Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

Some algorithms based upon a projection process onto the Krylov subspace $K_m = \operatorname{Span}(r_0, Ar_0, \ldots, A^{m - 1}r_0)$ are developed, generalizing the ...

In 1965 Broyden introduced a family of algorithms called (rank-one) quasi-Newton methods for iteratively solving systems of nonlinear equations. We show that when any member of this family is applied ...

Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Prereq., APPM 1360 ...

To learn math, students must build a mental toolbox of facts and procedures needed for different problems. But students who can recall these foundational facts in isolation often struggle to use them ...