Anonymous at Fri, 3 Jan 2025 20:43:24 UTC No. 16534312

finishing undergrad, what should i know by now for masters?

Anonymous at Fri, 3 Jan 2025 20:45:32 UTC No. 16534314

just finished Lang's basic mathematics, what's next

Anonymous at Fri, 3 Jan 2025 21:37:49 UTC No. 16534384

I need help understanding the Fundamental Theorem of Graphs

Anonymous at Fri, 3 Jan 2025 22:07:58 UTC No. 16534436

>>16534314

Anonymous at Fri, 3 Jan 2025 22:17:57 UTC No. 16534447

>>16534436
i have this one, do i need lang too

Anonymous at Fri, 3 Jan 2025 22:30:14 UTC No. 16534463

Nobody told me that a math degree is worth nothing. Nobody hires mathematicians. :(

Anonymous at Fri, 3 Jan 2025 22:35:44 UTC No. 16534471

>>16534463
Try applying at middle schools. Math teachers are always needed.

Anonymous at Fri, 3 Jan 2025 23:27:22 UTC No. 16534516

>>16534314
Stewart's Calculus

Anonymous at Fri, 3 Jan 2025 23:31:16 UTC No. 16534518

Which numbers are able to be the sum of consecutive cubes? Assuming that the cubes don't have to start from one. For example, one of such numbers could be 1584 because of the fact that 1584 = 7^3+8^3+9^3.

Do those numbers have a formula and how common would they be?

Anonymous at Fri, 3 Jan 2025 23:36:34 UTC No. 16534524

>>16534518
[math]( n - 1 ) ^ 3 + n ^ 3 + ( n + 1 ) ^ 3 = 3 n ^ 3 + 6 n[/math]

Anonymous at Fri, 3 Jan 2025 23:38:36 UTC No. 16534526

>>16534463
Try becoming a quant at Jane Street

Anonymous at Fri, 3 Jan 2025 23:42:14 UTC No. 16534528

I hate applied math, but the only way to do a master degree at my uni is in a statistic program.

🗑️ Anonymous at Fri, 3 Jan 2025 23:43:28 UTC No. 16534529

>>16534524
But isn't that just three consecutive cubes? What if there's a number which cannot be the sum of three consecutive cubes but is still the sum of some other number of consecutive cubes.

🗑️ Anonymous at Fri, 3 Jan 2025 23:47:07 UTC No. 16534531

>>16534524
That's only three consecutive squares. You can not make the number 1800 with that formula but yet 1800 is still able to be the sum of consecutive cubes.

Anonymous at Fri, 3 Jan 2025 23:48:32 UTC No. 16534533

>>16534524
That's only three cubes. You can not make the number 1800 with that formula but yet 1800 is still able to be the sum of consecutive cubes.

Anonymous at Sat, 4 Jan 2025 00:10:30 UTC No. 16534543

>>16534463
I became a code monkey.

Anonymous at Sat, 4 Jan 2025 01:31:17 UTC No. 16534597

>>16534543
all the physics and math majors end up becoming code monkeys, meanwhile i was ahead of the game at became a code monkey from the start. Now i see the writing on the wall though with how AI is going to fuck everything up, so i'm returning to my studies to learn everything i can to try to still have an identity after the great ai reckoning in all intellectual fields

Anonymous at Sat, 4 Jan 2025 01:39:07 UTC No. 16534605

>>16534516
>Stewart's Calculus
$200 bucks, why these textbook publishers always trying to scam students

Anonymous at Sat, 4 Jan 2025 01:40:01 UTC No. 16534606

>>16534605
it's free on libgen

Anonymous at Sat, 4 Jan 2025 01:42:29 UTC No. 16534608

>>16534606
i need the bound paper, unless it's physically sitting in my library daring me to read it, i'm not going to

Anonymous at Sat, 4 Jan 2025 01:56:05 UTC No. 16534615

>>16534605
Bro, I got my copy of Stewart's Calculus for $5 on thrift books.

