deep-dive

Since 2020, I embarked on a journey to write all my studies in mathematics through LaTeX. This process has enabled me to dive deeper into the development of proofs and engage in insightful discussions about a diverse range of mathematical constructions. With the hope of illuminating the path for fellow seekers of mathematical knowledge, I decided to share my collection of notes publicly.

Deep Dive is the evocative title I've chosen for this ever-evolving collection of personal notes. It represents a continuous and endless exploration of the realm of mathematics. To that end, I claim absolutely no originality in any of my writings, instead they can be thought as a compilation of books and papers I've read, written on my own words.

It must be stressed that this document is an endless work in progress and will never be finished. It primarily serves as a repository of personal notes created for my own benefit and enjoyment. Therefore, I must acknowledge the presence of numerous linguistic and mathematical errors scattered throughout this document. However, as time permits, I plan to revise and refine this work in some distant future. In doing so, I hope to rectify most of the silly mistakes and errors.

The first propulsor of this journey was a draft of Dongryul Kim titled A rough guide to linear algebra, which aims to give a sophisticated introduction to linear algebra; making extensive use of the language of category theory. My interaction with this draft settled my path to the world of abstraction in mathematics, and for that I'm profoundly grateful.

The source of Deep Dive is available on my GitHub at luizmugnaini/deep-dive. Additionally, a compiled version of the document can be found here. Please note that this document may frequently be out of date.