A study on the number of zeros of a polynomial in the real line

• Grant number: 19/07066-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2019
• End date: August 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Vanessa Avansini Botta Pirani
• Grantee: José André Oscar Pinto
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

This research project proposes the study of classical results related to the behavior of zeros of polynomials, with special attention to results which determine the number of zeros in the real line, as the Budan-Fourier Theorem, the Descartes' rule of signs and the Sturm Theorem, for example. Some applications involving the use of this rule will also be studied, such as in expressions of Financial Mathematics. In addition, it is a subject not completely covered within the disciplines of most of the courses of Degree in Mathematics in Brazil. Therefore, it is intended that the candidate conduct a study on the behavior of zeros of polynomials, in general, so that he acquires a solid base of knowledge in this area to extend his studies, in the future, in a post-graduate course.