Diophantine Geometry (In progress)
Topoi Theory (To Come)
Here is a compilation of pdfs that I have written, more precisely, I have taken multiple books in each field and have combined them each into a comprehensive study guide. Each pdf consists of the bulk/basics of each field, with proofs and examples being omitted. They are mostly complete, but will always be a work-in-progress. Whenever I commit to knowing/remembering something forever, I organize the material in such a way so that it is easy to engrain the information in my head… these books accomplish that.
I cannot proceed without giving credit to those authors whom I have learned most from, and whose material I have chosen to use in my references. They are: Tenenbaum, Montgomery, Vaughan, Apostle, Ireland, Rosen, Titchmarsh, Jarvis, Marcus, Alaca, Lang, Ash, Samuel, Neukirch, Tao, Vu, Nathanson, Ruzsa, Mac Lane, Leinster, Awodey, Hungerford, Dummit, Foote, Palka, Stein, Bass, Royden, Gordon, McNulty and Oxley.