- Animations of conjugate gradient.
- If you're given a particular (say 2D) shape, possibibly with some
knowledge of the properties (areas, lengths, etc), investigate
problems of cutting the shape into smaller shapes. For example,
say you're given a square that you want to cut into 5 smaller
squares of equal area. There could be costs associated with
different types of cuts, or maybe inaccuracies (e.g., cutting
in half is 1% accurate, cutting in thirds is 2% accurate, etc).
Which sorts of cuts minimize the costs / errors? Lots of other
- Can you use a tensor decomposition to compress video? Something
like an SVD for matrices, but in a third order tensor. Does
something like this already exist? Does it even make sense (i.e.,
do there exist something like singular values for higher order
tensors which tell you something about the rank)?
- Study some more on mechanics.
- Look into solving linear BVP's from the matrix.
- Make a video of plots of a second order boundary value
problem, to illustrate how the parameters change the
- Read more on Navier-Stokes equations, particularly weak solutions.
- Write notes on various topics, with illustrations on how the
definitions / theorems depend on one another.
- Write notes on tons of miscellanesous facts for 2x2 matrices, as an aid
for intuition and having quick ways to compute with them.
- Do some OpenGL-based animations of fluid models.
- OpenGL Starfox clone.
- Look at interpolating a signal via a cubic spline electronically.
- Readable comics illustrating various basic mathematical topics
(calculus, linear algebra, abstract algebra, etc.).