Anonymous No.11575950]

>>11575873
Only if you are working with hyperreals, in whichcase not all .9... are equal to each other, and none is equal to 1.

[Anonymous No.11575953]

>>11575946
When you enter a math major, you're already betting all your cards on the academia, there's no middle ground here

[Anonymous No.11575954]

>>11575922
Not a psychedelic, but if you're looking for something with antidepressant effects, I recommend 2-FDCK.

[Anonymous No.11575955]

>>11575936
>But actually Fomenko is why I'm learning to draw
Have you seen this https://www.springer.com/gp/book/9780387345420? It's not as creative, but the drawings are nice and the author would like to see illustrations be used more for intuition. Fomenko's art is absolutely gorgeous and I congratulate you for having a good taste.

[Anonymous No.11575956]

>>11575944
24, I know, I'm not old and shouldn't feel regrets, it just feel like all of my middle and high school years (and some of undergrad) were completely and totally wasted

[Anonymous No.11575959]

>>11575861
The second condition seems extraneous. Convergence of [math]\sum a_n[/math] is strictly stronger than convergence of [math]\sum a_n^2[/math] when all the terms are nonnegative.
I really doubt there's any kind of closed formula for this though. For example if you pick a_n properly you can set your sum equal to the first 66669 prime powers of c. I doubt there's going to be a formula for that simpler than just evaluating the whole sum.
I'm not sure you could even get particularly useful lower bounds without more information, but I might be wrong on that point.

[Anonymous No.11575962]

>>11575955
These actually look quite nice, I like the detail on the knots. Actually, that's possibly the best thing about Penrose's book, his illustrations are pretty great at times.

[Anonymous No.11575964]

>>11575945
I've never done DMT or ayahuasca. DMT supposedly has a high degree of time dilation, so that might help to cancel out the short duration. I have done DPT though, but it was underwhelming. I insufflated it, but the effects weren't very intense. I might try it again with a different ROA. I'm thinking of getting some Banisteriopsis caapi to act as a MAOI, and use it to make "dipropylhuasca".

[Anonymous No.11575966]

>>11575959
Ah sorry messed up the assumptions, I know that [math]\sum_i a_n < \infty[/math] and [math]\sum_i a_n^2 = 1[/math]. Does this help? Thanks.

[Anonymous No.11575974]

>>11575868
Mine
>Guitar
>Volleyball
>Learning French/German
>Youtube/Vidya

[Anonymous No.11575975]

>>11575974
>Learning French/German
Useless, learn japanese

[Anonymous No.11575978]

so we're just gonna drop the hot mathematician talk from last thread?

[Anonymous No.11575982]

>>11575966
That's still not an assumption that adds anything. You already knew [math]\sum a_n^2 = s < \infty[/math], so you can just rescale your original series by dividing by the constant [math]1/\sqrt{s}[/math] if you want. It's the exact same problem except maybe multiplied by a constant.

[Anonymous No.11575983]

>>11575975
That's the next one, followed by ASL

[Anonymous No.11575984]

>>11575950
wouldn't they all have a standard part equal to one though?

[Anonymous No.11575989]

>>11575950
thanks bud

[Anonymous No.11575992]

>>11575962
Oh and, of course, there is Escher with his tesselations and Möbius bands. I remember using the metric of the Poincaré disk to do some tesselations of my own. It's pretty fun, I recommend. All you need is a ruler, a compass and a calculator.

[Anonymous No.11575993]

>>11575946
>>11575953

[Anonymous No.11575994]

>>11575982
Right, I see. Is it at least possible to conclude that, when [math]c\to 1[/math], the series [math]\sum_n a_n c^n[/math] converges to something close to [math]\sum_n a_n[/math]?

[Anonymous No.11575998]

>>11575679
Oh please jesus god anons give me a hint. I've been trying this problem for a half fucking hour and I'm going to kill myself if I can't solve it.

What am I doing wrong?

[Anonymous No.11576016]

>>11575994
I think you can conclude that much, yeah.
If you have convergence in some interval around 1, then since power series are automatically continuous where they converge you get that [math]\sum a_nc^n \rightarrow \sum a_n[/math].
If you only have convergence to the left of 1 (i.e. any c > 1 makes the sum diverge) then you probably have to use Abel's convergence theorem, but it's still true.

[Anonymous No.11576019]

>>11575954
I'd rather not get addicted to stuff.

[Anonymous No.11576025]

>>11575998
So I guess in the xln(y) part since it's a multiplication derivative we're talking (f ')(g)+f(g'). Which means that, since the derivative of ln(y) is (1/y)(dy/dx), that we have a problem. Because now my equation for the left side looks like dy/dx(ln(y) + x/y(dy/dx)+5y^4. I have an extra dy/dx.

What the fuck.

[Anonymous No.11576028]

>>11575998
[math]\ln(y)+\frac{x}{y}\frac{dy}{dx}+5y^4\frac{dy}{dx}=\frac{6}{x}[/math]
Rearrange to get
[math]\frac{dy}{dx}=\frac{6y-xy\ln(y)}{x^2+5xy^5}[/math]
Ask on /sqt/ next time

[Anonymous No.11576029]

>>11575998
For future reference, homework goes in the stupid questions thread >>11565779
Anyway, you've fucked up the ln(y). It doesn't belong in the denominator; you differentiated the x term to get ln(y), not anything involving y, so there's no dy/dx in front of it. You only get dy/dx terms when you differentiate some function of y.

[Anonymous No.11576037]

>>11576029
Oh. 2 points.

1. Sorry for posting here, I didn't know the rule. WIll change next time.

2. While I'm here. Why is there not a dy/dx in front of the ln(y) stuff? I thought you give that to everything with a y in parentheses?

so like:

x(ln(x) wouldn't get it

but

x(ln(y) would.

[Anonymous No.11576043]

>>11576016
That's very nice, I just read about Abel's theorem and related results and a lot of my problems are solved it seems. Thanks.

Where do you learn about this kind of stuff? I'd love to read more.

[Anonymous No.11576053]

>>11576037
You put it in front of everything with a y __when you differentiate the y__. But since you're using the product rule to differentiate xln(y), you only differentiate the y stuff in one of the terms, not both. Only the term where y is differentiated gets a dy/dx. It might be easier to understand why once you get that implicit differentiation is basically just using the chain rule. You have some function f(y) involved, and you do this:
[eqn](\frac{d}{dx}x)f(y)+x(\frac{d}{dx}f(y)) = f(y)+x\frac{df}{dy}\frac{dy}{dx}[/eqn]

[Anonymous No.11576060]

>>11576043
It's in Rudin. It's probably in most serious real analysis textbooks. Unfortunately I don't have a better recommendation for you than the standard meme book, I never really studied analysis beyond the undergrad courses.

[Anonymous No.11576070]

>>11576060
>It's in Rudin.
Rudin is a meme.

[Anonymous No.11576080]

>>11576060
What's the difference between babu rudin and adult rudin? I know one is graduate level and the other is undergraduate, but what makes them different exactly?

[Anonymous No.11576081]

>>11575898
>What is the minimum IQ required to understand Inter-universal Teichmüller theory?
200 (up to indeterminacies)

[Anonymous No.11576089]

Threadly reminder to work with physicists.

[Anonymous No.11576091]

>>11576080
Totally different content. Baby Rudin deals with convergence of sequences/series of numbers or functions, differentiation and integration of functions on the real line, and some chapters in the back nobody reads.
Adult Rudin does abstract, measure-theoretic integration theory, functional analysis, and a bunch of complex analysis chapters in the back that I'm not sure anybody reads either.

