As a person who has to use a Screen Reader, math in PDFs is almost impossible to read for me. The problem is almost insurmountable if the PDF is a collection of images, but even if it is a LaTeX-generated PDF, reading anything but the simplest of equations is very, very hard. In these cases, having the LaTeX source to read is a godsend.
To the authors who publish the source of their books: thank you, thank you. I cannot express how grateful I am. To anyone who is related to /working in the publisher space: it would be incredibly useful if there was a process to get the LaTeX source of books upon request, although I understand how copyrights/etc might make this difficult.
Some other books I would like to point out for being open source: Apex Calculus, Open Data Structures.
You are very welcome. Glad to help. :-)
(I'll just say that the TeX Users Group is very interested in improving the PDFs that LaTeX outputs in this regard, and has projects in this direction. They are at https://www.tug.org.)
Even more damningly, I actually have no idea what it is the accessibility users do, because I’m sure I wouldn’t understand half of the maths notation I’ve read or typeset if someone just spelt it out for me. I simply can’t manipulate things that long without writing them out, and when comparing two equations nothing beats placing them one above the other. Surely computers must be capable of something more helpful than forcing everything into one-dimensional form?
(I should say that my personal involvment goes no further attending presentations at the annual conference.)
Can you elaborate on what / where those projects are? It's not clear from the tug.org website.
I love LaTeX and if I had a relevant skill set I'd be willing to help out.
Thank you.
They get digital versions of books from the publishers and make them accessible to people with print disabilities. This means adding image descriptions and offering various text alterations (different text sizes, special fonts and colors, etc.) to make them easier to read. They also offer math-based tools to make equations accessible.
Bookshare is 100% free to any US-based student who qualifies, and various other countries have agreements with Bookshare as well. They are part of the tech-for-good nonprofit Benetech and are based out of Palo Alto.
I consulted with the student and saw how the reader worked. All was fine, but it was slow because it said e.g. "backslash begin open brace equation close brace", so I made a perlscript to remove backslash and braces (and a few other things) and then it all worked really well.
People, especially those who don't use mathematics much, think latex is hard for humans. I think exactly the reverse is true.
I also laugh when teachers say they expend all this effort making "lesson plans". There are 3.7 million teachers just in the U.S. You'd think they could share them?
I would LOVE to use free textbooks and older books. I try to do so as much as possible. But the real problem (for me at least), is how can I get a copy for all of my students? I can't afford to print them all a copy of old stuff, and after about 5-10 years, the publishers stop printing the older books!
I came across this problem big time this school year -- planned on using a book I love and have been using for 10 years old to be told last minute it's now OUT OF PRINT. (It was in print just 6 months ago). sigh
Old is OK in many places, but only if you can get 50-100 copies of it each semester / year...
I'm not a teacher, but I think often when they talk about old textbooks, the issue is that they are physically falling apart, not just that they were published a long time ago. These books are in continuous use by children, so you can't compare it to a book you've had on your shelf for 40 years. As for lesson plans, most teachers don't have the luxury to just pick a plan they think is best. Every state, district, individual school might have its own rules about what can and must be taught, and teachers often aren't given much say in that.
But for the first point, as poor as research in education is, there have been improvements in educational methods. I read some examples about the Common Core mathematics pedagogy, prepared to be as angry as Feynman, but they were actually teaching kids how to do arithmetic the way I do (which is way better than New Math or brute force methods): 99x5 is 500-5 not 5+(4+5)*10+400. Are their changes more likely to be improvements rather than demerits? I do not know.
Old textbooks used to use white names. Now, many schools are required to throw out prospective textbooks that don’t have names representing multiple minorities.
In the US students are treated as a captive audience and publishers work hard to get professors and education authorities to specify particular books, which are then sold at a very high mark-up. The incentives ought to be purely academic but in practice are often material or financial.
Generally, writing textbooks is just hard and nobody really knows how to do it. Textbooks as they are usually understood[2] are, above all, books[3], that is, large flowing pieces of prose that tell a story about an area of knowledge in a generally linear manner.
This is not how knowledge works. At least the way I feel my knowledge is organized when I try to explain things is that I have a sprawling weighted (on a scale from “vague association” to “hard prerequisite”) graph with rather compact ideas as vertices of absolutely enormous degree (at least in regions I feel I have a decent understanding of). Only by several iterations of merciless pruning around the desired generating set can I get a subgraph that is concise enough that I have some hope of explaining it in the available time, parsimonious enough that I can toposort it onto the time axis without people’s heads spinning and stacks overflowing, and comprehensive enough that I don’t feel I’ve given people a horribly skewed impression and don’t risk choosing a perspective so narrow that would fail to engage some of them. Then comes the actual work of (choosing a) linearization, which I can kind of do in my head for stories of no more than a couple hours at the cost of something like 15 minutes of confusion-inducing backtracking per hour, but it gets exponentially harder as you go past these limits, and you have to go pretty far past them to reach good writing. All of these decisions are kind of like those in an optimizing compiler in that they really want to feed into each other, but actually letting them do so would cause the process to come to a grinding halt, so you interate and order and apply vague heuristics and make arbitrary choices and your inner perfectionist hates you the whole time you’re doing it. And you get to do this practically from scratch every single time because the given context and the desired focus are virtually never the same.
