Computational Mathematics: An Introduction to Deep Learning.

• Grant number: 25/23101-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2025
• End date: November 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Kauan dos Santos Loche
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Company: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC)
• Associated research grant: 23/14427-8 - Data Science for Smart Industry (CDII), AP.PCPE

Abstract

In this Scientific Initiation project, we will analyze some mathematical and computational concepts used in deep learning algorithms. The theoretical topics of interest in the project are part of the Numerical Linear Algebra and Numerical Calculus disciplines: concepts of vectors and matrices, the least squares method, matrix decompositions, eigenvalues ¿¿and eigenvectors, etc. Regarding computational strategies, this project will address methodologies such as dynamic matrix allocation, implementations for solving linear systems, optimization techniques, etc. In the final stage of the project, we will dedicate ourselves to studying applications involving machine learning and deep learning.