Gallery — Math

In this paper, we do exactly what the title implies: prove the Čebotarev Density Theorem. This is an extremely valuable theorem because it is a vast generalization of Dirichlet's Theorem on primes in an arithmetic progression. Our theorem goes even further to the case of other number fields; we will show that the prime ideals in an imaginary quadratic field K are virtually equidistributed among the conjugacy classes of Artin symbols in the Galois group of a Galois extension L over K. Note that L need not be abelian over K!

In this article we will discuss a new type of notation for homogenous polynomials of $3$ variables, and its applications in solving Olympiad inequalities using the AM-GM inequality, Muirhead’s Inequality, and Schur’s Inequality. I suggest reading [1] first for a clearer explantion on the mechanics of this notation. This article is more focused on the applications to Olympiad inequalities

A leaflet created for a Math class that I conduct during this term.

Sistemas Lineares

see title

CS 155 HW 9

Two Snow Plows Problem

This template can be used for typesetting solutions to homework assignments. We define a document class that includes a number of useful packages, defines shorthand macros for commonly used constructs and makes it easy to typeset answers to exercises. The template default content demonstrates how various tasks can be achieved in LaTeX as well: mathematical notation and many symbols, typesetting a table, including a figure, et cetera.

A non-rigorous proof of the Lorentz factor and transformation in Special relativity using inertial frames of reference.