Since 2020, I started documenting all of my studies in mathematics. This process ended up generating something that resembles a book. It is with the hope of illuminating the path for fellow nerds that I decided to share my collection of notes publicly.

Deep Dive is the title I've chosen for my ever-evolving collection of personal notes. I claim absolutely no originality in any of my writings, instead they can be thought as a compilation of lectures I've watched, as well as books and papers I've read --- but written down on my own words and with my own explanations.

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. Therefore, I must acknowledge the presence of numerous linguistic and mathematical errors scattered throughout this document. As time permits, I plan to revise and refine this work in some distant future --- rectifying most of my silly mistakes and errors I've made along the way.

The first propulsor of this set of notes 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 category theory --- it was probably my first introduction to actual modern mathematics. My interaction with this draft settled my journey in mathematics, and for that I'm profoundly grateful. For this exact reason I thought of making Deep Dive available for anyone that might be interested in this kind of writing.

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 Please note that this document may be frequently out of date.

Last update: 2025-01-06.