/sci/ - Science & Math » Thread #12987294

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/mg/ - maths general

Anonymous Sat 17 Apr 00:49:28 2021 No.12987294 View Reply Original Report

Quoted By: >>12987809 >>12989018 >>12989525 >>12994724 >>12996429 >>12998682 >>12999142

havard mathematics phd qualifying exam edition

previous: >>12979086

Anonymous

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Anonymous Sat 17 Apr 2021 01:04:55 No.12987344 Report

Quoted By: >>12987361 >>12987365 >>12987369 >>12987373 >>12987640 >>12988071 >>12988899 >>12989420 >>12993302

Very important message for all you aspiring alg*braists: do not retreat to algebra to escape the difficulties you face studying analysis.
There is no retreating from inadequacy in mathematics. You must confront your weakness head on!

Now it is certainly possible to attain greatness is algebraic pursuits, but never assume that the greats of the past "fled" to algebra by necessity.
Here's a very interesting note on Grothendieck's early career
>Grothendieck's early mathematical work was in functional analysis. Between 1949 and 1953 he worked on his doctoral thesis in this subject at Nancy, supervised by Jean Dieudonné and Laurent Schwartz. His key contributions include topological tensor products of topological vector spaces, the theory of nuclear spaces as foundational for Schwartz distributions, and the application of Lp spaces in studying linear maps between topological vector spaces. In a few years, he had turned himself into a leading authority on this area of functional analysis—to the extent that Dieudonné compares his impact in this field to that of Banach.

Remarkable, to be considered in league with Banach, that early in life. And this wasn't even his final form!
So next time you think "I want to be an algebraic whateverist just like X", keep in the mind that X in this case was probably 10x the analyst you are.

Anonymous

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Anonymous Sat 17 Apr 2021 01:06:48 No.12987352 Report

Quoted By: >>12987553 >>12987744

The majority has spoken. They want you to come back, anitranny.

Anonymous

Anonymous Sat 17 Apr 2021 01:08:34 No.12987361 Report

Quoted By:

>>12987344
While I dislike you as a person, I don't totally disagree. A lot of the most important breakthroughs bring in ideas from disparate areas of mathematics.

Anonymous

Anonymous Sat 17 Apr 2021 01:09:14 No.12987365 Report

Quoted By:

>>12987344
for me it was the other way around originally. i was filtered by algebra and stuck to analysis.
now slowly i'm becoming an algebra chad

Anonymous

Anonymous Sat 17 Apr 2021 01:10:02 No.12987369 Report

Quoted By:

>>12987344
idk I'm retreating to analysis because algebra makes me feel stupid

Anonymous

Anonymous Sat 17 Apr 2021 01:10:23 No.12987373 Report

Quoted By:

>>12987344
10 times 0 is still 0

Anonymous

Anonymous Sat 17 Apr 2021 01:28:58 No.12987438 Report

Quoted By:

Always remember:
When we prove a theorem or decide a proposition, we operate in a purely formal, syntactical manner. In doing mathematics, we do not discover pre-existing truths that were "already there without one knowing" —we invent mathematics, bit-by-little-bit.

Anonymous

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Anonymous Sat 17 Apr 2021 01:54:55 No.12987547 Report

Quoted By: >>12987562 >>12987611

>OP starts with exambait image
>Third post is trannybait
>Everyone ignores them and decides to talk about maths
I'm crying, I lived to see /mg/ become based for once, thank you

Anonymous

Anonymous Sat 17 Apr 2021 01:55:41 No.12987553 Report

Quoted By: >>12987744

>>12987352
I support the return of Little Miss Algebra

Anonymous

Anonymous Sat 17 Apr 2021 01:57:05 No.12987562 Report

Quoted By:

>>12987547
You must have very low standards anon

Anonymous

Anonymous Sat 17 Apr 2021 02:04:19 No.12987611 Report

Quoted By:

>>12987547
>exambait
what do you mean?

Anonymous

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Anonymous Sat 17 Apr 2021 02:08:09 No.12987631 Report

Quoted By: >>12988100

>Group analysis of differential equations combines the powers of analysis and algebra to develop an underlying structure of differential equations. The author L. V . Ovsiannikov has been a significant contributor to the development of this field during the past twenty-five years. It is especially useful in problems arising in physics, mechanics, geometry, numerical analysis, and other areas in which ordinary and partial differential equations play an important role.

Anonymous

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Anonymous Sat 17 Apr 2021 02:09:57 No.12987640 Report

Quoted By:

>>12987344
Grothendieck was a geometer.

Anonymous

Anonymous Sat 17 Apr 2021 02:33:14 No.12987744 Report

Quoted By: >>12987769 >>12987807 >>12989420

>>12987352
>>12987553
If I understood his post correctly, he left so these threads would be about math and not off topic. This is not what he would have wanted.

Anonymous

Anonymous Sat 17 Apr 2021 02:38:56 No.12987769 Report

Quoted By: >>12987807

>>12987744
That just means we need to make these threads even worse so he realizes him leaving won't change anything and comes back.

Lads, we need to shit /mg/ up. Do it for anime tranny.

Reported

Reported Sat 17 Apr 2021 02:50:58 No.12987807 Report

Quoted By:

>>12987769
>>12987744

Anonymous

Anonymous Sat 17 Apr 2021 02:51:11 No.12987809 Report

Quoted By: >>12987823 >>12987834

>>12987294
Does anyone know how to find papers that arent in print anymore?
I specifically want Barnes' The Theory of the G-function and P J Heawood's Geometrical relation between the zeros of f(z)=0 and f'(z)=0, Quarterly Jour. Math 38 (1907) 84- 107.
It seems the quarterly journal of math doesn't have online records that far back but I don't have any access to a university. I just play around with complex analysis in my free time and I want these papers.
If any of you guys with university accounts or a way to get these papers can help me I would appreciate it.

Anonymous

Anonymous Sat 17 Apr 2021 02:54:57 No.12987823 Report

Quoted By: >>12987855

>>12987809
have you tried sci-hub? works most of the time.

Anonymous

Anonymous Sat 17 Apr 2021 02:57:23 No.12987834 Report

Quoted By: >>12987855

>>12987809
The Barnes paper is on jstor, you can read 100 articles free a month on there currently with an individual account (free).

Anonymous

Anonymous Sat 17 Apr 2021 03:03:53 No.12987855 Report

Quoted By: >>12987876 >>12987888

>>12987823
Sci-hub needs a doi link for me. Searching by name seems to fail. Is that not the case with you?
>>12987834
Wow, I couldn't find it. Can you give me a doi? Thanks

Anonymous

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Anonymous Sat 17 Apr 2021 03:04:24 No.12987857 Report

Quoted By: >>12987861 >>12987878 >>12987910 >>12987981

I graduated with a BA in math from a very mediocre state school in US this past December and want to keep studying but have a wife and soon kid and no money so grad school isn’t in the cards. Between work and other obligations, I can reasonably do 90 minutes to two hours of studying a day. Starting with baby rudin (we used lay’s analysis w intro to proof in UG) and going through the chart, is it reasonable to think I could eventually get to a point where I make a meaningful contribution to the field despite not going to grad school? Is it dumb to wait until I’m very old to go if I keep doing math in the mean time?

Anonymous

Anonymous Sat 17 Apr 2021 03:05:47 No.12987861 Report

Quoted By:

>>12987857
Leonard Susskind had a kid when he was on grad school I think.
Then again, he was very smart and part of the tribe.

Anonymous

Anonymous Sat 17 Apr 2021 03:10:09 No.12987876 Report

Quoted By: >>12987882 >>12987888 >>12987924 >>12987929

>>12987855
The Barnes paper is here:
https://www.jstor.org/stable/90809
(you have to create an account but it's free)
Dunno if it has a doi, I couldn't find one.

Reported

Reported Sat 17 Apr 2021 03:10:31 No.12987878 Report

Quoted By: >>12987905

>>12987857
How old are you?

Anonymous

Anonymous Sat 17 Apr 2021 03:11:11 No.12987882 Report

Quoted By:

>>12987876
Unless that's the wrong paper, if so, sorry.

Anonymous

Anonymous Sat 17 Apr 2021 03:12:07 No.12987885 Report

Quoted By: >>12987900

I'm retarded.

Anonymous

Anonymous Sat 17 Apr 2021 03:12:45 No.12987888 Report

Quoted By:

>>12987855
you can put a jstor link in and it will try to grab it.
put >>12987876 his link in and you'll get the paper.

Anonymous

Anonymous Sat 17 Apr 2021 03:14:23 No.12987900 Report

Quoted By:

>>12987885
You've come to the right place.

Anonymous

Anonymous Sat 17 Apr 2021 03:15:15 No.12987905 Report

Quoted By: >>12987960 >>12987968

>>12987878
21, from a v devout religious family/background so we start families young

Anonymous

Anonymous Sat 17 Apr 2021 03:16:22 No.12987910 Report

Quoted By: >>12988062

>>12987857
>eventually
>meaningful
Depends on your definition of meaningful. If you mean publishable, sure? If you mean being the Galois of analysis, not a fucking chance unless you have some sort of 10 billion iq gigabrain with some random unique and useful angle to take the field. There are certain small fields that have some low hanging fruit that are likely achievable for an amateur mathematician, but you're not going to (re)solve the abc conjecture

Anonymous

Anonymous Sat 17 Apr 2021 03:18:44 No.12987924 Report

Quoted By: >>12987964

>>12987876
Sorry I think this IS the wrong paper as it cites the paper you want. I checked my university library it seems the journal no longer exists? Some older copies pre-1900 are digitized by google, but others are only available by paper and are in 'storage' at my library.
Not sure that they are online.

Anonymous

Anonymous Sat 17 Apr 2021 03:19:09 No.12987929 Report

Quoted By: >>12987964

>>12987876
Oh yeah, his paper "the theory of the G function" is an earlier paper. That paper is really interesting, but comes at the family of gamma functions through modular forms and doesn't have the specific stuff I was after.

Anonymous

Anonymous Sat 17 Apr 2021 03:28:14 No.12987960 Report

Quoted By:

>>12987905
You're really young. Do what you think is better for your, don't worry about mistakes so much for now, if you do make a mistake you still have time to fix it, just follow your own heart for now and enjoy the journey. Time is still a friend of yours, unlike for me. Good luck.

Anonymous

Anonymous Sat 17 Apr 2021 03:30:18 No.12987964 Report

Quoted By:

>>12987929
Yeah I realise that now, see my reply here: >>12987924
You'll probably have to get an interlibrary loan or find a library or something. Unless someoene else can find it.