[Anonymous No.11576114]

>>11575998
Thanks for the help. I finally got it right. I'm on the next problem and I'm as stuck as I was.

I'm a fucking physics major. I should just end it now.

[Anonymous No.11576118]

https://www.rationality.org/about/instructors

What went wrong?

[Anonymous No.11576125]

What were your goals when you decided to become a math major? Where are you now? Have you accomplished any of them or are you otherwise on your way to do so?

[Anonymous No.11576126]

>>11576118
>with an extensive background in category theory, algebraic topology, and related subjects.
That's what.

[Anonymous No.11576130]

>>11576125
>What were your goals when you decided to become a math major?
To do as little work as possible in uni
>Where are you now?
grad school
>Have you accomplished any of them or are you otherwise on your way to do so?
yes

[Anonymous No.11576133]

>>11576125
>What were your goals when you decided to become a math major?
I'm not sure I remember, and they don't matter anymore. They're probably retarded anyway.
>Where are you now?
I want to end it.
>Have you accomplished any of them or are you otherwise on your way to do so?
Non-applicable.

[Anonymous No.11576143]

>>11576114
Oh, sorry. I spoke too soon. I still got it wrong.

I WANT TO FUCKING DIE PLEASE KILL ME I DON'T DESERVE TO LIVE I'M FUCKING SCUM OMG OMG OMG OMGO MGOM EGAOWEGMIAWEMGOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOE

[Anonymous No.11576147]

>>11576125
>What were your goals when you decided to become a math major?
begum mathematician
less broadly, understand higher mathematics well enough to poke around it myself
>Where are you now?
4th semester undergrad
>Have you accomplished any of them or are you otherwise on your way to do so?
sure, i'm on track to finish undergrad a year early which would get me in grad studies learning the real shit soon

[Anonymous No.11576150]

>>11576143
sasuga physics major sama

[Anonymous No.11576155]

>>11576125
>What were your goals when you decided to become a math major?
To prove the Riemann Hypothesis and become a great mathematician
>Where are you now?
Still in undergraduation at 23, will probably finish by 26 with a lot of hardwork
>Have you accomplished any of them or are you otherwise on your way to do so?
No, I've already gave up on my dreams, now if I can get into a PhD program then graduate I'll be happy

[Anonymous No.11576161]

[Anonymous No.11576176]

>>11576118
who is this chong and why should i care

[Anonymous No.11576217]

>>11576125
>What were your goals when you decided to become a math major?
None. I just picked the only thing I've ever been decent at.
>Where are you now?
Trying to get a PhD.
>Have you accomplished any of them or are you otherwise on your way to do so?
I have a bunch of results that I will go through with my supervisor at some point, and then we will decide if they are sufficient to be sent somewhere to be published. I guess, even with my struggles with some concrete stuff like examples, I am making progress towards that end. I will make it, and therefore so will you people too!

[Anonymous No.11576263]

>>11575974
oops forgot about rollerblading

[Anonymous No.11576271]

What's your favorite math youtube channel?

[Anonymous No.11576279]

>>11576271
epic math time for style
Flammablemaths for consistency
Mathologer for quality

[Anonymous No.11576281]

>>11576271
>What's your favorite math youtube channel?
https://www.youtube.com/user/njwildberger

[Anonymous No.11576316]

>>11576279
flammable maths is fun times

[Anonymous No.11576417]

>>11576271
That channel with clickbait title who keeps solving IMO problems.

[Anonymous No.11576438]

>>11576417
What?

[Anonymous No.11576447]

>>11576438
https://www.youtube.com/watch?v=uJqbHaFqjmI

[Anonymous No.11576494]

>>11576417
>favorite

[Anonymous No.11576496]

>>11576494
What's wrong if I like it?

[Anonymous No.11576545]

What's your favourite definition of mathematics? I particularly like Poincare's

"Mathematics is the art of giving the same name to different things."

[Anonymous No.11576549]

>>11575868
Hanging out with friends/my gf
philosophy
making and listening to music
tv/anime/movies/etc

[Anonymous No.11576552]

>>11576545
>What's your favourite definition of mathematics?
Mathematics is not well-defined.

[Anonymous No.11576562]

>>11576125
>What were your goals when you decided to become a math major?
Learn math
>Where are you now?
At home
>Have you accomplished any of them or are you otherwise on your way to do so?
Yes

[Anonymous No.11576572]

>>11576271
I have a few ties:
https://www.youtube.com/user/XylyXylyX/playlists

https://www.youtube.com/channel/UCu5cg_Jd9XSJL_CHUskgkGw/playlists

These are physics but they are rigorous mathematically so I think it's okay:
https://www.youtube.com/channel/UCUHKG3S9N_QeIE2jQXd2-VQ/playlists
https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

[Anonymous No.11576871]

>>11576545
>Mathematics
That's not well-defined!

[Anonymous No.11576940]

Category Theory

[Anonymous No.11576984]

>>11575861
By your first assumption the convergence radius of this series (in the real line or even the complex plane) is at least 1. You can probably find a counter-example of an an such that the series doesn't converge for c > 1 (and c nonnegative).
It's utopic to imagine you could get a precise evaluation of the sum without further information on an. Your condition isn't that restrictive, pleny of sequels are going to meet it.

[Anonymous No.11577033]

>>11576940
stop hating on category theory

[Anonymous No.11577042]

>>11576545
>matheatics
Science analysing sets and constructions built of sets.

[Anonymous No.11577062]

>>11576940
Don't you think that's more like IUT?

[Anonymous No.11577093]

>>11576125
>What were your goals when you decided to become a math major?
I had to study something, I was reasonably good at it in school and had to make my cross somewhere...

>Where are you now?
Master thesis.

>Have you accomplished any of them
Yes. I successfully evaded the life of wage cucking, at least for now...

[Anonymous No.11577106]

>>11575868
>Vidya
>Reading
>Jujitsu
>Voluntary firefighter, but not really as of right now...
I also occasionally do some cycling and usually (but not right now) hang out with friends.

[Anonymous No.11577118]

bros... why am i so stupid?

[Anonymous No.11577134]

why is complex analysis so fucking terrible? who the fuck actually finds it enjoyable?

>mfw I see a complex integral

[Anonymous No.11577137]

>>11576281
same for me

[Anonymous No.11577140]

>>11576125
>What were your goals when you decided to become a math major?
My initial plan was to be a computer scientist, I just didn't want to bother with stupid programming coursework so I studied maths instead. I also wanted to explore some research opportunities in the department while I was there, and I liked it so much that I decided to stay for a PhD.
>Where are you now?
Postdoc in mathematical physics.
>Have you accomplished any of them or are you otherwise on your way to do so?
My goals changed and I gave up on working in computer science, although that's always the plan B if an academic career fails.

[Anonymous No.11577144]

>>11577118
Welcome to the club, friend.

[Anonymous No.11577426]

redpill me on holomorphic functional calculus

[Anonymous No.11577495]

>>11576549
Unvirgins are not welcome here. Begone with you, and never return.

[Anonymous No.11577498]

>>11577426
>holomorphic functional calculus
Complex analysis then?

[Anonymous No.11577531]

>>11577426
see >>11577134

[Anonymous No.11577542]

>>11577531
Does this mean that the blue pill would be some psychedelic that makes you see things similar to the "complex analysis is fun" propaganda pictures with all the shapes and colours?

