A friend with a math msc aluded at this, that it's kind of a math meme to call material "basic" or "introduction to" for rather advanced stuff.

I feel like it's some kind of misguided intellectual humility. Kind of feels vaguely related to how so many Haskell packages are version "0.*".

I think it is a matter of perspective. The book covers stuff you learn in the first two semesters when studying maths. So for someone who studied maths (probably the author) these are the basics.

You were learning spectral theorem applications in the second semester of math?

I learned the spectral theorem with a couple applications in the first semester of my electrical engineering graduate studies. First year graduate material is commonly called basics in my experience. Compared to the state of the art, it is. Compared to what an undergraduate freshman knows, not so much.

Right, it's material I covered in my senior year of undergrad taking hpc grad courses. If it were covered anywhere in the second semester of undergrad I would be shocked.

This is more like the first two years of mathematics course in the French Preparatory Classes for Great engineering schools Program.

This is book 1962 pages long. If this is basic, how long is the advanced book?!

Actually. many "advanced" texts are rather short (perhaps because they are more specialized or they do not need to be verbose or "entertaining" like many elementary texts are).

That reminds me of the seen in the first Antonio Banderas Zorro movie. Anthony Hopkins' character asks the wannabe Zorro how to fence, and wannabe Zorro says you stick the pointy end in the other guy. The "basic" stuff is actually everything you have to master to avoid getting killed in your very first duel.

It reminds me of Introduction to Algorithms, a classic book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest. It is over 1000 pages long. But they call it "Introduction..." :)

To be honest, Cormen et Al. is an actual introductory book. While it is humongous, it covers all of the basic math, logic and algorithms you see in the first 2 or 3 years of an computer science undergraduate course. It is an introduction in the sense that knowing and mastering the tools that the book provides you will set you up for more advanced topics in the many areas of computer science. For instance, a big number of important algorithms in machine learning, computational geometry and other topics use the basic strategies of greedy, divide-and-conquer or dynamic programming algorithms.

> “Math Basics” is quite the misnomer—it gives the impression that one would need to study all of the contents of this book to be an effective practitioner in CS or ML.

To me basics mean that if you study this entire book you won’t be able to understand ML otherwise it would say comprehensive. Furthermore the math presented in this book are all taught in 1st year courses for most CS programs I’ve encountered.

> Keep in mind it can take an hour, and sometimes way more, to really absorb a single page of a math.

Learning is a personal experience and happens at differing rates for different people. While I do agree this book is rather terse and would serve as a good reference any added explanations around the proofs would force a split to multiple publications so I can see why the authors chose to present it in the way they did.

Overall I have found this text easy to digest and well formulated and thank the authors and poster.

Which CS program? I think you’re more than exaggerating. They don’t teach topology, FEM and abstract algebra in “most” CS program. These are just three random examples; most of the book is wayyy more advanced than what I would expect to learn in freshman CS.

This book seems to be designed as a primer for PhD research students - which might include some talented final year undergrads heading in that direction.

If that's your level, it might reasonably be called "basic."

For everyone else - no.

> Furthermore the math presented in this book are all taught in 1st year courses for most CS programs I’ve encountered.

From what I see this book is much more complete than a first year course, or even the whole curriculum of a classical CS education.

I'm quite familiar with math, but I never encountered wavelet theory, Gauss-Seidel method, Rayleigh-Ritz theorem, and many more. My knowledge about other subjects such as Hermitian spaces, quaternions, finite elements is quite superficial.

And I've only listed elements of Part I.

You do need to look further than chapter one before making statements about the content and what grades you'd learn it in.

A lot of this is year 2 (and 3!) even in engineering physics.

Been writing software for over 15 years and its very rarely that I actually need to use any Maths. Occasionally yes, but very rarely.

I have been writing software for over 20 years and I very regularly find that I am presented a challenge to learn new math, but am still rewarded mightily even if I do not engage it.