Oct

24

2014

This talk serves as part II of a two-part elementary introduction to mathematical fluid mechanics. In this series of talks we will introduce and (at least partially) derive the Euler and Navier-Stokes equations modeling incompressible fluid flow in two and three dimensions. We will also discuss quantities of interest such as the velocity, pressure, vorticity, and particle trajectory map. For our discussion of inviscid flows modeled by the Euler equations, we will focus in particular on vortex motion, namely Kelvin's circulation theorem and the Helmholtz vortex theorems with applica

Oct

25

2014

Oct

27

2014

For the past 15 years I have been involved with research that seeks to understand how students can transition from more informal reasoning to more formal, mathematical reasoning. As part of this NSF funded research, we have developed curriculum to help students make this transition. In my current project our team is developing instructional materials appropriate for a first college course in linear algebra including the topics of (1) span and linear independence, (2) matrix multiplication and linear transformations, and (3) eigen theory, change of basis and diagonalization.

Oct

28

2014

For any permutations $\sigma \in S_n$ and $\pi \in S_k$, we say that $\sigma$ contains the pattern $\pi$ if $\sigma$ has a subsequence that is order isomorphic to $\pi$. In this case, we refer to $\pi$ as a pattern of length $k.$ We may endow a pattern $\pi=\pi_1\pi_2\cdots\pi_k$ with proximity restrictions, that is, requiring certain elements of the pattern to correspond to adjacent elements in the permutation $\sigma$. If the elements $\pi_i,\pi_{i+1}$ of the pattern $\pi$ are required to correspond to adjacent elements of $\sigma$, then we place an underscore beneath $\pi_i,\pi_{i+1}$.

Oct

30

2014