# About us

Welcome to the official blog of Dedekind’s Army.

## Who are we

**Dedekind’s Army** is a volunteer-driven project in Universidad Complutense de Madrid
which organizes classes covering introduction to diverse math topics. The classes are imparted by and for college students.

Two reasons have motivated the foundation of the project:

- We feel that there are many several topics of interest in math that are pushed aside in the standard curriculum. We want to promote self-study of such topics, and give students a way of sharing their passions.
- Many students are considering pursuing a life as teachers in college or institutes. In DA, they can try for themselves what teaching is like, and build the communication skills needed for it.

This webpage serves as both a repository of lecture notes and a central hub to announce and organize events.

Interested in collaborating or attending? Get in touch with us!

## The core team

### Jaime Sevilla

*Cofounder, site manager, organizer and teacher*

Jaime Sevilla is a Mathematics and Computer Engineering undergrad student in the Universidad Complutense de Madrid, Spain.

He is headed towards becoming a researcher in Safe Artificial Intelligence. He is a Summer Fellow of the Machine Intelligence Research Intitute and an alumni of the Center For Applied Rationality. He has spoken in several conferences about Artificial Intelligence, Rationality and Effective Altruism, as well as organized several workshops and activities related to those fields.

He has also lead a couple of entrepreneurship-related projects and has won several math contests and programming hackathons.

His research interests lie in logic, computability, complexity, probability, machine learning and the theoretical foundations of artificial intelligence, among other things.

In Dedekind’s Army, he teaches subjects related to the research of foundational safe artificial intelligence. Most of his classes fall within the scope of the topics listed in MIRI’s research agenda.

All the beautiful posters you see advertising DA’s classes are designed by him.

**Classes taught:**
Set theory -
Equinumerability -
Computability -
Löb’s and Gödel’s Theorems -
Modal logic

Contact **by mail**

### Diego de la Fuente

*Organizer and teacher*

Diego de la Fuente is currently an undergraduate student at Universidad Complutense de Madrid. He is in his third year and he is interested in all aspects of mathematics, in special in number theory and algebraic structures. Someday, he would like to be a researcher in any area of mathematics so he can spend his time studying.

His hobbies are reading and practising sports, specially table tennis, in which he has been a federated player for several years.

**Classes taught:**
Arithmetical Functions

## Contributors

Dedekind’s Army would not be anything without its contributors. The following people have generously volunteered their time and effort to help Dedekind’s Army become a successful project. We are proud to have collaborated with such a select group of people, and we hope to continue helping each other in the future.

### Diego Chicharro

*Cofounder, teacher and organizer of the Dedekind Olympiad*

Diego Chicharro is an undergraduate student at Universidad Complutense de Madrid, studying the joint degree in Mathematics and Physics. He aims to become a researcher in number theory, but he is also interested in other branches such as complex analysis and topology. *He could never resist a series*.

We ought the existence of this blog to his efforts.

**Classes taught:**
Elementary Number Theory

Contact **by mail**

### Gonzalo Gómez

*Teacher and organizer of the Dedekind Olympiad*

Gonzalo Gómez studies Mathematical Engineering in the Universidad Complutense de Madrid, Spain.

The first time he read a serious Mathematics Book from the University Library, he only got to the third page before realizing, in horror, that there were no pictures or diagrams. In fact, there were only definitions, theorems and proofs. Since that very day, Gonzalo fights a war against formalism that will never be won.

Meanwhile, he naively tries to find applications for mathematics in something that resembles reality, as well as solving problems that have a visual, intuitive solution.

His favourite topics are Group Theory, Combinatorics, Geometry, Game Theory, Chaos Theory, Complexity and Abstract Algebra, in that order.

**Classes taught:**
Axiomatic Origami - Groups in Games -
Degrees of freedom

### Garazi Muguruza

Garazi Muguruza is an undergraduate student of mathematics at the Complutense University of Madrid. She is mainly interested in analysis, whenever it is not related to solving PDEs.

She is the president of Hypatia Reading Club at the physics faculty and member of TEMat and ANEM editorial group, which hardly leaves her spare time.

**Classes taught:**
Fractals

### Mauro Sanchiz

Mauro is a student (of the Master in advanced Mathematics in the UCM), who feels interest for (mostly) everything and passion for (hardly) anything. As a graduated in Mathematics, he can speak with everyone about everything without saying anything relevant or not strictly logical. Because of his uncertain future and interest in mathematical research, he could run away from his academic life anytime, so you should talk to him about mathematics while you can and have common interests.

**Classes taught:**
Non compact surfaces

### Patricia Contreras

Patricia Contreras Tejada is a PhD student in the mathQI group at Universidad Complutense de Madrid. She studied Mathematics and Physics MSci at the University of Bristol and Philosophy of Physics MSt at the University of Oxford.

Patricia is interested in applying quantum information theory to the foundations of quantum mechanics, whether from a mathematical, scientific or conceptual viewpoint.

In her spare time she plays the piano and sings in a barbershop chorus, The Barbees.

**Classes taught:**
Bell’s Theorem

### Fernando Díaz

Fernando Díaz is currently an undergraduate physics student in the Universidad Autónoma de Madrid.

He is interested in the principles of both classical and quantum mechanics and their relation to linear algebra and functional analysis. He also likes reading about nonlinear dynamics and chaos, statistical mechanics and, essentially, anything related to physics.

As a hobby, he enjoys listening to classical music, reading or going to the theatre.

**Classes taught:**
Least action principle

### Gerardo García

Gerardo García Moreno is an undergraduate student of Physics at Universidad Complutense de Madrid. He is interested in theoretical and mathematical aspects of physics, mainly in foundations of quantum mechanics , quantum information ,quantum technologies and quantum field theory , among other things.

He likes spending his spare time doing outdoor activities such as trekking or (trail) running. He is also trying to learn how to play guitar.

### Guillermo Gallego

Guillermo Gallego Sánchez is an undergraduate student of Double Degree in Mathematics and Physics at Universidad Complutense de Madrid.

Guillermo is at the fourth year of five of the Double Degree and currently his interests are Lie groups and its relations to physics (elementary particles, spin groups, anyons), algebraic and symplectic topology, classical mechanics and dynamical systems. He is also a philosophy reader, defines himself as a materialist (in the philosophical way) and is interested on the philosophy of sciences.

He is a guitar player and he is the secretary of Asociación Cultural Lewis Carroll, a cultural and social club of the Faculty of Mathematics, which organizes several activities for students like film projections, a reading club, talks and jam sessions.

**Classes taught:**
Symplectic geometry

### Juan José Madrigal

Juan José Madrigal is a mathematician affiliated to the UCM interested in educational technology, willing to explore new ways to bring advanced mathematics to the world.

He is currently leading the Mathifold project, whose goal is to make mathematics accesible to everybody, completely free, based on open collaboration and the best pedagogical tools.

**Classes taught:**
Homology

### Guillermo Sánchez

Guillermo Sánchez Arellano is a Mathematics undergrad student in the Universidad Complutense de Madrid.

He is studying the fourth course of the degree and he has discovered that his interest lies on foundational math (things like sets, logic and categories), topology and algebra, but he knows that mathematics still has a lot of amazing things to show him.

He is collaborating now on Mathifold, a project in the University that tries to give another, “more visual”, point of view of math for their students. He also is studying English in CSIM and, in his spare time, he learns how to play guitar and is an instructor of children in his neighborhood.

**Classes taught:**
Banach-Tarski’s Theorem