Modern Differential Geometry
These are some of my notes from my Modern Geometry course in university. They cover some of the basics of differential geometry, and were taken from a combination of lectures and textbooks.
View/Download PDFMath & Physics Notes
Welcome to my collection of math and physics notes. This section is a work in progress, where I upload insights, research, and notes from my various projects. While primarily for my own use, I hope they may also be useful to others. I plan to expand this section and develop it more in the future.
Available Notes
Combinatorics
These are two interesting research projects I worked on a few years ago with Greg Dresden involving visual interpretations of integer sequences.
Tiling a 2 x n Board with Dominos and L-Shaped Trominos
We count the number of ways to tile 2 x n rectangles and bracelets using dominos and L-shaped trominos. We show that these 2xn tilings can be related to 1xn tilings with squares, dominos, and two colors of k-minos for k ≥ 3, and we discover some new identities for old sequences.
View/Download PDFConvolutions of Sequences with Similar Linear Recurrence Formulas
We show that a collection of convolution formulas involving the Fibonacci, Tribonacci, Pell, Jacobsthal, Narayana, and other number sequences can all be derived from a single elegant formula so long as the sequences follow certain mild requirements. We give many examples, both old and new.
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