Anonymous

Anonymous Sat 17 Apr 2021 03:31:03 No.12987968 Report

Quoted By: >>12988062

>>12987905
You're really young. Do what you think is better for your life right now, don't worry about mistakes so much for now, if you do make a mistake you still have time to fix it and you'll learn from it, it's better than someone here spoonfeeding you which will take away the experience learned from failure, just follow your own heart for now and enjoy the journey. Time is still a friend of yours, unlike for me. Good luck.

Anonymous

Anonymous Sat 17 Apr 2021 03:34:09 No.12987981 Report

Quoted By: >>12988062

>>12987857
What courses were in your senior year by the way? I'm not trying to knock you or anything, just curious why you didn't go beyond Lay's Analysis book, if it was due to a lack of interest?

Anonymous

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Anonymous Sat 17 Apr 2021 03:44:57 No.12988023 Report

Quoted By: >>12988032 >>12988124 >>12988175

Does anybody understand this notation? In particular, what the subscript of the random variable X means? And what does alpha do? I don't recall them ever going over this notation in the book, there was an entire chapter on random variables and I haven't seen anything that looks like this

Anonymous

Anonymous Sat 17 Apr 2021 03:45:57 No.12988032 Report

Quoted By: >>12988124

>>12988023
To clarify, the subscript that reads (1/(n+1),1/n)

Anonymous

Anonymous Sat 17 Apr 2021 03:55:45 No.12988062 Report

Quoted By:

>>12987968
Thank you lad, I appreciate that a lot.
>>12987910
Also thank you for the honesty. That makes sense.
>>12987981
I was in numerical analysis, matrix analysis, vector calculus/analysis(we already have a vector cal class but this was more proofs), then some elective about skepticism for my last semester

Anonymous

Anonymous Sat 17 Apr 2021 03:57:40 No.12988071 Report

Quoted By:

>>12987344
Just go into geometry. No one cares the 20 pages you needed to prove 1/2< x <3/4.

Anonymous

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Anonymous Sat 17 Apr 2021 04:07:44 No.12988100 Report

Quoted By:

>>12987631
Excellent taste anon. I actually know someone who has his book because he made photocopies of the entire book in his university library and brought it with him when he left the Soviet Union to emigrate to the United States.

Anonymous

Anonymous Sat 17 Apr 2021 04:09:59 No.12988107 Report

Quoted By: >>12988117 >>12988133 >>12988154 >>12988906 >>12992156 >>12992589

There are two kinds of people living in an island. One kind of people are honest who always say the true things. Another kind of people are dishonest who always say the incorrect things.
One day you visited the island and met three local people (We call them A, B and C). The following is their conversation:
A: B and C are lying.
B: I am not lying.
C: B is really lying.
Please tell me how many people are lying?

Anonymous

Anonymous Sat 17 Apr 2021 04:12:10 No.12988117 Report

Quoted By: >>12988158

>>12988107
All of them

Anonymous

Anonymous Sat 17 Apr 2021 04:13:50 No.12988124 Report

Quoted By: >>12988142

>>12988032
>>12988023
It means you skip the exercise and move on to the next one.

Anonymous

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Anonymous Sat 17 Apr 2021 04:16:13 No.12988133 Report

Quoted By: >>12988158 >>12992939

>>12988107
All, no way their names are A, B and C

Anonymous

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Anonymous Sat 17 Apr 2021 04:18:48 No.12988142 Report

Quoted By:

>>12988124
way ahead of you bro

Anonymous

Anonymous Sat 17 Apr 2021 04:20:56 No.12988152 Report

Quoted By:

Are there more than three spatial dimensions?

Anonymous

Anonymous Sat 17 Apr 2021 04:21:12 No.12988154 Report

Quoted By:

>>12988107
What race are they?
(2 are lying)

Anonymous

Anonymous Sat 17 Apr 2021 04:22:06 No.12988158 Report

Quoted By:

>>12988117
>>12988133
Fellas, nobody said A was lying but A is tired of their bullshit.

Anonymous

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Anonymous Sat 17 Apr 2021 04:24:22 No.12988175 Report

Quoted By: >>12988199

>>12988023
That's an indicator random variable
https://en.wikipedia.org/wiki/Indicator_function

What text btw? Now that I know measure theory I wanna study some probability theory now!

Anonymous

Anonymous Sat 17 Apr 2021 04:29:18 No.12988199 Report

Quoted By:

>>12988175
Ahhhhh I get it, it looked like a 1. So the subscript after the I/1 is just an interval for the indicator function. I'm retarded, thank you. It's Probability: Theory and Examples by Durrett

Anonymous

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Anonymous Sat 17 Apr 2021 04:41:59 No.12988253 Report

Quoted By: >>12988259 >>12988706

Which research area has no business being as popular as it is?
Number Theory is my pick.

Anonymous

Anonymous Sat 17 Apr 2021 04:42:51 No.12988259 Report

Quoted By: >>12988689 >>12990634 >>12990698

>>12988253
Why does everyone here pick on number theory? No one here ever claims to like it.

Anonymous

Anonymous Sat 17 Apr 2021 05:51:44 No.12988592 Report

Quoted By: >>12988608

>>12981318
You read both tomes?

Anonymous

Anonymous Sat 17 Apr 2021 05:57:01 No.12988608 Report

Quoted By: >>12988626

>>12988592
Yeah, are you surprised, brainlet?

Anonymous

Anonymous Sat 17 Apr 2021 06:03:15 No.12988626 Report

Quoted By:

>>12988608
Kek, calm down I wasn't trying to be rude. I never see people reading Vol 2 is all, and also I tought some of the suggestions you got were weird if you already had read the second tome

Anonymous

Anonymous Sat 17 Apr 2021 06:22:25 No.12988689 Report

Quoted By:

>>12988259
Probably a jaded undergrad with burnt out mathematical beauty receptors

Anonymous

Anonymous Sat 17 Apr 2021 06:28:56 No.12988706 Report

Quoted By:

>>12988253
>Which research area has no business being as popular as it is?
mathematics

Anonymous

Anonymous Sat 17 Apr 2021 08:03:57 No.12988899 Report

Quoted By:

>>12987344
grothendieck rediscovered the lebesgue integral at 18

Anonymous

Anonymous Sat 17 Apr 2021 08:06:12 No.12988906 Report

Quoted By:

>>12988107
between 0 and 3

Anonymous

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Anonymous Sat 17 Apr 2021 08:49:01 No.12989018 Report

Quoted By: >>12989244 >>12989252 >>12989256 >>12989276 >>12989883 >>12990788 >>12991836

>>12987294
>be me
>sit real analysis test
>"Prove that X is a topological space on R"
>I prove it
>write QED at the end
>prof deducts 5 points (equivalent of a moderate mistake) even if everything is correct
>ask him why
>"you wrote QED. you only write QED in academic papers."

is this true? am i in the wrong?

Anonymous

Anonymous Sat 17 Apr 2021 10:03:56 No.12989244 Report

Quoted By: >>12989252 >>12989260 >>12992165

>>12989018
>>"Prove that X is a topological space on R"
what a meaningful question

Anonymous

Anonymous Sat 17 Apr 2021 10:08:13 No.12989252 Report

Quoted By:

>>12989018
>>12989244
Has anyone really been far even as decided to use even go want to do look more like?

Anonymous

Anonymous Sat 17 Apr 2021 10:11:00 No.12989256 Report

Quoted By: >>12989260

>>12989018
I mean both of you are cunts and deserve to suffer dealing with each other.

Anonymous

Anonymous Sat 17 Apr 2021 10:13:13 No.12989260 Report

Quoted By: >>12997556

>>12989244
it wasn't just that but it was close to it
the prof took the papers from us

>>12989256
who hurt you

Anonymous

Anonymous Sat 17 Apr 2021 10:18:51 No.12989276 Report

Quoted By: >>12989319

>>12989018
define "a topological space on R"

Anonymous

Anonymous Sat 17 Apr 2021 10:34:23 No.12989319 Report

Quoted By: >>12989331

>>12989276
Probably means that they were given a subset of the reals with some topology, and then they were tasked to show it is a subspace of the real line. My conjecture.

Anonymous

Anonymous Sat 17 Apr 2021 10:38:24 No.12989331 Report

Quoted By:

>>12989319
>they were given a subset of the reals with some topology, and then they were tasked to show it is a subspace of the real line
this
again, I don't remember well the task because the prof took both the task sheet and the test paper

Anonymous

Anonymous Sat 17 Apr 2021 11:08:19 No.12989392 Report

Quoted By: >>12990149

Hello I am a big stupid high school dropout and I would like to ask for some help.

I want to know how many different axis I would need to be able to adjust to come up with at least 150 unique objects several thousands of times.

I am trying to study math in my spare time at work but I have only made it to prealgebra, I am sorry.

I dont even know how to start on my math problem.

Anonymous

Anonymous Sat 17 Apr 2021 11:20:16 No.12989420 Report

Quoted By: >>12989638

>>12987744
She never said or implied that.

>>12987344
The essence of this message is not only for algebrafags. All of you geometry, analysis, etc faggotes who have strong allergy towards algebra or any major area should stop being pathetic little bitches.
The most based strategy is neither to be a jack of all trades nor an ultra specialist who never leaves his filthy incestuous cave, but a sort of double/triple yielder who will specialize in two or three big fields in a way that he or she finds great synergy between those like no one ever found before.

Anonymous

Anonymous Sat 17 Apr 2021 11:54:16 No.12989488 Report

Quoted By:

What is Geometric Measure Theory?
I saw the book by Federer and it seems to have a minimal analysis prerequisite compared to other books (it seems to be self contained).

Anonymous

Anonymous Sat 17 Apr 2021 12:06:26 No.12989525 Report

Quoted By: >>12989638

>>12987294
Does "phd qualifying exam" mean the same as "comprehensive exam"? If that is the case, you do not need to do more than repeat stuff that you learned during courses.

Anonymous

Anonymous Sat 17 Apr 2021 12:59:47 No.12989638 Report

Quoted By: >>12989714

>>12989420
>sorry for being a nuisance
I interpret that as being a source of off topic, but this itself is off topic.

>>12989525
It's the exam you must pass in order to get to the next level if you start your phd stuff after bachelor.

Anonymous

Anonymous Sat 17 Apr 2021 13:36:16 No.12989714 Report

Quoted By: >>12989744

>>12989638
I see what you mean, but she meant to apologize to a supposed majority of posters who didn't want her posting, it's a subjective (but relevant) judgemenet rather than objective. Her own opinion of her posts could be different. We also have to take into account how overboard she goes when criticizing herself.

Anonymous

Anonymous Sat 17 Apr 2021 13:50:33 No.12989744 Report

Quoted By:

>>12989714
Maybe. Idk. Back by May is my guess.

Anonymous

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Anonymous Sat 17 Apr 2021 14:17:51 No.12989830 Report

Quoted By: >>12989878

is it good?