Anonymous at Sat, 4 Jan 2025 02:49:45 UTC No. 16534660

>>16534533
pardon me, I'm retarded and saw a 3 where there was none
for the sum of all cubes from [math]x[/math] to [math]y[/math] you have the mildly unpleasant formula [math]\frac {y^4 + 2y ^ 3 + y ^ 2 - x ^4 + 2 x ^3 - x ^2} {4}[/math]

which is ugly enough that I don't want to do heuristics to figure out how common numbers of that form are

Anonymous at Sat, 4 Jan 2025 04:00:21 UTC No. 16534706

>>16534526
Are you Indian?

Anonymous at Sat, 4 Jan 2025 04:01:32 UTC No. 16534708

>>16534528
Are you also Indian?

Anonymous at Sat, 4 Jan 2025 06:27:04 UTC No. 16534819

Why shouldn't I go to Columbia for their cash cow masters? I want it. I hate how the voices in my head are making me insecure about being self indulgent for doing something for myself, just for myself. There are people who waste their time and money restoring cars, or gardening, or even playing video games. I want to get a masters in math. No it won't matter, no it's not a PhD and I don't have the time and money for that. It's fine, I'm fine, and I can cope by thinking that what I'm putting in cash wise will fund math PhD students so everyone wins. I can't afford to lose my job no fucking way in today's economy is anyone in tech making 200k salaries anymore. There are kids being hired now, over five years later, for less than I did when I started.

I live in in the bay area, no I'm not going to move anywhere else for school. I need a fellow sperg here to hype me up to do this.

Anonymous at Sat, 4 Jan 2025 06:35:54 UTC No. 16534824

>>16534183
lol no undegrad program is going to ask for anything beyond your "freshman year".

Anonymous at Sat, 4 Jan 2025 08:20:10 UTC No. 16534870

>>16534183
>posted the meme list that noone has ever read one book from again

Anonymous at Sat, 4 Jan 2025 14:58:44 UTC No. 16535047

>>16534706
No, Slavic

Anonymous at Sat, 4 Jan 2025 16:56:54 UTC No. 16535154

Bros, How can I get a scholarship for a master's degree in mathematics?
My university has an agreement with the University of Paris Saclay, but since my country is garbage, they only let me apply for the master's degree in applied mathematics, but I would like to do pure mathematics.

I have been searching on different websites for scholarships but the only thing I have been able to find have been scholarships that only include tuition fees.
What I'm looking for are scholarships like the Sohpie Germain foundation, (https://www.fondation-hadamard.fr/en/our-programs/transversal-programs/graduate-program/apply-for-a-sophie-germain-scholarship/) , which give you money while you study so you can live.
Sorry for the repost.

Anonymous at Sat, 4 Jan 2025 17:11:38 UTC No. 16535177

>>16534708
????
>>16534543
But i hate coding. It makes me feel like ive wasted 4 years of undergrad. My uni only had one class of programing.

Anonymous at Sat, 4 Jan 2025 17:40:07 UTC No. 16535209

i got a book on Lie groups, i'm either going to understand higher mathematics or die trying

Anonymous at Sat, 4 Jan 2025 18:17:27 UTC No. 16535250

>>16535209
Sounds exciting (the part about dying)

Anonymous at Sat, 4 Jan 2025 19:56:40 UTC No. 16535362

>>16535047
Basically the same thing.
>>16535177
So, you admit you are?

Anonymous at Sat, 4 Jan 2025 20:00:21 UTC No. 16535364

>>16534183
Lean's syntax irritates the fuck out of me.
I don't know how people use this shit.

Anonymous at Sat, 4 Jan 2025 20:15:59 UTC No. 16535384

>picrel
thoughts gentlemen? I just want to blitz through precalc and this text is nice and condense, with better writing than stewart's

Anonymous at Sun, 5 Jan 2025 02:47:53 UTC No. 16535775

>>16535384
What is your motivation for learning this material? Having an end goal will help.