You might say at this point that this is what I get for choosing a wire representation (books and more generally stories) so unlike the in-memory representation (graphs of associations). That may be true to some extent[4], but it’s also important to realize that what is best for knowledge storage doesn’t have to be any good for knowledge acquisition[5]. In fact, the omission that bothers me most of the ones I made in the book-writing rant above is that I know of some things that are just so cute and smol sitting in my head, but when I try to get them out I either assume so many prerequisites that there’s nothing to get out or end up staring at a plan for what is at best a terse twenty-page essay I’m never going to write. I wish hard for viable alternatives to linear narrative, but I also realize I haven’t encountered any that were nearly as good or universally applicable. You can certainly point people at a pile of short-form hypertext, but that misses the issue of pruning: doing it effectively requires you to already know things you decide to prune and the general layout of the subject on a level that is, in classroom terms, several years beyond what you are trying to isolate; a learner is incapable of doing this or at the very least is going to waste tremendous amounts of time doing a mediocre job of it. (I certainly did when I was learning maths from Wikipedia.) I don’t mean to denigrate anyone’s intellectual capability here, or even dissuade them from literature surfing. Surfing in moderation is useful and efficient. I’m only saying that the apparently obvious solution of switching out books for a hyperlinked card catalogue fails and fails hard.
Teaching and books are hard and nobody really knows the secret to doing them well, even those who are brilliant at them. There are a lot of arbitrary choices (not really, but heavily reader-dependent, including factors unknowable to the writer or even the reader) involved in making a book. We solve that problem by throwing a lot of them at the audience and seeing what sticks to whom. But that means a perfect book is impossible—not “drink the ocean” impossible, but “draw a round square” impossible[6]. The problem doesn’t even make sense; what’s a perfect book to you can be a hideous book to me, and what’s a perfect book for me right now was an impenetrable book for me ten years ago. There are objectively good books and objectively bad books, but objectively perfect is something a book cannot be.
[1]: Nobody is going to count your Wikibooks contributions towards your tenure; also, Wikibooks and MediaWiki in general managed to find that sweet spot where they’re simultaneously so expressive you can’t reliably process them automatically and so limited they don’t make good self-contained books, neither fixed nor reflowable.
[2]: Let’s say pre-1970—I find modern trends in English-language secondary and basic undergrad texts positively cringeworthy, but I haven’t ever had to use them in either capacity.
[3]: Can’t help but be reminded here of Michele Audin’s deliciously snarky Tautology 2.3.1 from “Conseils aux auteurs des textes mathématiques”, <http://irma.math.unistra.fr/~maudin/newhowto.ps>.
[4]: The only tool or process I’ve found which is even remotely adapted to this data model is TiddlyWiki <https://tiddlywiki.com/>, which I tried, but never could get over its many quirks and primitive organizational features to make it useful even for notes to myself, let alone as an interface with others.
[5]: For example, fluent readers of Latin/Greek/Cyrillic-script languages generally work by recognizing shapes of words on a page, often for several words in parallel, but teaching children or non-Latin/Greek/Cyrillic-literate adults to read this way is a famously useless affair.
[6]: This also means mandatory texts for students and even mandated curricula for teachers are an atrocity which sacrifices a whole lot of adaptation capability for a modest bit of ease in detecting incompetence and bad faith. The more often a curriculum is nailed down to the time axis with tests and metrics the worse it is.
> [T]here are many books that violate the principle of having something to say by trying to say too many things. Teachers of elementary mathematics in the U.S.A. frequently complain that all calculus books are bad. That is a case in point. Calculus books are bad because there is no such subject as calculus; it is not a subject because it is many subjects. What we call calculus nowadays in the union of a dab of logic and set theory, some axiomatic theory of complete ordered fields, analytic geometry and topology, the latter in both the “general” sense (limits and continuous functions) and the algebraic sense (orientation), real-variable theory properly so called (differentiation), the combinatoric symbol manipulation called formal integration, the first steps of low-dimensional measure theory, some differential geometry, the first steps of the classical analysis of the trigonometric, exponential, and logarithmic functions, and, depending on the space available and the personal inclinations of the author, some cook-book differential equations, elementary mechanics, and a small assortment of applied mathematics. Any one of these is hard to write a good book on; the mixture is impossible.
... But I should probably explain the general picture somewhat for the reader who’s unable to follow the deluge of terminology here.
