Many universities use diagnostic tests to assess incoming students' preparedness for mathematics courses. Diagnostic test results can help students to identify topics where they need more practice and give lecturers a summary of strengths and weaknesses in their class. We demonstrate a process that can be used to make improvements to a mathematics…

By considering a general representation of proper rotation matrices, the eigenvalues and eigenspaces of those matrices are identified.

A general method is presented for evaluating the sums of "m"th powers of the integers that can, and that cannot, be represented in the two-element Frobenius problem. Generating functions are introduced and used for that purpose. Explicit formulas for the desired sums are obtained and specific examples are discussed.

Within the general framework of a multifactor term structure model, the fundamental partial differential equation (PDE) satisfied by a default-free zero-coupon bond price is derived via a martingale-oriented approach. Using this PDE, a result characterizing a model belonging to an exponential affine class is established using only a system of…