
Free and Open-Source Mathematics Textbooks - vo2maxer
http://dcernst.github.io/resources/free-and-open-source-textbooks/
======
westurner
This is a good list of books. Unfortunately many of the links are broken?
Probably just my luck, but the first few "with Sage" books I excitedly
selected unfortunately 404'd. I'll send an email.

> _Moreover, the American Institute of Mathematics maintains a list of
> approved open-source textbooks.[https://aimath.org/textbooks/approved-
> 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/](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...](https://ocw.mit.edu/courses/electrical-engineering-and-computer-
science/6-042j-mathematics-for-computer-science-spring-2015/)

There may be a newer edition than the 2017 version of the book:
[https://courses.csail.mit.edu/6.042/spring17/mcs.pdf](https://courses.csail.mit.edu/6.042/spring17/mcs.pdf)

~~~
throwaway17_17
Does anyone have a good strategy for archiving and downloading the textbooks
from aimath.org? They are all excellently formatted in HTML, but I am not
certain what the best way to get the complete book would be.

~~~
BlackLotus89
When I have books in form of webpages I normally write a small crawler in
python, extract the text div with beautifulsoup, add <hn> tags for chapter
names and throw them all together in html form. Add a cover image and combine
everything with pandoc.

Nothing fancy but works reliable in an automated fashion

------
gmfawcett
You might also enjoy /r/mathbooks (and /r/csbooks) on Reddit, where people
post links to freely-published math and CS textbooks. Most are not open-
source, but all are shared with permission from their authors and publishers.

[https://www.reddit.com/r/mathbooks/](https://www.reddit.com/r/mathbooks/)

[https://www.reddit.com/r/csbooks/](https://www.reddit.com/r/csbooks/)

~~~
creative-coder
Thanks for pointing out these Reddit pages. I wasn't aware of these

------
ericmaki
You might want to check out Open Math Notes, which is hosted by the AMS and
contains almost 100 notes in various subjects, at levels ranging from
undergraduate survey course notes to advanced research:
[https://www.ams.org/open-math-notes](https://www.ams.org/open-math-notes)

------
jimhefferon
Lots of nice links there, thanks.

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.

~~~
mpiedrav
Perhaps a combination of LaTeX/PreTeXt and Open Monograph Press [1] will do :D

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).

[1] [https://pkp.sfu.ca/omp](https://pkp.sfu.ca/omp)

------
oefrha
1\. For math textbooks, being “open source” doesn’t really add much value
(compared to just free).

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.

~~~
jimhefferon
> For math textbooks, being “open source” doesn’t really add much value
> (compared to just free)

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.)

~~~
oefrha
> it allows someone to take up a project if the original author dies.

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.

~~~
fortran77
> In practice I’ve yet to hear of a worthwhile monograph in mathematics
> written that way.

Look at new editions of "Calculus Made Easy". It was re-written from
infinitesimals to limits

------
cesarosum
Great idea to compile this list. One of my favourite mathematics books that is
available for free download is GeneratingFunctionology -
[https://www.math.upenn.edu/~wilf/DownldGF.html](https://www.math.upenn.edu/~wilf/DownldGF.html)

Well-written and incredibly rewarding.

------
abeppu
Everyone likes free stuff, and there's nothing wrong with this kind of list
per se, but I do think there's a trap here lurking for some people. That is,
it's easy to find a free resource appealing. You can grab dozens of free texts
of material you'd like to understand!

_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.

~~~
VovaPutin
> math doesn't really go stale

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/](http://measure.axler.net/)

Direct Link:
[https://link.springer.com/content/pdf/10.1007%2F978-3-030-33...](https://link.springer.com/content/pdf/10.1007%2F978-3-030-33143-6.pdf)

It's free.

~~~
throwawaymath
I have to imagine you know this if you're reading a book like that; but for
anyone else reading this comment: I recommend you don't read _Measure,
Integration and Real Analysis_ for a first introduction to real analysis. It's
"fun" to see Axler present measure theory first and foremost, but analysis is
typically a prerequisite to that.

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.

~~~
VovaPutin
> . 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.

------
zcdziura
Wow, it's a fun surprise to see Dana Ernst featured on Hacker News! Before he
moved to Arizona, he was a mathematics professor at Plymouth State University.
I had him as a Discrete Mathematics teacher, and he was awesome!

------
Koshkin
e-Books, to be exact. Some of us strongly prefer to work with paper books.
Borrowing those for free from a library is not always an option, so one ends
up buying them at whatever price point and the physical state they are
available in. Other considerations: it is still often true that you get what
you pay for; also, 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.

~~~
psv1
> it is still often true that you get what you pay for

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.

~~~
oefrha
> Hasn't been my experience at all - in fact I haven't noticed a relationship
> between quality and price of textbooks in either direction.

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).

------
ardavast
You can also add "An infinitely large napkin", and "Linear algebra done
wrong".

------
ipnon
These are books about mathematics that are free and open-source.

~~~
shocks
Not sure why you’ve been downvoted.

The title is ambiguous, it could mean open source textbooks that are free of
Mathematics!

~~~
wizzwizz4
It could only mean that if it were hyphenated. Given that "Open-Source" is
hyphenated, one can assume that hyphens have been made explicit, not left
implied, and hence this title does not contain that ambiguity.

~~~
ipnon
The title of the submission was changed after my initial comment. The original
title was "Mathematics Free Open Source Textbooks", which I interpreted as
"textbooks without mathematics that are open source." My initial comment was
intended to clarify the content on the submission for people reading the
comments.

------
amitkumar91
Good list of books. I could be helpful to majority of persons at larg.e

------
Jahak
Thank you very much

