The following project is in the field of combinatorics. It is a broad summary of the probabilistic method. Basic definitions and theorems, needed for the proper use of the probabilistic method, are introduced. Simple examples are provided in order to illustrate the theory in practice and to introduce the method itself. The project focuses on competitive problems from major national and international competitions, in whose solutions could be used probabilistic method, contributing to their briefness. One of our main aims is demonstrating the broad application of the probabilistic method not only in some theoretical fields of mathematics, but also in competitive problems. The problems in the abstract are with increased difficulty and we believe, they can serve as a preparation for mathematical olympiads and competititons.
This project provides a LaTeX document class suitable for writing academic dissertations and thesis according to the formatting rules established by the Alberto Luiz Coimbra Institute for Graduate Studies and Research in Engineering (COPPE/UFRJ).
The 'coppe' class contains a minimalist set of macro commands which allows its users to create the required textual elements following the COPPE/UFRJ dissertation/thesis guidelines. Among these elements, there are a front cover, a title page, cataloging details, native and foreign languages abstracts, table of contents, and list of bibliographic references.
Although it is tied to the COPPE/UFRJ guidelines, it can be easily ported to other institutions.
This version follows the document:
Norma para a Elaboração Gráfica de Teses/Dissertações COPPE/UFRJ Aprovada pela CPGP em 15 de julho de 2008 Com correção no Anexo III, páginas 19 e 20, em 01/10/2009 (Revisada em 10/09/2010) (Revisada em 26/11/2019 – Alteração da Folha Aprovação, Anexo III, páginas 22 e 23)
Important Notice - ReadMe first!
This project is NOT officially supported by COPPE/UFRJ. All of its content is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. It is under the GNU General Public License version 3.
Vicente Helano, George O. Ainsworth Jr, Paulo Laranjeira da C. Lage, Eduardo Mangeli