Anonymous

Anonymous Sat 17 Apr 2021 14:36:07 No.12989878 Report

Quoted By: >>12989910

>>12989830
No

Anonymous

Anonymous Sat 17 Apr 2021 14:37:10 No.12989883 Report

Quoted By:

>>12989018
>is this true? am i in the wrong?
No. Your teacher is just being a dick.

Anonymous

Anonymous Sat 17 Apr 2021 14:44:11 No.12989904 Report

Quoted By: >>12989917

Discrete math is ridiculously easy. Why did I need Calc 1 as a pre req?
Can I just focus on this, graph theory and combinatorics for the rust of my life? Don't really enjoy most other topics desu.

Anonymous

Anonymous Sat 17 Apr 2021 14:46:15 No.12989910 Report

Quoted By:

>>12989878
Aluffi is the best.

Anonymous

Anonymous Sat 17 Apr 2021 14:51:10 No.12989917 Report

Quoted By:

>>12989904
Not discrete math, but your discrete math course.

Go try some hungarian olympiad problems on those topics and you'll see how fucking hard it can get.

Anonymous

Anonymous Sat 17 Apr 2021 15:26:54 No.12990016 Report

Quoted By: >>12990070 >>12990089 >>12990615

For all the ESL anons here, are there good math books in your native language? To me it looks like the best books are in english.

Anonymous

Anonymous Sat 17 Apr 2021 15:46:42 No.12990070 Report

Quoted By:

>>12990016
I heard there are some good ones in German but whenever possible I use English materials.

Anonymous

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Anonymous Sat 17 Apr 2021 15:51:09 No.12990084 Report

Quoted By: >>12990123

I was originally planning to buy a whiteboard to mount on a wall but now I have no idea which one I should get for under <$60 USD.
Any recommendations anon? This one seems to have quality issues and the amazon one does too.

Anonymous

Anonymous Sat 17 Apr 2021 15:52:47 No.12990089 Report

Quoted By: >>12990116

>>12990016
Every book I've read in my language has just been some book translated from english

Anonymous

Anonymous Sat 17 Apr 2021 16:00:21 No.12990116 Report

Quoted By: >>12990156

>>12990089
What is your language?

Anonymous

Anonymous Sat 17 Apr 2021 16:02:08 No.12990123 Report

Quoted By: >>12990131 >>12990137 >>12991214

>>12990084
Those boards will have permanent marks from the pens as time goes on. If you want my advice, buy a black board or spend some money on a glass white board.

Anonymous

Anonymous Sat 17 Apr 2021 16:04:23 No.12990131 Report

Quoted By: >>12990135

>>12990123
>buy a black board
this and use a moderately wet sponge to minimize chalk dust

Anonymous

Anonymous Sat 17 Apr 2021 16:05:25 No.12990135 Report

Quoted By: >>12990145 >>12990265

>>12990131
Hagoromo chalks don't leave dust.

https://youtu.be/PhNUjg9X4g8

Anonymous

Anonymous Sat 17 Apr 2021 16:06:03 No.12990137 Report

Quoted By:

>>12990123
>If you want my advice, buy a black board or spend some money on a glass white board.
It'll be put in my bedroom so I should probably avoid the dust (place is already dusty as hell). I never knew glass white boards existed, good call, thanks anon.

Anonymous

Anonymous Sat 17 Apr 2021 16:07:54 No.12990145 Report

Quoted By:

>>12990135
japan ^___^ kawaii

Anonymous

Anonymous Sat 17 Apr 2021 16:08:59 No.12990149 Report

Quoted By:

>>12989392
I don't understand the question but any rotation can be generated by only 3 angles (Euler angles)

Anonymous

Anonymous Sat 17 Apr 2021 16:10:14 No.12990156 Report

Quoted By: >>12990168

>>12990116
Korean

Anonymous

Anonymous Sat 17 Apr 2021 16:15:10 No.12990168 Report

Quoted By: >>12990214 >>12990515

>>12990156
Sugoi, I love Korea. How hard is it to be accepted for a PhD there? Do I have to know korean?

Anonymous

Anonymous Sat 17 Apr 2021 16:27:35 No.12990214 Report

Quoted By: >>12990222 >>12990234

>>12990168
You won't need to know korean at KAIST or UNIST but most other universities I think you will
Admission is much easier for foreigners

Anonymous

Anonymous Sat 17 Apr 2021 16:29:34 No.12990222 Report

Quoted By: >>12990251

>>12990214
What's the point of going to Korea if you aren't going to learn Korean ahead of time?

Anonymous

Anonymous Sat 17 Apr 2021 16:32:25 No.12990234 Report

Quoted By: >>12990251 >>12990389 >>12990515

>>12990214
How hard is it to find a cute christian mathematician korean gf?

Anonymous

Anonymous Sat 17 Apr 2021 16:35:17 No.12990251 Report

Quoted By: >>12990292

>>12990222
That's a good question
>>12990234
Probably not that hard as there are many christian girls that you would interact with in the maths department

Anonymous

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Anonymous Sat 17 Apr 2021 16:35:57 No.12990256 Report

Quoted By:

Is Quiver based or cringe?

Anonymous

Anonymous Sat 17 Apr 2021 16:39:41 No.12990265 Report

Quoted By: >>12990303

>>12990135
No way, how can chalk NOT leave dust? There will be minuscule amounts of it, do you have a blackboard with that type of chalk? I'm genuinely curious.

Anonymous

Anonymous Sat 17 Apr 2021 16:46:58 No.12990292 Report

Quoted By: >>12990515

>>12990251
>many christian girls that you would interact with in the maths department
Sugeee, Korea is perfect

Anonymous

Anonymous Sat 17 Apr 2021 16:50:25 No.12990303 Report

Quoted By: >>12990444

>>12990265
If I knew I'd be rich making and selling it right now. Go ask the japanese, only they have the formula for it.

Anonymous

Anonymous Sat 17 Apr 2021 17:12:31 No.12990389 Report

Quoted By: >>12990402 >>12990410 >>12990434

>>12990234
>christian
Koreans are some of the least religious people in the world.

Anonymous

Anonymous Sat 17 Apr 2021 17:16:47 No.12990402 Report

Quoted By: >>12990418

>>12990389
>only 15% of the population declared themselves to be not religious in the sense of "atheism"

Anonymous

Anonymous Sat 17 Apr 2021 17:20:22 No.12990410 Report

Quoted By: >>12990433

>>12990389
you are off by a good 100 years

Anonymous

Anonymous Sat 17 Apr 2021 17:23:34 No.12990418 Report

Quoted By: >>12990625

>>12990402
Most irreligious people simply don't think or care about it enough to label themselves atheists. Just talk to some Koreans. They might have some mild superstitions but they have nothing approaching a religion or gods and they don't really care about it.

Anonymous

Anonymous Sat 17 Apr 2021 17:26:28 No.12990433 Report

Quoted By: >>12990439

>>12990410
>over 60% of 20 year olds have no religion

Anonymous

Anonymous Sat 17 Apr 2021 17:26:31 No.12990434 Report

Quoted By:

>>12990389
It's the japanese who turner to atheism, not the koreans.

Anonymous

Anonymous Sat 17 Apr 2021 17:27:34 No.12990439 Report

Quoted By: >>12990453

>>12990433
The amount of catholics in Korean more than doubled in the last ten or so years.

Anonymous

Anonymous Sat 17 Apr 2021 17:28:32 No.12990444 Report

Quoted By:

>>12990303
They sold it to the Koreans, who produce it under the same brand name.

Anonymous

View Same Google iqdb SauceNAO Untit33led.png, 2KiB, 180x53

Anonymous Sat 17 Apr 2021 17:29:06 No.12990446 Report

Quoted By: >>12990459

What the FUCK does it mean when, in an integral, the "dy" is actually being operated on by another function? Like this

Anonymous

Anonymous Sat 17 Apr 2021 17:30:57 No.12990453 Report

Quoted By: >>12990492

>>12990439
What are you looking at? I'm seeing a slight decline in Catholicism.

Anonymous

Anonymous Sat 17 Apr 2021 17:32:01 No.12990459 Report

Quoted By: >>12990484

>>12990446
It's the integral with respect to the probability measure. That's just the notation.

Anonymous

Anonymous Sat 17 Apr 2021 17:36:37 No.12990484 Report

Quoted By:

>>12990459
Huh, alright. I'll try not to let it get to me.

Anonymous

Anonymous Sat 17 Apr 2021 17:37:34 No.12990492 Report

Quoted By: >>12990528

>>12990453
https://www.vaticannews.va/en/church/news/2020-01/south-korea-cathoic-population-statistics.html

Anonymous

Anonymous Sat 17 Apr 2021 17:42:17 No.12990515 Report

Quoted By: >>12990531

>>12990168
>>12990234
>>12990292
God I wish mathematicians weren't so fucking cringe

Anonymous

Anonymous Sat 17 Apr 2021 17:44:11 No.12990528 Report

Quoted By: >>12990538

>>12990492
That doubling occurred between 2000 and 2005. The Catholic population has remained stable or declined slightly over the last 15 years.

Anonymous

Anonymous Sat 17 Apr 2021 17:44:31 No.12990531 Report

Quoted By: >>12990537

>>12990515
Lol, fuck off american.

Anonymous

Anonymous Sat 17 Apr 2021 17:45:30 No.12990537 Report

Quoted By:

>>12990531
I'm German.

Anonymous

Anonymous Sat 17 Apr 2021 17:45:32 No.12990538 Report

Quoted By: >>12990547 >>12990550

>>12990528
It's still growing slowly, there was a increase of 0.8% last year: https://catholicmissionarydisciples.com/news/koreancatholic

Anonymous

Anonymous Sat 17 Apr 2021 17:47:04 No.12990547 Report

Quoted By: >>12990562

>>12990538
Is that even outside the margin of error? Also, why all the Catholic news sources? They're likely to misrepresent the situation in favor of a growing Catholic population.

Anonymous

Anonymous Sat 17 Apr 2021 17:47:18 No.12990550 Report

Quoted By:

>>12990538
Wrong link, sorry. http://www.koreaherald.com/view.php?ud=20200427000801

Anonymous

Anonymous Sat 17 Apr 2021 17:50:59 No.12990562 Report

Quoted By:

>>12990547
Oh, the classic 'the Church is making up numbers to futher their narrative'. You realize the catholic Church was the biggest investor in science during the middle ages, right? You realize universities only exist because of the Church, right? You realize our society wouldn't even value knowledge if not for the efforts of the Church in the past right? You realize many academic works would have been completely lost if not for catholic monks, right?

Anyway, I just gave another source by the KoreanHerald just above. Feel free to keep whining.

