Teaching Resources

Here are a few resources that I have come across. I am not in any way endorsing these as correct. I am merely listing ones I find interesting, partly so that I can browse them as I have time.

I am not updating this page anymore.

For a nice listing of free textbooks, see section 5.1.3 of our UTMOST CCLI grant proposal.


  • Luke Campagnola gave one of my favorite 5-minute lightning talks at the 2015 Scipy conference (video). I love how Luke paces his talk and uses his slides to support his narrative.

General resources for Math

Mathematics in Society

  • Math in Society by David Lippman, which explores topics in a very introductory way. Topics include voting, dividing things, statistics, etc.
  • Fun Facts about mathematics


Here are a few free calculus textbooks.


  • Precalculus, used at University of Washington. This seems like a very nice book.

Standard Calculus

  • Hoffman’s Calculus
  • Calculus by Granville and then augmented by David Joyner. This includes lots of Sage examples for doing computations and graphs.
  • Whitman Calculus
  • Calculus by Gilbert Strang. This is a published book as well.
  • Calculus by Benjamin Crowell
  • Understanding Calculus by Faraz Hussain
  • Differential Calculus by David B. Massey. I’m confused by this one. It doesn’t seem really free (you can pay them to get the source to create your own customized version), but you can download a PDF and watch online video lectures. It’s may just be good supplementary material for students. There is also an Integral Calculus book by the same author, and apparently a multivariable text is on its way.
  • Paul’s Online Math Notes: Calculus I, Calculus II, and Multivariable Calculus.
  • Heiner’s web page includes two links to calculus books he’s written.
  • Calculus: Modeling and Application by David A. Smith and Lawrence C. Moore. When you click on the word “Copyright” on this page, you learn that “If and when MAA chooses the publish these materials, they will no longer be available without charge from this public site. In the meantime, we are eager to have teachers and students use these materials freely and provide feedback on their experiences, good or bad. Such educational use is explicitly permitted in the conditions below.” Please read that page fully to see the full terms of use.
  • http://www.e-booksdirectory.com/listing.php?category=4 - Lots of free calculus textbooks (including some of the ones mentioned above)

Multivariable calculus only

Sage Worksheets

Multivariable Calculus

Advanced Calculus

Calculus (other material)

Ordinary Differential Equations


Numerical Analysis



The following OpenCourseWare courses seem like they overlap with our numerical analysis course: * http://ocw.mit.edu/OcwWeb/Mathematics/18-086Spring-2006/CourseHome/index.htm * http://ocw.mit.edu/OcwWeb/Mathematics/18-335JFall-2006/CourseHome/index.htm * Computational Science and Engineering

Here are a few other course outlines: * http://persson.berkeley.edu/128A/ * Short course


  • MPIR - MPIR is an active fork of the long-established GMP project, implementing multiprecision integers and rationals.
  • MPFR - multiprecision correctly-rounded floating point computations.
  • An overview of software which comprises an appendix in the Cheney/Kincaid numerical analysis book.
  • A freely-available reference floating-point libm made by Sun
  • Eigen - what looks like a very nice C++ library for doing matrix arithmetic. This library looks like it has a very nice API.

Sage Worksheets


  • Tom Sederberg’s book on computer graphics, including very nice explanations of splines and Bezier curves.
  • Notes from a class on numerical computing with python
  • http://www-users.math.umd.edu/~dlevy/books/na.pdf – A set of Numerical Analysis notes by Doron Levy at University of Maryland
  • Stephen Pav’s Numerical Analysis book follows roughly the treatment in Cheney and Kincaid. This book is free to modify and redistribute, and uses a smattering of Octave or Matlab in the exercises. You can also contribute through the open-source version repository.
  • MPIR Documentation (algorithms chapter) contains a good overview of methods for doing computer arithmetic. You can also see the GMP documentation.
  • Modern Computer Arithmetic by <img style=’’ src’/img/< wp “Richard Brent (scientist)|Richard Brent” >’> (think Brent’s algorithm) and <img style=’’ src’/img/< wp “Paul Zimmermann” >’> (who helps develop MPFR). These gentlemen know what they are talking about.
  • Matters Computational – This book (and accompanying software) describes a wide variety of algorithms, including combinatorial and numerical algorithms.
  • Holistic Numeric Methods Institute has a large number of tutorials and videos about lots of different numerical methods topics.
  • Data Analysis for Politics and Policy by Edward Tufte, a recognized authority in presenting information clearly
  • Computational Mathematics
  • A free online text from University of Waterloo also seems to be pretty impressive.


