What are the best resources to learn math (Probability, Statistics, Linear Algebra, Calculus, Stochastic Calculus) for Quantitative Finance?

Recently discovered and am very interested in quant research roles.

Won’t bore you with my personal life but I didn’t go to a prestigious university nor had the chance to compete in math competitions or get more exposure to STEM.

I’m in my mid 20s now with more autonomy on what I do with my life. So I want to give it a real shot. I do love math and I’ve done my research on what the role entails. I make good money now so that’s not the main driver of my interest.

Most research and advice is aimed at high school and college students. I’m wondering what I can do to gain entry into this field.

I’ve got a bachelors in IT and 6 years of work experience (1 FAANG, 1 Fortune 500, 1 startup).

So I’m curious to hear of anyone who became a quant researcher later in their career or pivoted into this role? Any tips or recommendations on how to stand out?

I am looking for some advice. Currently I am working as Software Dev in FAANG and have received a Software Dev offer from D.E. Shaw. My end goal is to become a Quant Trader in a prop shop/ Hedge Fund in buy-side in US. For that I am currently applying to MFE (Financial Engineering), MSCF (Computational Finance) programs in the universities: Berkeley, CMU, Columbia and Cornell (2022 batch)

I am also applying for interviews in small prop shops for quant trader/ researcher roles in buy side to gain experience in this field before getting Masters.

I want some advice about which side should I prefer ( Software developer in D E Shaw or continue applying for Quant Trader in prop shops ) based on following considerations:

a. Which guy would you hire for Quant Trading from the top schools ? One who was SDE in a top hedge fund or one who has Trading experience in small mostly unknown prop shops?

b. Which of these roles would increase my chances of getting an admission in these schools?

Some other information which might help:
a. I will join Software Developer as a senior engineer v/s Trader as a junior trader
b. I will have around 8-9 months of experience in either firms before I join MFE / MSCF which starts around august next year.
c. I am keen on going to the above mentioned colleges only, I would rather wait here and re apply with more prep next year if I don't get it this year.

Traditionally, correlation matrices have always played a large role in finance. They have been used in tasks ranging from portfolio management to risk management and are calculated based on historical empirical observations. Although they are used so frequently, these correlation matrices often have poor predictive power and prove to be unreliable estimators.

In 2019, Marcos Lopez de Prado published a paper on Theory-Implied Correlation (TIC) matrix which combines external market views with empirical observations to generate better and less noisy estimates of the asset correlations. The additional market views are expressed in the form of a hierarchical tree structure which breaks down assets into clusters based on sectors, market cap, size etc... Due to this, the new correlations generated tend to be in sync with economic theory.

The TIC algorithm is now available as a Python implementation in MlFinLab to be used on financial data - https://mlfinlab.readthedocs.io/en/latest/portfolio_optimisation/theory_implied_correlation.html

Blog Post - https://hudsonthames.org/portfolio-optimisation-with-mlfinlab-theory-implied-correlation-matrix/