Id go with optimization theory. u dont even need to understand the equations if u know how to fit the parameters. im talking everything from bgfs to variational inference to MCMC. currently i kinda understand those topics but not at a professional level

second would be probablistic graphical networks. bayesian networks, factor graphs, conditional random fields, HMMs, etc

Probability Theory easily

Data structures/algorithms

I know it’s elementary but a mastery of this pretty much ensures any high paying job you want granted you get the interview

is this true? thats the first real course for CS majors, ive taken it at undergrad and graduate level, feels like thats not rly enough to stand out

yea this gets really hairy, i mean u basically need to know about fields like the abstract algebra s*** to fully understand this, it sounds simple but this is a very advanced field. my thing tho is most of that theory u dont rly need to apply statistics, its interesting but very theoretical

The operative word is “mastery” everyone knows it but actually mastering that s*** is a lot harder. That’s how you solve Leetcode problems in a fast amount of time

yea i guess, i mean algorithms is a kinda broad idea, like yea if u could just understand any algorithm that would be very beneficial. but the specific class called data structures and algorithms is not rly advanced like that is all im saying

That would make you a master in A***ysis as well pretty useful

Nah not too much AA here though there are sigma algebras of course

yea i dont rly understand that s*** at all tbh, i just saw the term "field" and i knew i was in too deep

my understanding of advanced algebra/complex numbers and those concepts is pretty weak, im more of a calculus/physics/stats type guy

For money ML

For doing cutting edge research quantum computing

For me personally graph theory

I mean complex numbers are a huge part of physics

At a certain point physics becomes extremely mathematical to the point that many advances in math come from physics. Ed Witten the greatest physicist alive is just as much a mathematician

If you do calculus you can understand fields and other AA concepts, it just requires thinking differently. The definitions are very detailed and intricate but the actual concepts are straightforward

Like a field, all that means is a set where it behaves how you'd want. The real numbers are a field for example

nah i know, they pop up a lot in differential equations, but in my experience knowing what they are is enough you dont have to be a master of group theory or something to understand a model that involves complex numbers. maybe i mispoke because tbh i dont know what i dont know u feel me, im a math minor i just took calculus 1-3 some stat classes an some computer science courses (along with ODEs)

yea every time i try to get into abstract algebra i just forget everything, i dont use a lot of math on a daily basis besides statistics

i feel this, graph theory is part of what im learning right now, TAing a class in probablistic graphical networks

Ah, yeah you're right you don't need anything beyond the complex basics to use models with them

ODEs was a fun class for me but its one if those that really depends how its taught. Can get really deep or be more of a catalog of methods to solve. Each has its place imo

Comp sci major?

Feel free to hit me with any questions on that

Currently distracting myself from work reading about all the ones you posted earlier itt, variational inference in particular looks interesting

Yeah I’m referring to DSA, like the s*** you learn early in college. Like I said, knowing it is one thing, but MASTERING that s***, like graph algorithms and the different kinds of trees and s*** takes you far as far as making money

i think of ODEs and physics in the same way really, my lab does mathematical modeling in the context of physics, its really cool stuff and its actually usually not terribly complex (finding solutions is not easy but most common equations have well known solutions)

to answer ur other posts, im not a comp sci major technically i was a biology major but i do computational biology, primarily image a***ysis, getting into the ML side more and more.

im glad to hear u found one of the topics interesting yea variational inference is a beautiful display of math, a little tricky but not too bad. I find that if im ever confused youtube is a great resource

hmm yea tbh most of my coding jobs havent been algo heavy, usually just doing some sort of mundane task or leveraging some unnecessarily complicated grouping of services like microsoft azure

i dont know much about the job market for CS majors since im technically not a CS major, but i do remember doing a lot of leetcode problems in undergrad

i work at a small place doing uninteresting work but i’ve interviewed at the most prestigious places and honestly it all boils down to a mastery of data structures and algorithms

id love to have a coherent understanding of addition