Narrow Results

In this report we highlight significant advances in university mathematics education research as well as areas that are in need for additional research insights. We add here to the rich set of literature reviews within the last several years. A novel aspect of this literature review is the fact that the areas of accomplishment and areas for growth were identified based on thematic analysis of survey responses from 119 experts in the field. The review provides a useful overview for both seasoned scholars and those new to research in university mathematics education.

The growth of a second derivative of the logarithm of the maximum modulus of an entire function provides information about the location of zeros of the function and its sections. We present a survey of work on this topic along with some recent sharp results and open questions.

Let Ω be a periodic unbounded domain in ℝⁿ. It is well-known that the spectrum of the Neumann Laplacian in L₂(Ω) is a locally finite union of compact intervals called bands. The neighbouring bands may overlap, otherwise we have a gap in the spectrum. Our goal is to construct such periodic domain Ω that the spectrum of the corresponding Neumann Laplacian has at least m gaps (m ∈ ℕ is a given number) and these gaps are close to predefined intervals.