The Undergraduate Teaching Assistant (UTA) Program at the University of Arizona exposes students to many different aspects of teaching an undergraduate mathematics course. The program's breadth generates various qualitative and quantitative benefits. Some of these benefits are that the UTAs improve their mathematics and communications skills, instructors have additional support both inside and outside the classroom, and mathematics students in classes with UTAs enjoy their mathematics classes more than students in similar classes without UTAs.

The Karhunen-Loève (KL) decomposition is widely used for data which very often exhibit some symmetry, afforded by a group action. For a finite group, we derive an algorithm using group representation theory to reduce the cost of determining the KL basis. We demonstrate the technique on a Lorenz-type ODE system. For a compact group such as tori or SO(3,R) the method also applies, and we extend results to these cases. As a short example, we consider the circle group S(1).

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