Gallery — Math

This is the template of a regular article to Mathematica Applicanda — the Annales Societatis Mathematicae Polonae Series III published by Polish Mathematical Society.

HoTT

Easy PSET template with examples.

Latex assignment of the definition of a derivative

Linear regression is one of the most widely used statistical methods available today. It is used by data analysts and students in almost every discipline. However, for the standard ordinary least squares method, there are several strong assumptions made about data that is often not true in real world data sets. This can cause numerous problems in the least squares model. One of the most common issues is a model overfitting the data. Ridge Regression and LASSO are two methods used to create a better and more accurate model. I will discuss how overfitting arises in least squares models and the reasoning for using Ridge Regression and LASSO include analysis of real world example data and compare these methods with OLS and each other to further infer the benefits and drawbacks of each method.

A short look at how to compute the domain of a composite function.

This is a report on the Dijkstra's Algorithm

Teoría de números

Identifying whether a degree matrix has an edge-disjoint realization is an NP-hard problem. In comparison, identifying whether a tree degree matrix has an edge-disjoint realization is easier, but the task is still challenging. In 1975, a sufficient condition for the tree degree matrices with three rows has been found, but the condition has not been improved since. This paper contains an essential part of the proof which improves the sufficient condition.