Lebesgue integral, functional analysis and linear algebra

• Grant number: 13/05199-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2013
• End date: April 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Hildebrando Munhoz Rodrigues
• Grantee: Bernardo Augusto do Prado Rivas
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main objective of this project is the study of fundamental concepts of Analysis, Lebesgue Integral and Functional Analysis, in order to deepen the knowledge of students in mathematics and gives them a solid foundation to improve their academic and professional lives. This project is divided into two parts. The first is intended for the study of the measure theory, more specifically the Lebesgue integral and their applications, such as the integrated function of parameters depending on the derivation and integration signal. For this purpose, "Principle of Mathematical Analysis" by Walter Rudin and "An Integral de Lebesgue e suas Aplicações" by C. S. Hönig is going to be the books studied. In the second part, we will study topics in operator theory of finite-dimensional vector spaces, ranging from the basics of vector spaces and normed vector spaces to positive matrices. This module will be mainly used the book "A Short Introduction to Perturbation Theory for Linear Operators" by T. Kato. We will use other reference books as convenient, whose relationship is presented in the references. As a complement, the students will become familiar with the software AMS-LaTeX, which will be used for writing the partial and final reports. (AU)