Mueller completed a Ph.D. in 1997 at the University of Nebraska–Lincoln. Her dissertation, Inverse Problems in Singular Differential Equations, was supervised by Thomas S. Shores.[3] After postdoctoral research at the Rensselaer Polytechnic Institute she joined the Colorado State Mathematics Department in 2000, and became a founding member of the School of Biomedical Engineering in 2007. She was promoted to full professor in 2011.[4]
Book
With Samuli Siltanen, Mueller is the author of the book Linear and Nonlinear Inverse Problems with Practical Applications (SIAM, 2012).[5]