These are some notes I wrote down starting from 2018, as a way of documenting the way I thought about things then and to explain things to myself. Apologies for typos and such.

The dates in the files are the date of last editing. Unfortunately I did not keep track of when the files were created (my computer does remember however, but it seems to be an unnecessary effort at this point). The labels listed below are somewhat vague.

I have tried to provide the appropriate references wherever possible. (Often I have linked an online resource using hyperlinks and this may not show up on your browser, however you could try clicking the title of the reference so listed; sorry about that. If it doesn't work, send me an email :)

To view the title that may have been truncated, hover over it if you are on desktop. If on a mobile device try long pressing the title and ideally the title should show on top of the drop down menu that appears.

In the second year of my BMath, I wrote down solutions for our Graph Theory course: course notes, solutions. There may be mistakes.

During the initial months of the lockdown, I spent some time working out a proof of Jordan Curve Theorem. You can look at it here. The bulk of it involves proving certain results about regions covered by finite polygons in the plane. More specifically, it involves 1. To subdivide the polygons in a nice way so that the interiors don't overlap. 2. Having found a procedure for 1, what do the boundaries of regions look like? 3. Use these results to find a "nice" covering of arcs/curves and prove the Jordan Curve Theorem. This has been accepted for publication in The Mathematics Student Vol. 91.

Documents related to a project on Morse Theory during the third semester of my MMath:

• Midsem presentation (held online)
• Some notes I have made on the subject
• A small result on displacing critical points of a function on a manifold with boundary.