[Anonymous No.11577545]

>>11577542
Man stop using /pol/ language here it's cringe bro

[Anonymous No.11577551]

>>11575679
kill this mofo will u

[Anonymous No.11577552]

>>11577545
True, /pol/ is pure cringe.

[Anonymous No.11577557]

>>11577552
>>11577545
post nose

[Anonymous No.11577567]

I'm returning to university to finish my math/physics degree after a many years hiatus. Ive started right where I left off, however I'm struggling to remember everything from first year. What exactly would one need to already know heading into 2nd year physics snd math?

[Anonymous No.11577578]

>>11577557
Does my jewish heritage triggers you? Ara, how cute, now end yourself

[Anonymous No.11577583]

>>11577567
That depends on what you did during your first year. So what did you do during your first year?

[Anonymous No.11577584]

>>11577567
The essentials are:
Calculus
Vector Calculus
Linear Algebra
Abstract Algebra
Analysis
University Physics (Freedman)
Classical Mechanics

[Anonymous No.11577610]

>>11577583
Well in my country for first year math and physics you just have general papers
Calc A
Calc B
Algebra
Physics A
Physics B
For second year they start to be more specific ie,
Classical mechanics
Electrostatics
Multivariable calculus
Differential equations
Linear algebra.

The problem I seem to be facing is every time I think I've covered all I need to start diving into the later topics I run into something else, and I'm trying to make sure I cover everything without wasting too much time on things like integral approximation methods (trapexoid/simpson/rienmann sums, etc).

[Anonymous No.11577618]

https://youtu.be/DZGINaRUEkU

The Symphony of Science - The Quantum World

So... what are we really made of?
Dig deep inside the atom
And you'll find tiny particles
Held together by invisible forces.
Everything is made up
Of tiny packets of energy
Born in cosmic furnaces.

The atoms that we're made of have
Negatively charged electrons
Whirling around a big bulky nucleus.
The Quantum Theory
Offers a very different explanation
Of our world.

The universe is made of
Twelve particles of matter
Four forces of nature.
The universe is made of
Twelve particles of matter
Four forces of nature
That's a wonderful and significant story.

Suppose that little things
Behaved very differently
Than anything big.
Nothing's really as it seems.
It's so wonderfully different
Than anything big!

The world is a dynamic mess
Of jiggling things!
It's hard to believe
That Quantum Theory
Is so strange and bizarre
Even Einstein couldn't get his head around it.

In the quantum world,
The world of particles,
Nothing is certain.
It's a world of probabilities.
The quantum theory
Offers a very different explanation
Of our world.

The universe is made of
Twelve particles of matter
Four forces of nature.
The universe is made of
Twelve particles of matter
Four forces of nature.
That's a wonderful and significant story

It's very hard to imagine
All the crazy things
That things really are like
Electrons act like waves.
No they don't exactly.
They act like particles.
No they don't exactly.

We need a theory of everything (need theory of everything)
Which is still just beyond our grasp (still just beyond our grasp)
We need a theory of everything (need theory of everything)
Perhaps the ultimate triumph
The ultimate triumph of science.

The Quantum Theory
Offers a very different explanation
Of our world

I gotta stop somewhere...
I'll leave you something to imagine!

[Anonymous No.11577622]

>>11577584
Basically I'd like to know the subsections of these that are essential, and what ones you need to know before being able to tackle another.

For example do I need to know multivariable calculus before I can do classical mechanics, if not what principles do you need to get my head around first?

[Anonymous No.11577623]

>>11577610
Recap the approximation methods, l'Hôpital and stuff like that to take care of the calcs, then the basic group theory stuff like subgroups, normality, cosets, Lagrange, homomorphisms, and the basics of fields to cover algebra. For physics just see what you remember of those two and you will be fine.

[Anonymous No.11577629]

>>11577622
>do I need to know multivariable calculus before I can do classical mechanics
Obviously, classical Mechanics has a lot of multivariable calculus, man, just download the books and take a look at them to remember somethings, just focus on vector calculus, classical Mechanics and university physics, since those will probably be more useful to you. Don't worry too much, when the courses start again you'll get the hang of it soon.

[Anonymous No.11577633]

>>11576545
Poincare is based and this is by far the best description I've seen of what math is as a whole. Most mathematicians just blank when you ask them this.

[Anonymous No.11577662]

>>11576545

[Anonymous No.11577663]

>>11577629
My university offers multivariable the semester after classical, hence why I wasn't sure.
>>11577623
>l'Hôpital and stuff like
That's basically what I've been trying to do. L'hôpital rule, partial fractional integration, trig substitution, disck, washer and shell methods, arc length, surface area of revolution... About to refresh myself on Taylor and maclaren series

[Anonymous No.11577664]

>>11577662

[Anonymous No.11577667]

>>11577664

[Anonymous No.11577671]

>>11577662
>>11577664
>>11577667
Logicomix unironically made me choose maths.

[Anonymous No.11577687]

>>11577671
Mathematics+philosophy+physics+literature is the best combo

[Anonymous No.11577709]

is it possible for a 35 year old cooder to learn real analysis? I just always wanted to know what its all about. Seems like the mathematics culture is to present problems that are just barely outside of the students reach to torture them and make them feel inferior. Then the professor shows them the magic trick after the student wasted hours the night before and they bow down and suck his cock. I'm too old for this type of game. Is there a better way to learn? It seems even textbooks take part in this mindfuckery.

[Anonymous No.11577716]

>>11577709
Abbott's book is the go-to if you're struggling with Analysis, it explains everything to the minimum detail, if you can't understand Analysis after that book then idk.

Basically Analysis is a rigorous study of calculus, but that's not the definition of Analysis, it's hard to define it, I guess I could say Analysis is the study of 'things' that converges.

[Anonymous No.11577734]

>>11577662
>>11577664
>>11577667
wittgenstein in logicomix was an excellent character

[Anonymous No.11577737]

>>11577709
Hello there.

>is it possible for a 35 year old cooder to learn real analysis?
I don't see why age should matter. It make take more of less time depending of how much math you know and how much you've forgotten.

>Seems like the mathematics culture is to present problems that are just barely outside of the students reach to torture them and make them feel inferior. Then the professor shows them the magic trick after the student wasted hours the night before and they bow down and suck his cock.
It depends of the math course. Some courses just have the goal to become familiar with mathematical tools and being able to use them for practical purposes. Math courses oriented to physicists, engineers, biologists, etc. are often of this nature.

Math math-oriented courses do indeed have that kind of a approach. The goal is to train the student to find mathematical proofs, with problems "just barely outside their reach", because this is the reality of everyday research.

For studying Real Analysis I recommend Terence Tao Real Analysis Vol. I and II. These books are wonderfully written, and you'd be able to read them just like a novel.
Stephen Abbott's Understanding Analysis is also a really good alternative.

You may also find Rudin books recommended in Analysis, I'd avoid them for now. They're heavily math-oriented, and its concise slick proofs may be harder to follow at this point.

[Anonymous No.11577766]

>>11577709
>It seems even textbooks take part in this mindfuckery.
This is true and an absolute shame. I love it when textbooks at least include answers to the exercises - it allows me to learn so much quicker and better - but very very few of them do that. Self-studying math is a fucking chore.

[Anonymous No.11577768]

What's a good book for functional analysis? What about advanced functional analysis?

[Anonymous No.11577779]

>>11577709
the chinks are the worst for this.

