i will sequeze in real Analysis between complex analysis and measure theory.
Basic Math Textbook: The Napkin Project
31–40 of 76 posts
Re: Basic Math Textbook: The Napkin Project
#32The 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.
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.
Re: Basic Math Textbook: The Napkin Project
#33The 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.
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 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.
Re: Basic Math Textbook: The Napkin Project
#34The 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 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.
Re: Basic Math Textbook: The Napkin Project
#35If 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 understand the concepts themselves.
For example, Baby Rudin (the standard textbook for Analysis for math majors) covers Sequences, Series, Continuity, Differentiation, and the Riemann integral in less than 100 pages (including exercises).
Re: Basic Math Textbook: The Napkin Project
#36Earlier quoted context omitted.
You need to be careful about this ... I believe that in France (for example) zero is regarded as both positive and negative. So in France: Non-negative integers: 1, 2, 3, 4, 5, ... Positive integers: 0, 1, 2, 3, 4, 5, ... Similarly, for some countries "Whole Numbers" is equivalent to all the integers, while in other countries it's the set { 0, 1, 2, 3, 4, ... } while in still other countries it's { 1, 2, 3, 4, ... }…
> I believe that in France (for example) zero is regarded as both positive and negative. That would cause all kinds of problems, so I'd be pretty surprised if it turned out to be true. I note that this is the heading of the relevant wikipedia page: > Un nombre négatif est un nombre réel qui est inférieur à zéro, comme −3 ou −π. ( https://fr.wikipedia.org/wiki/Nombre_n%C3%A9gatif ) It'd be hard to be more explicit tha…
If you're going to quote wikipedia:
> "Zéro est le seul nombre qui est à la fois réel, positif, négatif et imaginaire pur."
From: https://fr.wikipedia.org/wiki/Z%C3%A9ro#Propri.C3.A9t.C3.A9s...
It's hard to be more explicit that it is considered both.
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Added in edit
In speaking with a French colleague, he says that "inférieur" often means "less-than-or-equal-to" rather than "strictly-less-than", so the passage you quote would still imply that 0 is negative (and most likely also positive).
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Second edit:
> In France, "positive" means "supérieur à 0", and "supérieur à " means "greater than or equal to". Similarly, "négative" means "inférieur à 0", that is "less than or equal to 0".
> (We have the similar reaction towards the anglosaxon world and the introduction of nonnegative…)
-- https://mathstodon.xyz/@antoinechambertloir/1153275891164575...
Re: Basic Math Textbook: The Napkin Project
#37For 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 absolute goldmine.
Most basic math books assume no knowledge of the subject but a familiarity with general math that is unreasonable - it’s like saying you don’t need to know what a deadlift is but you need a back that resists 200kg… It’s a borderline fictional audience in practice.
Cummings manages to understand the novice far, far better.
Re: Basic Math Textbook: The Napkin Project
#38I 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?
While there are a lot of of textbooks flown around, I'd like to prop up ROB201 textbook, which I came across recently, also aims to cover a lot of ground and is accompanied by videos.
https://grizzle.robotics.umich.edu/education/rob201 - "ROB 201 Calculus for the Modern Engineer"
Re: Basic Math Textbook: The Napkin Project
#39For 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
Re: Basic Math Textbook: The Napkin Project
#40I feel like “basic” and “light” might be an overstatement (or should I say understatement). Feels like the audience needs at least a 1 year in a maths tangential uni course