Math modeling


Hidden Markov Models

Other notes

Linear Algebra


  • Immersive Linear Algebra. This book has interactive visualizations for lots of concepts in linear algebra.
  • Linear Algebra by Jim Hefferon. This seems like a nice, standard book that is easy to read.
  • A First Course in Linear Algebra by Rob Beezer. This is a very careful, nice book. If you have questions about the details of how something works, this is a great reference, as *everything// is cross-referenced to appropriate theorems, definitions, etc.
  • Linear Algebra by Ben Woodruff. This is a radically different approach to a course in linear algebra compared to more standard texts. I think this approach has a lot of potential, and plan to use it in teaching soon.
  • MIT Linear Algebra uses Strang’s book and has a number of other helpful resources, like a glossary.
  • Linear Algebra (in-progress PDF): my edited version of Ben Woodruff’s linear algebra book.
  • Terry Tao’s online notes covering the subject look very interesting. For example, in week 3, Terry brings up nice ideas about treating bases as “units” of a vector space, so that
    ) is a quantity, but a “foot” is a basis, and one foot is just a vector with coordinate 1 in the basis of “foot” and coordinate 12 in the basis of “inch”. The concept of linear transformations also has examples in this.
  • While not free, Carl Meyer’s Matrix Analysis textbook is available as a pdf download.
  • George Benthion has a number of notes on his site, including what looks like a very nice book on numerical linear algebra.
  • Solving large-scale eigenvalue problems is a book-length set of course notes.


Labs and Projects


Here are some very specialized packages for computing in linear algebra.

  • BLAS
  • LAPACK (and cousins)
  • Sage
  • ExpoKit - One of the most advanced software libraries for computing matrix exponentials
  • Eigen - what looks like a very nice C++ library for doing matrix arithmetic. This library looks like it has a very nice API.
  • http://www.netlib.org/utk/people/JackDongarra/la-sw.html A nice list of linear algebra software packages.

Sage Worksheets

Graph Theory

Statistics and Probability



Other books

Collections of materials

Math History

Math Videos

Programming books


Here are some great resources for learning scientific python:

  • A tutorial covering a lot of the scientific tools that you may be using
  • The Python bootcamp at Berkeley in August 2012
  • A collection of IPython notebooks highlighting a number of different areas.

Here are some general Python resources




Other collections

Computational Complexity

  • Computational Complexity: A modern approach by Barak and Arora was recommended to me as one of the best textbooks on computational complexity out there. The website for the book has an early draft and other supplementary material.
  • A compendium of NP problems.

Information Theory


This comment on HackerNews suggests that Rosalind is a good way to get into bioinformatics.

Random thoughts on licensing

Random thoughts on teaching

Random Quotes

Mathematician: noun, someone who disavows certainty when their uncertainty set is non-empty, even if that set has measure zero.

{{{ 99 instances of bugs in the code… 99 instances of bugs, …. code one out, mark it out (without running full tests), 106 instances of bugs in the code… 106 instances of bugs in the code… 106 instances of bugs, …. }}} (from here)

A tongue-in-cheek history of computer languages.

Walking on water and developing software from a specification are easy if both are frozen.

Other Random stuff

  • For those that read Russian, a Slashdot comment mentions “USSR science textbooks. Seriously, they are great (with some obvious exceptions :) ) and they are out of copyright. For example, Fichtenholz’s “Differential and Integral Calculus” is THE best textbook on calculus ever created. It’s so clear and written in so beautiful language that I had actually re-read it just for fun. I don’t know if there are translations into English, alas. Landau and Lifshitz’s “Course of Theoretical Physics” is the one of the best reference books for the modern physics, and it’s available in English. It’s out of copyright but its translations might be copyrighted.”
    • (ǀᴉɐɯə uo əɹnʇɐuɓᴉS) ¿uʍop əpᴉsdn ədʎʇ noʎ uɐɔ

Research resources

Here are a few good resources for analyzing numbers and sequences.


Here are some interesting-looking ipod apps that I might try someday.