Anonymous at Sun, 5 Jan 2025 03:16:22 UTC No. 16535809

>>16534183
Do any of you know of a software package that can do efficient kernel density estimation using a beta distribution?
I'm currently using the scipy.stats implementation, but it's slow.

🗑️ Anonymous at Sun, 5 Jan 2025 05:44:12 UTC No. 16535943

>>16534471
They don't teach actual math until you go to college and study something STEM--public school math is a debauchery of actual math.

Anonymous at Sun, 5 Jan 2025 08:01:22 UTC No. 16536004

How do you feel about cs students in your classroom?

Anonymous at Sun, 5 Jan 2025 13:32:57 UTC No. 16536148

>>16536004
The smartest person in my graduate level probability class was an ML guy.

Anonymous at Sun, 5 Jan 2025 14:12:33 UTC No. 16536165

>>16536004
I firmly believe we should return theoretical CS to math departments. The difference between them and the baby brain webdev /g/tards is so much larger than them and like a statistician, physicist, or mathematician.

Anonymous at Sun, 5 Jan 2025 15:51:40 UTC No. 16536222

>>16536165
as a CS guy I support this, automata and formal languages and complexity theory is math not computer science

Anonymous at Sun, 5 Jan 2025 17:50:57 UTC No. 16536320

So a Lie Group is a differential manifold and also a group. So it's basically bridging together topology and group theory?

Anonymous at Sun, 5 Jan 2025 20:42:16 UTC No. 16536515

>>16536320
it is simpler to think about it as a way of defining smooth group actions and their derivatives. it isn't really a bridge, just a subject which uses differentiable manifolds and group theory as tools.

Anonymous at Sun, 5 Jan 2025 21:14:10 UTC No. 16536541

>>16536004
at least some of them actually like math.
my course is FULL of tryhards with no passion for the subject but they really want good jobs, it's embarrassing desu

Anonymous at Mon, 6 Jan 2025 01:44:29 UTC No. 16536780

>>16536541
it was the same way in CS, 90% of people had no real interest in the subject and just wanted a high paying job

🗑️ Anonymous at Mon, 6 Jan 2025 01:46:55 UTC No. 16536783

Here's a cool way to solve cubics.
[math]\text{For cubic p, let a, b be solutions to the quadratic equation: }3p(x)p''(x)-2p'(x)^2 = 0.\\
\text{The zeros of p are given by: }z=\cfrac{a(-\frac{p(b)}{p(a)})^{1/3}+b }{(-\frac{p(b)}{p(a)})^{1/3}+1}.[/math]

Anonymous at Mon, 6 Jan 2025 02:05:30 UTC No. 16536797

>>16536783
wtf formatting. I'll try again
Here's a cool way to solve cubics.
[math]\text{For cubic p, let a, b be solutions to the quadratic equation: } 3p(x)p''(x)-2p'(x)^{2} = 0.\\
Zeros\ of\ p: z= \cfrac{ a(-\cfrac{ p(b) }{ p(a) })^{1/3}+b }{ (-\cfrac{ p(b) }{ p(a) })^{1/3}+1 }.[/math]

Anonymous at Mon, 6 Jan 2025 13:51:41 UTC No. 16537207

Let [math]G[/math] be a connected Lie group with Lie algebra [math]\mathfrak{g}[/math] and adjoint representation [math]\mathrm{Ad}_G : G \to \mathrm{Aut}(\mathfrak{g})[/math].

I'm desperate for a reference of the following (hopefully true) claim: Assume [math]G[/math] is semisimple and let [math]u \in G[/math]. Then [[math]\mathrm{Ad}_G (u)[/math] is unipotent w.r.t [math]\mathfrak{g}[/math]] if and only if [for some/any representation [math]\rho: G \to \mathrm{GL}(V)[/math] on a finite dimensional real/complex vector space, [math]\rho(u)[/math] is unipotent w.r.t [math]V[/math]].

