Articles — Math

The Schroeder-Bernstein theorem

A simple derivation of the relationship between dot products and cosines. I wrote this reacquaint myself with LaTeX.

The lecture notes are based on the number theory topics course on 3 Feb, 2016.

Based on the paper Sometimes Newton's Method Cycles, we first asked ourselves if there were any Newtonian Method Cycle functions which have non-trivial guesses. We encountered a way to create functions that cycle between a set number of points with any initial, non-trivial guesses when Newton's Method is applied. We exercised these possibilities through the methods of 2-cycles, 3-cycles and 4-cycles. We then generalized these cycles into k-cycles. After generalizing Newton's Method, we found the conditions that skew the cycles into a spiral pattern which will either converge, diverge or become a near-cycle. Once we obtained all this information, we explored additional questions that rose up from our initial exploration of Newton's Method.

Geometría Analítica

Fluid Report

A Statistics paper on Correlation and Linear Relationships.

A very quick and easy to understand introduction to Gram-Schmidt Orthogonalization (Orthonormalization) and how to obtain QR decomposition of a matrix using it.

An overview of the Cantor Set and its connection to counting.