OneRaynyDay

anyways, thanks for the context, I really appreciate it :) see you guys around

oh then you'd do great in manhattan!

it's like listening to 3 songs in your spotify playlist on repeat for the rest of your life

I want to dig a little deeper to understand why things really work and not just "we see this pattern", "oh ya just assume brownian motion and use ito's lemma", or "shrink that estimator"

Everything at work, works great due to the simplicity of the ideas and the execution. I'm a little bored of all the approximations we have to do to do things practically

(as much)

Nothing wrong, I just don't care about money

i.e. I don't really care if the professors pay me while I stay there

I've saved up quite a bit slaving for quant finance, so I was hoping I could alleviate some of that funding pressure with that

I see. I'm not even sure which grad programs I would be interested in. I'm not opposed to going back to UCLA since some of the professors still remember me from back then

Ah ok understood.

Are you expected to have been presented with Every Big Idea TM at the end of the first two/three years

When you say it's impossible, is it under some certain time frame?

I'm only curious about pure math as a means of peeling back the onion on the applied layers. If the grad text authors approach it by separating the two (fear of presenting it as a machine for one applied context) it sounds demotivating

hmm I see

Why is this the case? Why can't authors just add a bit of personality into their texts to make things more entertaining for the reader? Maximizing utility can't be the only objective here

oh no :(

currently reading another cambridge press book by David Williams (probability theory & martingales) and really liking the presentation style and humor

In real analysis honors I also read Metric Spaces, Cambridge University Press, by E. T. Copson which I found to be much more enjoyable

compared to typical grad school texts it's not dry?

It was a bit dry but it got the job done

Yeah Rudin was a required text

Great! Thanks for the recommendation :) I'm really excited to read it when I have the chance

Nice, I just ordered it on amazon. When it comes to "interesting", what do you mean? The author has a sense of humor? Their approach is aggressive in how general it attempts to be at the start? Writing style(terseness, etc) or a mix of all of the above?

I understand. What do you recommend as a starter text that's heavy on proof exercises?

yes, the honors series is always focused on proofs: math.ucla.edu/~totaro/115ah.1.15f (I didn't take specifically this professor's course, but the syllabus should be uniform)

I've been overextending a bit in the analysis side, currently learning measure theory (as a means to an end to understand stochastic calculus to e.g. price options at work). Do you have suggestions on what's the most effective way to get started on algebra?

I've gotten some basic topology & analysis from my undergrad experience, but not so much algebra

Unsure what defines as "pure", but I went to UCLA, took terrence tao's (or rather, his postdoc's) real analysis honors course, his graduate complex analysis, honors linear algebra, probability theory & stochastic processes (but not from a measure theoretic perspective, so I wonder if this can be considered pure), computability theory

Unfortunately, I have a cs degree and I'm not sure which professor would take someone who came from industry with no graduate math course experience besides complex analysis. I've thought about doing a masters but haven't found any programs for "non-applied math", i.e. I don't want to take applied math courses as a means to an end to find a career, but rather just to understand things from a more general perspective

Hey, I've been lurking around a while but was curious about something: ever since undergrad I've been interested in going to grad school for math that's more on the abstract side. I've been in the industry for more than 3 years now and I'm wondering what I should do if I want to plan to go back to grad school in the next few years :) does anyone have advice?

Hi yall! It's been a while. I was snooping around in the cPython implementation and found that they use a particular sequence to generate all $2^n$ elements. Could anyone take a look real quick at this puzzle? I have no idea how to approach it :P math.stackexchange.com/questions/3771774/…

In this case if $K_n$s were open we would need to first take their closures, so finding closed balls were just 1 step-expedited

Ah, for anyone also wondering - it's because for a set $A$ to be nowhere dense, $(\overline{A})^o = \emptyset$

Yeah... not really seeing where the closedness is important here

Then simply take some $x \in (l^q \cap (l^p)^c)$, then $||x||_q = C$, then divide the sequence elementwise by some large enough constant and you get it's within $n$ radius of the origin

To show $K_n$ is nowhere dense in $l^q$, we just need to show that there exists some sequence $x \in l^q$ such that $||x||_q < n$ and $||x||_p = \infty$ right?

So what if it's open? $l^p = \cup_{n \in \mathbb{N}} K_n$ where $K_n$ is the open ball centered around zero with radius $n$

I'm a bit confused on why we need to show that the individual $A_n$'s used in the construction needs to be closed?

Hi guys, following the proof on why $l^p$ is first category in $l^q$ if $p < q$: math.stackexchange.com/questions/1097869/…

I guess that banks on the fact that $\overline{C_a}$ is also connected, but I think intuitively that makes sense

Hi guys, if given $(X,d)$ MS, $a \sim b$ means $\exists A \in X$ such that $A$ connected and $\{a,b\} \in A$, how can we prove that the equivalence classes $C_a = \{b \in X : b \sim a\}$ is closed?

Anyone fancy to take a look?

Hi, getting ghosted on current problem on MSE: math.stackexchange.com/questions/3036268/…

the proof I gave above is meant for the general proof to any real number (just replace zero w/ any real number)

I'm not sure you know what your question is @mathsresearcher

$x$

\$ x \$

literally put dollar signs around your expression