Anonymous

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Anonymous Sat 17 Apr 2021 17:53:00 No.12990570 Report

Quoted By: >>12990574 >>12990592

$\text{1.}\ \ \text{ What textbooks, papers or text did you read today?}$
$\text{2.}\ \ \text{ What non-textbooks did you read today?}$
$\text{3.}\ \ \text{ Did you write something today?}$
$\text{4.}\ \ \text{ Did you do some programming today?}$
$\text{5.}\ \ \text{ Did you build something today?}$
$\text{6.}\ \ \text{ Did you clean up something today?}$
$\text{7.}\ \ \text{ Did you plan something today?}$
$\text{8.}\ \ \text{ Did you manage to work off some bureaucracy/paper work today?}$
$\text{9.}\ \ \text{ Did you practice any skills today? If so, which?}$
$\text{10. Did you do sports/cardio/weightlifting today?}$
$\text{11. What were you eating today?}$
$\text{12. How much sleep did you get yesterday?}$

Anonymous

Anonymous Sat 17 Apr 2021 17:53:28 No.12990574 Report

Quoted By:

>>12990570
i jack off today

Anonymous

Anonymous Sat 17 Apr 2021 17:56:44 No.12990592 Report

Quoted By:

>>12990570
Take you blogpost elsewhere, fiend.

Anonymous

Anonymous Sat 17 Apr 2021 18:00:53 No.12990615 Report

Quoted By: >>12990623 >>12990643 >>12991214

>>12990016
Yes, many. Here are some quality textbooks
Berger: Géométrie
Boyer: Algèbre et géométrie
Caldero-Germoni: Histoires hédonistes de groupes et de géométrie
Dieudonné - Calcul infinitésimal
Dolbeault: Analyse complexe
Mneimné-Testard: Introduction à la théorie des groupes de Lie classiques
Rouvière: Petit guide de calcul différentiel

Also some excellent lecture notes (available online):
Debarre: Algèbre I and II
Le Gall: Intégration, Probabilités et Processus Aléatoires
Paulin: Any set of lecture notes he has ever written honestly, eg. Géométrie différentielle élémentaire or Géométrie riemannienne

Anonymous

Anonymous Sat 17 Apr 2021 18:02:27 No.12990623 Report

Quoted By:

>>12990615
Ah oui le baguette

Anonymous

Anonymous Sat 17 Apr 2021 18:02:57 No.12990625 Report

Quoted By:

>>12990418
There are many extremely religous christians in Korea
For some reason Koreans are very attracked to pseudo-christian extremists cults as well

Anonymous

Anonymous Sat 17 Apr 2021 18:04:23 No.12990634 Report

Quoted By:

>>12988259
Curiously enough everyone I know seems to like it.

Anonymous

Anonymous Sat 17 Apr 2021 18:07:14 No.12990643 Report

Quoted By:

>>12990615
Their english counterparts are better. Cope.

Anonymous

Anonymous Sat 17 Apr 2021 18:07:49 No.12990646 Report

Quoted By:

The surreal numbers are awesome. Such a rich structure arising from such simple and intuitive rules.

Anonymous

Anonymous Sat 17 Apr 2021 18:19:01 No.12990698 Report

Quoted By:

>>12988259
I don't dislike number theory, I just like it less than most things, including but not limited to geometry, analysis, algebra and combinatorics.

Anonymous

Anonymous Sat 17 Apr 2021 18:40:01 No.12990788 Report

Quoted By: >>12994137

>>12989018
Literally nobody uses QED anymore. Just use a Halmos Tombstone or a tranny flag.

Anonymous

Anonymous Sat 17 Apr 2021 18:42:24 No.12990802 Report

Quoted By: >>12990818 >>12990902

Is that a real exam? It seems retarded to ask shit about many fields

Anonymous

Anonymous Sat 17 Apr 2021 18:45:57 No.12990818 Report

Quoted By: >>12991465

>>12990802
Why would that be retarded?

Anonymous

Anonymous Sat 17 Apr 2021 19:03:50 No.12990902 Report

Quoted By: >>12990909 >>12990944 >>12990995 >>12991465

>>12990802
It's a PhD comprehensive exam. It is literally the final big test before you get a math PhD, so it'd better test all major areas.

Anonymous

Anonymous Sat 17 Apr 2021 19:06:02 No.12990909 Report

Quoted By: >>12990920

>>12990902
So it's not too bad if I can't solve them as an undergrad?

Anonymous

Anonymous Sat 17 Apr 2021 19:08:36 No.12990920 Report

Quoted By:

>>12990909
It is a little bad, yes...

Anonymous

Anonymous Sat 17 Apr 2021 19:12:54 No.12990944 Report

Quoted By: >>12990977

>>12990902
>It is literally the final big test before you get a math PhD
Wait, I thought this was the exam you need to pass to qualify for entry into the PhD program? Not the one you take at the end of the program

Anonymous

Anonymous Sat 17 Apr 2021 19:18:45 No.12990977 Report

Quoted By: >>12990985

>>12990944
You need to learn how to read before trying to do mathematics, kid.

Anonymous

Anonymous Sat 17 Apr 2021 19:20:55 No.12990985 Report

Quoted By: >>12991028

>>12990977
*tips fedora* that was epic ownage my friend, simply epic. take my upvote

Anonymous

Anonymous Sat 17 Apr 2021 19:22:26 No.12990995 Report

Quoted By:

>>12990902
>It is literally the final big test before you get a math PhD
False.

Anonymous

Anonymous Sat 17 Apr 2021 19:28:48 No.12991028 Report

Quoted By:

>>12990985
Awwn, that's wholesome bro, that's so wholesome. Thank you dude.

Anonymous

Anonymous Sat 17 Apr 2021 19:43:54 No.12991153 Report

Quoted By: >>12991186

??????

Anonymous

Anonymous Sat 17 Apr 2021 19:48:17 No.12991186 Report

Quoted By: >>12991212

>>12991153
Very cool bro, now post "1+1 = 2" to /jp/djt and you've united us

Anonymous

Anonymous Sat 17 Apr 2021 19:51:34 No.12991212 Report

Quoted By:

>>12991186
?????

Anonymous

Anonymous Sat 17 Apr 2021 19:51:39 No.12991214 Report

Quoted By:

>>12990123
Just use some expo spray every once and a while

>>12990615
>Histoires hédonistes de groupes et de géométrie
That's a fun name, I'll add Cours d'algèbre by Assem and Leduc that one of my profs recommended but I haven't read

Anonymous

Anonymous Sat 17 Apr 2021 20:08:39 No.12991280 Report

Quoted By:

Now that animetranny left for real, I'm leaving as well. Good luck with this dead general now. You chose this.

Anonymous

Anonymous Sat 17 Apr 2021 20:39:18 No.12991414 Report

Quoted By: >>12991448 >>12993500

I can't tell if I like measure theory or not. Learning the construction of the Lebesgue measure and integration wrt to a measure was really cool. I enjoyed solving all the practice problems.
But something about it also feels really silly, but I can't really express what feels wrong about it all.

There's this quote due to Hamming:
>Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.

Now of course most of you are keen to dismiss this objection as completely worthless, but it does seem to reveal there is something odd about Lebesgue integration.
I enjoy working with the theory but it also feels like I'm way too far up my ass studying this shit. But that's mathematics I guess.

Anonymous

Anonymous Sat 17 Apr 2021 20:43:41 No.12991448 Report

Quoted By: >>12991655

>>12991414
>I can't tell if I like measure theory or not.
You stupid? It's pretty simple: are you having fun while studying it? If you do then you like it, if you don't then you don't like it. Lmao.

Anonymous

Anonymous Sat 17 Apr 2021 20:45:34 No.12991465 Report

Quoted By: >>12991478

>>12990902
>>12990818
What the Fuck? No one does a PhD on "math" you are supposed to produce new results in a particular field not know minute shit of all major fields.

Anonymous

Anonymous Sat 17 Apr 2021 20:47:35 No.12991478 Report

Quoted By: >>12991496

>>12991465
>No one does a PhD on "math"
uuuh yes we literally do...
>you are supposed to produce new results in a particular field
that part is right though

Anonymous

Anonymous Sat 17 Apr 2021 20:51:51 No.12991496 Report

Quoted By: >>12991968

>>12991478
Well yes but if someone asks you what are you doing your PhD on? no one answers
>just general math lol today we saw the Meyer-Viertoris sequence the projective plane and extrinsic curvature of curves. Tomorrow we start with intro to functional analysis and intro to algebraic geometry. Next fall we start with baby number theory!
You take courses relevant to your research it not to waste time with whatever sounds interesting.

Anonymous

Anonymous Sat 17 Apr 2021 20:55:58 No.12991516 Report

Quoted By: >>12991539

Does PhD and Doctorate mean the same thing?

Anonymous

Anonymous Sat 17 Apr 2021 21:00:20 No.12991539 Report

Quoted By: >>12991595 >>12991612

>>12991516
No. In some countries a doctorate is required as qualification for a full professorship.
On average it takes around five years after PhD to get it.

Anonymous

Anonymous Sat 17 Apr 2021 21:07:29 No.12991572 Report

Quoted By:

We have two random values that are generated from the normal distribution with mean 0 and stddev 1. If we always choose the larger of these two values, what would the mean be?

Anonymous

Anonymous Sat 17 Apr 2021 21:13:07 No.12991595 Report

Quoted By:

>>12991539
PhD doesn't exist in my country, it's an alien concept to me. Only masters and doctorare exist, what do I do?

Anonymous

Anonymous Sat 17 Apr 2021 21:16:14 No.12991612 Report

Quoted By:

>>12991539
Are you sure you didn't mix that up with docent?

Anonymous

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Anonymous Sat 17 Apr 2021 21:26:48 No.12991654 Report

Quoted By: >>12991915 >>12991986

Can someone help me with this?
The definition of regular I'm using doesn't needs to be a $T_{1}$ space.
I picked a $x$ and a closed set $F$ . I decided to do two cases, one where the closed regular neighborhood, which I'm calling $N$ , intersects $F$ and one where it doesn't.
For the later I just picked the open set derived from the neighborhood and the complement of $N$ .
For the former I tried constructing open sets with the following. Since $N$ is regular, then there two disjoint open sets $U,V$ in $N$ which separate $x$ and $F\cap N$ . I can build an open set for $x$ which doesn't touch $F$ , using the open set from the neighborhood and the open set $U'$ in $X$ such that $U=U' \cap N$ . However, I'm having trouble building an open for $F$
Is there any other way?

Anonymous

Anonymous Sat 17 Apr 2021 21:27:12 No.12991655 Report

Quoted By:

>>12991448
I'm having fun sorta, but I also feel kind of strange.
My head is scrambled overall. I get weird negative associations with certain topics just based on """""feel""""" but I can't say why.

