**Dr. Warren Christiansen**

*North Dakota State University***Investigating mathematics in the upper-division physics: Examples of Linear Algebra and Non-Cartesian Coordinate Systems**

There is an expectation that students completing the mathematics sequence of Calculus I, II, III, Linear Algebra, and Differential Equations, should have a wealth of conceptual and procedural knowledge that can be used in upper-division physics courses. However in practice, it seems that many students come into our physics courses lacking many of these skills. My group is conducting multiple studies across content in courses of Quantum Mechanics and Math Methods. We investigate the extent to which students possess these ideas as well as the context sensitivity. This talk will focus on student thinking about matrix multiplication and how their thinking appears to be influenced by their framing of the problem as either a mathematics or physics question. This work uses the framework of* Framing and Resources* to describe a single student's thinking during an interview. Using an interview protocol written by mathematicians from a study in Mathematics Education, we explicitly probed mathematical thinking, and investigated if (and when) students attempted to relate mathematical problems to physics. Additionally, I will discuss new work on student sense making with non-Cartesian coordinate systems.