Expository Papers

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Here is a collection of notes and expository papers I've written over the last few years. Please note that the majority of these papers began their lives as personal notes, so let me know via email if the writing is not so clear!

Geometry

A neat way to compute the lines contained in a projective hypersurface.
A note on (12₃)-configurations from Grünbaum's book, including a word on deficiency complices.
Exterior Products and Plücker Coordinates.
An outline of computing the canonical divisor of ℙ² using an explicit by-definition construction.
Some of my notes from first learning about Chern classes and Schubert cycles.
A short demo on why the group law of a nodal cubic curve is multiplicative (and why the nodal cubic is rational).
A dive into Weierstrass points on an algebraic curve.
How points and tangent lines can determine conics in ℙ². This explains some of the gadgets in my gallery.
The 27 lines on a cubic surface are the complete intersection of the cubic with a nonic surface, proven using divisors.

Algebra

Combinatorics

Probability

Calculating the probabilities of AB and AA appearing in a string of n random Latin letters.