Free and Open-Source Mathematics Textbooks
dcernst.github.io
dcernst.github.io
> Moreover, the American Institute of Mathematics maintains a list of approved open-source textbooks. https://aimath.org/textbooks/approved-textbooks/
I also like the (free) Green Tea Press books: Think Stats, Think Bayes, Think DSP, Think Complexity, Modeling and Simulation in Python, Think Python 2e: How To Think Like a Computer Scientist https://greenteapress.com/wp/
And IDK how many times I've recommended the book for the OCW "Mathematics for Computer Science" course: https://ocw.mit.edu/courses/electrical-engineering-and-compu...
There may be a newer edition than the 2017 version of the book: https://courses.csail.mit.edu/6.042/spring17/mcs.pdf
Levin http://discrete.openmathbooks.org/dmoi3.html
Hammack https://www.people.vcu.edu/~rhammack/BookOfProof/
the early parts of Newstead https://infinitedescent.xyz/
Nothing fancy but works reliable in an automated fashion
There needs to be a CMBAN, a Comprehensive Math Book Archive Network. It would fight link rot, allow an author to upload versions as they change and give a blurb as well as version notes, and allow a downloader to know if the book is free or Free, etc. There are some sites that archive some sets but I know of no site that tries to be comprehensive.
The idea is to allow authors using LaTeX/PreTeXt to pipeline the document+sources to a repository (think GitHub Pages for math textbooks), as well as preserving existing free content whose sources are lost (e.g., old out-of-print books).
2. Don’t limit yourself to free textbooks. I would urge people to not hesitate to pirate PDFs of good, non-free textbooks if you can’t afford them or find them too much of a financial burden (textbooks are usually outrageously priced in the U.S.) A good textbook vs a mediocre one probably doesn’t matter for entry-level topics (think freshman, sophomore, or even junior level topics for math majors), but for advanced topics, good textbooks can be markedly more insightful than a mediocre one, or sometimes you need to approach the same topic with different mindsets by learning from multiple texts.
That is wrong. For one thing it allows someone to take up a project if the original author dies.
> I would urge people to not hesitate to pirate PDFs of good, non-free textbooks if you can’t afford them or find them too much of a financial burden
That is also wrong. Authors spend a significant part of their lives on a book and are entitled to do with it as they like. The best way to get free access to a for-cost text is to use your library. (BTW, I write books that are freely distributed.)
That was for the 2nd edition of Volume 1, which came out in 1967, and for the 2nd edition of Volume 2, which came out in 1969.
$19 in 1976 dollars is about $86 in 2019 dollars.
Apostol's "Calculus" is still available from Wiley, and is still used in a few schools for their proof-oriented calculus courses (Caltech, MIT, Stanford, for example).
Wiley wants $283.95 for the current edition of each volume.
Guess what edition they are up to now?
The answer is the 2nd edition, from 1967 for Volume 1 and 1969 for Volume 2. They haven't even given them a new cover design in the last 50 years as far as I can tell. The design on the new copies today are the same as on my 1976 copies. All they've changed there is lightening the shade of the background.
(NOTE: this means that there is no downside to buying the international paperback edition. Sometimes publishers keep the international edition a few years behind the American edition, so for frequently revised textbooks the international edition might not match your course. Not a problem with these books. The international editions can be found for around $20 per volume, including shipping. Abebooks is a good place for this).
So...what changed since the 1970s to explain the $283.95 Wiley wants for these books instead of the around $86 we might expect based on the 1976 price?
The other big name in proof-oriented introductions to calculus, Spivak's "Calculus" was $70 when I bought a copy of the third edition in 2004. That one has had one new edition since then, which is currently $100. $70 in 2004 would be about $95 in today's dollars which is close enough to $100 that I can believe that one's price is explained by inflation plus revision costs for a new edition.
But for Apostol, where it's all just reprints of 50 year old books, I can't see anything other than "because we can" to explain the price.
So what's changed since the 1970s is that the market has been captured and book publishers can charge anything they want for books because you fail the class if you don't have the latest book with the one time use code for the exercises on the website.
Sure, in theory. In practice I’ve yet to hear of a worthwhile monograph in mathematics written that way.
> The best way to get free access to a for-cost text is to use your library.
Not all libraries stock for-cost texts of advanced mathematics. Not all people, including gifted high schoolers, live anywhere close to a library. These are especially true in poorer countries. When people make remarks like yours underprivileged demographics always seem to be forgotten.
Anyway, readers can do with the Internet as they like, and sorry if you’re offended.
Look at new editions of "Calculus Made Easy". It was re-written from infinitesimals to limits
Of course they are. But we are entitled to do the same with the copies of it.
No, that's not how copyright works.
It's amazing that some people consider it legitimate today still.
I've also heard that it also makes it easier to get it professionally printed and bound if one so desires, as printing services are otherwise wary of infringing copyrights.
When it comes to textbooks, with a few exceptions, math textbooks are a lot cheaper than other technical fields.
Maybe not the ones your university is requiring for introductory courses (e.g. Stewart's calculus), but there are plenty of cheap, equally good calculus textbooks out there.
