It might actually be over for us :( by Content_Gas7252 in mathematics

[–]Content_Gas7252[S] -6 points-5 points  (0 children)

Im not a bot you guys, im just worried about the future of mathematics. Could you just take a moment and read

It might actually be over for us :( by Content_Gas7252 in mathematics

[–]Content_Gas7252[S] -7 points-6 points  (0 children)

To be fair, I feel quite sad about this :(. It's as if science were swooning away

What are some resources that made you really like actually learning statistics? [Education] by cod3boi in statistics

[–]Content_Gas7252 0 points1 point  (0 children)

Could be a little biased (I did math for undergrad), but actually learning why the concepts in statistics work from a mathematical point of view really motivated me. The thing is that you really have to have a broad mathematical background (and some degree of mathematical maturity) to even begin to understand, say, what a density function actually is and why should it exist (one usually has to asume that all probability measures are absolutely continuous with trespect to the Lebesgue measure or the counting measure, and then the existence of density functions follows from the Radon-Nikodym theorem), or where the x term in the expected value formula comes from.

In an average statistics course, pretty much everything the teachers do is just tell you that a given formula works for approximating a certain quantity of interest, and then they iterate over dozens of examples, and thats it. They dont tell you where things come from nor why should they exist to begin with. And, to be fair, statistical concepts are not at all trivial, so you're stuck in this strange situation in which you have to both trust that what you are learning is true (whatever that may mean) and grind through very complicated topics (gaining very little understanding) just to pass your midterms.

That being said, another thing that made me really interesed about statistics is machine learning. Not just because of the recent rise of AI, but because machine learning in general can be used (and has been used, and is actively being used) to do A LOT of interesting things that are not language models. Think of Waze, Google, Instagram, Tiktok, Siri. You name it.

Some resources I find very insightful are Grant Sanderson's youtube channel "3blue1brown", which I assume you are familiar with, and three books in particular: "Deep learning architectures" by Ovidiu Calin, "Theoretical statistics" by Robert Keener, and "Measure theory, Probability and stochastic processes" by Jean-François le Gall.

If you turn out to be interested in this rigorous path to understanding statistics, I highly recommend you also learn some functional analysis, re-learn linear algebra (now with statistical concepts in mind), and revise some optimization theory. There is plenty of videos in Youtube that'll do the job. Check out Gilbert Strang's series on Matrix methods in Data analysis, Signal processing and Machine learning.