Basic Math Textbook: The Napkin Project • Hacker News Board

Re: Basic Math Textbook: The Napkin Project

#41

Post by zozbot234 » Mon, Oct 06, 2025, 1:46 PM UTC

loose-cannon wrote: post #19

If you just pick one of those subjects, you'll probably find a textbook just as long as his entire PDF trying to cover 13+ subjects. Sorry to be negative Nancy over here, but you're going to need more than 54 pages to cover calculus. There is value in organizing the major theorems in the different disciplines. But, to be honest, this doesn't really serve the beginner.

I don't quite get how it's supposed to introduce calculus/analysis - the introductory chapters just start talking about metric spaces without even bothering to properly introduce the real numbers or their peoperties. I don't think that's quite sensible. For comparison, mathlib4 of course does it right by starting from topological spaces - and it manages to nicely simplify things throughout, by defining a basic "tends to" notion using set-theoretic filters.

Re: Basic Math Textbook: The Napkin Project

#42

Post by qwertytyyuu » Mon, Oct 06, 2025, 1:53 PM UTC

commandersaki wrote: post #17

ptsneves wrote: post #12

Earlier quoted context omitted.

> Centred around AI Where do you see the centered around AI? I have used it a lot and have not touched a single subject around AI. > - Seems geared around edutech (which is what I gather from the site) What is edutech and why is it unsuitable? Finally, have you _used_ MathAcademy at all?

Where do you see the centered around AI? From https://www.mathacademy.com/how-it-works : > Math Academy is an AI-powered, fully-automated online math-learning platform. Math Academy meets each student where they are via an adaptive diagnostic assessment and introduces and reinforces concepts based on each student’s individual strengths and weaknesses. What is edutech and why is it unsuitable? I don't want a computer…

The “ai” is an expert system yes to calibrate to your ability to answer questions it throws at you. The questions are all human written. I had your initial scepticism as well, I can reassure you that the ai is not an LLM. Also the guy Justin skycak who built it has put a lot of thought into its pedagogy

Re: Basic Math Textbook: The Napkin Project

#43

Post by seanhunter » Mon, Oct 06, 2025, 1:58 PM UTC

I would strongly recommend getting, and working through Serge Lang's book "Basic Mathematics" for people who want to self-study what is normally considered "basic maths" (ie the stuff you might have covered in high school plus some of what in the US is called "college algebra" (in the UK and Europe that is just covered in high school and "algebra" at university generally means abstract algebra.

I did it to get my very rusty high-school maths back up to snuff before starting to self-study for a maths degree and it helped a lot. The problems are really excellent and since it's Serge Lang, he treats you like a mathematician right from the beginning even though he really is doing basic stuff.

Re: Basic Math Textbook: The Napkin Project

#44

Post by seanhunter » Mon, Oct 06, 2025, 2:05 PM UTC

stared wrote: post #13

nxobject wrote: post #3

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.

It follows a good tradition of textsbooks in STEM - is it starts with "Introduction to..." it is neither short or simple.

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.

[1] This is a really good book in my opinion btw.

Re: Basic Math Textbook: The Napkin Project

#45

Post by loose-cannon » Mon, Oct 06, 2025, 2:09 PM UTC

morcus wrote: post #35

loose-cannon wrote: post #19

If you just pick one of those subjects, you'll probably find a textbook just as long as his entire PDF trying to cover 13+ subjects. Sorry to be negative Nancy over here, but you're going to need more than 54 pages to cover calculus. There is value in organizing the major theorems in the different disciplines. But, to be honest, this doesn't really serve the beginner.

Two thoughts here: 1. I don't think it is at all intended to serve the beginner. It's geared towards readers wait a reasonable amount of mathematical maturity already (it explicitly says that in the landing page). 2. Many, many of the pages of most introductory calculus textbooks are spent on exercises and on the specifics of computing integrals and derivatives of particular functions - none of this is necessary to u…

So this is aimed at somebody who has mathematical maturity but prefers... less content and detail? The point is that you are losing something in a shortened presentation. You're not just losing "unnecessary exercises" as you put it.

Re: Basic Math Textbook: The Napkin Project

#46

Post by [deleted] » Mon, Oct 06, 2025, 2:22 PM UTC

diegof79 wrote: post #29

I love projects like these. Even when I took algebra and calculus in university, it’s good to refresh and go deeper into the concepts many years later. However, a small critique to the author: the audience of this book is not clear. It says “basic” math, but then in chapter 1, the group's explanation starts with this sentence: “The additive group of integers (Z,+) and the cyclic group Z/Zm.” Maybe it was a draft note…

[deleted]

Re: Basic Math Textbook: The Napkin Project

#47

Post by sota_pop » Mon, Oct 06, 2025, 2:38 PM UTC

nxobject wrote: post #3

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.

“The proof is self-evident, and been left as an exercise for the reader.”

Re: Basic Math Textbook: The Napkin Project

#48

Post by HelloNurse » Mon, Oct 06, 2025, 2:42 PM UTC

diegof79 wrote: post #29

I love projects like these. Even when I took algebra and calculus in university, it’s good to refresh and go deeper into the concepts many years later. However, a small critique to the author: the audience of this book is not clear. It says “basic” math, but then in chapter 1, the group's explanation starts with this sentence: “The additive group of integers (Z,+) and the cyclic group Z/Zm.” Maybe it was a draft note…

That is clearly a "note to self" that remained in the full text. The following paragraph has a regular definition of group.

Re: Basic Math Textbook: The Napkin Project

#49

Post by moi2388 » Mon, Oct 06, 2025, 2:43 PM UTC

What a fantastic read. I’ve never had higher maths. Having read the first few pages, this perfectly fits my level of knowledge. It makes next paragraphs intuitive by using the remarks and asking me to think. I can’t wait to read more!

Re: Basic Math Textbook: The Napkin Project

#50

Post by thibley » Mon, Oct 06, 2025, 2:43 PM UTC

The content is great but static PDFs with minimal hyperlinking is a lost opportunity.

Learning and internalizing higher math is largely about connecting lots of ideas, terms, definitions, named theorems, lemmas, etc. If the book were instead built for the modern web stack with heavy use of tooltips, it would be lots more engaging and fun, supporting a more active learning process.