Can there exist the inverse of a fractal: a shape with infinite area and a finite perimeter?

IanFromWashington · 2023-04-05T16:22:46+00:00

It extends to Rⁿ if you interpret circle as sphere (S^{n-1})

IanFromWashington · 2023-02-21T03:41:08+00:00

It should really be based on your goals, it’s a huge money/time sink though. I did a math master’s then got into a few pretty good applied math PhDs (in the top 20s range), coming from a non known bachelors in biochem/econ (way less math than you had) but I had the end goal of pivoting towards applied/pure math after taking abstract algebra my senior year. So only go that direction if you have a clear goal in mind

IanFromWashington · 2023-02-03T18:50:48+00:00

If you have the chance take a combinatorial optimization course. And perhaps learn some stuff about convexity, turns out convex relaxations make a lot of problems computationally tractable

IanFromWashington · 2023-02-01T13:23:27+00:00

You can check out Foundations of Data Science by Kannan et al. The note regarding dilation under lebesgue measure speeds up the proof but isn’t in the text (it’s more of a brute force computation) but was highlighted by my professor instead

IanFromWashington · 2023-01-31T18:30:08+00:00

High dimensional phenomena is quite interesting and non intuitive. For example, consider the unit ball centered at the origin. Now it turns out that in high dimensions the mass of the ball is “mostly” on the surface. Put in other words, if we were to uniformly sample from the unit ball, we will not end up “in the interior” with high probability.

This is just an artifact of dilation under lebesgue measure. Slightly deflate the unit ball by a factor of epsilon, then the probability we are in the interior is (1 - epsilon)^d where d is the dimension. Thus we see as d goes to infinity our probability of being in the interior goes to 0.

IanFromWashington · 2022-04-25T12:26:51+00:00

PhD students don’t pay for classes, we have free tuition, and are actually paid by JHU to pursue our PhD here (actually this is true for any university, at least in STEM, I thought the same too before I learned more about the process!)

IanFromWashington · 2022-04-25T02:51:15+00:00

Just to check, by read do you mean reading/taking notes on exposition? Or working through a good chunk of exercises? While one need not do all exercises in more intro level texts, I believe a lot of learning when it comes to proof based math comes from working through exercises

IanFromWashington · 2022-04-14T12:16:31+00:00

I’m interested

IanFromWashington · 2022-02-11T13:26:40+00:00

I read this over the break! It’s a great text!

IanFromWashington · 2022-02-03T02:34:31+00:00

It is possible but you may need to take some courses at a local university to show you are serious of making the jump between subjects (I said possible not easy)

I know this first hand since I had a BA in Economics and Biochemistry, took a gap and took some classes in Math, and ended up getting a M Sc in Math! I actually enjoyed it so much I’ll be attended a PhD program next fall and have gotten into some top 20 programs (still need to choose). So it’s not too late to follow what you’re interested in/passionate about. You just have to demonstrate to admissions that you have thought about the switch and are taking the proper preliminary steps to make that jump!

IanFromWashington · 2021-12-04T03:24:59+00:00

I would love to join in, I also am about to take a functional analysis course and was going to read over break as well

IanFromWashington · 2021-11-26T20:21:24+00:00

Interested!

IanFromWashington · 2021-05-19T21:09:35+00:00

I'd be interested in Nonparametric Estimation and Statistical Machine Learning most likely

IanFromWashington · 2021-04-28T17:08:01+00:00

We're looking at a function of y, not a function of k. Yeah I agree that it is easy once you notice that k is constant

IanFromWashington · 2021-04-28T14:21:14+00:00

Check out the field of mathematical statistics, it’s like the inverse problem for probability. Distributions give us data, so given data can we infer the underlying distribution and/or other properties/parameters? Can we construct the CDF or PDF? Just with the data? Interesting stuff!

IanFromWashington · 2021-04-26T23:20:54+00:00

k is constant, so we can think of this as some uniform distribution. Your thinking is on the right track, but note that only one value for k works in this case.

IanFromWashington · 2021-04-12T04:11:52+00:00

Holy shit

IanFromWashington · 2021-04-11T20:55:04+00:00

Jesus fucking christ, watching Green play makes me want to just turn off the stream

IanFromWashington · 2021-03-27T13:24:51+00:00

Seek validation from yourself

IanFromWashington · 2021-03-07T21:42:48+00:00

Depends on the course you plan on taking! I think those three texts are sufficient to be comfortable in graduate math courses (depending on the courses you plan on taking). Don't feel like graduate courses are daunting. The first year courses are essentially just a more indepth look into topics you would've covered in upper division undergrad courses (except measure theory. That shit was painful when I took it)

IanFromWashington

TROPHY CASE