Proposal
The Gauss Bonnet Theorem
I am planning to create a website that presents the Gauss Bonnet Theorem: a general overview, its necessary background information, and its consequences.
Website Features
Audience
At the most narrow level, my target audience would be members of the Directed Reading Program within the UCSB Math Department interested in gaining supplemental information about the topic I present at the end of the year. These are all UCSB undergraduate students, probably ranging in age from 18-24, in math-adjacent majors, if not specifically studying math or applied math. The readers will probably have more capabilities to understand the presented information than the general public as they hold at least some amount of advanced mathematical skills. I will present the topics with the impression that my readers understand proofs, as this is a requirement of being a member of the DRP. There will be curious, interested, and intelligent attitudes possessed by my readers since I’m sure they are not familiar with this topic prior to traversing the website. This website has the capability to circulate outside of the DRP, but most likely will stay within the math department, as those visiting the site must be interested in abstract topics in math.
This website doubles as a way to organize what I learn within my program throughout the quarter while also presenting it in a way accessible to outside audiences so they can learn more about the specific topic. My three main purposes are to explain, describe, and define in a comprehensive and aesthetically pleasing manner. I hope that my website serves as a second, more in depth option to what I cover in the DRP symposium at the end of spring quarter. I think I will write in a very clear, concise, and serious manner, as my main purpose is to educate the audience. A less serious tone may make what is being learned seem less credible.
Purpose
Text
I plan to integrate lots of media into my website so as to ensure it does not present itself as too text heavy. This can be done by using graphics to demonstrate many of the theorems and ideas needed to understand the resulting proof of the Gauss Bonnet Theorem. These graphics will be a mix of short videos and images. For example, it is necessary to be familiar with the concepts of curvature and surfaces prior to seeing the proof of the theorem, in which animations of the movement of a curve will prove very helpful to the reader’s understanding. I also hope to include a few links to credible explanations of certain harder concepts on YouTube.
I would hope that this website will circulate following the DRP symposium at the end of spring quarter. I intend to put a small QR code on my poster that I present that takes those in attendance to the website in order to gain supplemental information. Thus, this website will be reached by UCSB math and math adjacent majors, as well as their graduate student mentors.