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.
The UTMOST Project experimented with a variety of approaches for integrating open source mathematics software with open textbooks in undergraduate mathematics courses. The Sage Cell Server is a new tool, developed as a major part of this grant by Professor Jason Grout and his students at Drake University, that allows embedding interactive computational sessions in web pages or electronic textbooks. Sage is open source software for advanced mathematics and the Sage Cell Server makes it extremely easy for a student to run short computations through communication with a running instance of Sage on a public server. Authors can add Sage cells to electronic textbooks, such as we have done with Beezer's "First Course in Linear Algebra" and Judson's "Abstract Algebra: Theory and Applications," or as the Mathematical Association of America is doing with their electronic calculus textbook, "Calculus: Modeling and Application." Faculty and students may add Sage cells to web pages with a minimum of effort or technical skill. We have successfully converted open source textbooks from their LaTeX source to the Sage notebook format, as a collection of Sage worksheets. Faculty and student use of the Sage notebook servers provided by this grant has demonstrated that the Sage notebook server needs to be replaced in light of technological changes, in order to better serve larger communities of users beyond a small workgroup. This effort, initiated as part of this grant by Professor William Stein, is the Sage Math Cloud, which provides a collaborative online environment for students, teachers and researchers to interact with Sage and with each other. It has Sage worksheets, powerful LaTeX editing features and a full Linux computer, all running in a standard web browser. The Sage Math Cloud has attracted many users, and development continues on this new tool for mathematical collaboration. Textbook conversion from LaTeX source has demonstrated the need for a new source-level language that unambiguously specifies the structure and content of a document without making any assumptions about presentation. We have used XML as the base syntax for a new specification, MathBook XML. With standard XML processing we are producing multiple output formats (print, PDF, HTML, EPUB, iPython, SageNB, Sage Math Cloud) from one source. This project was initiated during the grant, which also supported user interface design and development for the web page output. Professor Robert Beezer, in collaboration with Dr. David Farmer, will continue to develop MathBook XML. The Open Textbook Initiative at the American Institute of Mathematics (AIM) was initiated as one of the activities for this grant. It is now recognized as the leading authority on the quality of freely-available undergraduate mathematics textbooks. It continues to advocate for, and evaluate, open textbooks in mathematics under the leadership of Dr. Kent Morrison at AIM. Our materials and tools were tested at eight undergraduate institutions, including two Minority Serving Institutions. Faculty from these schools, in addition to other faculty interested in our efforts, participated in the four productive workshops we held at the University of Washington each June. We have learned a great deal about the best ways to provide Sage and course material to students in electronic forms, and ways to effectively combine the two. The Sage Cell Server, the Sage Math Cloud and MathBook XML are new and significant technological achievements which will greatly assist the project's goals of making computation more readily available to students through electronic course materials.
