Gallery — Math

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Dicas para a preparação de listas de exercícios da disciplina MAC0239 (Introdução à Lógica e Verificação de Programas) no IME-USP. Tips for preparing exercises for MAC0239 (Introduction to Logic and Program Verification) at IME-USP.

In this project, students create a two-dimensional shape with nonuniform density, finds its center of mass, and hang it from a mobile. The various portion of the project address the differences and relationships between computing the center of mass of a discrete set of point masses and a lamina. Included here is also a sample solution to help students formulate their own well-written solutions. Also, in the LaTeX code are a few comments to address some of the basics of LaTeX and Overleaf.

Lecturas tomadas de la clase de M.Sc. Fidel Ordoñez, Carrera de Matemática UNAH, 2014

It's easy to find out how many combinations you can have if you know the total number of items, and the number of items you are combining. It's a little harder to do that in reverse. This document shows how to find the total number of items if you know how many are combined at a time, and the total number of combinations.

Experiment on events

This is a math homework template

In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in \(T\) \(\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.\)

Resuelva la ecuación