Research and instruction in intermediate mathematical methods courses

For several years, we have been engaged in research and curriculum development in the context of the so-called math methods courses that is part of many undergraduate physics degree programs. Along with several student researchers, we have investigated student understanding of specific content areas including series, basis vectors, matrix multiplication, Fourier series, and ordinary differential equations. This work and that of others have informed the development of a suite of instructional materials. In this presentation we draw upon these studies and others to provide broader perspective on our findings and the implications they suggest for instruction in mathematical methods as well as the use of mathematics in physics classrooms.