[Anonymous No.11577781]

>>11575861
Abel transform can give you a expression for the n-th partial sum in terms of a_n and the n-th partial sum of the c_n.
Taking the limit of the partial suns it should look like Sum c^n*(a_{n+1}-a_{n}) (the first term of the transform going to zero as n->\infty)

[Anonymous No.11577785]

>>11577766
are... you saying you look at the answers to exercises?
>>11577768
stein and shakarchi is good for functional analysis

[Anonymous No.11577786]

>>11577768
>functional analysis
Folland
>What about advanced functional analysis?
Folland

[Anonymous No.11577791]

>>11577766
Dude you won't learn anything if you keep looking at the answers, believe me, I've been there

[Anonymous No.11577802]

>>11577785
>are... you saying you look at the answers to exercises?
if you don't know how to solve an exercise, having a solution lets you learn a new technique that you weren't able to come up by yourself. without solutions or a professor to ask, there's a chance you will literally just never know how to solve it. and even if you do know how to solve the exercise, looking at the solution to check if you didn't miss any assumptions or to see alternative proof methods is very helpful.

there are literally so many advantages to having solutions in a textbook, but I guess every author wants their textbook to be used in US universities and get shitloads of money from it so they won't include solutions.

[Anonymous No.11577806]

>>11577781
Sorry, I'm retarded, it should be
[math]\sum_{n = 0}^{\infty} (\sum_{m=0}^{n}c^m)(a_{n+1}-a_{n})[/math]

[Anonymous No.11577860]

Any books that would explain why mathematicians have accepted the obviously dumb and wrong axiom of induction?

[Anonymous No.11577863]

>>11577806
Also, forgot a - in front of it.
Plus, if (a_{n+1}-a_n) is \Omega(1/(n^s)) then the sun is asymptotic to \frac{c\psi^s(c) - \gamma(s)}{c-1} where \psi^n is the n-th polygamma function.
I don't think there's a simple closed form tho

[Anonymous No.11577872]

>>11576118
I don't know him personally, so I can't say, but I think 1) he was put onto and unfruitful topic and got disillusioned with math a bit and 2) he wasn't comfortable being an incel.

[Anonymous No.11577874]

>>11577860
Why's it wrong and dumb?

[Anonymous No.11577875]

>>11577860
Deepak Chopra.

[Anonymous No.11577877]

>>11577860
https://www.math.wustl.edu/~chi/310notesIV.pdf

[Anonymous No.11577895]

>>11577042
>Science analysing sets and constructions built of sets.
Intriguing. Would you expand this idea?

[Anonymous No.11577899]

>>11577860
Read about Löwenheim–Skolem theorem (although I don't think you can understand this article) https://en.wikipedia.org/wiki/Löwenheim–Skolem_theorem

[Anonymous No.11577902]

>>11577877
The well-ordering principle is also dumb and wrong.
>>11577874
Because it's empirically wrong.
>>11577899
I already know about it, but thanks anyway.

[Anonymous No.11577904]

Is the "soundness" of a math system the same as the "sound" property in deductive reasoning.
I'm confused.

[Anonymous No.11577911]

>>11577902
>empirically wrong
Prove it.

[Anonymous No.11577913]

>>11577902
>The well-ordering principle is also dumb and wrong.

[Anonymous No.11577923]

>>11577874
>>11577877
Well-ordering principle
Let S be the set of natural numbers of grains of sands which make up a big pile of sand. S is nonempty because a pile made up of 10000000 grains of sand is a big pile. Clearly if n grains make up a big pile of sand, removing one grain won't make it small, it will still be a big pile of sand. Hence S has no least element.
Axiom of induction:
1 grain of sand is a small pile of sand
If a pile made up of n grains of sand is small, adding one more grain won't make it big.
Hence every pile is small. But that's clearly wrong.

[Anonymous No.11577930]

>>11576572
based

[Anonymous No.11577931]

>>11577923
Sand isn't well ordered dumbass

[Anonymous No.11577937]

>>11577931
Well-ordering principle wrongly states that the natural numbers are well-ordered.
Each pile of sand is made up of natural number of grains.
Nowhere did I say that sand is well-ordered. That doesn't even make sense.

[Anonymous No.11577939]

>>11577923

[Anonymous No.11577951]

>>11577937

[Anonymous No.11577954]

>>11577939
>>11577951
Which part of my proof of the falsehood of the axiom of induction and the well-order principle do you dispute?

[Anonymous No.11577962]

>>11577954
I dispute the claim that you are mentally sane and should not kill yourself

[Anonymous No.11577970]

>>11577954
The part where you mistake fuzzy statements with traditional logic is pretty annoying. The part where you use your "intuition" and what clearly amounts yo layman understand and definition of a few words to create some kind of "gotcha" is what makes it insufferable.

[Anonymous No.11577972]

>>11577970
How would you describe this pile of sand?

[Anonymous No.11577978]

>>11577970
If you make a stick the length of which is one light year and then you push it one cm, you get information travelling faster than light. :^)

>>11577972
A motherfucking shitload.

[Anonymous No.11577980]

>>11577972
With natural language, as you did. Of course natural language isn't precise, and so formal logic's appliableness is dubious at best. Now stop being a faggot

[Anonymous No.11577982]

>>11577972
A collection of identical objects, grains of sand.

[Anonymous No.11578000]

>>11575679
Are there any good lecture series on HoTT?

[Anonymous No.11578001]

I dont understand how to prove a function is always greater than some given value. DESU I dont understand how proofs about real valued functions make sense.

Like, if I want to show a function is monotonically increasing on some interval, I take the derivative and show that on that interval the derivative is positive. That makes sense to me because of what the derivative is. But what I dont get is how do you show that the derivative is always positive on that interval. I can't just go "Here's the graph, see! it's always positive" that's fucking stupid, but if I try to do it algebraically it would involve taking an uncountable amount of inputs and showing that they are all positive valued on the output. So there must be a way to do it, because non-algebraic "proofs" are not real and not worth any degree of consideration.

So what is the algebraic way to show that some function f(x) is always greater than some value v, or to show on some interval (a,b) some function g(x) is monotonically increasing, and such?

[Anonymous No.11578005]

>>11577972
A group called a "pile" equipped with an operation "x" which acts on two piles A and B such that A x B = C, where C is denoted the union of all "sand" elements of A with B.

[Anonymous No.11578006]

>>11578001
Use inequalities you god-damned mong

[Anonymous No.11578011]

>>11578001
you know you can quantify over uncountable sets right

[Anonymous No.11578028]

>>11578001
If you want to show that [math]f(x)>r[/math] for all [math]x\in [a, b][/math], find the values of [math]x[/math] for which [math]f(x) = r[/math]. Then there are basically 3 options: never, one such value, many values. If there are no such values, then you just evaluate the function at some easy value [math]x_0[/math] and then see if [math]f(x_0)>r[/math]. If there is one such [math]y\in\mathbb{R}[/math], and if [math]y\not\in [a, b][/math], just evaluate [math]f(x)[/math] for any [math]x\in [a, b][/math] and compare. If there are two or more values, then you choose those between which the interval lies and between which there are no other [math]y: f(y)=r[/math]. Evaluate at some easy value between those and compare.

[Anonymous No.11578030]

>>11575868
>Rowing for uni
>Reading
>Chess
>Hanging out with my art student friends because they are attractive and not autists like math students.

[Anonymous No.11578114]

>>11578028
How does showing f(x) = r for some values of x show that it's always greater than or equal to r. You've not shown that it must be the case for all x in (a,b) that f(x) >= r. You have not shown anything about how, on the interval, every single point on that interval is greater than r.

