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I am a sophomore studying computer science and mathematics at Carnegie Mellon University. I am also a CS251 teaching assistant.
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.
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 and , the existence of an injection and an injection implies the existence of a bijection from to .
The composition factors of a group (if a composition series exists) are unique up to isomorphism and permutation; every finite group has a composition series. This is a partial analogue of the Fundamental Theorem of Arithmetic for finite groups. Based on a series of lectures in Algebra I (21-610) by Dr. James Cummings.
I am teaching a variant sudoku puzzle StuCo in the spring of 2024. Its course code is 98-049. If you have any interest in logic puzzles or learning about them I hope you consider taking the course.
Unlike the previous logic puzzle StuCo, my class will be entirely variant sudoku puzzles.
You can find the current course curriculum at its Git repository. All details stated there are tentative too.