Mathematics & Computing Science Student, Programmer, Researcher

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About Me

I am currently a student at University of Alberta majoring in Computing Science Specialization alongside Mathematics. As of Summer 2019 I am working at The Maple Lab with Professor Karim Ali. I am also a developer of Asymptote alongside Professor John C. Bowman, specializing in GUI design and rendering engine. Apart from that, I also tutor at Decima Robinson Support Centre as an undergraduate tutor.


My Interests
\[ \oint_{\gamma} f(z) \, dz = 2\pi i \sum_{i=1}^n \nu(\gamma, z_i) \text{Res}(f,z_i) \]
The Residue Theorem, perhaps in my opinion the most elegant formula out there.

My primary interests lies in Pure Mathematics, particular in Complex Analysis, Algebra including Number Theory and an intersection between analysis and algebra which includes Analytic Number Theory. Recently, I have been studying Algebraic Number Theory alongside Measure Theory, which deals which how prime numbers behave in various algebraic field extensions and what results can be derived from them. In particular, one has the Class Number Formula which describes the size of the Ideal Class Group of each number field. That formula is generally derived from both Algebra and Analysis and serves as a foundation for further study.

\[ a^{\varphi(n)} = 1 \; (\text{mod } n), \quad \text{for all } a\in \mathbb{Z}_p^{\times} \]
Euler's Theorem, a result that establishes modern public-key cryptography.

In my secondary interests, I am also interested in Artificial Intelligence Development, Algorithm Design and analysis of programs. In particular, I am interested in how we can use logic and theory to mechanize proofs and develop further methods of program analysis. Many of my work as of recently are in Theoretical Computing Science, focusing on detailed analysis of algorithms, methods of AI and as stated, mechanizing proofs alongside development of test cases in string problems.



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