[Anonymous No.11578123]

>>11575953
>>11575946
it is claimed that the largest employer of mathematicians in usa is the nsa

[Anonymous No.11578140]

>>11578123
They're not hiring academia rejects though

[Anonymous No.11578150]

>>11578001
We will prove that [math] f(x)=\ln(x)\geq0[/math] on the interval [math][1,\infty)[/math]. Notice that [math] f'(x)=\frac{1}{x}[/math] which is positive so long as [math]x>0 [/math] so the function is increasing on [math](0,\infty)[/math]. Also note that [math]f(1)=0[/math] and so we have proven our claim.

[Anonymous No.11578166]

>>11578150
>Notice that f(x)=1x which is positive so long as x>0
This is not proven, again what you're doing is just going "look at the graph! see, it's positive" this is not algebraic and thus is not valid. Just going "notice" is not mathematically rigorous and not valid.
Give me ALGEBRAIC proof, otherwise it's not real.

[Anonymous No.11578171]

>>11578150
>Notice that [math]f(x)=1x[/math] which is positive so long as [math]x>0[/math]
I think anon's point is how can you know this? Of course that's it's "obvious" it's true, but how do you rigorously proof that [math]1/x[/math] doesn't simply decide to start decreasing somewhere near infinity?

[Anonymous No.11578173]

>>11578166
I'm sorry, I just copied the text, it's supposed to say
>f(x) = 1/x is positive so long as x>0

[Anonymous No.11578180]

>>11578166
A fraction is positive so long as both the numerator and denominator have the same sign

[Diracula No.11578184]

anyone have that comic about how girls ruin DnD sessions?

[Anonymous No.11578185]

>>11575898
IQ is just speed dude. If you're 120 IQ you can understand everything there just fine, but it'll take more time than if you were 150 IQ

[Anonymous No.11578196]

>>11578114
Yes I did. If the function [math]f[/math] is continuous, then so is [math]g(x) = f(x) - r[/math], and so [math]g[/math] can change sign only after being 0 at some point. If you know all the points where you get 0, you get the sign of [math]g[/math] between any consequent such points by evaluating the function at any point between them. If [math]g(x) > 0[/math], then [math]f(x) > r[/math].

[Anonymous No.11578205]

>>11578180
Why? You can think that anon's question is stupid but at least make an effort to understand him. His question is trivial to answer in the naturals if you accept the principle of induction, but how do you actually formally prove that some arbitrarily large irrational value of [math]x[math] doesn't cause [math]f[/math] to start decreasing (at least until the next natural)?

[Anonymous No.11578215]

>>11577954
The induction step is wrong. This is the same flaw as in the 'proof' that all horses are the same color.

[Anonymous No.11578309]

This one's funny, Lex Fridman asks Stephen Wolfram on the role of Ego and he gives an excuse for himself

https://www.youtube.com/watch?v=ez773teNFYA&t=2151s

[Anonymous No.11578315]

>>11578205
If you want to be ridiculously pedantic, we could show that it holds for all rational numbers (on the function [math]\frac{1}{x}[/math], by definition, don't even ask) and then continue by stating that the rationals are dense in R, and then you prove that its continuous on [math][1,\infty)[/math](the interval which we're concerned about) and so it would hold for the irrationals. I'm sure an algebraist could give you a simpler answer.

[Anonymous No.11578318]

F

[Anonymous No.11578334]

>>11575942
Not that anon, but thanks for that rec. I was actually going through this gallery considering printing some of these
http://chronologia.org/en/math_impressions/images.html

[Anonymous No.11578337]

Did Mochizukawaii solve all the maths yet?

[Anonymous No.11578346]

>>11578334
Was meant for
>>11575936

[Anonymous No.11578356]

>>11578315
>I'm sure an algebraist could give you a simpler answer.
Well, that's the whole point. Anon wants to see it proven, not just argumented for (although your argument should be good enough to at least convince him that there's a way to maybe prove what he wants to the desired level of detail).

[Anonymous No.11578438]

>>11578114
You didn't read his post right.

[Anonymous No.11578445]

>>11578315
>>11578356
holy fuck what an autistic discussion
if x > y > 0
then multiply both sides by 1/xy which is a positive number
you obtain 1/y > 1/x
gooodbye problem

[Anonymous No.11578449]

>>11578166
Holy fucking shit you're fucking dumb
LOOK UP ORDER RELATIONS AND LOOK UP THE DEFINITION OF THE ORDER ON R
IT IS PROVABLY COMPATIBLE WITH THE OPERATIONS ON R IN CERTAIN WAYS
YOU CAN FIND THESE THINGS IF YOU JUST. FUCKING. LOOKED.

[Anonymous No.11578451]

>>11578445
Why is 1/xy a positive number?

[Anonymous No.11578457]

>>11578166
>positive numbers are positive
>NOOOO YOU DIDN'T PROVE THIS
There comes a point when you're no longer being rigorous and simply being that obnoxious 2 year old who figured out he can ask "but why?" to every single statement.

[Anonymous No.11578467]

>>11578445
>>11578449
>>11578457
Sir, this is a maths general. You need to calm down.

The guy hasn't even asked for anything super weird. Do you also get this ignited when set theorists prove "obvious" shit because they're being overly pedantic?

[Anonymous No.11578479]

>>11578467
>Do you also get this ignited when set theorists prove "obvious" shit because they're being overly pedantic?
Yes. Nobody reads those chapters.

[Anonymous No.11578497]

>>11578479
Confirmed for inferior "intuitionist" (in terms of style) mathematician. Please don't talk to my superior logician self anymore.

[Anonymous No.11578513]

>>11578318
fucking hell what a terrible month for math
at least he wasn't another COVID victim

[Anonymous No.11578515]

>>11578451
1/x is positive number
1/y is positive number
two positive numbers multiplied give a positive number

[Anonymous No.11578526]

>>11578513
Spain is in bad shape and I know some nice mathemagicians from there. I hope they are ok. And an old guy in Paris, too.

[Anonymous No.11578539]

>>11578467
STOP FUCKING POSTING

[Anonymous No.11578546]

>>11578515
Why are 1/x and 1/y positive numbers?

[Anonymous No.11578557]

>>11578526
I feel you, man. the guy who was my undergrad advisor is an old fart with COPD.
thankfully my country's not being hit too hard yet compared to others, but there are a couple hundred cases in that city

[Anonymous No.11578576]

>>11578526
Bad shape? 2 weeks from now Brazil will have more than a million cases, I think I might die.

[Anonymous No.11578578]

>>11578557
I wish Corona-chan would take me instead of someone who can actually get or has already got something done. Let me a sacrifice to Nurgle, so that actual maths folk can carry out their work.

[Anonymous No.11578580]

Is computational geometry CS or Math?

[Anonymous No.11578588]

>>11578576
At least you stopped drinking bleach. Try not to die, and the same for mr. Verbitsky (assuming you are not him posting the reading list over and over again)! Stay alive, anons. Your contribution is needed.

[Anonymous No.11578645]

>>11578580
It's CS, but some applied mathfags also do it. It's also mostly rediscovering 19th century algebraic geometry results, or so one of my professors says

[Anonymous No.11578716]

>>11578588
>Your contribution is needed
Not that guy but contribution to what? My thesis is bunk and I know it, my motivation to work is dead, intellectually I am inferior to hundreds of well known mathematicians and phycisists... I don't plan on killing myself but if I died the world wouldn't stop turning for 1 second because my contributions are nil...

