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Basic Math Textbook: The Napkin Project
- qwertytyyuu 1y agoI 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
- tocs3 1y agoI 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?
- _hao 1y agoSubscription to Math Academy might be more suitable for that.
- commandersaki 1y agoRed flags of Math Academy: - Centred around AI - Seems geared around edutech (which is what I gather from the site) Green flags for Napkin: - Covers advanced undergraduate and graduate topics - Encourages pencil & paper way of learning (took me way too long to learn this is the best appraoch)
- ptsneves 1y ago> 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?
- commandersaki 1y agoWhere do you see the centered around AI? From https://www.mathacademy.com/how-it-works 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 in the loop when I learn math, plain and simple. My preferred style of learning is instructor led with a mix of Socratic method and hand holding. But bar that, reading texts and using a pen and paper. Finally, have you _used_ MathAcademy at all? Nope, doesn't look like my cup of tea.
- delichon 1y agoMy experience with MathAcademy is very positive. So is my experience using ChatGPT 5 as a math teacher in learning mode. I'm as fed up with AI slop as most people, but for me this is a domain where it excels.
- yorwba 1y agoAs far as I can tell, most of its value comes from having a reasonably thorough dependency tree of math topics and corresponding exercises (which can be solved with pen and paper) and describing it as "AI" is how you get investors to fund a math textbook. See also How Math Academy Creates its Knowledge Graph https://www.justinmath.com/how-math-academy-creates-its-knowledge-graph/ https://www.justinmath.com/how-math-academy-creates-its-know... "We do it manually, by hand."
- qwertytyyuu 1y agoThe “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
- barrenko 1y agoWhile 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 https://grizzle.robotics.umich.edu/education/rob201 - "ROB 201 Calculus for the Modern Engineer"
- BeetleB 1y agoTry the Princeton Companion.
- j2kun 1y ago+1 this is a great reference text
- eapriv 1y agoIf 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.
- j2kun 1y agoI wrote one: https://pimbook.org https://pimbook.org
- rramadass 1y agoThere is no one book which can give you the overall sweep of Mathematics. However, you might find the following (though not textbooks per se) useful. 1) The Princeton Companion to Mathematics by Timothy Gowers et al. and The Princeton Companion to Applied Mathematics by Nicholas Higham et al. - The closest you have to a Modern Encyclopedia of Mathematics. You get unmatched breadth after which you can move on to dedicated books as needed. Well worth the money. 2) Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov et al. - Absolutely brilliant overview of Basic Mathematics. Published by Dover and hence very affordable. 3) Elements of Mathematics: From Euclid to Gödel by John Stillwell - Written as sort of an update to the great Felix Klein's Elementary Mathematics from an Advanced Standpoint books. The Topics are particularly well chosen given modern advances; they include Arithmetic, Computation, Algebra, Geometry, Calculus, Combinatorics, Probability, Logic.
- nxobject 1y agoThe 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.
- spankibalt 1y agoFrom 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.
- schoen 1y agoIt 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.
- qsort 1y ago> 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.
- avdelazeri 1y agoThat's common with mathematics books. Weil's Basic Number Theory is enough to give the unsuspecting quite the fright, despite the name
- auggierose 1y ago> The set ℕ is the set of positive integers, not including 0. Hell yeah! I've agonised over this quite a lot over the decades. Not including 0 is more intuitive, but including 0 is more convenient. Of course, both approaches are correct. My main reason for not including 0 is that I hate seeing sequences numbered starting with 0.
- qsort 1y agoI used to write and review problems for math competitions. This is why we avoided saying "natural numbers". We used "nonnegative integers" or "positive integers" instead.
- ColinWright 1y agoYou 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, ... } There is no approach that uses "natural language" and is universal, and being aware of this is both frustrating and useful. Whether it is important is up to the individual.
- thaumasiotes 1y ago> 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 https://fr.wikipedia.org/wiki/Nombre_n%C3%A9gatif ) It'd be hard to be more explicit that zéro is not a negative number.
- ColinWright 1y agoIf 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_arithm.C3.A9tiques_et_alg.C3.A9briques 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. ================ 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). ================ 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/115327589116457527 https://mathstodon.xyz/@antoinechambertloir/1153275891164575...
- qsort 1y agoIt's that Evan Chen. Thanks for teaching me the way of the bary, senpai!
- WillAdams 1y agoPrevious discussion: https://news.ycombinator.com/item?id=20168936 https://news.ycombinator.com/item?id=20168936 Need to see how this looks on my Kindle Scribe --- I suspect that it will push me over to updating to the newly announced colour model when it becomes available.
- cubefox 1y agoHe uses the word "group" 1297 times. This might be a new record.
- loose-cannon 1y agoIf 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.
- morcus 1y agoTwo 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).
- loose-cannon 1y agoSo 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.
- bonoboTP 1y agoFrom 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.
- aap_ 1y agoReally cool! This is the sorta thing that, just yesterday, I wished existed. And it's already on the HN frontpage. It's hard to see the forest for the trees in many math books, a bird's eye view is a really valuable perspective. I highly appreciate this approach: "As i have ranted about before, linear algebra is done wrong by the extensive use of matrices to obscure the structure of a linear map. Similar problems occcur with multivariable calculus, so here I would like to set the record straight" Math education and textbooks are doing an awesome job obscuring simple ideas by focusing on weird details and bad notation. Always good to see people trying to counter this :)
- j2kun 1y agoSheldon Axler's book is the common (now decades old) example of a book doing linear maps first.
- lesser-shadow 1y ago[dead]
- diegof79 1y agoI 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. To be fair the paragraphs that follow attempt a more basic explanation of groups, but even my “Algebra I” book at the university was friendlier than that.
- deleted 1y ago[deleted]
- HelloNurse 1y agoThat is clearly a "note to self" that remained in the full text. The following paragraph has a regular definition of group.
- jackallis 1y agoi will sequeze in real Analysis between complex analysis and measure theory.
- torben-friis 1y agoFor 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.
- rmonvfer 1y agoUNED by any chance? Broken indeed
- torben-friis 1y agoBingo. I’m guessing you went through the same song and dance?
- mna_ 1y agoTry the Open University.
- seanhunter 1y agoI 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.
- dave7 1y agoThank you for the recommendation, that sounds much more like my level at the moment!
- seanhunter 1y agoYou are very welcome. The other resource I found excellent was Khan Academy which is free (donation supported) and has videos and supporting resources covering a very wide range on mathematical topics. I would recommend the “precalculus” playlist which is just a general grab bag of topics covering algebra, basic vectors and matrices and a few other things.
- moi2388 1y agoWhat 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!
- thibley 1y agoThe 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.
- BeetleB 1y agoFor many people, learning a heavy topic like mathematics is a lot easier on paper than on a screen.
- thibley 1y agoDef 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.
- TRiG_Ireland 1y agoPresumably started before Evan Chen's recent discovery of Typst.
- golem14 1y agoIs there a way to get a nicely bound hardcopy ? Doing a single one-off is expensive, I wonder if a hundred people got togehter, would a larger run be more cost effective ? Are there services for those larger runs ? Qwen3 recommends Blurb Lulu BookBaby Mixam For a 1000 page book, it suggest pricing of ≈$120 for single copies, down to $15-25 for a run of 1000.
- golem14 1y agoI can also get a coil binding machine for $50, and can print the book for maybe $15 and spend 1h printing and binding chapters… Maybe cheap child labour is called for…