All teaching materials linked below are in Spanish.
Centro de Investigación en Matemáticas (CIMAT), Guanajuato (2019–2020)
Fall 2020: Teoría de números algebraicos.
Introductory course of algebraic number theory. Online due to COVID (videos available on YouTube).
Fall 2019: En torno de las funciones zeta aritméticas.
A series of lectures about Hasse–Weil zeta functions, with some calculations and Dwork’s proof of rationality.
Some activities for school kids
Fall 2021: Un repaso de geometría.
An interactive presentation/quiz with some theorems in geometry.
Fall 2021: Teoría de números en ejercicios.
Some exercices in elementary number theory.
Universidad de El Salvador (2016–2019)
In 2016–2019 I collaborated with the Ministry of Education of El Salvador (Central America) and the Department of Mathematics of the University of El Salvador, giving lectures to undergraduate and master students. It was a very exciting endeavor overall. I spent three full semesters in San Salvador: Spring 2018, Fall 2018, and Spring 2019. Here is a list of my major teaching activities there.
August 2019: Teoría de esquemas.
An advanced seminar/minicourse explaining the definition of a scheme (for master students who took an introductory course of algebraic geometry).
Spring 2019: Bases de Gröbner.
A course of computational commutative algebra: Gröbner bases, with examples in Macaulay2.
Spring 2019: Álgebra I.
An undergraduate algebra course; first semester, starting from rings. (This was my last semester in San Salvador, and another professor took over the course for the second semester.)
A master course of commutive algebra, loosely based on the first chapters of Eisenbud’s book.
June 2018: Categorías.
A minicourse for master students treating the basic notions of categories, functors, natural transformations, adjunctions, etc.
April 2018: Números p-ádicos.
An introduction to p-adic numbers for master students. This was given as a part of a standard point-set topology course, to show what happens with ultrametric spaces.
Spring and Fall 2018: Álgebra I y II.
A fairly standard one-year undergraduate course of algebra: groups, rings, fields, etc.
February 2017: Números de Bernoulli.
A minicourse for undergraduates about Bernoulli numbers, assuming almost no special background.
August 2016: Álgebra homológica.
An intensive minicourse of homological algebra: abelian categories, derived functors, etc.
Here is a separate page where you can find my teaching materials prepared in San Salvador:
- Mis cursos en la Universidad de El Salvador (2016–2019)
I plan to eventually share all LaTeX source code for my teaching materials. I have found it helpful for myself to have old lecture notes within easy reach, to be able to copy and paste some complex diagrams and pictures. You may already find some materials at my GitHub page: https://github.com/alexey-beshenov/.
Anything else is available upon request.
Any use is encouraged and any feedback is welcome.