[Anonymous No.11578754]

How to roll into math?

[Anonymous No.11578777]

>>11578588
>Verbitsky
Not him, but I've been to his room at IMPA once, I thought of knocking on the door and talking to him about his chart and math, but I got scared and left kek

[Anonymous No.11578788]

>>11578716
Then we are the same.

>>11578777
Your trips will protect you. Please do have a chat with Misha!

[Anonymous No.11578907]

>>11578166
[math] f'(x)=\frac{1}{x}\to xf'(x)=1 [/math]
by cases

[math]x[/math] positive
[math]\to f'(x)[/math] positve because we have a positive product
[math]x[/math] negative
[math]\to f'(x)[/math] negative because we have a positive product

[math]x[/math] is given as positive
[math]\to f'(x)[/math] is positive for all such [math]x[/math]. [math]f(x)[/math]
is therefore increasing for all these [math]x
\ \square[/math]

I think that's sufficient

[Anonymous No.11578935]

>>11578907
You're just shifted the problem to "prove that every product of two positive numbers is positive", which is again obviously true but if anon accepted that he'd also accept that [math]1/x, x > 0[/math] is always positive. You're just appealing to the definition of product over the reals without grounding it in an inductive reasoning that actually "shows" that every product will be positive (i.e., you're just playing games with symbols and anon doesn't accept that they necessarily capture the problems of all real numbers).

I think the only way to satisfy that autist is with >>11578315's reasoning.

[Anonymous No.11578940]

>>11578935
*problems -> properties

[Anonymous No.11578948]

>>11578935
unless I missed something his last post was >>11578173
I thought he might just be a legit brainlet that couldn't see why a fraction with positive numerator and denominator must be positive
the person questioning the legitimacy of that was >>11578205 who appears to be a different anon

[Anonymous No.11578951]

What is domain of [math]cos \sqrt x[math] and why is it a set of real numbers?

[Anonymous No.11578958]

What is domain of [math]cos \sqrt x[/math] and why is it a set of real numbers?

[Anonymous No.11578968]

>>11575998
Just take the total differential

[Anonymous No.11578976]

>>11578958
you need to pick a domain
if you mean the real valued function, then the domain is obviously [math] [0, \infty ) [/math]. If you mean a complex valued function, then it's defined on [math] \mathbb{C} \setminus R [/math] where [math]R[/math] is a ray on which you take a branch cut.

[Anonymous No.11579000]

>>11578976
>real valued function
The problem is that for [math]x<0[/math] you can write [math]\cos \sqrt{x} = \cos \sqrt{(-1)(-x)}=\cos{i \sqrt{-x}}=\cosh{\sqrt{-x}}[/math]

[Anonymous No.11579018]

What is your preferred notation for the set of bijections from a set on itself?

[Anonymous No.11579024]

>>11579000
be careful with that sort of reasoning, it isn't true in general and similar stuff can give you garbage
[math]\sqrt{1}=\sqrt{-1\cdot -1}[/math]
[math]\sqrt{-1\cdot -1}=\sqrt{-1}\sqrt{-1}[/math]
[math]\sqrt{-1}\sqrt{-1}=i\cdot i= -1[/math]
[math]1=-1[/math]
this has to do with branch cuts
it does work in this case, see here: http://davidbau.com/conformal/#cos((e%5E((log(%7Cz%7C)%2Biarg(z)%2Bi2npi)%2F2))) so you could argue for a definition of [math]\cos\sqrt{x}[/math] such that that is the definition for negative reals, though not through your math, you'd need to use more rigorous stuff that takes into account the multivalued square root and then show that both values net the same result (essentially since cos is even)

[Anonymous No.11579025]

>>11579018
[math]S_X[/math] (symmetric group of X)

[Anonymous No.11579041]

>>11579024
[math]\cos x = \sum_{n=0}^{\infty} \frac{(-1)^nx^{2n}}{(2n)!}[/math]
If i substitute x with [math] \sqrt x[/math] I get [math]\sum_{n=0}^{\infty} \frac{(-1)^nx^{n}}{(2n)!}[/math] that is convergent for every real number. Rigorous enough?

[Anonymous No.11579049]

>>11579041
yep, that works

[Anonymous No.11579075]

>going through Velleman's How to Prove It
>Spends one day reading a section of a chapter
>Spends the next day doing all the exercises of that section
Is it normal or am I really really slow? Do you guys usually read the entire section of a book then proceed to do the exercises immediately? I'm doing all exercises, reading the sections very carefully to understand everything but I'm realizing that this method is really slow, I'll finish the book in 50 days if I keep this pace, but I don't know, what do you guys think? Is this fine or should I speed things up?

[Anonymous No.11579103]

>>11579075
>doing all the exercises
in books i read I tend to do the exercises that don't seem immediately obvious or intuitive + a few simple exercises to make sure I actually understand how to work with what i just read
taking a day to go through a section depends a lot on the book. For some that's my pace, for others I blast through several sections in a few hours. but that's more about the subject matter and the book than the person reading it in my opinion.

You're being very thorough, which is good, it means you'll likely need to refer back to the book less often later on.

[Anonymous No.11579105]

>>11579075
I don't do exercises. I read chapters and immediately absorb all the knowledge within them; Exercises are a waste of time because they're just for applying what I just learnt.

[Anonymous No.11579112]

>>11579105
they're more for making sure you didn't misunderstand some principle and to make sure you understand the full implications of what you read

[Anonymous No.11579117]

>>11579075
Take your time, you'll slowly become faster. Most math books are planned to be studied for a full semester (sometimes even 2). You're fine. How to Prove It is an specially important book if you're beginning to learn math, so take your time.

[Anonymous No.11579118]

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

[Anonymous No.11579148]

is this worth a damn?
https://mathvault.ca/math-test/
i kinda wanna know how i'm doing as an undergrad mathlad

[Anonymous No.11579154]

>>11579118
Wow that's bad

[Anonymous No.11579192]

Stupid question about proofs.

It's a common argument in analysis to say: the sequence [math](a_n)[/math] converges to 0, so for any [math]\epsilon>0[/math] we can choose [math]N[/math] so that [math]\sum_{n=N}^{\infty} a_n < \epsilon[/math].

Can I do the same thing when I have a countable set of convergent sequences? That is: the sequences [math](a_{n}^{(i)})[/math] converge to 0 for each [math]i[/math], so we can choose [math]N[/math] so that [math]\sum_{n=N}^\infty a^{(i)} < \epsilon[/math] **for all [math]i[/math]**?

What if there are uncountably many [math](a^{(i)}_n)[/math]?

Not sure if I'm overthinking this.

[Anonymous No.11579196]

>>11577662
>>11577664
>>11577667

[Anonymous No.11579209]

>>11579196
Where can I read logicomix online?

[Anonymous No.11579210]

>>11579209
it sucks, but there's some funny panels like the ones ITT

[Anonymous No.11579214]

>>11579192
Nope, if you took a epsilon for every sequence there's no guarantee that the epsilons have a lower bound different from zero.
Consider a_n^i = 1/(i*n)^2 the epsilon for i+1 needs to be smaller than the one for i ad infinitum.

[Anonymous No.11579215]

I like the scene with russell's nightmare of gauss

[Anonymous No.11579222]

>>11579210
Why it sucks?

[Anonymous No.11579229]

>>11579222
half of the comic is about how they made the comic

[Anonymous No.11579231]

>>11579222
half of the comic is about how they made the comic

[Anonymous No.11579234]

>>11579214
so if I want to have the same epsilon, I need to choose a different N for each (a^i_n) and then it works, right?

