Gregory V. Bard

Associate Professor of Mathematics
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Sage-Related Stuff


(Scroll down for lots of cool resources.)

What is Sage?

SageMath (or Sage for short) is the free, open-source competitor to Maple, Mathematica, Magma, and Matlab. It is a computer-algebra system ideally suited to students of mathematics, and all other STEM fields, vastly more sophisticated and advanced than any graphing calculator. Moreover, Sage is based on the popular programming language Python. That means if you use Sage in a mathematics, statistics, physics, or data-science class, you will learn Python along the way. Lots of other STEM fields are using Sage too, such as chemistry and geology.

There are four really great ways to use SageMath:

  • SageMathCell --- this is perfect for simple tasks requiring 1 to 10 lines of SageMath code. I use this all the time when teaching Math-154: Calculus ii at UW Stout.

  • CoCalc.com --- this is an awesome many-featured system, that was once called SageMathCloud.com. You can collaborate with others, have chats that can include mathematical formulas, add/remove collaborators, and publish your work to the web. Moreover, you have access to every version of every file, unlike a typical jupyter notebook. You can use many languages, such as Python, R, Octave, Java, C++, C, and even FORTRAN, in addition to SageMath, plus all the major Python libraries, like NumPy, SciPy and SymPy. There is even a full course-management system for those who teach online.

  • A local installation --- not recommended for beginners, this can be great for those who do not have reliable access to a high-speed internet connection. Most Sage users access Sage via the internet. There is almost never any reason to do a local install of Sage on your laptop or home computer. The exception is if you have limited or no internet connectivity, such as in rural areas. 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.

  • 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 clicking here, and I've made a few myself, which you can find by clicking here. For using the interacts, NO KNOWLEDGE of Sage whatsoever is required! However, making your own interacts is neither too difficult nor very easy, and is covered in Chapter 6 of my book, Sage for Undergraduates. You can download that book for free, using the rainbow link at the top of this webpage.

  • The commands used are the same in all cases, because that's the SageMath part, the computational engine at the heart of the system. Even better, SageMath is based off Python, so students naturally become good Python programmers while using Sage, instead of learning a proprietary language when using Maple, Mathematica, MATLAB, or Magma.

Sage is great for calculus, differential equations, linear algebra, data science, abstract algebra, discrete mathematics, graph theory, physics, numerical computing, machine learning, and many other courses. Sage also includes a full copy of R for those who use statistics or those who want to learn data science, and other open-source systems like Maxima, Pari, and GAP.


Resources for Sage

Here are some of my favorite resources for Sage. However, this page is woefully incomplete. The Sage community involves hundreds of developers and thousands of contributors world wide.

  • 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] Click here.
    • 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.

  • The book Calcul mathematique avec Sage was only available in French until the middle of 2018, when a translation into English was released. I have enjoyed consulting this book frequently over the years, but I'm glad that it is now available in English, because very few of my students have studied French. In some ways, this book can serve as a sequel to my own. The translation is Computational Mathematics with SageMath. (click here to download)

  • There is a tutorial for Sage, by Prof Michael E. O'Sullivan (at San Diego State University in California). This is an excellent entry-point for faculty, PhD-students in mathematics, and senior math majors about using Sage for all sorts of problems. (click here)

  • 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. :-)

  • Aimed at students in Calculus 1, Prof Hieu Nguyen (at Rowan University in New Jersey) has made a guide for his students, SageMath Advice for Calculus. However, I think it is also very useful for Calculus 1 instructors. (click here to download)

  • For matrices and linear algebra, Prof Robert Beezer (at the University of Puget Sound) has written an excellent textbook that uses Sage examples throughout. The book, A First Course in Linear Algebra also teaches the writing of proofs. Even if you're using a different textbook, you can steal all the Sage examples. Best of all, the book is free in electronic form. (click here to download)

  • In any case, the directions for a local install can be found by clicking here.


Videos about Sage

  • Here is a series of videos/screencasts introducing Sage. They are made by William Stein, the founder of Sage.

  • Here are some videos that I've made to introduce my students to the basics of using Sage with its most simple interface, the SageMathCell Server. (All are less than five minutes.)

    • Part One covers functions, derivatives, integrals, and 2D plotting.

    • Part 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.

    • 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 are coming soon!!

Last updated August 8th, 2018.
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