A complete guide to linear algebra, calculus, and probability theory

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Machine learning is built on three mathematical pillars: linear algebra, calculus, and probability theory. Linear algebra describes models through vectors, matrices, and transformations. Calculus enables model training through differentiation and gradient descent optimization. Probability theory provides the framework for making predictions under uncertainty, including concepts like expected value, entropy, and information theory. The guide covers essential topics from vector spaces and matrix operations to multivariable calculus and Bayes' theorem, providing a structured learning path from beginner to advanced understanding of neural networks.

The Roadmap of Mathematics for Machine Learning

In the future, “school will still exist ‘because you still need childcare’” and that “AI will handle the teaching”. He is not wrong about it. I see this happening.
I wanted to improve my skills in one X domain. So I went on ChatGPT, asked it to be my career coach at first and explained my goals. It told me that I need to improve my skills in certain areas. So it gave me an amazing outline, on how to learn these skills. It agreed to not give me any code straight up and actually refused to give it to me, unless I try it out first.
I can already here the rebuttal, (1) so can an university teacher and (2) this does mean change will happen for young kids.
(1) The university/college teacher. They could. Except that to change the curriculum for something that just came out it would take anywhere between 5 to 20 years. They were still teaching PROLOG in 2010 in Principles of Programming. Some more Clojure or some Scala would have helped me a lot more, but I’d rather not rant. My point is that they take a very long time to rewrite and approve curriculums. An AI can change it right away. It can make mistakes, but in 2-5-10 years, these mistakes will be few and far between.
(2) What about the kids? This is where it’s a gray area, because across the planet the educational systems vary and the way kids are taught really really varies. I will be honest I cannot think of a single that’s a one-size fits all. I just know that at one point in the curriculum you start doing things like Math, Physics and Chemistry. The basics. AI can really help there. Now I’m not expecting AI, yet, to teach you how to write an essay, but give technology time. I have not yet tried it… It would be a good idea. I’ll ask it “I’ve never learned how to write essays. How do you do it? Can you ask me some questions to judge my current knowledge and then can you tell me step-by-step and guide me to write essays, going from beginner simple essays to research papers”. I would be surprised if it fails, but you still need practice and children love to cheat the system. I know because I loved to ignore the teacher. So… teachers are still required, but teachers can use AI to adapt to today and use AI to adapt material to every student so that someone weaker at Math can still get the basics, without boring an insufferable-Hermione-like-math-know-it-all 🙋‍♂️ (me!).
This may have been a long message and again. I cannot cover all the bases, but more or less he is not wrong. I can see AI teaching us directly or using AI to teach us depending on the student and on the class. I do not know what the future will be, but it will include AI. 😉
EDIT: None of the above has been proofread or checked through an AI. The above may have grammatical errors and syntax problems. It was a think-to-keyboard operation in pure keyboard warrior-style. I did not expect it to be this long. If I made any grammar/syntax errors, as a Canadian, I am saying “Sorry!” and I apologize profusely “My bad!”.

This is one of those articles that make it work to have daily.dev. Bookmarking it. This is a goldmine of an article.

In the 2025 there are more resources out there,
But I am still confused 🤔 which one is good for me, and how to learn things clearly