[Anonymous No.11579237]

>>11579231
Where can I read it online though?

[Anonymous No.11579238]

>>11579231
Is that supposed to be Papadimitriu? Lmao he looks like a meme boomer

[Anonymous No.11579244]

>>11579238
The guy in the yellow shirt is Perelman my man

[Anonymous No.11579245]

>>11579234
That should work

[Anonymous No.11579248]

>>11579244
I read christos and computer scientist and just assumed. Well, he kind of look like Perelman

[Anonymous No.11579255]

>>11579244
>>11579248
nah this is him in real life

[Anonymous No.11579263]

https://vocaroo.com/eXOMjfkYjHk

[Anonymous No.11579288]

>>11579248
It's not fucking Perelman kek, I'm joking you idiot

[Anonymous No.11579291]

>>11579237
it's a fucking book
not a webcomic
go away

[Anonymous No.11579298]

>>11579288
Can you stop fucking posting?

[Anonymous No.11579304]

>>11579234
>>11579214
Wait, I'm retarded. The reasoning is right but the series is wrong. You want the sum of the series to get slightly bigger as i grows, not smaller. Sorry.

[Anonymous No.11579310]

>>11579304
In that case then there's no global epsilon.
Yes, that works.

[Anonymous No.11579332]

>>11579310
>there's no global epsilon.
what do you mean by that?

[Anonymous No.11579341]

>>11579332
Of every sum is a bit larguer than the anterior then you can't take any finite epsilon to work for all sequences while keeping N fixed.
The first example fails because you don't actually need to take a smaller epsilon (in fact the epsilon for the sequence with i = 1 should work for all of them, because each one is a bit smaller than that one).

[Anonymous No.11579354]

>>11579117
>Most math books are planned to be studied for a full semester (sometimes even 2).
Most math books also aren't planned to be studied in full at all. Books almost always include substantially more material than you could reasonably teach in a course, for lots of reasons (it gives the instructor choices to customize his course without having to write up his own notes, it gives interested students bonus content, it makes the book more useful as a reference, etc.)
People who self-study almost always seem to want to power straight through the entire book preface to index. This isn't always a bad idea, but it's hardly ever what happens in universities so it slows you down compared to traditional students unless you work like a madman.

[Anonymous No.11579448]

>>11575956
I feel exactly the same way. I know I enjoyed the time but I can’t help but feel like if I was exposed to what I like now I would appreciate it even more and also be better.

[Anonymous No.11579489]

[math]\mathbb{Z}_n[/math] is the set of the remainders of all natural numbers modulo [math]n[/math]
(where [math]n[/math] is an integer greater than [math]1[/math])
how is [math](\mathbb{Z}_n,+)[/math] a group when it doesn't exhibit an inverse property? thank you, i'm sorry.

[Anonymous No.11579499]

>>11579489
(a + (b-a+1) mod b) = 1

e.g. with a=3 and b=7,
3 + (7-3+1) = 3 + 5 = 8
so in Z_7, 5=-3, i.e. 5 is the inverse of 3

[Anonymous No.11579501]

>>11579489
(a + (b-a)) mod b)= b mod b = 0

e.g. with a=3 and b=7,
3 + (7-3) = 3 + 4 = 7
so in Z_7,
3 + 4 mod 7 = 0
so 4=-3, i.e. 4 is the inverse of 3

[Anonymous No.11579502]

>>11579489
Let [math]a[/math] be a remainder mod [math]n[/math]. Naturally, [math]n-a[/math] is a remainder mod [math]n[/math]. Then, [math]a + (n-a) = n[/math], which has remainder [math]0[/math] mod [math]n[/math]. [math]0[/math] is the identity element in [math]\mathbb{Z}_n[/math].

You may be thinking of multiplication, in which, no, not every element has an inverse.

[Anonymous No.11579506]

You're a mess, Anon. Skulking around [math] \mathbb{R}_n [/math]? Dodgy place. Don't want no one to see you there. People will think you're up to no good.

[Anonymous No.11579528]

>>11575868
lifting, video games, bricklaying, binging wikipedia about history economics and technology, surfing,

[Anonymous No.11579551]

>>11579501
>>11579502
i thought it would have to be something about messing with inverse moduli... but i wasn't very confident. thank you.

[Anonymous No.11579595]

>>11575884
>>11579528
clones?

[Anonymous No.11579628]

This isn't exactly /mg/ related, but I can't think of a better place on which to talk about this (maybe /adv/).

I'm a euro finishing their comp sci msc. The programme was ok, nothing to write home about but not bad either. I had plans to pursue a phd immediately after presenting my dissertation, but as the date nears I'm starting to think that it'd be better to take a year or two off to look into doctoral programmes at other unis. En part this is because I've come to realise I am tired of the environment in my current uni and really have no wish to continue working here.

My questions are: do you guys think this is a good idea? I know people who've done it successfully, but I'm afraid of losing my motivation to go back for a phd after I start working (+ there's some loss of knowledge as time goes on). What are some good things (topics, books, papers) to study in preparation for a comp sci phd? Obviously I can't give too many details about what area I'm interested in for fear of self-doxing, but it's reasonable to assume that I have at least a passing interest from "algebra" (as a broad term) all the way to memegory theory. I am also interested in foundational works in mathematics, since I should also take the chance to revise my knowledge.

I'd be happy to hear about your own experiences doing anything similar. Salutes to all for taking the time to read my shit.

[Anonymous No.11579633]

>>11579595
are you the first ID? if so yeah mate lol i guess we have similar tastes

[Anonymous No.11579638]

>>11579633
nah, that ain't me, your post gave me deja vu tho and made me go look for the other one

[Anonymous No.11579643]

>>11579638
lol, well i guess a lot of people have wikipedia addictions too lol

[Anonymous No.11579671]

>>11579628
I took two years off before I started my PhD (not deliberately, due to health issues) and I had no issues going back.
Rustiness is not a big deal. You derust really fucking fast (within weeks) once you start up again, and ideally you should be spending a little time each day on studying even when you're working, so you won't be totally out of practice anyway.
Losing your motivation is a serious possibility, but this is a good thing, IMO. The people who lose motivation when they take a break are the people who didn't really want to stay in academia all that badly but were just trying to hide from entering the real world. Once they find out the real world isn't that terrifying, they lose their reason to go back. These sorts of people usually struggle in grad school anyway, so it's better for everybody that they realize they fit better somewhere else.
If you have serious intrinsic motivation to go back and do a PhD, the kind that actually belongs in a PhD program in the first place, that's not going to go away.

[Anonymous No.11579766]

>>11579628
There are some books written by Krantz aimed at people entering a PhD, it might help you, look on /sci/'s wiki, I forgot the title of the book

[Anonymous No.11579795]

>>11579628
I took a year off before heading into my Phd and boy was it worth it. I think the experience will do you well anon. That being said, as >>11579671 pointed out, if you don't feel like going back after a year, that's a strong sign the program isn't a good fit for you. I would say that you should have a goal of at least reading one comp sci related text over the span of the year that you're out of school, that way you still retain a bit of the stuff you've learned and possibly have a better transition back into comp sci. You could also learn some discrete math.

[Anonymous No.11579967]

/MG/… I HAVE BEEN WONDERING… WHAT’S IT ALL ABOUT? SERIOUSLY? WHEN YOU GET RIGHT DOWN TO IT?