Clarification: A linear operator [math]T[/math] on a vector space [math]V[/math] is called unipotent if [math]I_V - T[/math] is nilpotent.

Anonymous at Mon, 6 Jan 2025 17:04:21 UTC No. 16537333

Starting a math degree in your late 20s is a gamble. You’ll face a steep learning curve, especially if you're transitioning from a different field, and the workload can be overwhelming. While it may open doors in academia or research, the reality is that most jobs in industry require more applied skills than pure math. At that age, competing with younger students who have been immersed in the subject for years might feel discouraging. The payoff in terms of salary is often low, especially in academia, and breaking into high-paying fields like tech or finance usually requires additional qualifications. Balancing school with other life responsibilities, like work or family, can be draining.
The shift toward programming and data science is tempting for many math majors, as it's seen as a way to make the degree more practical. However, the rise of AI tools is making it harder to stand out in these fields. While you might have a background in math, automation and AI are already taking over many data science and programming tasks, making it harder to compete with younger, more specialized candidates. The market for skilled professionals is shifting fast, and as AI systems evolve, the demand for human programmers or data scientists may shrink, leaving many to question if the time and effort invested in this path will be worth it in the long run.

Anonymous at Mon, 6 Jan 2025 20:26:59 UTC No. 16537501

>>16537333
You literally described how i feel.
A a math major but hadn't been able to find a proper job, all my classmates went to data "science" and are making a lot of money. I think a master degree will solve my problems.

Anonymous at Mon, 6 Jan 2025 20:49:14 UTC No. 16537524

>>16537501
>You
That's a chatbot.

Anonymous at Mon, 6 Jan 2025 21:27:55 UTC No. 16537567

Which of the remaining Millenium Prize problems do you think is most likely to be solved next?

Anonymous at Mon, 6 Jan 2025 21:43:13 UTC No. 16537577

>>16537567
You may as well use a magic 8-ball to answer that one. It's effectively impossible to know.

Anonymous at Mon, 6 Jan 2025 21:48:41 UTC No. 16537582

>>16534312
>what should i know by now for masters?
your plan to afford grad school besides shoveling on more loans

Anonymous at Tue, 7 Jan 2025 02:13:35 UTC No. 16537795

I'm starting to realize that I'm probably too retarded and also not ambitious enough for academia. I'm almost finished with my master's and I'm experiencing some sort of crisis right now.
Is there anything in-between the two extremes of either becoming another npc codemonkey or trying to larp my way through a phd? As in, are there some fulfilling jobs outside of academia that I'd be qualified for?
I'm from Europe btw if that matters (yes this shit is keeping me awake at night)

Anonymous at Tue, 7 Jan 2025 04:40:33 UTC No. 16537898

>>16537795
Crypt keeper

Anonymous at Tue, 7 Jan 2025 09:04:24 UTC No. 16537989

>>16537795
You're right. No other jobs exist out there for someone with a math degree, none at all.

Anonymous at Tue, 7 Jan 2025 09:57:49 UTC No. 16538019

>>16534312
https://users.itk.ppke.hu/~vago/all-the-mathematics-you-missed.pdf

Anonymous at Tue, 7 Jan 2025 10:23:31 UTC No. 16538030

>>16534447
Strang's book is more applied/computational. I recommend the linear algebra problem book by Paul Halmos as a supplement to whatever. It takes you from the level of https://www.3blue1brown.com/topics/linear-algebra to the theoretical side.

Firedberg, Insel, and Spence or the book by Hefferon are some entry-level linear algebra books

Anonymous at Tue, 7 Jan 2025 10:38:17 UTC No. 16538042

>>16534819
Can you do a local master's after work?

