Gallery — Math

Short Sectioned Assignment LaTeX Template Version 1.0 (5/5/12) This template has been downloaded from: http://www.LaTeXTemplates.com Original author: Frits Wenneker (http://www.howtotex.com) License: CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)

As part of the NASA IMPACT program to model mechanical interactions with bodies in space such as comets, asteroids, and other Near Earth Objects (NEOs), the Colorado School of Mines team is designing a motor stage apparatus to interact with JSC-1A regolith simulant surfaces. This initial study involved development and testing of a prototype motor stage apparatus which was used to drive three types of probes into JSC-1A surfaces while collecting force data under standard Earth atmospheric conditions. The probes used were a conical-tipped probe, a wedge-tipped probe, and an anchoring probe. Main goals of the prototype system were to acquire general force trends for each interaction, and to isolate the most important design features for a more-complex in-vacuum system. Our data revealed force interactions that were very small in magnitude—on the order of tenths of Newtons—and more complex than our simple stiff beam probe and mount model could accurately predict. Our results lead us to recommend a more complex experimental model that can accurately represent deflection in the probes while also allowing for better measurement of regolith movement near the tip of the probes. Specifically, we recommend the following design features for the in-vacuum system: a load cell capable of measuring at very low ranges (thousandths of Newtons), reliability of structural axis alignment between trials, a robust mounting system that can accommodate each different type of probe, and consistency of sample preparation between trials.

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A LaTeX template for notes-taking.

Skabelon til midtvejsrapporten for kurset Førsteårsprojekt i matematik ved Institut for Matematiske Fag, Københavns Universitet

A sample of some problem types and LaTeX commands that may be useful in a math exam. Uses the exam document class.

This template does not comply with the design manual at the University of Oslo from 2022. Beamer theme for the Department of Mathematics at the University of Oslo. Documentation: https://github.com/martinhelso/MathDept

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!

Brief LaTeX file for HHO section