The UTMOST Project (Undergraduate Teaching in Mathematics with Open Software and Textbooks) is coupling the use of Sage - comprehensive free open source mathematics software - with existing free open textbooks, to make it possible for faculty and institutions to more easily bring the power of mathematics software to their students. Authors of open source software and open textbooks provide licenses that permit free copying and editing of their work, allowing others to adapt or extend them to suit their needs or make improvements. A major project activity is to convert existing open textbooks into web-based dynamic e-texts that integrate traditional mathematical exposition with Sage code and hands-on demonstrations. The intellectual merit of this project lies in its use of the innovative Sage environment and its active community of users and practitioners. Eight diverse undergraduate institutions are helping to test and refine these materials using a comprehensive, professional evaluation procedure. The main goal driving this project is to create technical and pedagogical tools and methods that greatly simplify the deployment and use of powerful software to increase learning and experimentation in undergraduate mathematics. The potential broader impacts of this project are strong given the distributed nature of both development and deployment.
Sage is a comprehensive open source mathematical software system. The Sage Cell server (https://sagecell.sagemath.org), a new online service developed as part of this grant by Jason Grout and students at Drake University, allows embedding interactive Sage computations and results in web pages or electronic textbooks. Students, educators, and researchers use these live computation cells, either embedded in a web page or as a link in an email or pdf file, to check their work, explore variations on a computation, or communicate short results with teachers or collaborators quickly and easily, without having to install software or log into a service. Embedded Sage cells can produce 2d and interactive 3d graphics, as well as buttons, sliders, and other controls to explore a computation (via the Sage or IPython interactive widget infrastructures). Embedded Sage cells can also include computations in R, Octave, Python, Gap, GP, Singular, or other mathematical software systems for which Sage provides an interface. Authors add these interactive cells with a few lines of javascript and html, or by using an easily-generated web link or QR code, such as in Rob Beezer's "First Course in Linear Algebra" (http://linear.ups.edu/) or the Mathematical Association of America's electronic calculus textbook "Calculus: Modeling and Application" (http://calculuscourse.maa.org/). See https://sagecell.sagemath.org/static/about.html for instructions to embed a computation with a minimal amount of effort or technical skill and for other places educators are using Sage cells. We also provide plugins to easily embed computation cells in wikis and to call Sage from the Webwork online homework software to create problems or check student answers. The Sage Cell server also powers the Sage Android and iPhone/iPad apps. In addition to the underlying service, as part of this grant, we have also rewritten the Sage interact system to be more powerful and general and have significantly contributed to the IPython widget infrastructure. We developed the pythreejs open source project (https://github.com/jasongrout/pythreejs) for interactive 3d graphics in both the Sage Cell server and the IPython notebook. The Sage Cell server, in conjuction with materials and other resources created as part of the collaborative UTMOST project, provides an easy way for authors, educators, and students everywhere to use free open source mathematical software in education and collaboration.
