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I have discovered that the only way I am capable of holding on to information is by writing up notes on the subject. The result is a collection of expository notes of varying quality which I have compiled here.
Core Class Notes:
As preparation for my qualifying exams, I wrote up a set of notes for each of the three core classes
Algebra Core Notes.pdfAnalysis Core Notes.pdfDiff-Geo Notes.pdfNumber Theory Stuff:
Here are some notes I have written as I have studied various things in number theory.
Personal Hodge Theory Notes.pdfProof of Mordell's Theorem.pdfReductions via Wach Modules.pdfChaotic Dynamics:
When I was an undergraduate, I studied discrete dynamical systems under Robert Devaney. In particular, we concentrated on systems which exhibited chaotic behavior. As part of my senior thesis, I wrote a program which generated Julia and Mandelbrot sets for a new family of complex polynomial maps which I include here.
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