I do like the Lebesgue theory so far. It's actually pretty elegant as far as analysis goes. I also like how it formalizes probability theory, very elegant.

Anonymous

Anonymous Sat 17 Apr 2021 22:08:06 No.12991836 Report

Quoted By: >>12994137

>>12989018
he's autistic and you should report him for being autistic.
unless he specifically stated before that you shouldn't use qed.

Anonymous

Anonymous Sat 17 Apr 2021 22:28:25 No.12991915 Report

Quoted By: >>12991986 >>12992194

>>12991654
Pretty sure closed neighborhood gives you $x \in W \subset N$ with $W$ open (in $X$ ), $N$ closed.

So you can do (using your notation) $U' \cap W$ and $V' \cup N^c$ and those should be the disjoint open sets you want

Anonymous

Anonymous Sat 17 Apr 2021 22:37:32 No.12991948 Report

Quoted By: >>12991993

Is there any nice formula for sums of powers? I'm talking about stuff like
$<br />\sum_{k=1}^n k^p<br />$
for positive integer p. They exist for all p, but is there a quick way of me telling you a p and you giving me the formula? I know how to get it supposing I know p-1, so theoretically I could compute them, but it's infeasible for large p.

Anonymous

Anonymous Sat 17 Apr 2021 22:45:05 No.12991968 Report

Quoted By: >>12992294

>>12991496
Well typically the qualifying exam is taken before you start your PhD research. That's what you 'qualify' for. So you are expected to know stuff from a wide range of mathematics before you specialize.

Anonymous

Anonymous Sat 17 Apr 2021 22:51:19 No.12991986 Report

Quoted By: >>12992194

>>12991654
>>12991915
Without that open $W$ you're basically stuck, I think.
It just doesn't look like its possible to guarantee that $U'$ and $V'$ (where $V = V' \cap N$ ) will be disjoint, which seems to be the problem you were having.

Anonymous

Anonymous Sat 17 Apr 2021 22:53:37 No.12991993 Report

Quoted By: >>12992081

>>12991948

https://en.wikipedia.org/wiki/Faulhaber%27s_formula

Anonymous

Anonymous Sat 17 Apr 2021 23:07:01 No.12992044 Report

Quoted By: >>12992149 >>12992186

Is there no math for solving functional equations other than guessing? Has it been proven that there's no general methods for solving them? Does functional analysis has anything to do with it?

Anonymous

Anonymous Sat 17 Apr 2021 23:17:04 No.12992081 Report

Quoted By:

>>12991993
Thanks my dude.

Anonymous

Anonymous Sat 17 Apr 2021 23:22:03 No.12992112 Report

Quoted By: >>12992154

https://en.wikipedia.org/wiki/Schizophrenic_number

Wow, math needs to be cancelled. This term is very problematic and negative towards the mentally divergent!

Anonymous

Anonymous Sat 17 Apr 2021 23:29:31 No.12992149 Report

Quoted By: >>12992186

>>12992044
Functional equation is an extremely general concept. Of course there are not going to be general methods: Any type of morphism between structures ? That solves a functional equation. L-functions ? These solve functional equations. Differential equations ? These are functional equations.

Anonymous

Anonymous Sat 17 Apr 2021 23:30:55 No.12992154 Report

Quoted By:

>>12992112
I'm schizophrenic and I agree, it makes me feel very unsafe when I heard fellow mathematicians using that term like that.

Anonymous

Anonymous Sat 17 Apr 2021 23:31:24 No.12992156 Report

Quoted By:

>>12988107
B and C make precisely opposite claims, so exactly one of them is lying.
This contradicts A's statement, so A is lying too.

Therefore, there are two liars. Either A and B, or A and C.
There's not enough information to determine which one of B or C is lying.

Anonymous

Anonymous Sat 17 Apr 2021 23:33:15 No.12992165 Report

Quoted By:

>>12989244
You know they meant "X is a topology on R" i.e. "(R, X) is a topological space".
This bullshit is semantics, not maths.

Anonymous

Anonymous Sat 17 Apr 2021 23:36:32 No.12992186 Report

Quoted By:

>>12992044
I agree with >>12992149

E.g. for the equation
f(x+y) = f(x) + f(y)

over the reals, you'll easily see that f(x):=c·x is a solution for any c.
If you adopt the Axiom of Choice, then there are infinitely many other solutions.
Hard to imagine to find a nice theory sensitive to this.

Anonymous

Anonymous Sat 17 Apr 2021 23:37:45 No.12992194 Report

Quoted By:

>>12991915
>>12991986
Thanks. I was missing the $V' \cup N^c$ , lel. I didn't knew why I didn't thought of that before.

Anonymous

Anonymous Sat 17 Apr 2021 23:55:57 No.12992294 Report

Quoted By: >>12992296 >>12992371

>>12991968
Algebraic topology as a general requirement? Galois theory?

Anonymous

Anonymous Sat 17 Apr 2021 23:56:28 No.12992296 Report

Quoted By: >>12992332

>>12992294
I only have an undergraduate degree and I've taken courses in both those topics.

Anonymous

Anonymous Sun 18 Apr 2021 00:04:30 No.12992332 Report

Quoted By: >>12992351 >>12992366 >>12992367 >>12992371

>>12992296
They should be electives. There is no fucking reason to require Galois theory as a general requirement. A basic abstract algebra course it what you need.

Anonymous

Anonymous Sun 18 Apr 2021 00:07:18 No.12992351 Report

Quoted By: >>12992375

>>12992332
Galois theory is the end of my mandatory undergrad algebra, seems pretty reasonable. Maybe you need to cope and seethe harder

Anonymous

Anonymous Sun 18 Apr 2021 00:09:52 No.12992366 Report

Quoted By: >>12992401

>>12992332
What is 'basic abstract algebra' then? I don't agree with you, I think you should have a broad education in mathematics before specializing, and obviously Harvard agrees with that approach. If you specialize too early you aren't going to generate good researchers. Given I've seen a lot of the material on that test and only have an undergraduate degree a PhD student at harvard knowing all of it after a year or two doesn't surprise me.

Anonymous

Anonymous Sun 18 Apr 2021 00:09:53 No.12992367 Report

Quoted By:

>>12992332
I agree. In fact, we should just reduce the entire math undergrad to intro to proofs, basic group theory and calculus, and everything else should only be learned if you want to specialize in it.

Anonymous

Anonymous Sun 18 Apr 2021 00:10:35 No.12992371 Report

Quoted By:

>>12992294
>>12992332
A lot of Americans will need to do a Masters before a PhD. Not every undergrad is the same. You can absolutely graduate with a math degree and never take Algebraic Topology as an undergrad.
Or you could be a very tryhard undergrad and take a lot of graduate level courses, but which ones you choose to take will be very optional when it comes to actual graduation requirements.

Also some schools will have a math major vs math "honors" distinction, the latter requiring some amount of graduate level courses.

Anonymous

Anonymous Sun 18 Apr 2021 00:11:13 No.12992375 Report

Quoted By:

>>12992351
not him, but at my uni it's also not a hard requirement. one may do it to fill up a credit requirement for honors/non-honors if they so desire.
the standard abstract algebra course is a requirement in both paths.

Anonymous

Anonymous Sun 18 Apr 2021 00:16:55 No.12992401 Report

Quoted By: >>12992435

>>12992366
Basic definitions of groups rings and fields. Isomorphisms and isomorphism theorems groups actions finite groups some applications.

Anonymous

Anonymous Sun 18 Apr 2021 00:24:01 No.12992435 Report

Quoted By: >>12993492

>>12992401
And then after that if you're not specializing in an algebra related field you don't think you should know anything more?

Anonymous

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Anonymous Sun 18 Apr 2021 00:24:42 No.12992437 Report

Quoted By: >>12992447 >>12992501 >>12992512 >>12993314 >>12999151

havard mathematics phd qualifying exam spring 2018 days 1,2 and 3.

Anonymous

Anonymous Sun 18 Apr 2021 00:26:21 No.12992447 Report

Quoted By: >>12992512

>>12992437
They also require you learn another language. (Harvard that is): [...] students are required to demonstrate the ability to read mathematics in French, German, or Russian by passing a two-hour, written language examination. Students are asked to translate one page of mathematics into English with the help of a dictionary.

Anonymous

Anonymous Sun 18 Apr 2021 00:28:29 No.12992457 Report

Quoted By: >>12992464 >>12996128

What field has the highest fun/creativity to writing ratio? Analysis just has so much fucking writing. My hand gets cramped and tired. I am considering selecting my field specialization based on just this.

Anonymous

Anonymous Sun 18 Apr 2021 00:29:53 No.12992464 Report

Quoted By:

>>12992457
Consider typing things instead.

Anonymous

Anonymous Sun 18 Apr 2021 00:36:15 No.12992501 Report

Quoted By:

>>12992437
The exam has six topics Algebra, Algebraic Geometry, Algebraic Topology, Differential Geometry, Real Analysis and Complex Analysis.
You have to get 20/30 in each subject.
I see no problem with this, to be a good researcher you need a broad knowledge and this is just the basics in 6 areas. If you don't know this shit after 6 (4 undergrad + 2 graduate) years of courses in mathematics you won't make it.

Anonymous

Anonymous Sun 18 Apr 2021 00:37:58 No.12992512 Report

Quoted By:

>>12992437
Wow okay I feel pretty dumb

>>12992447
>They also require you learn another language.
Oh but THIS would be a breeze hell yeah. I could do one without a dictionary in about ten minutes and probably a second with a dictionary. So at least I have that going for me?

Anonymous

Anonymous Sun 18 Apr 2021 00:54:24 No.12992589 Report

Quoted By: >>12994695

>>12988107
Just C. B's claim is true by definition. C's and A's claims are therefore false.

Anonymous

Anonymous Sun 18 Apr 2021 01:56:05 No.12992939 Report

Quoted By:

>>12988133
kek

Anonymous

Anonymous Sun 18 Apr 2021 02:15:01 No.12993052 Report

Quoted By: >>12993064

Most american unis' quals are no where near as autistic as harvard's
Usually there are just analysis and algebra, and sometimes topology/geometry. Usually you only need to pass two of the three

Anonymous

Anonymous Sun 18 Apr 2021 02:18:03 No.12993064 Report

Quoted By:

>>12993052
Yeah, mine has Algebra & Analysis (though analysis does cover some complex analysis, and algebra does cover Galois theory which some people here think is odd for some reason) plus one other subject of your choice you have to pass.

Anonymous

Anonymous Sun 18 Apr 2021 03:40:57 No.12993302 Report

Quoted By:

>>12987344
Algebra scares me, I don't understand it and the men who study it seem so intimidating, strong, virile. I simply can't complete.
As well, none of the algebraists in my department have reciprocated my homosexual advances.
So, I've decided it best to restrict myself to Analysis, where everyone is an impotent faggot with Dunning-Kruger effect, just like myself.

