
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability, and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models, and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
One approach I've found effective: start with a conjecture, visualize it with matplotlib, then prove it formally. The instant feedback loop helps develop both computational thinking and mathematical rigor. Tools like Jupyter notebooks make this workflow seamless.
For anyone interested in similar resources, "Mathematics for Machine Learning" by Deisenroth et al. and 3Blue1Brown's linear algebra series complement this beautifully by bridging theory and computation.
I used those along with a few exercise books and a Casio FX-82ES Plus 2nd Ed.
My advice: keep practising maths every day, or you’ll just forget it again.
You can also copy and paste complex maths problems or papers directly into an LLM - it does a decent job of explaining them. If you get stuck, try the "Explain it like I’m n" trick, decrementing n until it makes sense.
Because I am still in the academic process, I had the opportunity to take a couple of classes on the subject. Three books that I would recommend going over to make sure your foundation in ML and mathematics are solid are
-Pattern recognition and machine learning by Christopher Bishop
-Mathematics for Machine Learning by Peter Deisenroth
-Deep Learning by Courville, Bengio and Goodfellow
All three are legally available online in some form. I can't say I have any experience in finding a job related to ML though.
The Linear Algebra chapter links to 'longer' courses the chapter is based on:
>Pavel Grinfeld’s series on linear algebra: http://tinyurl. com/nahclwm
>Gilbert Strang’s course on linear algebra: http://tinyurl. com/29p5q8j
>3Blue1Brownseries on linear algebra: https://tinyurl. com/h5g4kps