In my spare time, I enjoy writing expository notes.

machine learning

• Supervised Learning – An exposition to basic machine learning concepts such as gradient descent, k-nearest neighbors, soft-margin SVM from a mathematical viewpoint, using real-world examples. (34 pages)

mathematics

• A Brief History of Mathematics and Physics – A timeline of major developments in mathematics and physics over the past 400 years, with an emphasis on the interplay between the two fields and the universal importance of symmetry. (10 pages)

• Almost Integers – An introduction to the number theory behind the existence of numbers such as $e^{\pi\sqrt{163}}$, which are mysteriously close to being integers. (6 pages)

• Hartogs’s Phenomenon – An exposition of one of the most striking results in the theory of complex analysis in several variables. (6 pages)

• Modular Curves – An overview of the basic theory of modular curves as spaces of isomorphism classes of elliptic curves. (12 pages)

• Algebraic Geometry – Some introductory notes on classical algebraic geometry. (20 pages)

• The Ring of Cyclotomic Integers – This note contains a derivation of the ring of integers in a cyclotomic field $\mathbb{Q}(\zeta_{n})$. By passing to the $p$-adic numbers, we are able to avoid many of the technicalities in the standard proof of this fact. (3 pages)