Mathematical analysis and linear algebra with applications

• Grant number: 18/19642-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2019
• End date: December 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: Abimael Alves de Oliveira Neto
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main purpose of this project is the study of Mathematical Analysis, with the goal of giving the students a more profound knowledge of the field and to help them develop their academic and professional careers. The students will present lectures in English, alternating between them. The subjects to be studied are numerical sets (and its properties), basic notions of topology in metric spaces, continuous and differentiable functions, sequences and series of complex numbers and complex functions as well as measure theory and integration, more specifically Lebesgue integral and its applications. The references for the study will be the books "Principles of Mathematical Analysis" by Walter Rudin and "A Integral de Lebesgue e suas Aplicações" by C. S. Hönig. These books will also help a future study of the theory of linear operators in vector spaces in finite dimensions, which includes from basic notions of vector spaces to positive matrices. In this case the main source will be the book "A Short Introduction to Perturbation Theory for Linear Operators" by T. Kato.