Factoring the Sum/Difference of 𝑛th Odd Powers with De Moivre's Theorem and Roots of Unity

February 26th, 2024

I sought to factor the sum and difference of 𝑛th Odd powers in an alternate form using De Moivre's Theorem and roots of unity, deriving an interesting equality that is helpful in evaluating certain trigonmetric summations.

Python Implementation of the Quadratic Sieve Algorithm to Break RSA

March 31st, 2024

I learned about the quadratic sieve algorithm and wrote an algorithm (with some help) that employs it to break the RSA encryption scheme.

Magnetic Field Generation for Tau Disaggregation in Alzheimer's Disease, Part 1: Motivations and Magnetic Field Generation

May 29th, 2024

In this first article outlining my summer research project at USC, I briefly describe the therapeutic motivations for exposure of Tau protein, a key player in Alzheimer's Disease, to both static and alternating magnetic fields. Then, I spend the rest of the article explaining my DIY magnetic field generator.

Magnetic Field Generation for Tau Disaggregation in Alzheimer’s Disease, Part 2: Potential Mechanisms

Jun 20th, 2024

In this second article outlining my summer research project at USC, I fully outline my motivations for using magnetic fields to combat Alzheimer's Disease from a variety of physiological angles.

Supplement: Extending Roots of Unity Factorization Method to the Sum and Difference of nth Even Powers and Discussing More Advanced Applications of the Theorem

Jun 21th, 2024

In this supplement to my first article on this site, I extended by Roots of Unity Factoriztion Method to the sum and difference of even powers. Likewise, I found more complex trigonmetric summations to share! Beware, they're exercises for the reader!

Final Supplement to Proof: On the Generalized Evaluation of Ordered Sums of Cosine Products with Arguments Progressing in an Arithmetic Sequence

October 12th, 2024

In this final supplement to my first article on this site, I use my formula for the sum/difference of nth odd powers to derive a generalized closed-form expression for the ordered sum of cosine products.