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TEACHING

DOCENCIA NA USC. Durante o curso 2023-2024 impartín as seguintes materias.

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Álxebra Linear e Multilinear (2º curso). Libro con teoría e problemas. Calquera comentario e benvido.

Xeometría Linear (2º curso). Libro con teoría e problemas (aínda en preparación, pendente de acabar).

Matemática Discreta (1º curso, Grao en Intelixencia Artificial).

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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).

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COURSES TAUGHT AT WARWICK UNIVERSITY

  • Iwasawa theory (Fall 2021). TCC course (16 hours course for graduate students at Warwick, Oxford, Imperial, Bath and Bristol).

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TEACHING ACTIVITY DURING MY PHD (At UPC-BarcelonaTECH)

  • Integral Calculus (Fall 2020, problem sessions, 30 hours). 2nd course, Bachelor in Mathematics.

  • Real Analysis (Spring 2020, problem sessions, 30 hours). 2nd course, Bachelor in Mathematics.

  • Differential Calculus (Spring 2020, problem sessions, 30 hours). 1st course, Bachelor in Mathematics.

  • Complex Analysis (Spring 2019, problem sessions, 30 hours). 2nd course, Bachelor in Mathematics.

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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).

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I have supervised 3 bachelor thesis at UPC, a 4th year project (Warwick) and one more bachelor thesis in Santiago.

-> 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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  • Alguns problemes resolts de Càlcul Integral. Aquí.

  • Alguns problemes resolts de Càlcul Diferencial. Aquí.

  • 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.

  • Class from Maths Foundations: Introduction to arithmetics. Here.

  • 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.

  • 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.

  • I am interested in politics and the analysis of different electoral systems. Here some comments about the last Spanish elections (in Spanish).

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