Here is my contribution to the pool of resources for Cambridge Mathematics Tripos. My guiding philosophy while writing the notes has been to put the content into a coherent narrative first and foremost, and make all ideas as intuitive as possible. These resources are best used as auxiliary reading material to solidify intuitions or look at alternative perspectives.
Methods for Puremos
An attempt at reorganising the methods course which emphasises strong connections with Linear Algebra. Hopefully this makes methods more bearable if you are more inclined towards pure mathematics.
Analysis and Topology (but mostly Metric Spaces)
An experimental approach to the theory of metric spaces that puts everything in a more coherent narrative, and paves the way for topology. Initially an attempt at writing a full set of notes for the course, I stopped halfway through topology and the project remains unfinished. The sections that have been written, however, are essentially complete and capture the main intuitions I wished to convey.
In particular, the sections on Hamilton’s method and Legendre transform are attempts at making those concepts feel more natural, something that the lecture notes fail to do.