<p>a really heavy math related research topic
for my senior project</p>
<p>I am trying to think of something really creative that I can self-teach myself the basics of</p>
<p>I maybe wanted to do something with Chaos Theory but I don't know where to teach myself that or its practical applications</p>
<p>any ideas to get me started?</p>
<p>Thanks.</p>
<p>Many years ago (when computer graphics was a new thing), I did an intersting project related to granular packing, and calculation of the “voids” volume. It involved random placement of spheres with varying radius… think rocks vs sand.</p>
<p>Maybe a modeling project? Those are the most straightforward to self study. Like car traffic jams, perturbation theoretical models of atoms on a quantum level, or chaotic systems (you might want to learn some diff’eqn’s), fluid mechanics modeling, numerical algorithms to partial diff eqn’s ??</p>
<p>Just throwing some random ideas out there, hope it helped?</p>
<p>There’s graduate research even in the most… accessible areas, e.g. decimal expansions etc.! I remember there was a GRE (strange, I forgot the name… graduate whatever exam) where they wanted the examinees to find the diagonal across a cuboid - which is really easy for all of us here. But they made the mistake of drawing a cylindrical rod to represent the diagonal, and asked them to find the length of the rod instead. Now, the more… perfectionist ones thought they wanted them to find the length of the diagonal, then correct the ‘small gaps’ at both corners. And obviously they couldn’t do it. Now, that’s screwed up integral calculus there. I don’t know what’s the name of the problem already, I recall it’s called “coin in corner redux” or something… it’s in one of the 2005-2009 College Mathematics journals, and it was actually unresolved.</p>
<p>So, chaos theory is fine, really. It’s the quality of the research that matters. If you’re interested in chaos theory, you could start your self-study with real analysis -> applied analysis for dynamical systems.</p>
<p>If you’re looking for something esoteric, quantum field theory, advanced cryptography, string topology, differential geometry etc. are nice.</p>