Math: my Biggest Passion
For many years, I have been passionate about mathematics. I have entered into some math competetions, and I study math outside of school. What I love most about it is its intriguing and wonderful nature.
Ways I enjoy mathematics
Over the years, I have experienced mathematics in many different ways. I have joined Euler Circle, which exposes high school students to undergraduate-level maths. In school, I was part of the advanced problem solving class, which participated in many math competetions on behalf of the school. I have made many friends at the Alphastar Camp. I enjoy comptetitions, and I have pariticpated in the AMC 12as well as the AIME. I particiapted, as well, in the Stanford Math Circle
My Favorite Areas of Math
Complex Analysis
Complex analysis is one of my favorite areas of mathematics . It is truly beautiful and wonderfully marries complex numbers with calculus. So many of the theorems of real analysis gain new light in complex analysis
Type Theory
Type theory solidified my understanding of the relationship between computers and mathematics, and how mathematics can directly be applied to computer science. By having computers execute proofs using type theory I gained a new appreciation for rigor of proofs.
Abstract Algebra
Abstract Algebra demonstrated to me that mathematics is all about abstraction. I now see groups everywhere, from vectors to the complex numbers, and I feel I can now look at the world of mathematics through the lens of groups, rings and fields.
Read My Papers
Automata Thoery
on Automata Theory, Generating Functions, and Finite State Machines
Perron Frobenius Theorem
Applications of the Perron Frobenius Theorem
Error Correcting Codes
Error correcting codes as they are used, and on their derivations
Real Projective Geometry
A new kind of geometry, and how constructions work in it.
Boolean Algebras
An introduction to Boolean Algrebras and the Stone Theorem.
Continued Fractions
How continued fractions are used in irrationality proofs
Elliptic Curves In Cryptography
The application of ellpiptic curves to cryptography (ECC)
Consequences of the Riemann Hypothesis
What is the impact of the most famous conjecture: the Riemann Hypothesis
The Continuum Hypothesis
The unresolvable question in set theory, and its applications
Proof of Unique Factorization from the axioms of integers
Prof. Jim Fowler said
"Unique factorization is a theorem that
people are insufficiently appreciative of"
Denotational Correct Computer Arithmatic
Using the denotational design technique of Conal Elliott to prove the formal correctness of computer circuits
Denotational Correct Computer Arithmatic Talk
Using the denotational design technique of Conal Elliott to prove the formal correctness of computer circuits