LaTeX templates and examples — Math

Teoría de números

A rigorous construction of the field of real numbers: the unique (up to isomorphism) completely ordered field with the least upper bound property; along with various formulations of completeness and with a postlude on the measure of sets.

We describe what mimetic interpolation is and why it is critical for some pre- and post-processing tasks. A simple test case shows how using bilinear interpolation for a flux calculation introduces numerical errors that depend on the grid, the number of segments and the number of quadrature points. In contrast, mimetic interpolation will return the exact result regardless of the grid resolution and the number of segments.

Template to use in PUC-Rio Optimization course 2019.1

A LaTeX template for preparing documents for the Mathematical Modeling and Boundary Value Problems Conference. This is a LaTeX template (version from 2019 Feb. 25) for preparing documents for All-Russian Scientific Conference of the Mathematical Modeling and Boundary Value Problems [Matem. Mod. Kraev. Zadachi, Samara, Russian Federation]. It was submitted by an author writing for the 11th All-Russian Scientific Conference with international participation (MMiKZ’19). The various components of your paper [title, text, heads, etc.] are already defined on the style sheet, as illustrated by the portions given in this document. Author: Mikhail N. Saushkin (msaushkin@gmail.com)

Can there be a polynomial with infinite solutions? If so, would it be a polynomial? Also, would it have an infinite solution set? Let's find out.

A template Ximera activity.

Stručný přehled vzorců a vztahů z předmětu PST. Neobsahuje všechny triviální věci (pravděpodobnost jevu) a některé komplikovanější, které se nedají snadno stručně shrnout (CLT, Markova nerovnost etc.). Veškerou většinu ostatní potřebné výbavy na zkoušku ale ano.

This research paper aims at exploiting efficient ways of implementing the N-Body problem. The N-Body problem, in the field of physics, predicts the movements and planets and their gravitational interactions. In this paper, the efficient execution of heavy computational work through usage of different cores in CPU and GPU is looked into; achieved by integrating the OpenMP parallelization API and the Nvidia CUDA into the code. The paper also aims at performance analysis of various algorithms used to solve the same problem. This research not only aids as an alternative to complex simulations but also for bigger data that requires work distribution and computationally expensive procedures.