Anonymous

Anonymous Sun 18 Apr 2021 03:46:48 No.12993314 Report

Quoted By:

>>12992437
>typed up in word
Nigger school

Anonymous

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Anonymous Sun 18 Apr 2021 03:57:53 No.12993342 Report

Quoted By: >>12994786 >>12995031

havard mathematics phd qualifying exam 1970 days 1,2 and 3.

Anonymous

Anonymous Sun 18 Apr 2021 04:05:40 No.12993364 Report

Quoted By: >>12993390

>algebraists: strong independent women
>analysts: seething incels

Anonymous

Anonymous Sun 18 Apr 2021 04:13:38 No.12993390 Report

Quoted By:

>>12993364
I remembered this guy who was always the smartest in my undergrad algebra classes, decide to look him up, must be doing great things now. PhD candidate, name Abigail she/her/hers. That's what it says.

Anonymous

Anonymous Sun 18 Apr 2021 04:46:05 No.12993492 Report

Quoted By: >>12993532

>>12992435
No? Its enough to be prepared to tackle shit that comes typically in higher level maths but why the fuck do you think you need more? I have never in all my research years used anything remotely close to galois theory. The algebraic topology shit is just some few results and some representation theory. But that's all.

Anonymous

Anonymous Sun 18 Apr 2021 04:48:28 No.12993500 Report

Quoted By:

>>12991414
learn the ito integral now
https://en.wikipedia.org/wiki/Stochastic_calculus

Anonymous

Anonymous Sun 18 Apr 2021 05:03:27 No.12993532 Report

Quoted By: >>12993680 >>12993750

>>12993492
Dunno what to tell you, Harvard seems to think it's necessary and they probably know better than I do. I took it as an undergrad and it's required on the qualification exam for my school too (they only require algebra & analysis though to be fair).

Anonymous

Anonymous Sun 18 Apr 2021 05:48:51 No.12993680 Report

Quoted By:

>>12993532
Harvard is an an elitist institution with enough demand to put such a test. It works as a somewhat fair filter if you want to get the best of the best but it is not a fucking requirement.

Anonymous

Anonymous Sun 18 Apr 2021 06:11:53 No.12993750 Report

Quoted By: >>12993759 >>12995085

>>12993532
That's not the point of the quals. The point isn't to have you learn all fields thoroughly. It's to make sure that you know the basics of a broad enough base that you can do research properly, learn to see connections between areas, and so on.

Anonymous

Anonymous Sun 18 Apr 2021 06:16:11 No.12993759 Report

Quoted By:

>>12993750
I agree with that, but apparently learning algebra beyond what this person said was necessary is required to pass these exams at a lot of schools.

Anonymous

Anonymous Sun 18 Apr 2021 08:44:00 No.12994137 Report

Quoted By: >>12994178

>>12990788
I like using QED, it makes me feel cool

>>12991836
>unless he specifically stated before that you shouldn't use qed.
he never said that
he himself uses QED sometimes in his lectures the massive cunt

Anonymous

Anonymous Sun 18 Apr 2021 08:55:21 No.12994178 Report

Quoted By:

>>12994137
What race is he and what race are you?

Anonymous

View Same Google iqdb SauceNAO IMG_20210418_113344600_HDR~3.jpg, 4MiB, 3455x3072

Anonymous Sun 18 Apr 2021 09:38:46 No.12994268 Report

Quoted By: >>12994285 >>12994681 >>12994800 >>12997437

What's the next book you're gonna buy?

Anonymous

Anonymous Sun 18 Apr 2021 09:50:22 No.12994285 Report

Quoted By:

>>12994268
Laura Warholic by Alexander Theroux

Anonymous

Anonymous Sun 18 Apr 2021 11:15:56 No.12994491 Report

Quoted By: >>12994493 >>12994632

Good day lads,
can someone recommend me a book that gives a basic introduction to degrees of maps between manifolds? Preferably from a topological standpoint

Anonymous

Anonymous Sun 18 Apr 2021 11:16:39 No.12994493 Report

Quoted By: >>12994632 >>12994796

>>12994491
Milnor: Topology from the differentiable viewpoint

Anonymous

Anonymous Sun 18 Apr 2021 12:26:51 No.12994632 Report

Quoted By: >>12994796

>>12994491
you mean smooth degree or topological degree? if the first, then >>12994493. if the second, then Bredon

Anonymous

Anonymous Sun 18 Apr 2021 12:48:34 No.12994681 Report

Quoted By:

>>12994268
wtf is with your obsession of the rotenturmstraße

Anonymous

Anonymous Sun 18 Apr 2021 12:53:08 No.12994695 Report

Quoted By:

>>12992589
How is B's claim true "by definition"?

It might help to reframe it that way: Imagine there are knights and knaves, knights tell the truth, and knaves lie.
If some person says "I am a knight", they could be a knight telling the truth, or they could be a knave lying that they are a knight.

Anonymous

View Same Google iqdb SauceNAO IMG_20210418_205856.jpg, 2MiB, 3999x1391

Anonymous Sun 18 Apr 2021 13:00:03 No.12994714 Report

Quoted By: >>12995012 >>12997437

Pugh with the based exercises

Anonymous

Anonymous Sun 18 Apr 2021 13:06:13 No.12994724 Report

Quoted By:

>>12987294
I passed my two comprehensive exams two years earlier than these. We had to apply imaginative approaches to solving the problems. These look more like asking for definitions and some standard examples.

Anonymous

Anonymous Sun 18 Apr 2021 13:38:32 No.12994786 Report

Quoted By:

>>12993342
it is, haha wtf

Anonymous

Anonymous Sun 18 Apr 2021 13:41:12 No.12994796 Report

Quoted By: >>12994817

>>12994493
>>12994632
Thanks for the answers. Which book by Bredon? "Topology and Geometry"?

Anonymous

Anonymous Sun 18 Apr 2021 13:43:56 No.12994800 Report

Quoted By:

>>12994268
No more for me right now. I've got Algebra Chapter 0 and Elements of the Theory of Functions and Functional Analysis Vol I & II to chew on.

Anonymous

Anonymous Sun 18 Apr 2021 13:50:14 No.12994817 Report

Quoted By:

>>12994796
>Which book by Bredon? "Topology and Geometry"?
yes, this one. he does the degree stuff better than Hatcher IMO.

Anonymous

Anonymous Sun 18 Apr 2021 14:47:50 No.12995012 Report

Quoted By: >>12995365 >>12995804

>>12994714
Do I have to be ESL to hear the rhyme?

Anonymous

View Same Google iqdb SauceNAO classical vs constructive existe (...).jpg, 143KiB, 1404x672

Anonymous Sun 18 Apr 2021 14:53:57 No.12995031 Report

Quoted By: >>12995063

>>12993342
>Do not use or prove general existence theorems, but write a formula for f.
Based Harvard BTFOing false mathematicians.

Anonymous

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Anonymous Sun 18 Apr 2021 14:57:16 No.12995042 Report

Quoted By: >>12995164 >>12995168

how does this actually work /mg/? t. was good at calculus like 5 years ago but barely used it since and never did real analysis or anything

Anonymous

Anonymous Sun 18 Apr 2021 15:02:44 No.12995063 Report

Quoted By:

>>12995031
?

Anonymous

Anonymous Sun 18 Apr 2021 15:05:09 No.12995069 Report

Quoted By: >>12995074 >>12995106 >>12995166

Any good source on group theory?

Anonymous

Anonymous Sun 18 Apr 2021 15:07:19 No.12995074 Report

Quoted By: >>12995087

>>12995069
yeah

Anonymous

Anonymous Sun 18 Apr 2021 15:10:00 No.12995085 Report

Quoted By: >>12995171

>>12993750
The fields are heavily skewed towards certain areas. "All fields" is impossible to thoroughly learn. No having basic shit knowledge about certain fields will not aid you in doing research.

Anonymous

Anonymous Sun 18 Apr 2021 15:10:35 No.12995087 Report

Quoted By: >>12995093

>>12995074
Mind to share?

Anonymous

Anonymous Sun 18 Apr 2021 15:11:35 No.12995093 Report

Quoted By:

>>12995087
no

Anonymous

Anonymous Sun 18 Apr 2021 15:14:07 No.12995106 Report

Quoted By:

>>12995069
start with the definition of a group and derive all groups and their properties from there

Anonymous

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Anonymous Sun 18 Apr 2021 15:30:31 No.12995164 Report

Quoted By:

>>12995042
* shizo answer: the reals are retarded and you'd be better off just not using them as much
* there is no paradox, the length of the jagged/blue line is always the same integer value. That sequence of jagged/blue converges pointwise to the arc with the nice smooth parametrization and irrational length, but not more. The lengths of the two things don't converge and that's that.
* big brain answer: the reals are retarded and you'd be better off just not using them as much

Anonymous

Anonymous Sun 18 Apr 2021 15:31:24 No.12995166 Report

Quoted By:

>>12995069
Gorenstein

Anonymous

View Same Google iqdb SauceNAO anbYYo5_700b.jpg, 61KiB, 700x750

Anonymous Sun 18 Apr 2021 15:31:45 No.12995168 Report

Quoted By:

>>12995042
* shizo answer: the reals are retarded and you'd be better off just not using them as much
* academic answer: there is no paradox, the length of the jagged/blue line is always the same integer value. That sequence of jagged/blue converges pointwise to the arc with the nice smooth parametrization and irrational length, but not more. The lengths of the two things don't converge and that's that.
* big brain answer: the reals are retarded and you'd be better off just not using them as much

Anonymous

Anonymous Sun 18 Apr 2021 15:32:11 No.12995171 Report

Quoted By:

>>12995085
>No having basic shit knowledge about certain fields will not aid you in doing research.
It will significantly aid you actually.

Anonymous

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Anonymous Sun 18 Apr 2021 15:42:35 No.12995217 Report

Quoted By: >>12995302 >>13000542

here's your "math" bro

Anonymous

Anonymous Sun 18 Apr 2021 16:03:57 No.12995302 Report

Quoted By: >>12995738 >>12995783 >>13000542

>>12995217
Rep theory is like the post-modernism of mathematics. No one understands what they're saying, and they love it.

Anonymous

Anonymous Sun 18 Apr 2021 16:18:24 No.12995365 Report

Quoted By:

>>12995012
Yes, it'd only rhyme if you have shit pronunciation of "bounded"

Anonymous

Anonymous Sun 18 Apr 2021 17:23:20 No.12995687 Report

Quoted By: >>12995695

Number theory and geometry/topology are the only fields of math that are acceptable for men to study. All other fields are for women and trannies.

Anonymous

Anonymous Sun 18 Apr 2021 17:24:37 No.12995695 Report

Quoted By: >>12995776

>>12995687
Combinatorics isn't?

