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Basic Math Textbook: The Napkin Project

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Re: Basic Math Textbook: The Napkin Project

#51

Post by avdelazeri »

bonoboTP wrote: post #33
spankibalt wrote: post #5

Earlier quoted context omitted.

From the books advice corner: "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 m…

True. There's Morita's a mathematical gift for the same audience

Re: Basic Math Textbook: The Napkin Project

#52

Post by BeetleB »

thibley wrote: post #50

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.

For many people, learning a heavy topic like mathematics is a lot easier on paper than on a screen.

Re: Basic Math Textbook: The Napkin Project

#54

Post by bonoboTP »

loose-cannon wrote: post #45
morcus wrote: post #35

Earlier quoted context omitted.

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.

From the book

> Philosophy behind the Napkin approach

> As far as I can tell, higher math for high-school students comes in two flavors:

> • Someone tells you about the hairy ball theorem in the form “you can’t comb the hair on a spherical cat” then doesn’t tell you anything about why it should be true, what it means to actually “comb the hair”, or any of the underlying theory, leaving you with just some vague notion in your head.

> • You take a class and prove every result in full detail, and at some point you stop caring about what the professor is saying.

> Presumably you already know how unsatisfying the first approach is. So the second approach seems to be the default, but I really think there should be some sort of middle ground here. Unlike university, it is not the purpose of this book to train you to solve exercises or write proofs, or prepare you for research in the field. Instead I just want to show you some interesting math. The things that are presented should be memorable and worth caring about. For that reason, proofs that would be included for completeness in any ordinary textbook are often omitted here, unless there is some idea in the proof which I think is worth seeing. In particular, I place a strong emphasis over explaining why a theorem should be true rather than writing down its proof.

Re: Basic Math Textbook: The Napkin Project

#55

Post by eapriv »

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.

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.

Re: Basic Math Textbook: The Napkin Project

#56

Post by dooglius »

eapriv wrote: post #55
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.

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.

"undergrad math" might be a better phrase to use; "basic" and "advanced" mean very different things to people with different backgrounds

Re: Basic Math Textbook: The Napkin Project

#57

Post by eapriv »

tocs3 wrote: post #2

I have been looking for a general all around math text since last century (as an amateur / recreational mathematician). I m starting to look at this. It seems to cover lots of ground. Any observations?

If I were to write such a text, it would have a lot more about building intuition for advanced mathematical concepts. This intuition is extremely valuable, but missing from almost all advanced-level texts. On the other hand, it’s very difficult to put into words, and probably quite personal.

Re: Basic Math Textbook: The Napkin Project

#58

Post by morcus »

loose-cannon wrote: post #45
morcus wrote: post #35

Earlier quoted context omitted.

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.

As I said, intro calculus books will spend a large amount of time teaching you the mechanics of finding closed form solutions for integrals and derivatives of various kinds of functions. Look at https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/pa... for an example. Most of that content is not that important to understand the concepts.

And yes, with more mathematical maturity you definitely don't need as much detail. The proofs get terser as you're expected to be able to fill out the more straightforward details yourself.

Re: Basic Math Textbook: The Napkin Project

#59

Post by torben-friis »

rmonvfer wrote: post #39
torben-friis wrote: post #37

For another approach at teaching math in an accessible (and self-teaching friendly) approach, I can’t recommend Jay Cummings enough. I recently tried to go for a math degree in my free time using my countries’ remote learning option, and even though the attempt didn’t last long because the format is hopelessly broken (Mediterranean bureaucracy), I’m still engaging in self learning through his books and they’re an abs…

UNED by any chance? Broken indeed

Bingo. I’m guessing you went through the same song and dance?

Re: Basic Math Textbook: The Napkin Project

#60

Post by thibley »

BeetleB wrote: post #52
thibley wrote: post #50

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.

For many people, learning a heavy topic like mathematics is a lot easier on paper than on a screen.

Def true. I often mark up math papers and books with DIY-hyperlinks. It's very easy for me to skip over an important, foundational clause just because some term isn't immediately familiar, and if that happens frequently in some reading, then I'm mentally checking out.

For the Napkin book, if the underlying metadata were in the latex source, we could have PDF annotations in a sidebar, e.g., ("def: p.123, key application: p.234, ..."), as well as live tooltips for a modern web experience. That would be totally wonderful for this text and its audience.

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