Online Mathematics Textbooks
June 18, 2017 10:09 AM   Subscribe

"The writing of textbooks and making them freely available on the web is an idea whose time has arrived. Most college mathematics textbooks attempt to be all things to all people and, as a result, are much too big and expensive. This perhaps made some sense when these books were rather expensive to produce and distribute--but this time has passed."
posted by jenkinsEar (32 comments total) 77 users marked this as a favorite
 
woohoo! I was expecting to need to write in to ask for inclusion of the book I co-authored, but it's already there (in position 73). (Therefore: Great list! Though a bit more organization might be nice.)

We wrote the first draft of our intro linear algebra book while teaching it, with the intention of making something that actually fit our course plan, instead of using another expensive, kitchen-sink textbook. We then went through and cleaned things up during a subsequent term, and then I left and another co-author joined and reworked a big portion of it. Another big goal was including 'hybrid' content in a really meaningful way - like online homework sets for 'drill' problems that 'everyone should have to do but no one should have to grade,' as well as written problem sets to build skills reasoning and writing about the concepts.

It was a pretty big time investment, but I don't feel like I lost any research time while doing it, which is usually the criticism of textbook writing for young people. In fact, I think we need more young mathematicians writing publicly accessible material (textbooks or otherwise). We need textbooks with a mix of creativity, care for the subject, and attention to the UX of the students (both in the class and afterwards); I tend to think that it's hard to have all of these things after 30+ years of teaching from shite textbooks... 'Visual Group Theory' is a fantastic example of a book which approaches a subject in a completely fresh and accessible way; the sort of thing that we should be aspiring to write.

(An example of UX research: One of the better things I did while we were writing the linear algebra book was go and ask a bunch of grad students from other departments what parts of linear algebra they actually used and/or wish they had gotten from their undergrad courses; we ended up putting a lot more focus on linear regression as a result.)
posted by kaibutsu at 10:31 AM on June 18 [26 favorites]


The American Institute of Mathematics also has an open textbook initiative.

I used one of the recommended ones the last time I taught our proofs course. But I ended up not liking the book much. It didn't really have enough, or enough of the right type, of exercises. The fact I had access to the LaTeX source was nice, though.

But I was just talking to a friend last night about the problem of really expensive math textbooks. My favorite linear algebra text (Lay) is almost $200, and my favorite proofs text (Ensley and Crawley) is maybe $240, which was just too much.

If you can find a book with Dover, that's awesome, though, and I'm really excited by some of the MAA's new textbooks. I'm going to use one next fall for Combinatorics, and probably one in the spring for geometry as well (but I haven't decided. Any recommendations?). The Dover books are quite cheap, and the MAA books run about $50.
posted by leahwrenn at 10:34 AM on June 18 [2 favorites]


It didn't really have enough, or enough of the right type, of exercises

...and so you typeset several of your own exercises of the right type and released them into the wild published them on your web page. Right?

Right?
posted by erniepan at 10:48 AM on June 18 [3 favorites]


Isn't part of the attraction of the big expensive books the exercises and teacher's answer books and other goodies that publishers provide to make the lives of authors and lecturers and examiners easier? Does the free ecosystem have a way to consistently provide those things?
posted by clawsoon at 10:50 AM on June 18


The AMS Open Math Notes seem relevant.
posted by busted_crayons at 10:53 AM on June 18


"Buy this $250 mandatory textbook of close to zero long-term value, different from last year's only by virtue of the numbered exercises and I'm-sure-only-coincidentally written by the prof of the course."

Textbooks, like most academic publishing, has been a thinly veiled extortion scheme for a long time. I'll be happy to see the back of that, and society will be better off for it.
posted by mhoye at 11:54 AM on June 18 [9 favorites]


Isn't part of the attraction of the big expensive books the exercises and teacher's answer books and other goodies that publishers provide to make the lives of authors and lecturers and examiners easier?

Coming up with exercises that are any good is really quite difficult, but I think the other "goodies" don't really exist. Okay, Stewart's calculus has a solutions manual which is handy for the occasional atrociously unclear problem but that's about it. Most of the books on the list are for courses for which there are no ancillary materials provided by publishers.