Anonymous at Tue, 7 Jan 2025 10:40:33 UTC No. 16538045

>>16535809
https://www.researchgate.net/publication/374879305_DELTD_An_R_Package_for_Kernel_Density_Estimation_using_Lifetime_Distributions

Anonymous at Tue, 7 Jan 2025 15:24:42 UTC No. 16538199

How do you feel about EE students in your classroom?

Anonymous at Tue, 7 Jan 2025 16:13:51 UTC No. 16538252

>>16538199
As someone who has been that EE student in the classroom, we tend to occupy the extremes. Every EE student I've seen in math grad programs tend to either be the most stereotypical braindead engineer who can't into math, or they tend to be way ahead of everyone.

I've done both. I was way ahead of just about everyone in my introductory complex analysis course (just because we get so used to analytic functions of complex variables in undergrad) and then got my shit repeatedly rocked in measure and functional analysis.

Anonymous at Tue, 7 Jan 2025 19:37:38 UTC No. 16538408

Why do "they" keep it suppressed? Why don't "they" want us to know about Geometric Algebra?

Anonymous at Tue, 7 Jan 2025 19:55:24 UTC No. 16538421

>>16538408
A treatment of exterior algebra is found in any good linear algebra textbook.

Anonymous at Tue, 7 Jan 2025 22:14:21 UTC No. 16538557

>>16534183
Any PhD havers have advice for getting through the burnout/slump phase? I'm a fourth year and I would rather do literally anything except work on my problem. I've been distracting myself reading other stuff (I do rep theory/categorification). Wanted to ditch my advisor's seminar today to go to a QFT seminar. I don't have the heart to tell my advisor I didn't do shit over winter break except read about tensor categories.

Anonymous at Tue, 7 Jan 2025 22:41:01 UTC No. 16538583

what am I missing

Anonymous at Tue, 7 Jan 2025 23:27:45 UTC No. 16538636

>>16538583
Which of those have you spent time reading/feel like you have a mastery of? Having a gigantic collection of unread textbooks (which I am also guilty of) is worth far less than a smaller collection of textbooks you actually have a mastery of.

Anonymous at Tue, 7 Jan 2025 23:42:32 UTC No. 16538648

>>16538636
i am a master of nothing, barely qualified to do arithmetic, I just like collecting books

Anonymous at Tue, 7 Jan 2025 23:42:33 UTC No. 16538649

>>16538636
>Having a gigantic collection of unread textbooks (which I am also guilty of)
Why is this so common? Is it just consumerism?

Anonymous at Tue, 7 Jan 2025 23:49:00 UTC No. 16538663

>>16538649
NTA but for me it's a mixture of procrastination, OCD and books that I don't really intend to read and only use as a reference.

Anonymous at Tue, 7 Jan 2025 23:49:23 UTC No. 16538664

>>16538649
for me it's just general curiosity, i've been reading bits and pieces from them and combining it with internet learning, trying to understand the full scope of mathematics before diving too deep into any particular topic

Anonymous at Tue, 7 Jan 2025 23:54:18 UTC No. 16538668

>>16538649
In my case, my PhD has required that I have a really large amount of reference material. What ends up happening is I realize that some area I'm researching has a lot of related requisite material for some part of it, I end up getting textbooks on that requisite material, and I read one or two chapters and that's it.

As an example, I think I have a dozen probability theory/statistics related textbooks, and it's always because of one or two chapters in each that are different enough that it's useful to have both as a reference.

I don't think I own any textbooks I've never opened/used in some capacity, but the majority of them I've needed one or two chapters of their specific reference material and that's it. So I end up having a ton of textbooks in the "I'll get around to reading the whole thing some day" pile, after only using the bit of reference material I needed and moving on.

Anonymous at Tue, 7 Jan 2025 23:56:22 UTC No. 16538669

>>16538648
Ah, then I guess it just depends what you want to look at. Personally, I like probability theory, so I'd say get a book or two on that and related subjects. I quite like Bremaud's Discrete Probability Models book and it also covers some information theory and graphical models as well.

