Gallery — Math

We'll show that probability and uncertainty can be convert each other through quadratic equation. And, we'll also show that the quadratic equation can be transform to homogeneous equation, and some assumptions generate symmetric forms.

The classes smfbook and smfart are intended to help the preparation in LaTeX of the monographs and articles to be published by the French Mathematical Society.

A basic understanding on Bayes' theorem and how to apply it to baseball statistics.

Aufgaben zum Thema Grundrechenarten werden mit LuaLaTeX automatisch erzeugt. LuaLaTex provides math problems for the four basic arithmetical operations automatically.

A short note on the motivation for n-gram frequency discounts in the context of the Katz backoff algorithm.

A simple proof of Riemann's Rearrangement Theorem. Also called Riemann's series theorem.

A Statistics paper on Correlation and Linear Relationships.

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.

A footnote in OpenIntro Statistics, 3rd Edition, Section 5.5.2, Analysis of Variance (ANOVA), relates an identity for the sum of squared errors (SSE).