The author’s doing themselves a disservice by using the word “basic” - it doesn’t describe either the mathematics or the description. Perhaps it refers to its focus on the basics of a field.
"As explained in the preface, the main prerequisite is some amount of mathematical
maturity. This means I expect the reader to know how to read and write a proof, follow logical arguments, and so on."
Yeah, that's way beyond what's called basic math instruction, e. g. in schools. A more specific, as in accurate, subtitle (or description) is in order.
The preface has "I initially wrote this book with talented high-school students in mind, particularly those with math-olympiad type backgrounds."
Apparently the author tried to somewhat expand the audience from that, but to me it seems still mostly appropriate for smart high schoolers who have heard some pieces of lore from friends about these topics, but they can't put that puzzle in order in their minds yet.
It's most definitely not aimed at the average student. You need to be highly curious, motivated and find math fun already.
And I think that's a perfectly fine thing. It's great to have books for that kind of audience.
It would make more sense to include the term "higher math" (from the author's own description) in the page title, like "Basic Higher Math Textbook" or "Introductory Higher Math Textbook".
Higher mathematics isn't necessarily very strictly defined anyway, but I guess most people who've heard the term would apply it to branches of math that are developed using formal definitions and at least moderately rigorous proofs, and that usually aim at a level of generality beyond their originally motivating examples.
> that's way beyond what's called basic math instruction, e. g. in schools
I'm not saying you're wrong, I know for a fact that you aren't: unfortunately most high-school students fall extremely short of that bar, but it's not necessarily that way. Many teenagers can and do develop that kind of mathematical maturity.
In this context "basic" means "it doesn't require knowledge in the field", and by and large this book can indeed be followed with no other requirement than the mathematical maturity it talks about. Many classic books self-describe in similar way.
This is such a common misunderstanding it's worth explaining.
If you get a book in stem called "an introduction to x" it isn't claiming to be short or simple at all. What "introduction" means is that it is intended for a first course in that topic (ie it does not have prerequisites within that topic).
So if I get "an introduction to mechanics" by Kleppner and Kolenkow[1] for example (to pick one off my bookshelf), it is a challenging first course in classical mechanics but it doesn't require you to know any mechanics before reading it.
I think it's not just some kind of humblebrag. I know this trope that college students feel like it says it's intro but it's hard so it's not an intro. But you only think this when you don't know the topic well. The "thing itself" is in the journals, at the conferences, and in the professional work of researchers, and (if applicable) the real-world applications of the content in various contexts. Any normal-sized book can really only be an introduction to all that for most topics taught in undergrad or master's level.
The actual website never says "Basic Math Textbook", only the submitter typed that in the title here on HN, I guess because "An Infinitely Large Napkin" or "The Napkin Project" would sound ambiguous without a topic context.
I submitted it, and the word “basic” is mine, because the author doesn’t really go deep into what I would consider “advanced” mathematics. It can be a good prerequisite for advanced things, though.
As elsewhere in the thread, I'd advocate for "basic higher mathematics" or "introductory higher mathematics" (which would make clear that it's for people actively studying math as a subject and not as a standard part of primary or secondary education, or a prerequisite in an engineering major or something).
The author says that this is largely aimed at high school students who are doing self-study, which is a realistic audience but not a context where a lot of people would naturally apply the word "basic". But this material is basic for mathematicians, I guess (although even a lot of mathematicians may not have quite as broad a knowledge of mathematics as the author does!).