Stanley's EC1 is missing. (Or maybe the fact the PDF may have errors that don't appear in the printed version eliminates it?)
posted by hoyland at 12:01 PM on June 18 [2 favorites]


I use my Stewart's calculus textbooks as a computer stand. I think that it's literally the most expensive piece of furniture that I own.
posted by Kutsuwamushi at 12:44 PM on June 18 [7 favorites]


Textbook 65 is a great introduction to differential equations for engineers, our primary (maybe only) audience at the college I teach at. This summer is the third semester I have used it as a text. There are one or two sections I have to supplement, but in general, the explanations and exercises are excellent. And, the author has a good sense of humor.
posted by wittgenstein at 12:57 PM on June 18 [1 favorite]


Thanks for the link. My Dad is a college professor who feels textbooks are a racket also. He's in humanities, but finding things like this are always good fodder for making the point of using free and open sourced online resources.
posted by Samizdata at 1:26 PM on June 18 [1 favorite]


I've been reading up on mathematics pedagogy papers and this one math professor has a post on how college calculus is evil and taught completely inappropriately (that students end up mislearning mathematics in the process, mispreparing them for more advanced work in math), and although doesn't specifically point a finger at Stewart, corroborates other professors' criticism of Stewart that I've heard in the past.
posted by polymodus at 1:50 PM on June 18 [1 favorite]


Textbooks, like most academic publishing, has been a thinly veiled extortion scheme for a long time. I'll be happy to see the back of that, and society will be better off for it.

Then we just need to pair that with a US Open/Free University.
posted by leotrotsky at 1:58 PM on June 18


There are some math textbooks available at the Rice University-based openstax.org. (Samizdata, for your father -- there's a single U.S. history textbook listed under "Humanities" at the link.)
posted by Iris Gambol at 1:59 PM on June 18 [1 favorite]


openstax.org.!?!?!?

I am excite!

Oh.

I am disappoint.
posted by stet at 2:32 PM on June 18 [3 favorites]


I understand why I would want an online book. It's free.
What's the incentive to write one?
Not that I disagree with the 'extortion' idea...
posted by MtDewd at 5:56 PM on June 18


I had a prof that wrote his own textbook and sold it for $25 and gave any proceeds to the university scholarship. For him, it was a threefold benefit- the book covered exactly what he wanted to cover, his students didn't have to pay a high price (he encouraged buying used copies), and he gave back to the school.
posted by Monday at 6:44 PM on June 18 [6 favorites]


Looks like a great list, fantastic project that should grow and grow. The only small caveat is the media, as someone who's tried to read some texts on kindle/small tablet/phone (yea nuh) and various laptops, the typography of equations and graphs can be magnitudes better on a well printed book. Needing to double check a complex exponent can take a really hard problem into impossible territory.
posted by sammyo at 6:46 PM on June 18


What's the incentive to write one?
That's the central problem here. I'm sure there are lots of professors who see the need and would like to do the work, they just don't want to do it completely for free on top of all their other responsibilities. And the universities don't want to pay them to do it, since by definition it benefits everyone else in the anglosphere just as much as their own students, so it gives them no edge in terms
of recruitment. Are accreditation bodies in a position to bully universities into setting aside a certain small percentage of their budget for open-source textbooks? Or if not who is?

It seems possible that some major University by itself, or a group of universities, could just set out and start doing it and ignore that they're taking on all the cost and only a fraction of the reward, but I guess something has to spur them to do it.
posted by bracems at 7:01 PM on June 18 [1 favorite]


What's the incentive to write one?

I know it's kind of shocking, but a lot of people in academia really do care about people learning stuff. That's a little bit snarky, but honestly not that much so--it really isn't the usual way of things, I realize that. I have a good friend who's this kind of person. He just wants to teach math. He likes teaching math. He wants to be able to teach math as effectively as possible. As long as his university continues to pay him enough to make ends meet, that's all he requires as far as monetary reward; the rest of what he wants to get out of life is a lot more abstract than that.

Not everybody in the field cares that much about teaching versus other aspects of their academic work, and nobody should be faulted for that, but some people really do just do this kind of thing just for its own sake, as long as they're given enough freedom to do so.
posted by Sequence at 7:05 PM on June 18 [10 favorites]


Textbooks, like most academic publishing, has been a thinly veiled extortion scheme for a long time. I'll be happy to see the back of that, and society will be better off for it.

I used to think that. But I've tried not assigning textbooks a few times now, and my students rebel. I use readings and exercises from a variety of different sources that I make available online on the class website (they have to click a link that goes through to the library's online version of the reading). This semester after a class where not a single one of the students had done the week's reading or the exercises, I did a sort of focus-group, plus a survey of the whole class, and found that they desperately want a paper-based actual textbook by a single author. They hate the contrasting viewpoints they get in the multiple-author sourced readings (although, tbh that was kind of the point), and they hate having to print things out or read them electronically, and they hate that terminology might be subtly different among the different readings and exercises.

