Robotics

 So, I had been told a bajillion times at topology math conferences that robotics is a big area for applications of manifold topology and geometric group theory, but I never really took the statements seriously: that was "applied math".

Low and behold, as I was Googling for applications of manifold topology and Larangian mechanics to geometric control theory, thisYouTube video playlist popped up https://www.youtube.com/watch?v=4Y1_y9DI_Hw&list=PLZaGkBteQK3HQFSWDM7-yRQWTd86DeDIY&index=1 and I don't think my life will ever be the same.

Robotics is the application of manifold topology and Lagrangian mechanics for which I had been looking for, I think, my whole life. So, their 4x4 transformation matrices, which are really representations of the special Euclidean group, $SE(3) = \mathbb{R}^3 \rtimes SO(3)$, are just wonderful mathematics, and DH tables are a fabulous ways of encoding and automating the process of creating transformation matrices.

So, I now have a new purpose in life. I am considering postponing my MS in Control Engineering at UW-Platteville to seek a (hopefully online) BS or BS Certificate in Mechanical Engineering and then, with that credential in place, completing an MS or Ph.D. in Control Engineering, either at UW-Platt or U Washington (in Washington State).

 I think a future in Robotics Engineering could be a very bright and rewarding future for me indeed.