Aug

12

2022

In this dissertation, we will consider some localization methods for estimating solutions to partial differential equations related to fluids models. In particular, we focus on two non-local systems, the Navier-Stokes (and Euler) equations describing incompressible fluid behavior, and the aggregation equations. We introduce compactly supported weights and algebraic weights, and use them to inspect solutions of these models. Via compactly supported weights, we derive short-time existence of solutions to the Euler equations in $H^s_{ul}(\R^d)$ for sufficiently nice initial data.

Aug

15

2022

Aug

17

2022

Realistic Mathematics Education (RME) is a body of educational theory which is a common point of inspiration among mathematics educators focused on reform towards active learning at the undergraduate level. This paper presents the origin and major components of RME theory, placing particular attention on the thought of Dr. Hans Freudenthal, the founder of the theoretical school. The theory is further elucidated through the perspective of a curriculum generating developmental research project, Teaching Abstract Algebra for Understanding (TAAFU or IOAA).

Sep

26

2022

Oct

03

2022