Dennis Chen
I have written what (accidentally) became a small book on graduate-level abstract algebra. It is not meant to be thorough, it is just meant to give you an idea of the content you might encounter and a base of intuition. I am writing a difficult honors high school geometry textbook, entitled A brief foray into Euclidean geometry. A preview of the third chapter is available. Many references are broken; specifically, those to theorems/problems/etc of other chapters of the text. Additionally, hints and solutions still need to be written, and the chapter will occasionally be updated with new hints and solutions. Why I study mathematics On “well-defined” functions A proof of the Principle of Inclusion-Exclusion Notes from my Fall 2023 math contest course. The Cantor Schroeder-Bernstein Theorem A proof, via direct construction, that given sets 𝐴 and 𝐵 , the existence of an injection 𝑓 : 𝐴 → 𝐵 and an injection 𝑔 : 𝐵 → 𝐴 implies the existence of a bijection from 𝐴 to 𝐵 . Jor