reference request / study plan - to build a solid foundation in mathematics for research in ML and optimisation
2026-03-28 10:04:02.1774692242
reference request / study plan - to build a solid foundation in mathematics for research in ML and optimisation
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First of all, delete group theory and all successor nodes. You can also probably safely get rid of algebraic and differential topology, unless you are 100% sure that you want to work on manifold learning or topological data analysis, which I wouldn't necessarily recommend if you're just starting out.
But I'm not going to go through it node by node, because the diagram is fundamentally broken for a simple reason: there is no actual machine learning anywhere in it. If you spent 4+ years learning all of that, at what point would you have learned about logistic regression, or principal component analysis, or neural networks? You can understand all of those things with only linear algebra, multivariable calculus, and probability theory. Most of the other topics in the diagram are used at best for niche algorithms which address niche use cases.
Here's an alternative plan: 1. Get a copy of Pattern Recognition and Machine Learning by Bishop (PDF available for free online) and start reading the first 5 chapters. 2. If you get to a point where it's all gibberish, fill in the relevant technical background - probably that will be either probability theory, linear algebra, or multivariable calculus. 3. Try to read Part II of Goodfellow's deep learning book (available free online). 4. Now go find a paper that you want to read and work through it, using Goodfellow as a reference.
Odds are you'll have the technical background to work on a research problem by this point. You could conceivably need some real analysis / measure theory depending on what you want to do, but other than that you should just focus on picking up what you need to solve your problem.