The problem with calculus, in terms of my parent comment, is that it hasn’t been a singular cluster or clique of ideas in any working mathematician’s association graph since the time of Euler; the list of topics that is presented under that name has never been such—it’s both anachronistically rich in trying to include insights from Weierstrass’s rigour to Tychonoff’s point-set topology and anachronistically poor in avoiding Newton’s motivation from algebraic geometry and differential equations or Euler’s motivation from complex analysis and homotopy theory.
So, if we don’t have a justification from either history or state of the art, why do we insist on this low-resolution camrip of Newton and Leibniz’s writings sprinkled with an arbitrary selection of later work? I don’t know, but I suspect that this is simply the best people could fit into the allotted time when they last tried to incorporate actual, live mathematics into the general curriculum at the beginning of the 20th century, after a hundred years of vulgarization erosion and haphazard contradictory pushes for modernization and practicality.
Why should you even care how mathematicians think now or thought in the past? You don’t have to, of course, though in that case I would much prefer that you avoid diluting the brand “mathematics” by attaching it to the result[2]. But a course should be about something; either you’re teaching mathematics as a matter of culture and way of thought (you sure as hell don’t have time to teach it as a field of study), or you’re reaching for a particular application (but you better know which one, because an applied course left adrift soon becomes a patchwork zombie).
Either way those funny mathematicians in their ivory towers can be of use for you, because they haven’t simply spent all these years playing with impractical abstractions: they broke every subject including old-school calculus into patterns, distilled those patterns into their most elementary possible forms in the form of impractical abstractions, then went back and rearranged their understanding of each subject to make the forms they found more evident, then did it again and again. For decades.
Unfortunately for us lovers of simple answers, their conclusion was, “calculus is not a single thing”. Is there a course or two struggling to come out in the general vicinity so labelled? Yes, but while I have some speculations as to what they are, I don’t have a actual plan—that takes years of regular experimentation with and on classes of real students. It probably includes more varied topics compared to the current approach, certainly some formal series and a glimpse beyond dimension one, probably even a bit of linear algebra as a geometric foundation for it all. (Also a pony while we’re at it.) Should we teach them when combinatorics is infinitely more accessible and probability theory is infinitely more practical? I think so, if not for the cultural significance and life wisdom[3], then because any physics worth speaking of is practically inexpressible without it.
Sorry, I don’t have an answer for you; if I had, it would’ve already been one of those many, many books.
(Took me until the middle of the second of my two answers to realize they both essentially say “Your question is ill-posed” from different points of view; hope they are a bit more helpful than just that.)
[1]: https://www.mathematik.uni-marburg.de/~agricola/material/hal...
[2]: https://www.maa.org/external_archive/devlin/devlin_03_08.htm...
[3]: <https://www.basicbooks.com/titles/jason-wilkes/burn-math-cla...>, <https://www.blackdogandleventhal.com/titles/ben-orlin/change...>
Here are two publishers releasing in the open:
https://www.reddit.com/r/teachingresources/
https://www.reddit.com/r/edtech/
https://www.reddit.com/r/matheducation/
https://www.reddit.com/r/ScienceTeachers/
I donated to Openstax as well: https://riceconnect.rice.edu/donation/support-openstax
The explanation of impedance (volume II, chapter 14) was the first one that made intuitive sense to me, after struggling with the concept for years. The whole thing is beautiful, but that chapter especially.
It would be nice if there was something like OpenStax, maybe even a fork of it, that could be held in a Git repo and anyone could make pull requests.
There's a couple of variations available - it was written by some professors at Georgia Tech, one of which moved to Duke and teaches off of it there - but the UBC version is my favorite, as it makes some changes in the lesson order to teach vectors before matrices.
If you need inspiration for good alt descriptions of STEM / computer science / software engineering related images, just look at how Openstax does it. I'm a screen reader user myself and I'm very impressed.
if you read the latex source, there are even some easter eggs in the comments
Stuff like this exists, and is possibly pretty reasonable monetarily, but not being in the U.S., exchange rates hit me hard.
I've bookmarked this and will look into this more, though, thanks!
If you're a screen reader user, the context menu may not open for reasons unknown. Try routing your mouse to the equation and simulate a right mouse click, that should do it. Moving your focus to the equation with the tab key may also be an option. Alternatively, you can just use Voice Over for MacOS, it can do it just fine.
Unfortunately, this doesn't quite work on OpenStax-I can't get LaTeX, all I can get is MathML, and that's not very easy to read. There's a way to navigate the math (using something called mathplayer), but it's quite inefficient as compared to LaTeX, specially as I go into higher math. The books are still very, very good, though.
Alternatively play with MathPlayer's settings (in the control panel), some of the other reading modes work better in certain contexts.
If you can, also try VoiceOver on the Mac, it has its own math support, which works pretty well.
We seem to be in similar situations, if you want to share tips or something, my hn username at gmail dot com.
in case, link: https://jeffe.cs.illinois.edu/teaching/algorithms/
