# Math

• 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 problems, too.
• 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 solutions space.
• 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.

# Programming

• Do some OpenGL-based animations of fluid models.
• OpenGL Starfox clone.

# Electronics

• Look at interpolating a signal via a cubic spline electronically.

# Art

• Readable comics illustrating various basic mathematical topics (calculus, linear algebra, abstract algebra, etc.).