Gregory V. Bard
Associate Professor of Mathematics
Preserving the look-and-feel of the World Wide Web as it was, in 1998.
What is Sage?
Sage is the free, open-source competitor to Maple, Mathematica, Magma, and
Matlab. It is a computer-algebra system ideally suited to students of mathematics.
This page is woefully incomplete. The Sage community involves hundreds of developers
and thousands of contributors world wide.
Last but not least, I've made some videos for introducing students to Sage.
- Interacts (sometimes called interactive webpages, applets, apps, or interactive
figures) are a really fun way to demonstrate a complicated math topic. A large repository
of them (made by the Sage community) can be found by
and I've made a few myself, which you can find by
clicking here. (For using these,
NO KNOWLEDGE of Sage whatsoever is required!)
- Here are some links for my book Sage for Undergraduates,
published by The
American Mathematical Society in February of 2015.
- Graciously, the AMS has permitted me to place a pdf file of the book on my webpage.
- Here is a link
to the black-and-white version.
- Here is a link
to the color version.
- The online electronic appendix covers plotting in color, complex functions, and
3D graphics. Those subjects are not suited to a black-and-white book, and therefore cannot
be printed inside the book itself. [Rough Draft]
- Chapter 6 of the book teaches the reader how to make their own interactive webpages
or applets. To save readers from having to retype my
code into their computers,
I promised a zip-file with
some source code of the examples used.
- Here are some videos that I've made
to introduce you to the basics of using Sage with its most
simple interface, the SageMathCell Server. Both are less than five minutes.
One covers functions, derivatives, integrals, and 2D plotting.
Two covers factoring, 3D plotting, gradients, and symbolic solving.
- After watching both videos (or even without them) you'd find it very easy to just dive
on into Chapter 1 of my book, linked above.
- At the bottom of this page, I have some other videos about matrices and about linear
- Want to give Sage a try?
- For short and medium-sized problems (especially in 100-level and 200-level courses, but
even in higher-level courses too), the best way to use Sage is the SageMathCell Server.
(That's the competitor to WolframAlpha, and until recently it was called Sage-Aleph.)
- The first bullet on this page talks about interacts (sometimes called applets or interactive
webpages) and those can be used by anyone, with no knowledge of Sage or computing required at all.
- For longer problems (especially those that will require collaboration, writing your
own programs, or using data sets) the
server is the way to go. (This service was called SageMathCloud until the Summer of 2017. It is the
same service, just renamed, because the tool is being used by computer scientists, physicists,
engineers, and even geologists, not just math people.)
- The beauty of Sage is that it works through the internet. There is almost never any
reason to do a local install of Sage on your laptop or home computer. This is good news,
because it saves a lot of headaches and hassles (especially for students), that you would
have to suffer if you were using Mathematica, Maple, Matlab, or Magma. The exception is if you
have limited or no internet access, such as in rural areas. In any case, the directions
for a local install can be found by
- This is an excellent tutorial
for faculty, PhD-students in mathematics, and senior math majors about using
Sage for all sorts of problems.
- Here is a large collection of quick-reference
cards for Sage, by various people, for various branches of mathematics, in many languages.
Personally, I think having a printed quick-reference card out next to the laptop while using
Sage is really handy. :-)
- Here is a series of videos/screencasts introducing Sage. They are
made by William Stein, the founder of Sage.
- Here is a video for how to find the Reduced Row Echelon Form (RREF) of
a matrix. For example, you might do this to solve a linear system of equations.
- For solving Linear Programming Problems (i.e. maximizing or minimizing a many-variable
linear function subject to several multivariate linear inequalities), I have three videos:
- More is coming soon!!
Last updated July 26th, 2017.