Anonymous at Wed, 8 Jan 2025 05:55:18 UTC No. 16538919

hi guys im horrible at math, i am trying to write a program. so the x input will always be 1, 2, 3, 4 etc increments of 1. the y is random it doesnt matter.
how do i find an equation that matches like this graph so when the input is 1 itll give me the y input. the way i imagine it is multiple linear lines that zig zag like that graph. i dont know how to say what im tryna say.

someone point me into what to look into to get what im trying to do. the equation isnt a linear equation i dont know what equation it is but i think it looks like that graph i dont care about 1.5 2.5 on the x line only increments of 1. maybe it also doesnt have to be straight lines but up and down parabolas.

Anonymous at Wed, 8 Jan 2025 05:58:43 UTC No. 16538922

>>16538919
You're looking for a piecewise linear function, or a linear interpolation. Take a look at a numerical analysis textbook for interpolation and you'll find what you need. Burden is the standard one. Or just read articles and posts about spline-based interpolation online.

Anonymous at Wed, 8 Jan 2025 06:00:54 UTC No. 16538924

>>16538922
thanks for the keyword ill check it out

Anonymous at Wed, 8 Jan 2025 14:44:44 UTC No. 16539128

Any recommendations on books that provide an overview of discrete math? I want something targeted at CS students, even something midwitish like "so well there are graphs and there's Djikstra alg which is just non-heuristic A* alg" will do just fine as long as most things are somewhat covered.

Anonymous at Wed, 8 Jan 2025 15:38:26 UTC No. 16539166

>>16539128
Graphs, Networks and Algorithms by Jungnickel.

Anonymous at Wed, 8 Jan 2025 15:39:33 UTC No. 16539168

>>16539128

Anonymous at Wed, 8 Jan 2025 16:49:41 UTC No. 16539261

Greetings mathematicians!

How can I prove the following statement?

Let \( f: \mathbb{R}^n \to (X, \rho) \) be a function, where \((X, \rho)\) is a metric space. If \( f \) is continuous with respect to one of the metrics \( d_1, d_2, d_\infty \), then it is continuous with respect to all the others.

I just cant figure out how to get one or another metric using the other(s).

Thanks in advance

Anonymous at Wed, 8 Jan 2025 16:52:03 UTC No. 16539266

>>16539261
I will read your question if you properly format it.

Anonymous at Wed, 8 Jan 2025 17:15:19 UTC No. 16539296

>>16539261
Try to show (for example) that [math]d_1 \leq \sqrt n d_2 \leq n d_\infty[/math] pointwise.

Anonymous at Wed, 8 Jan 2025 17:21:53 UTC No. 16539307

aaaand i'm failing for real

Anonymous at Wed, 8 Jan 2025 17:23:11 UTC No. 16539309

>>16539266

Let [math]f: \mathbb{R}^n \to (X, \rho)[/math] be a function, where [math](X, \rho)[/math] is a metric space. If [math]f[/math] is continuous with respect to one of the metrics [math]d_1, d_2, d_\infty[/math], then it is continuous with respect to all the others.

Anonymous at Wed, 8 Jan 2025 17:24:34 UTC No. 16539311

>>16539296
Hmm. How is that definition of continuity pointwise based in that inequality?

Anonymous at Wed, 8 Jan 2025 17:33:52 UTC No. 16539324

>>16538557
Probably your advisor cares less about you and your thesis than you think, and will not really care if you check out for a while and come back. If learning about other fields of math or physics keeps your overall interest level up that is maybe a good thing. But do come back to your main project. If you are really honestly stuck somewhere that is your advisor's responsibility too, and maybe you can work on something else more interesting and fruitful.

Anonymous at Wed, 8 Jan 2025 17:54:45 UTC No. 16539339

>>16539311
https://proofwiki.org/wiki/Lipschitz_Equivalent_Metrics_are_Topologically_Equivalent

Anonymous at Wed, 8 Jan 2025 18:16:40 UTC No. 16539360

>>16539339
>lipshit
I'm not into that.

