TEACHING
DOCENCIA NA USC. Durante o curso 2023-2024 impartín as seguintes materias.
Álxebra Lineal e Multilineal (2º curso). Libro con teoría e problemas publicado en Edicións USC.
Xeometría Linear (2º curso). Libro con teoría e problemas (aínda en preparación, pendente de acabar). Comentarios benvidos.
Matemática Discreta (1º curso, Grao en Intelixencia Artificial). Apuntamentos de teoría (versión preliminar). Comentarios benvidos.
TFGs e TFMs.
Se estades interesados en que vos dirixa un TFG ou un TFM, escribídeme un mail ou vide polo despacho.
No relativo aos TFGs, teño diferentes propostas:
-> TFGs de introdución á teoría de números (problemas relacionados con curvas elípticas, formas modulares, teoría alxébrica de números).
-> TFGs orientados á ensinanza secundaria, especialmente relacionados con temas de Olimpíadas Matemáticas.
-> Se tedes algunha outra proposta, tamén estou aberto a discutila!
Os TFMs que oferto están relacionados coa teoría de números, en concreto coas formas modulares, as representacións de Galois e os aspectos p-ádicos desta teoría (teoría de Iwasawa, por exemplo).
COURSES TAUGHT AT WARWICK UNIVERSITY
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Iwasawa theory (Fall 2021). TCC course (16 hours course for graduate students at Warwick, Oxford, Imperial, Bath and Bristol).
TEACHING ACTIVITY DURING MY PHD (At UPC-BarcelonaTECH)
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Integral Calculus (Fall 2020, problem sessions, 30 hours). 2nd course, Bachelor in Mathematics.
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Real Analysis (Spring 2020, problem sessions, 30 hours). 2nd course, Bachelor in Mathematics.
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Differential Calculus (Spring 2020, problem sessions, 30 hours). 1st course, Bachelor in Mathematics.
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Complex Analysis (Spring 2019, problem sessions, 30 hours). 2nd course, Bachelor in Mathematics.
Between January 2017 and December 2018, I was the responsible of the Problem Workshop from the Faculty of Mathematics, addressed to answer doubts and questions from 1st year students (similar to TA in the anglosaxon system).
I have supervised 3 bachelor thesis at UPC, a 4th year project (Warwick) and many bachelor and master thesis in Santiago.
-> Jorge Gómez (academic year 24-25): Curvas elípticas e formas modulares.
-> Gabriel Fernández (academic year 24-25): O teorema de densidade de Chebotarev.
-> Lucas López (academic year 24-25): Unha andaina polo último teorema de Fermat.
-> Lucía Vendrell (academic year 24-25): Teoría de corpos de clase.
-> Inés Aguín (academic year 24-25): Teoría alxébrica de grafos.
-> Borja Quintela (master thesis 24-25): Introdución á teoría de Iwasawa.
-> Javier Polo (master thesis 24-25): A función L p-ádica dunha forma modular.
-> Lois Omil (master thesis 23-24): Familias de Hida.
-> Juan Carlos Regueiro (academic year 23-24, cosupervised with Daniel Cao): Formas modulares e sumas de cadrados.
-> Héctor Varela (academic year 23-24, co-supervised with Felipe Gago): A teoría da multiplicación complexa.
-> Laura Antela (academic year 22-23, co-supervised with Felipe Gago): A xeometría do triángulo nos problemas de olimpíadas.
-> Lewis Howard (academic year 21-22): Ribet's lemma.
-> Marta Altarriba (Spring 2019): La conjectura de Sato-Tate (On the Sato--Tate conjecture).
-> Andreu Tomas (Spring 2019): Mock modular forms.
-> Carles Checa (Spring 2018): Una aproximació a la teoria de cossos de classe (An approximation to class field theory).
I sometimes collaborate with the training for the Mathematical Olympiad. In the past I wrote some training materials, that you can find here (mainly in Spanish). I hope to post them once I have time to write them in a more suitable way!
Here you have some miscellaneous materials of other courses I have taught in the past:
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Book (in Catalan). Una inroducció a l'anàlisi real. 100 problemes resolts. Amb S. Boza i J. Rué.
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Alguns problemes resolts de Càlcul Integral. Aquí.
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Alguns problemes resolts de Càlcul Diferencial. Aquí.
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Classe d'aplicacions del càlcul de primitives (C1V; FME, 3/12). Aquí. Classes de càlcul de primitive (C1V; FME, 23/11 i 30/11). Solucions primitives. Aquí.
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Class from Maths Foundations: Introduction to arithmetics. Here.
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In April 2017 I taught the course Basics of statistics at Harbour Space (Barcelona). It was a 60 hours course who tried to give mathematical tools from probability and statistics to economists and businessmen. Here you can find the syllabus, some short notes (summaries), the list of problems and assignments (with solutions) as well as the exams and quizzes.
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I once wrote (in Spanish) some detailed notes about the proof of the inverse function theorem that I explained to students of the first year. Here.
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I am interested in politics and the analysis of different electoral systems. Here some comments about the last Spanish elections (in Spanish).