Math

In this section, you will Find a selection of the coursework I completed throughout my master's studies.

1st Semester - FALL 2022

•  Abstract Algebra

Homework list (in Spanish) 

• Algebraic Topology Principal Reference: Allen Hatcher. "Algebraic Topology", Cambridge University Press, 2005 

• Ordinary Differential Equations

2nd Semester - SPRING 2023

• C* Algebras. Principal Reference: R. Kadison and J. Ringrose. "Fundamentals of the Theory of Operator Algebras". Vol. 1. American Mathematical Society, 1997.

Homework list (in English and Spanish)

• Complex Analysis. Principal Reference: First 21 pages of Lars Hörmander. "An Introduction to Complex Analysis in Several Variables". North Holland; 3rd edition (January 16, 1990). 

• Problem-solving Seminar

• Functional Analysis. Principal References: 

  1. 1. 1. 1. 1. 1. 1. 1. S. Axler, Measure Integration and RealAnalysis, 2020 

                       2. Mohammad Jabari, Functional Analysis notes.

3rd Semester - FALL 2023

• von Neumann Algebras. Principal Reference: R. Kadison and J. Ringrose. "Fundamentals of the Theory of Operator Algebras". Vol. 1. American Mathematical Society, 1997.

Homework list (in English)

• Free Probability. Principal References: 

  1. 1. 1. 1. 1. 1. 1. 1. A. Nica & R.Speicher. Lectures on the Combinatorics of Free Probability. Cambridge University Press

                       2. J. Mingo & R. Speicher. Free Probability and Random Matrices. Springer.

• Special Activities (Thesis advances)

4th Semester - SPRING 2024

• Category theory

• Thesis Seminar

General Exams Approved 

• Abstract Algebra

• Topology

• Measure Theory