Anonymous at Wed, 8 Jan 2025 18:22:29 UTC No. 16539364

>>16539339
Thank you

Anonymous at Wed, 8 Jan 2025 20:02:08 UTC No. 16539458

>>16534608
Print it then

Anonymous at Wed, 8 Jan 2025 20:48:56 UTC No. 16539497

>>16534518
[math]Re[\int\limits_{m-1/2+\frac{i}{\sqrt{12}}}^{n+1/2+\frac{i}{\sqrt{12}}}x^3dx][/math]

Anonymous at Thu, 9 Jan 2025 00:59:51 UTC No. 16539726

>>16539339
Now theres something I am confused about. The statement of equivalences of metrics is true if the inequality holds, but the reciprocal is false. So, assuming the inequality I cannot go further on proving why those are equivalents, neither how it can prove the main problem. What can I do there?

Anonymous at Thu, 9 Jan 2025 07:51:37 UTC No. 16540058

IQ
Hardest math you can do in your head

Anonymous at Thu, 9 Jan 2025 11:22:19 UTC No. 16540156

This is Grok:
If a spherical object triples its surface area, we need to understand how this affects its volume (and hence its weight, assuming uniform density).

First, let's define some terms:

Let A0
be the original surface area of the sphere.
Let V0
be the original volume of the sphere.
Let r0
be the original radius of the sphere.


The surface area A
of a sphere is given by:
A=4πr2

The volume V
of a sphere is given by:
V=43πr3

If the surface area triples:
3A0=4πrnew2

Solving for rnew
:
rnew2=3A04π

rnew2=3r02

rnew=r03

Now, let's find the new volume:
Vnew=43π(r03)3

Vnew=43πr03⋅33

Vnew=33V0

Thus, the new volume is 33≈5.196
times the original volume.

Since weight (or mass) is proportional to volume for a uniform density object, the sphere gains approximately:

5.196−1=4.196
times its original weight.

Therefore, if the sphere triples its surface area, it would gain about 4.196 times its original weight.

Anonymous at Thu, 9 Jan 2025 11:27:22 UTC No. 16540164

>>16538649
Yep, literal funko pops collecting. But because they are made out of paper and not plastic it's somehow ok.
>BUT BOOKS ARE USEFULLLLL
No, they are not, a free PDF on your computer is way more practical (hyperlinks embedded in the textbook etc). Watch everyone seethe now.

Anonymous at Thu, 9 Jan 2025 12:12:05 UTC No. 16540192

>>16540164
I have read quite a few math textbooks and all of the textbooks I've read I've read on my computer screen. I have a handful of textbooks on my shelf and I never read them. Sometimes I read the same textbooks I have physically but on my computer because flipping pages is much more difficult than scrolling/pressing page down.
Also another perk with a PC is that you can have two copies of the book opened at the same time which I find extremely useful, because what often happens is that some part references another and you want to quickly switch between them. Physically flipping pages loses context and it's harder to return to where you were before as well as physically taxing. With ebooks I just alt tab.
As for hyperlinks, that's definitely a perk, however most of the time the ebooks I read don' t have any hyperlinks and I just manually scroll to the referenced lemmas/theorems. And to be honest I'm not sure how much having hyperlinks would help, since my scrolls are typically quite fast, just a few seconds (I use sumatraPDF and scroll using the scrollwheel on the scroll bar which makes it scroll very fast).

Anonymous at Thu, 9 Jan 2025 14:56:52 UTC No. 16540302

>>16534183
So, are there any books that reflect Gian Carlo Rota's thoughts? Or should I just pick any book and use attached article as a filter for the content/chapters?

I don't mind reading, but many ODE books are voluminous and if half the stuff is truly obsolete, then I'd rather not waste time and focus on the important stuff.

Anonymous at Thu, 9 Jan 2025 15:52:38 UTC No. 16540339

What is this guy talking about? Someone explain it to me in English.

