Here’s the the honors components I’ve completed during my stay at community college:
First-semester freshman under Professor Wolfson for Calculus III:
Obtaining the Shortest Distance Between Two Points on a Surface
Paper is dedicated to the discussion of functionals, calculation of variations, and the derivation of the geodesic on a surface.
Second-semester freshman under Professor Wolfson for General Physics I:
Applying Quaternions to Rotating Reference Frames
Discussing quaternions, deriving the formulas for motion in a rotating reference frame, then combining the two together. Appendix is dedicated to discussing quaternion’s algebraic properties.
I also did a culminating honors project in Galois Theory my third semester. I didn’t like the result to be honest, it’s a bit long (~35 pages). Perhaps I’ll eventually edit it down then upload it here.
At a new school now (transferred after third semester). Over here I’m a first-semester sophomore now. I’ll update this if I do something. Probably will soon enough.