Hello Julians, need an advice on several topics, please.

(1) A starting point from the scratch into AI (ML example: not fit/predict/dashboard, but rather scientifical way) is Calculus, Linear Algebra and Probability Theory. Is this statement correct?

(2) If (1) is true, next question is about proper literature. I assumed (1) was true and already did some investigation and found next books which looked like “the right ones”:
Calculus - Thomas’ Calculus: Early Transcendentals,15/e, 15th edition Joel R. Hass, Christopher E. Heil, Maurice D. Weir, Przemyslaw Bogacki
Linear Algebra - Linear Algebra and its Applications, 6th edition, David C. Lay, Judi J. McDonald, Steven R. Lay
Probability Theory - Introduction-Probability-Data-Science-Stanley/dp/1607857464/](https://www.amazon.com/Introduction-Probability-Data-Science-Stanley/dp/1607857464/)
The question is if scientific community knows ‘better texts’ (in quotes, because of course there is no best book, but, for example, there is a B. Stroustrup for C++ and others, I mean this), especially related to JuliaLang (mine calculus and linalg books have practical parts designed for Maple)?

(3) AIMA. Is presented as a ‘big book about all AI topics’. Question is how can you rank this text in terms of a ‘starting point from scratch’ ?

In your case I would not recommend using separate textbooks for linear algebra, probability, etc.
There are good introductory textbooks that mix all of these topics, such as Mathematics for Machine Learning.

Artificial Intelligence: a Modern Approach is indeed a big book but it is slightly outdated by today’s standards. In particular, it is very poor on the ML side, and covers “classical” planning more in depth.
The best book on modern ML is probably Probabilistic Machine Learning: An Introduction (which also has an amazingly thorough “Foundations” part that could answer your question 2).

I had overlooked the “Julia” part of your question. Unfortunately the ML literature is mostly illustrated with Python these days (sometimes Matlab or R).
The most prominent Julia book I’ve heard of is Statistics with Julia

You may also want to consider MOOCs.
Those of the MIT MicroMaster “Statistics and data science” (free to attend if you don’t need the piece of paper) are excellent and go very deep in math.
But they are not much in programming nor in practical things, for that you may want to couple it with the Julia MOOC “Computational Thinking”.

It also depends on which path towards AI/ML you take. The research path or an engineering or applied research path.

What you mentioned in 1 & 2 are the pre-requisites that you need to be good at to start your AI/ML journey and the books in the marked solution will be of great help to start from scratch.

a) One good way would be to browse through research literature regularly. Usually authors mention the mathematical equations or scientific algorithms used in their research. So you will get an understanding of the fundamentals that way also.

b) Don’t think of AI as a monolith. Choose a problem area you are interested in and find out how AI/ML is used in that area. This will help you practice your techniques and later help you think about applying existing techniques to general problems.

c) This is especially useful for JuliaLang where there are many specific packages for specific AI/ML problem areas.

d) Join the software and specific domain communities to collaborate and exchange views about techniques and new ways of testing your ideas.