I think we are going back to textbooks next semester.
posted by lollusc at 7:05 PM on June 18 [7 favorites]


They hate the contrasting viewpoints they get in the multiple-author sourced readings

On the one hand I can sympathize with your students here because as an undergrad it's hard to tell what's worthwhile and what isn't so there has to be at least a small degree of "indoctrination" (in the most benign sense of the term) for guidance sake before you get into the actual education.

On the other hand your students need to step up their fucking game because wrestling with different worldviews and theoretical models is kinda the whole point of college and if you're not willing to do that work you're limiting yourself to passively, uncritically, receiving information for the sake of information rather than actually learning how to think.
posted by bracems at 7:29 PM on June 18 [2 favorites]


As a current math undergrad, the textbook situation is pretty good in my department. Every math textbook I've bought has been 55$ or less, and most significantly less than that. It seems like every conceivable math subject you would want to learn as an undergrad has a good, cheap, textbook available. [1] You just need professors who a) care enough to find them; b) have enough time to choose exercises and grade them, rather than have some fancy digital assistant do it for them.

That said, I've been shocked at how awful the situation is at some other universities' math departments. I'm not convinced that the problem is the textbooks out there: it's the departments that absolutely do not care about finding these textbooks and supporting their profs enough to let them be used.

[1]: Possibly not for differential geometry. But is there a good undergrad book on differential geometry at any price?
posted by sidek at 7:33 PM on June 18


On the one hand I can sympathize with your students here because as an undergrad it's hard to tell what's worthwhile and what isn't

Yeah, which is why we have this weird thing called lectures and tutorials where they come to class and get some guidance on how to interpret the stuff we assigned them to read. Except that half of them don't come to class, and the other half don't read. So ¯\_(ツ)_/¯

(Can you tell it's the end of the semester and I'm feeling a little burnt out?)
posted by lollusc at 7:36 PM on June 18 [7 favorites]


Have you tried making half the grade quizzes on the reading and failing everybody? (/s but not really.)
posted by bracems at 8:00 PM on June 18 [1 favorite]


I understand why I would want an online book. It's free.
What's the incentive to write one?


People write novels all the freaking time, and the financial return on that is not measurably different from zero.
posted by escabeche at 8:10 PM on June 18 [1 favorite]


In other words: you have a vision! You want to share it with people!
posted by escabeche at 8:10 PM on June 18 [1 favorite]


I would like to invite everyone to contribute to Wikibooks.
posted by koavf at 8:45 PM on June 18


This is a fantastic resource, but I find the idea of (for example) a $250 dollar undergraduate discrete mathematic textbook baffling. In the UK (or at least at Cambridge, where I studied) lecturers prepare their own notes, which are either transmitted the old-fashioned way (blackboard) or via printed (LaTeX'ed) notes. I can't remember a single class where I was told, or even recommended, to buy a textbook. Of course, the quality and scope of the notes varied, but the had the virtue of being free...

There's a big archive of notes for cambridge undergraduate and graduate classes here
posted by Omission at 9:39 PM on June 18 [6 favorites]


I think it's true that the Cambridge way is super super unusual, though I need to check with maths folk from other places.
posted by lokta at 2:50 AM on June 19


This is definitely a good start, in that the first books that come to mind are listed here. But I would like to see a more complete version of this - there are way more math books available online than are on this list!

(Am I going to have to do this myself? But who will pay me? Maybe I'll write a novel instead, there's money in that.)
posted by madcaptenor at 9:07 AM on June 19 [1 favorite]


The only small caveat is the media, as someone who's tried to read some texts on kindle/small tablet/phone (yea nuh) and various laptops, the typography of equations and graphs can be magnitudes better on a well printed book.

In the Open Textbook Initiative link leahwrenn posted, you can read about MathbookXML (soon to be renamed PreTeXt), an XML application for authoring articles and books, written by the author of textbook #36 from the OP. With it, you can output to pdf or html, and "texts" there seem to render very nicely on mobile. See the project's main page for some examples. Or visit it on Github.
posted by klausman at 10:05 AM on June 19


I would like to invite everyone to contribute to Wikibooks.

I have a 500 page computer science textbook that I will be happy to contribute. Where is the "Import from LaTeX" button?
posted by victotronics at 10:28 AM on June 19 [1 favorite]


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