November 14 Math Colloquium

Ian Anderson, Utah State University

Googling Einstein and Wikipeding Cartan

Recent software advances in computer algebra systems such as Maple and in laptop and desktop computing power have now given mathematicians effective tools for research in computational intensive fields such as differential geometry and its applications. In this talk, I will discuss new ways in which we can use computer algebra systems, ways which go well-beyond the use of such systems for long, complex computation.

First I want to show how Maple can be used to create dynamic, interactive data-bases of mathematical or  mathematical physics knowledge and how this knowledge can be made accessible to a broader audience. As a case study, we will look at the subject of exact solutions to the Einstein equations of general relativity. I will describe our efforts [1] to create a comprehensive  data-base of known solutions; [2] to verify the correctness of these solutions; [3] to calculate an extensive set of properties of these solutions; [4] and to develop an easy-to-use search engine to access this data-base.

Second, I want to give a brief demonstration of how Maple can be used to create rich interactive documents for teaching advanced mathematics. Here we will look at the structure theory of simple Lie algebras. This classification was begun by W. Killing, completed by E. Cartan in his PhD thesis, and cast into its current form by E. Dynkin. This material is covered in many text books and is readily available on the web. I'll show how one can use Maple to  present this same material in a dynamical new way which makes the material much easier (and more fun!)  to learn.

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