This is a collection of notes I have made during my graduate and undergraduate studies. They are primarily intended for personal use, but may be useful to others.
Notes on Margulis construction of high-girth 4-regular graphs: pdf (heavily based on the book by Davidoff, Sarnak and Valette).
Combinatorics (English) (pdf, changelog)
Notes based on the lectures given by Oriol Serra and Simeon Ball in the fall of 2021.
Advanced undergraduate course in combinatorics. Some sections are incomplete.
Estructures algebraiques (Catalan) (pdf, changelog)
Notes based on the lectures given by Jordi Guardia in the fall of 2020.
Introduction course to abstract algebra. It does not follow the usual order: it starts with rings, fields, and only at the end introduces groups. The second part of the chapter on groups and the last chapter about modules are missing.
Teoria de la probabilitat (Catalan) (pdf, changelog)
Notes based on the lectures given by Anna de Mier in the fall of 2020.
They cover the first half of the course, until the midterm exam.
Matemàtica Discreta (Catalan) (pdf - last updated on 11/06/20)
Notes based on the lectures given by Oriol Serra in the spring of 2020.
First half of an undergraduate course for freshmen that intends to be an introduction to combinatorics.
Quantum Physics (English) (pdf - last updated on 20/05/20)
Notes based on the lectures given by Jordi José and Manuel Linares in the fall of 2019.
Introductory course to quantum physics. It presents the historical developments that led to quantum physics, introduces Schrödinger's equation, derives the Hydrogen atom orbitals, and introduces some techniques for dealing with multiple-electron atoms. It does not use bra-ket formalism.
OIE geometry training 2026 (Spanish) (pdf)
Solutions to some computational geometry problems aimed at high-school students preparing for the International Olympiad in Informatics.