Maths foundations for statistics and machine learning

While (and after) being a COVID hermit, I took/re-took a journey from basic maths to try to use the momentum to get better at "formal" (i.e., real) mathematics for statistics and machine learning. It was a winding path but these were the most useful resources, in order (the first 6 steps anyway) - prerequisites are very much non-skippable. For an interested psychology student missing a solid maths background, I think even the first 3 will make a big difference in understanding stats.
  1. Back-to-basics to make sure you're not missing anything that'll trip you up later: The first four parts of the MathTrackX series on edX: Polynomials, Functions and Graphs; Special Functions; Differential Calculus; Integral Calculus. You can also finish the series with the last two courses, Probability and Statistics, but I'd still continue on as suggested below after those.
  2. I didn't cover this again in my last run, but it's needed in the list at this point: A good introduction to basic linear algebra. (Currently liking the look of Savov's No Bullshit Guide to Linear Algebra, chapters 2 through 4, for this.)
  3. Introduction to Probability (STAT110x) on edX: Really well designed and accessible online introduction to foundational probability maths.
  4. Introduction to Probability by Hwang & Blitzstein. This is the book the online course is based on, but the next step after completing the course is to really work through the book - including the (standard) exercises - you can trust the authors that they're doable. It's a time investment but I found it very worth it. Subsequent topics in this list will assume a good grasp of probability concepts covered here (although which specifc ones will vary per topic).
  5. A bit more linear algebra as a basis for things like Principal Component Analysis. (The content of chapters 5 through 6.6 of Savov's No Bullshit Guide to Linear Algebra.)
  6. Regression by Bingham & Fry, fully covers linear regression including the contents of the usual mathematical black box where Psychology statistics teaching ends.
  7. Principal Component Analysis: e.g., chapter 15 in Shalizi's Advanced Data Analysis from an Elementary Point of View.
  8. The Elements of Statistical Learning by Hastie, Tibshirani and Friedman. This isn't particularly accessibly written (although that's all relative! but let's say it won't handhold and will assume foreknowledge or willingness to look up further information) but it's the Bible of machine learning - I recognized a lot of the book in other texts on machine learning after reading it. I just read this through for the concepts and used relevant parts for reference when working in detail on something.
  9. Sutton & Barto's Reinforcement Learning. The Bible of reinformcement learning, working up to, e.g., actor-critic models.
  10. Probability and Measure by Billingsley. Another one I just read versus doing exercises, but even that's worth it to see what the fuss is about and to not be intimidated by talk about sigma algebras.