Anonymous at Thu, 9 Jan 2025 16:15:05 UTC No. 16540362

>>16540164
>>16540192
Maybe I'm just retarded, but I find (especially for self study on something difficult) that if I don't have the book, I won't be as serious in reading it. It's a sort of "accountability" thing where having a PDF of the book is easily "out of sight, out of mind." Instead, having a copy of the book near my desk staring at me makes me far more likely to actually spend my free time going through it.

Anonymous at Thu, 9 Jan 2025 17:16:23 UTC No. 16540452

Just finished reading and doing all the exericses in Atiyah&Macdonald AMA

Anonymous at Thu, 9 Jan 2025 17:24:52 UTC No. 16540458

>>16540452
Is it worth it

Anonymous at Thu, 9 Jan 2025 17:27:13 UTC No. 16540461

>>16540362
Nah, I feel this too, but for me it depends on the content and pacing of the book, I think.
Books with shorter chapters (more dense thus requiring more notes) and longer problem sections are better for me on PC whereas the reverse is better for books.

Anonymous at Thu, 9 Jan 2025 17:31:15 UTC No. 16540466

>>16540458
Too early to tell. However the book itself was very interesting and fun to read. I feel like learned a lot.

Anonymous at Thu, 9 Jan 2025 20:40:47 UTC No. 16540629

Bros, a very retarded and personal question, but let's assume that you are going to do a master's degree in mathematics. Would you rather do a master's degree at a university that is recognized worldwide as the university with the best mathematics department and is in the top 3 of the Shanghai ranking but the master's degree is in an area of mathematics that you don't like or do a master's degree in something that you do like but at a university that is in position 300 in that range.

Anonymous at Thu, 9 Jan 2025 20:47:43 UTC No. 16540633

>>16540629
The latter

🗑️ Anonymous at Thu, 9 Jan 2025 20:53:48 UTC No. 16540640

>>16539726
>>16539309
If I understand correctly your question, what you want to prove is that if the function is continuous with one of the three norms then is continuous with the other two. So, assume is continuous the [ math ] d_1 [ /math ] metric the is continuous with the [ math ] d_2, d_{\infty} [ /math ]. So assume without loss of generality that [ math ] f [ /math ] is continuous with respect to the [ math ] d_1 [ /math ] norm. Then by the inequality you have that there is some constant [ math ] C >0 [ /math ] such that [ math ] d_2(f(x), f(x_0)) \leq Cd_1(f(x), f(x_0)) [ /math ]
And since [ math ] f [ /math ] is continuous then [ math ] d_2(f(x), f(x_0)) \rightarrow 0 [ /math ] as [ math ] x [ /math ] approaches [ math ] x_0 [ /math ]. And similarly with the infinite norm.

Anonymous at Thu, 9 Jan 2025 21:03:29 UTC No. 16540647

>>16539726
>>16539309
If I understand correctly your question, what you want to prove is that if the function is continuous with one of the three norms then is continuous with the other two. So, assume is continuous the [math] d_1 [/math] metric the is continuous with the [math] d_2, d_{\infty} [/math]. So assume without loss of generality that [math] f [/math] is continuous with respect to the [math] d_1 [/math] norm. Then by the inequality you have that there is some constant [math] C >0 [/math] such that [math] d_2(f(x), f(x_0)) \leq Cd_1(f(x), f(x_0)) [/math]
And since [math] f [/math] is continuous then [math] d_1(f(x), f(x_0)) \rightarrow 0 [/math] as [math] x [/math] approaches [math] x_0 [/math], implying that [math] f [/math] is continuous with respect to the [math] d_2 [/math] norm. And similarly with the infinite norm.

Anonymous at Thu, 9 Jan 2025 22:03:57 UTC No. 16540691

>>16540647
>So, assume is continuous the [math]d_1[/math] metric the is continuous with the [math]d_2,d_\infty[/math].
Anon did you have a stroke? Are you ok?