Anonymous

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Anonymous Sun 18 Apr 2021 17:25:37 No.12995696 Report

Quoted By:

>whiteboard/blackboard/glass board all makes you stand up and move your arms, thereby making you and your 10am brain more active
You guys were hiding this from us the entire time weren't you

Anonymous

View Same Google iqdb SauceNAO IMG_20210418_192900632~2.jpg, 2MiB, 2424x4018

Anonymous Sun 18 Apr 2021 17:33:37 No.12995738 Report

Quoted By: >>12995754 >>12995783 >>13000542

>>12995302
I assume it's QFT, but it doesn't look pretty

Anonymous

Anonymous Sun 18 Apr 2021 17:37:23 No.12995754 Report

Quoted By: >>12995981

>>12995738
>Fanged Noumena

Anonymous

Anonymous Sun 18 Apr 2021 17:40:46 No.12995776 Report

Quoted By:

>>12995695
Only enumerative combinatorics because it has epsilon and Fourier transforms. Algebraic combinatorics is for femoids.

Anonymous

Anonymous Sun 18 Apr 2021 17:42:11 No.12995783 Report

Quoted By: >>12995981

>>12995738
>>12995302
here's the paper
https://msp.org/agt/2013/13-6/p15.xhtml

Anonymous

Anonymous Sun 18 Apr 2021 17:45:54 No.12995804 Report

Quoted By:

>>12995012
Nah, I'm not a linguisticschad but at least the way I speak, the final d of bounded and t of it are both about the same sound, a sorta glottal stoppy type deal.

Anonymous

Anonymous Sun 18 Apr 2021 18:20:17 No.12995940 Report

Quoted By: >>12995981 >>12997952

Anyone else have trouble deciding what topics NOT to learn?
There's so much interesting mathematics out there, so its hard not to want to learn a bit about everything.

Anonymous

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Anonymous Sun 18 Apr 2021 18:31:39 No.12995981 Report

Quoted By:

>>12995783
I'm glad nobody is forcing me to read this.

>>12995754
Staged it for meme purposes.

>>12995940
I like to make notes sketching stuff out and focusing on things that fill some gaps.
My second, related strategy is to write about something and try to capture the math necessary to pin it down properly.

Anonymous

Anonymous Sun 18 Apr 2021 18:40:53 No.12996029 Report

Quoted By: >>12996038 >>12996065 >>13000629 >>13000841

How do I cope with the fact that I'm just about to start uni at age of 23?

I will never succeed this late in life, I AM A FAILURE

Anonymous

Anonymous Sun 18 Apr 2021 18:43:00 No.12996038 Report

Quoted By: >>12996040

>>12996029
are you cis?

Anonymous

Anonymous Sun 18 Apr 2021 18:43:32 No.12996040 Report

Quoted By: >>12996056

>>12996038
I'm bisexual, is that cis?

Anonymous

Anonymous Sun 18 Apr 2021 18:45:10 No.12996056 Report

Quoted By:

>>12996040
still less of a failure than trannies. godspeed.

Anonymous

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Anonymous Sun 18 Apr 2021 18:46:41 No.12996065 Report

Quoted By:

>>12996029
nobody succeeds in life, succeeding in life is a meme

Anonymous

Anonymous Sun 18 Apr 2021 18:55:38 No.12996128 Report

Quoted By: >>12996135

>>12992457
None, any serious math will require you to do some kind of ugly computation

Anonymous

Anonymous Sun 18 Apr 2021 18:57:01 No.12996135 Report

Quoted By: >>13000569

>>12996128
Even category theory?

Anonymous

Anonymous Sun 18 Apr 2021 19:07:25 No.12996192 Report

Quoted By: >>12997759 >>12997950 >>12997952 >>12998136

>forgets how to prove basic property learned years ago
>too mad and prideful to look up how it's done
>hours and hours spent trying to re-reinvent the wheel

Tell me why I shouldn't suicide.

Anonymous

View Same Google iqdb SauceNAO N.jpg, 46KiB, 1280x721

Anonymous Sun 18 Apr 2021 19:17:49 No.12996256 Report

Quoted By: >>12996415 >>13000745

Anonymous

Anonymous Sun 18 Apr 2021 19:40:23 No.12996415 Report

Quoted By: >>13000745

>>12996256
lmao so heckin based
libtards seething!!

Anonymous

Anonymous Sun 18 Apr 2021 19:42:37 No.12996429 Report

Quoted By: >>12996645

>>12987294
What’s the hardest part of the first differential equations course a student would take?

Anonymous

Anonymous Sun 18 Apr 2021 20:21:52 No.12996645 Report

Quoted By:

>>12996429
Not being bored to death.
Those courses are mainly about following instructions. You are presented with a bunch of different types of equations, and are shown step by step how to solve them.
Doing well is just a matter of getting enough practice so that you can adequately memorize and apply all the solution techniques.

Though I guess it is possible that certain topics could provide conceptual difficulties.
If linear algebra confuses you then systems of differential equations could be hard.
There's also Laplace Transform which is technically a complicated topic, but they won't teach the actual theory it. So solving problems with it boils down to following instructions and treating the transform as a magical black box.

Anonymous

Anonymous Sun 18 Apr 2021 22:53:27 No.12997437 Report

Quoted By:

>>12994268
fuchs fomenko or pinter probably

>>12994714
lmao

Anonymous

Anonymous Sun 18 Apr 2021 23:27:32 No.12997556 Report

Quoted By:

>>12989260
>who hurt you
I want reddit to leave

Anonymous

View Same Google iqdb SauceNAO 1505169726119.png, 268KiB, 750x750

Anonymous Mon 19 Apr 2021 00:13:36 No.12997661 Report

Quoted By: >>12997666

>tfw switched form texstudio to visual studio code
it's...so much better....

Anonymous

Anonymous Mon 19 Apr 2021 00:14:25 No.12997666 Report

Quoted By: >>12997883 >>12997887

>>12997661
For me, it’s Texmaker.

Anonymous

Anonymous Mon 19 Apr 2021 00:47:17 No.12997759 Report

Quoted By:

>>12996192
This is me and I'm also considering suicide :)

Anonymous

Anonymous Mon 19 Apr 2021 01:16:41 No.12997883 Report

Quoted By: >>12997902

>>12997666
For me it's Lyx

Anonymous

Anonymous Mon 19 Apr 2021 01:18:14 No.12997887 Report

Quoted By:

>>12997666
I like Texmaker too. I use it over the SpaceVim LaTeX extension (which has some features that I think are just really, really stupid)

Anonymous

Anonymous Mon 19 Apr 2021 01:24:23 No.12997902 Report

Quoted By: >>12998051

>>12997883
Redpill me on Lyx, anon.

Anonymous

Anonymous Mon 19 Apr 2021 01:43:03 No.12997950 Report

Quoted By:

>>12996192
This is me but also

>have to calculate a matrix
>wonder wether i should kill myself
>muster the discipline to actually do the thing
>it's the wrong fucking matrix

every time...

Anonymous

Anonymous Mon 19 Apr 2021 01:43:18 No.12997952 Report

Quoted By: >>12999089

>>12996192
I can never remember how to prove the half-dozen or so basic analysis inequalities. I remember Cauchy-Schwarz because there's geometry that makes it easy to remember but stuff like AM-GM and the Young-Holder-Minkowski trilogy I can't for the life of me remember how the proofs go no matter how many times I see them. I took real analysis with a harmonic analyst and he told us he had to spend an afternoon rederiving them all every time he taught the class because he could never remember either.
>>12995940
Thinking of it as deciding NOT to learn something is a bad way to frame it. The decision you're making is what's most important for you to learn _right now_. You're not deciding to never learn the other stuff, just leaving it for later. I keep a giant list of papers/videos/books/general topics I want to get to eventually partitioned roughly based on how important they are. It grows way faster than I can cut it down, and I will probably never get around to a lot of it, especially the less important stuff, but writing it down makes it feel less swampy and overwhelming and stops me from spending most of my time thinking about what I should think about.

Anonymous

Anonymous Mon 19 Apr 2021 02:16:29 No.12998051 Report

Quoted By:

>>12997902
Tex but with office-like ui.

Anonymous

Anonymous Mon 19 Apr 2021 02:29:32 No.12998081 Report

Quoted By: >>12998112 >>12998115 >>12998187

Does anybody know of a good series of intro real analysis lectures on youtube?

Anonymous

Anonymous Mon 19 Apr 2021 02:40:46 No.12998112 Report

Quoted By: >>12998631

>>12998081
https://youtu.be/KH-8lZBa76E

Anonymous

Anonymous Mon 19 Apr 2021 02:41:30 No.12998115 Report

Quoted By: >>12998147

>>12998081
I like Winston Ou’s lectures on analysis. He teaches out of the first 7 chapters of Rudin.

Anonymous

Anonymous Mon 19 Apr 2021 02:47:06 No.12998136 Report

Quoted By:

>>12996192
Remember: add zero or multiply by one and then use the triangle inequality.

Anonymous

Anonymous Mon 19 Apr 2021 02:50:41 No.12998147 Report

Quoted By:

>>12998115
I second these, they're the best available it seems. It'd be nice if someone would have some proper lectures with good audio and video but they are good enough.

Anonymous

Anonymous Mon 19 Apr 2021 03:01:03 No.12998187 Report

Quoted By: >>12998604

>>12998081
Look for the Kreysig book if you're looking for an introductory text.
"Introduction to Functional Analysis with Applications"
You can understand everything going on there if you've taken your first Advanced Calculus class.
https://physics.bme.hu/sites/physics.bme.hu/files/users/BMETE15AF53_kov/Kreyszig%20-%20Introductory%20Functional%20Analysis%20with%20Applications%20(1).pdf

Anonymous

Anonymous Mon 19 Apr 2021 04:46:30 No.12998604 Report

Quoted By: >>12998876

>>12998187
I wonder if its worth studying Functional Analysis if you don't know enough about Lebesgue measure to understand the theory of L^p spaces.
Without that background, are there really any complete function spaces you can even consider?

Anonymous

Anonymous Mon 19 Apr 2021 04:53:14 No.12998631 Report

Quoted By: >>12998693 >>12998979

>>12998112
that channel is ass

Anonymous

Anonymous Mon 19 Apr 2021 05:06:44 No.12998682 Report

Quoted By:

>>12987294
How much chance do i have to publish as an engineer bsc in the math department?

Anonymous

Anonymous Mon 19 Apr 2021 05:11:00 No.12998693 Report

Quoted By: >>13000596

>>12998631
It sure is. We had a discussion a while back about his crappy books that a 'pure math' major uses and they were all engineering level books from one prominent publisher.