[Anonymous No.11580294]

Has the Continuum Hypothesis (CH) been solved?
Vote here
https://strawpoll.com/7geke189

[LMC !!6bFXHDKL67m No.11580491]

>>11580294
Why don't you read cohen and find out?

[Anonymous No.11580509]

>>11580491
Why would you think I haven't read and understood Cohen's proof of independence of CH of ZFC?

[Anonymous No.11580540]

A mighty fine morning to everyone. To those working on something today: good luck with your attempts - and to the rest: have a nice day!

[Anonymous No.11580734]

>>11580540
look at me im so happy and cute and nice ^____^ fuck off

[Anonymous No.11580768]

>>11580294
Your 1 and 2 aren't really very different.

[Anonymous No.11580813]

>>11579628
taking time off in the middle of a global meltdown which is likely to cause the biggest crash in job opportunities in recent history (especially in academia) might not be the best idea. if you're dead set on doing a PhD, just do it now while good scholarships etc. are still available. but I would seriously reconsider the PhD in case you want to go into industry - just getting a job now and sticking with it might be safer.

[Anonymous No.11580814]

>>11579291
>it's a fucking book
And?

[Anonymous No.11580823]

>>11579192
>It's a common argument in analysis to say: the sequence (an)(an) converges to 0, so for any ϵ>0ϵ>0 we can choose NN so that ∑∞n=Nan<ϵ∑n=N∞an<ϵ
It is?
1/n certainly converges to zero. But certainly the series converges for no N...

Am I missing something?

[Anonymous No.11580824]

>>11580823
the series is not 0 for any finite n, the point is that it gets very small for large N. you can't choose epsilon=0

[Anonymous No.11580843]

>>11580824
>the point is that it gets very small for large N.
No. Absolutely not. The sum from N to infinity of 1/n does not exist for any N.

[Anonymous No.11580854]

>>11580843
uhh right, that argument applies to summable sequences, >>11579192 just didn't specify this I guess.

[Anonymous No.11580857]

>>11580854
Oh, sure, then it is okay.

[Anonymous No.11580943]

How does one show that a simply-connected open subset of the Euclidean plane is contractible?

[Anonymous No.11580958]

>>11580943
is it true though? an open unit ball in R^3 minus the origin is simply connected & open, but not contractible

[Anonymous No.11580961]

>>11580958
That's why I said the plane.

[Anonymous No.11580973]

>>11580734
you're stinky

[Anonymous No.11581067]

>>11580961
my bad you're right
then I think this would be a sketch of a solution: call the subset X, then
1) find sequence of sets [math]U_k \subseteq X[/math] s.t. [math] U_1 \subseteq U_2 \subseteq U_3 \dots [/math], each U_k is basically a polygon (possibly with holes), and [math] \bigcup_{k \geq 1} U_k = X[/math]
2) let [math]\Gamma_k[/math] be the outermost boundary of U_k, this is a loop contained in a simply connected set X, based on this prove that in fact everything "inside" [math]\Gamma_k[/math] is a subset of X, so you may as well assume that [math]U_k[/math] is a polygon (without holes) with boundary [math]\Gamma_k[/math]
3) every U_k is contractible; find contractions [math]F_k:[0,1] \times U_k \rightarrow U_k[/math] such that F_k agrees with F_l on [math][0,1] \times U_l[/math] whenever k > l. Then just taking union of F_k gives you a contraction of X.

[Anonymous No.11581098]

>>11581067
What do you mean by " basically a polygon (possibly with holes)" ?

[Anonymous No.11581100]

How relevant are computer programs/numerical approximations in physics? I have the option to take some modules in fluid dynamics in my maths BSc next year.

I'm interested in DEs from an analytical perspective which naturally comes up a lot in physics, but I don't want to be writing or using computer software.

[Anonymous No.11581120]

>>11579489
>[math]\mathbb{Z}_n[/math] is the set of the remainders of all natural numbers modulo [math]n[/math]
[math]\bf W [/math] [math]\bf R [/math] [math]\bf O [/math] [math]\bf N [/math] [math]\bf G[/math]
[math]\mathbb{Z}_n[/math] is the set of [math]n[/math]-adic integers. You're thinking of [math]\mathbb{Z}/n\mathbb{Z}[/math].

[Anonymous No.11581126]

>Direct proof
>Contrapositive
>Proof by contradiction
Are those the only proof techniques?

[Anonymous No.11581132]

>>11581126
>>11581126
modus ponens and induction off the top of my head

[Anonymous No.11581134]

>>11581126
Induction.

[Anonymous No.11581167]

How would you prove that this graph has no hamiltonian paths?

[Anonymous No.11581171]

>>11581120
I hate it when there's [math]\mathbb{Z}_n[/math] in a paper and the author doesn't tell which one they mean.

[Anonymous No.11581172]

>>11581120
Exactly in the same sense as a "set" in mathematics is WRONG, because a set is actually a unit used in the scoring system for the game of tennis.

[Anonymous No.11581181]

>>11581172
This is /sci/'s /mg/. When we refer to the word "set", we unambiguously refer to the mathematical object.
If you think about tennis, you can fuck off to >>>/sp/tennis

[Anonymous No.11581188]

>>11581126
Contradiction doesn't actually prove anything.

[Anonymous No.11581192]

>>11581098
this

[Anonymous No.11581199]

>>11581188
kys, the law of excluded middle is true. Name one (1) example of it not being applicable.

[Anonymous No.11581212]

>>11581199
>the law of excluded middle is true
Only true if taken as an axiom.

[Anonymous No.11581223]

>>11581212
Yes, as anyone sensible would do. Name one reason not to take it as an axiom.

[Anonymous No.11581224]

>>11581181
there's many incarnations of sets, though,
e.g., sets in ZF, sets in anti-foundation theories, sets in Homotopy Type Theory, etc.

[Anonymous No.11581226]

>>11581212

[Anonymous No.11581231]

>>11581223
>Name one reason not to take it as an axiom.
The burden of proof is on you to explain why it should be assumed.

[Anonymous No.11581233]

>>11581224
This was pretty clear I was referring to a set as defined in ZFC. Because I was talking about Z/nZ and Zn.

[Anonymous No.11581235]

>>11581132
Are those all? What about modus tollen?

[Anonymous No.11581239]

>>11581231
So you can use proofs by contradiction, which are pretty useful.

[Anonymous No.11581240]

>>11581167
loop over all the paths and go make a sandwich

[Anonymous No.11581244]

>>11575868
violently masturbating

[Anonymous No.11581264]

>>11581126
Construction of the object

[Anonymous No.11581272]

>>11581264
pretty much count as direct proof.

[Anonymous No.11581301]

>>11575679
0.666666... = 6

[Anonymous No.11581322]

>>11581313
CS faggotry is not mathematics.

[Anonymous No.11581326]

Just saw there's already a new one, reposted
>>11581263

[Anonymous No.11581386]

>>11581326
Holy shit bro, you need to wait some more time before creating a new thread

[Diracula No.11581495]

>>11576545
>>11577633
That sucks as a definition and doesn't tell me anything useful.

I think this is much more suitable:

>Mathematics is a sub branch of logic concerning the behaviours of well defined objects following well defined rules.

I think this covers just about everything?

[Anonymous No.11581749]

>>11581188
https://youtu.be/LmpAntNjPj0?t=770

[Anonymous No.11582845]

>>11578497
>Please don't talk to my superior logician self anymore.
Wanting to see proof for the most trivial shit possible does not make you a logician: it only means you're an undergrad who has finally discovered rigor.