The main exceptions are Springer-Verlag text books. And even some of those are not too expensive. I'm looking at one of my analysis text books - it's $36. My grad level abstract algebra textbook is $47 (also Springer).
Almost everything by Dover is cheap, and many of them are excellent books.
In general, if your goal is to learn, and are not required to buy for a class, math textbooks can be had for relatively cheap new, and fairly cheap used.
Sorry, coming from an engineering background, everything in mathematics looks very affordable. Occupational hazard :-)
Well-written and incredibly rewarding.
_But_ because old texts are pretty cheaply available (because publishers love making new editions with trivial changes like tweaked exercises, and because math doesn't really go stale), almost always the cost of acquiring a non-free book can is waaay less than the time you'd spend to read it, do problems, and really understand the material. Caring too much about "free" is letting the tail wag the dog.
I apologize for taking this out of context, but I'd thought I'd comment. Even though math in textbooks doesn't change, presentation totally does.
For example, "Measure, Integration & Real Analysis" by Axler [0] is a beauty to behold. Honestly, no books from as recent as aughts match the pics, the font, the color of this book...even the explanations and examples leave many (if not most) real analysis textbooks of the past and present in the dust.
[0]
The Book Page: http://measure.axler.net/
Direct Link: https://link.springer.com/content/pdf/10.1007%2F978-3-030-33...
It's free.
The more pedagogically appropriate way to learn analysis is with heavy emphasis on basic topology (metrics) and with the language of geometry. Geometry is useful in calculus and analysis for intuition. Measure is beautiful and helpfully simplifies/generalized a lot of results, but it's really abstract and (in my opinion) unmotivated if you've never encountered rigorous integration or differentiation before.
I'd recommend Tao's, Pugh's or Stein & Shakarchi's analysis books over this one if the focus is analysis. I agree with your broader point that the structure and presentation of math can substantively change, even if the fundamental content doesn't at the undergraduate and graduate levels.
That was my main point. I wasn't intending to recommend intro analysis book. But now that you mentioned it,
for introduction to real analysis, there are even better textbooks out there. For bare-bones hand-holding stuff, there are "How to Think About Analysis" by Lara Alcock and "Real Analysis" by Jay Cummings. The former spends a lot of pages explaining the concepts of convergence and boundlessness and the latter, in addition to what Alcock does, introduces a bit of topology on the real line. Speaking of topology necessary for analysis, Rafi Grinberg's "Real Analysis Lifesaver" kicks ass. It tackles topology and convergence in the Euclidean Spaces (a leg up on the above-mentioned books). These extremely easy to read books (read in the given order) would easily prepare a dedicated student for tacking modern analysis.
If a student wants to see worked out example after worked out example (in extreme detail), Indian authors have you covered. Such STEM books seem to be a tradition there.
My favorite elementary analysis books by an Indian author are "Real Analysis" and "Sequences and Infinite Series" by N.P. Bali (No idea what the initials stand for; all I know is this author is Indian).
A book that serves up elementary analysis in bite sized portions and gives you only what's unavoidable (not simply necessary) is "Intro to Analysis" by Mikusinskis. It has no fat and no excess whatsoever. It aims to save you time as much as possible and wherever possible. Such style is usually reserved for grad level books.
Out of the three books you recommend, the ones by Tao and Pugh require an instructor nearby. If I recall correctly, Tao starts out by carefully laying down the basics of naturals in a way that's sure to leave most any math novice (especially those interested in analysis) bored and lost in the weeds. Pugh, on the other hand, is roughly at the level of, say, baby Rudin (if a bit less formal and austere) which makes it a VERY tall order for a beginner. At this point, the student might as well read Axler's book as it has more material, is more advanced and Axler is a phenomenal writer.
If a student is taught to fear and avoid anything that is "outside the scope of this class", "graduate level" etc, there's "Lebesgue Integral" by Johnston and "Friendly Approach to Functional Analysis" by Sasane. An average high school student can read these books :)
I own all these books.
Hasn't been my experience at all - in fact I haven't noticed a relationship between quality and price of textbooks in either direction.
> you spend so much time and effort seriously working through a math book that whatever money you paid for it looks like something that does not matter at all.
You'll spend the time if the book is good. That's an advantage of free books - you can discard the bad ones without wasting money.
Maybe gp was referring to cheaper “international editions” available for certain popular texts. I heard they intentionally add errors to the cheaper editions (or at least shuffle exercises to make students’ lives miserable if their instructors assign textbook problems).
And eBook is ... well, free. A single copy might run you $40, as here: https://www.bookbaby.com/single-book-printing
Used/resale markets for existing texts are of course an option. And many photocopy shops can throw a usable binding on a text, though photocopy costa alone will be comparable to the price cited above, at $0.07 - $0.08 per page generally.
In many cases, ebooks become a very reasonable compromise.
On multiple occasions I've simply printed the PDF, gone to FedEx and had them bind it. Very cheap, including cost of paper, toner, etc.
A B/W laser printer is fairly cheap, if you don't have one. I was so glad once I bought one.
The title is ambiguous, it could mean open source textbooks that are free of Mathematics!