Anonymous

Anonymous Mon 19 Apr 2021 05:25:09 No.12998719 Report

Quoted By: >>12999163

Does the study of real analytic functions essentially just reduce to complex analysis?
By that I mean, is there any reason not to imagine real analytic functions as restrictions of suitable complex analytic functions? Is there anything to be gained by $\mathbf{not}$ passing to the complex domain?

Anonymous

Anonymous Mon 19 Apr 2021 06:30:45 No.12998876 Report

Quoted By: >>12998902

>>12998604
He just treats L^P spaces as completions of the corresponding space of Riemann functions if I recall correctly. I liked the book –obviously it's not the same as a heavy FA text, but it presents enough for mathematically minded applied people/undergrads, and he's a great writer.
Still, I don't think Kreyszig is good advice for someone who wants an intro to real analysis. It's neither an intro analysis book (i.e., completeness, compactness, Riemann integration, etc.), nor is it an intro to real analysis topics like measure theory

Anonymous

Anonymous Mon 19 Apr 2021 06:40:45 No.12998902 Report

Quoted By: >>13000706

>>12998876
It does look like a cool book. I would have really enjoyed reading it back when I was an undergrad, curious about functional analysis, but not brave enough for a graduate level text.

Anonymous

Anonymous Mon 19 Apr 2021 07:03:08 No.12998979 Report

Quoted By:

>>12998631
I don't care for the channel, the joke was the "video series" for real analysis was just "read rudin lmao"

Anonymous

Anonymous Mon 19 Apr 2021 07:13:57 No.12999012 Report

Quoted By:

sist... bros i did some category theory https://www.youtube.com/watch?v=EgKdyHcZJcs

Anonymous

Anonymous Mon 19 Apr 2021 07:40:07 No.12999089 Report

Quoted By: >>12999175

>>12997952
>I can never remember how to prove the half-dozen or so basic analysis inequalities.
How important is it to just know a fuck ton of random inequalities when doing analysis?
Seems like such an essential skill to just be able to recognize when you can invoke John McNobody's random obscure bumfuck inequality to crucially simplify an expression.

Anonymous

Anonymous Mon 19 Apr 2021 07:59:09 No.12999142 Report

Quoted By:

>>12987294
nice set of problems

Anonymous

Anonymous Mon 19 Apr 2021 08:05:00 No.12999151 Report

Quoted By: >>12999178

>>12992437
holy fuck I can only do problem 3 (day 2). how do I learn this shit niggas?

Anonymous

Anonymous Mon 19 Apr 2021 08:09:13 No.12999163 Report

Quoted By:

>>12998719
>Is there anything to be gained by notnot passing to the complex domain?
Fewer dimensions to deal with I suppose.
The fact that the complex conjugation $z\mapsto \bar z$ is nowhere in ${\mathbb C}$ differentiable is something that might be true, but a pure distraction when doing real analysis.

Anonymous

Anonymous Mon 19 Apr 2021 08:16:29 No.12999175 Report

Quoted By:

>>12999089
generally useful but you'll pick it up as you go
I find that complex analysis relies on inequalities significantly less and you have a much cooler toolbox to play around with

Anonymous

Anonymous Mon 19 Apr 2021 08:18:08 No.12999178 Report

Quoted By:

>>12999151
Relax, that problem you can do is dead easy with residues. That should tell you about the difficulty of the others. It's just meant to test your breadth of knowledge, not depth. It's just there to check you've mastered the basics.
So the answer to your question is just get out and read more.

Anonymous

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Anonymous Mon 19 Apr 2021 08:41:23 No.12999229 Report

Quoted By: >>12999231 >>12999238

Fuck, just used algebraic topology to solve an analysis problem. Is there something wrong with me?

Anonymous

Anonymous Mon 19 Apr 2021 08:42:22 No.12999231 Report

Quoted By:

>>12999229
No, it's totally fine.

Anonymous

Anonymous Mon 19 Apr 2021 08:45:23 No.12999238 Report

Quoted By: >>12999248

>>12999229
what was the problem?

Anonymous

Anonymous Mon 19 Apr 2021 08:49:35 No.12999248 Report

Quoted By: >>12999255 >>13000499

>>12999238
Apostol 13.7b

Anonymous

Anonymous Mon 19 Apr 2021 08:53:01 No.12999255 Report

Quoted By: >>12999263

>>12999248
There is absolutely something wrong.

Anonymous

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Anonymous Mon 19 Apr 2021 08:55:39 No.12999263 Report

Quoted By: >>12999281

>>12999255
dubs of truth i guess...

Anonymous

Anonymous Mon 19 Apr 2021 09:00:15 No.12999281 Report

Quoted By:

>>12999263
hi tranny

Anonymous

Anonymous Mon 19 Apr 2021 14:17:15 No.13000219 Report

Quoted By: >>13000225 >>13000689

Yo I'm having trouble understanding this proof that the natural numbers are not bounded.
Assume that the natural numbers are bounded above, let a = sup N
consider a - 1, since a -1 is not an upper bound of N there exists an n in N such that a - 1 < n
add one to each side
a < n + 1 , therefore there exists a natural number greater than a

The logic here seems circular to me. The proof is basically saying "pick the number that you think is the biggest natural then add one" but why are we allowed to add one in this case? Don't we need to prove that you can always add one to any natural number first?

Anonymous

Anonymous Mon 19 Apr 2021 14:17:41 No.13000221 Report

Quoted By:

Bruhs ahlfors is filtering me a little bit. All of his exercises are either super long computations or proofs that alternate between trivial and super hard. Am I doing it wrong?

Anonymous

Anonymous Mon 19 Apr 2021 14:18:36 No.13000225 Report

Quoted By:

>>13000219
Fairly certain that every natural number has a successor is part of their definition

Anonymous

Anonymous Mon 19 Apr 2021 14:23:47 No.13000244 Report

Quoted By: >>13000724

As it turns out reading some problem sets that colleges are assigning with ahlfors, trying to work the problems in the later parts of his third chapter may be a mistake, no one is assigning them

Anonymous

Anonymous Mon 19 Apr 2021 15:29:36 No.13000499 Report

Quoted By:

>>12999248
Post it

Anonymous

Anonymous Mon 19 Apr 2021 15:38:50 No.13000542 Report

Quoted By: >>13000689

>>12995217
>>12995302
>>12995738
Is Representation Theory important in QFT?

Anonymous

Anonymous Mon 19 Apr 2021 15:44:19 No.13000569 Report

Quoted By:

>>12996135
That's not mathematics, it's logic.

Anonymous

Anonymous Mon 19 Apr 2021 15:52:35 No.13000596 Report

Quoted By:

>>12998693
Which books?

Anonymous

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Anonymous Mon 19 Apr 2021 15:58:49 No.13000619 Report

Quoted By: >>13000632

>it's another episode of remember your useless trig identities or suffer

Anonymous

Anonymous Mon 19 Apr 2021 16:04:32 No.13000629 Report

Quoted By:

>>12996029
Would you rather be 27 with a degree or just 27?

Anonymous

Anonymous Mon 19 Apr 2021 16:05:22 No.13000632 Report

Quoted By:

>>13000619
it's a basic identity, it's not useless
you can't seriously be filtered by this

Anonymous

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Anonymous Mon 19 Apr 2021 16:19:18 No.13000689 Report

Quoted By: >>13000841

>>13000542
Extremely. This holds for mechanics in general.

>>13000219
>Don't we need to prove that you can always add one to any natural number first?
When you say "consider a - 1" at the start, it seems you went far beyond just that assumption. Might help to state the framework you're working in.

If your numbers aren't given materially, in terms of other things, then what I can tell you is that your proof will require induction.
This is because if you drop it, you get
https://en.wikipedia.org/wiki/Robinson_arithmetic
and this has a nonstandard model with "a natural" $w$ that has $w+1=w$ .

Anonymous

Anonymous Mon 19 Apr 2021 16:22:34 No.13000706 Report

Quoted By:

>>12998902
Hmm yeah I feel you. Stein and Shakarchi's measure theory book is pretty friendly. Some overlapping material with the Kreyszig but at a more advanced level.
Honestly though, I'd recommend leafing through Kreyszig if you're interested. You can burn through a good amount of it quickly, and if you've never dealt with Hilbert/Banach spaces, it's a pretty beautiful ride. And if you have, you can skip to the spectral theory parts, which is super nice.
One super compact book which you might enjoy casually leafing through instead is Widom's lectures on integral equations. Lots of the same material, but only the pieces which are necessary to develop the theory

Anonymous

Anonymous Mon 19 Apr 2021 16:25:53 No.13000724 Report

Quoted By:

>>13000244
Haven't read Ahlfors, but yeah I'd stick to assigned p-sets when self-studying for this reason. I remember Rudin has a problem in the first/second chapter which involves constructing the Cauchy sequence eq. class definition of the real numbers and proving its completeness. I can't imagine doing that in the second/third week of studying proof-based math for the first time...

Anonymous

Anonymous Mon 19 Apr 2021 16:29:05 No.13000745 Report

Quoted By:

>>12996256 >>12996415

$\mathbb{N}\hat\imath gg\varepsilon rs \quad btfo$

Anonymous

Anonymous Mon 19 Apr 2021 16:50:16 No.13000841 Report

Quoted By: >>13001043

>>12996029
>>13000689
>Extremely. This holds for mechanics in general
Guess I'll do my undergraduate research in it then. I like Algebra, Logic and Physics so this seems like the natural course to take, what do you think?

Anonymous

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Anonymous Mon 19 Apr 2021 17:31:33 No.13001004 Report

Quoted By:

Anonymous

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Anonymous Mon 19 Apr 2021 17:40:15 No.13001043 Report

Quoted By: >>13001195

>>13000841
Not sure what undergrad research is, but if you are just about to start uni, then you got some time.

Anonymous

Anonymous Mon 19 Apr 2021 17:42:20 No.13001058 Report

Quoted By:

or what it is 4u

Anonymous

Anonymous Mon 19 Apr 2021 17:49:58 No.13001103 Report

Quoted By:

>>13001099
>>13001099
>>13001099

Anonymous

Anonymous Mon 19 Apr 2021 18:03:51 No.13001195 Report

Quoted By:

>>13001043
It's exactly what it is, undergraduate research.
>if you are just about to start uni
I'm halfway through.

Anonymous

Anonymous Tue 20 Apr 2021 00:23:03 No.13002745 Report

Quoted By: >>13002826

In my topology exam this semester, we are being tested on Euler characteristics and classification of compact surfaces.
However, the textbooks for the class don't discuss these at all really. Does anyone have any suggestions for materials that I can use to study these two things?

Anonymous

Anonymous Tue 20 Apr 2021 00:47:15 No.13002826 Report

Quoted By:

>>13002745
Hatcher, munkres probably

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