(I highly recommend Bad Bunny's new album.)

Some cool pictures of proofs of nice math results

Some time ago I posted some fun and interesting math proofs (in spanish) on my Instagram profile which was linked to my YouTube channel. Nevertheless I believe many non-spanish speakers will be able to follow them since they are mostly written with math symbols and just some spanish here and there to clarify things. For time reasons I stopped uploading them, but I've decided to upload the content here, so feel free to take a look:

• On the Quicksort algorithm
• pi+e and pi*e can't be both rational
• Ulam's spiral
• Don Zagier's proof of the infinity of primes
• (x+y)^p = x^p + y^p (mod p)
• Every logical proposition can be written only using the NOR operator

Courses that I've enjoyed

I wanted to keep a record of some of the courses that I've enjoyed the most during my time as a student. This space serves as a reminder of the topics I've enjoyed the most and the professors that have inspired me. I've included some references and books that I used in several of these courses, hoping that it will be useful for someone else in the future. Please note that this list is neither exhaustive nor complete.

• Number Theory I (UNAM, 2019)
• Lecturer: Prof. Julio César Guevara
• Relevant refences include "An Introduction to the Theory of Numbers" by I. Niven and "The Book of Primer Number Records" by Paulo Ribenboim.
• Linear Algebra I-II (UNAM, 2020)
• Lecturer: Prof. Dr. Diana Avella Alaminos
• Based on "Linear Algebra Done Right" by Axler and "Linear Alegbra" by Fridberg.
• Calculus I-IV (UNAM, 2019-2021)
• Lecturer: Prof. Javier Fernández García
has been the best professor I've ever had in my entire life.
• Any standard univariante and multivariate differential and integral calculus book will do (Piskunov, Apostol, Spivak, etc).
• Mathematical Analysis II: Functional Analysis (UNAM, 2022)
• Lecturer: Prof. Dr. Mónica Alicia Clapp
• The course was entirely based on her extraordinary book "Análisis Matemático"
• Mathematical Logic I-III (UNAM, 2021-2022)
• Lecturer: Prof. Dr. Carlos Torres Alcaraz
has been one of the funniest and most inspiring lecturers I've ever had.
• The course was entirely based on his extraordinary book "Hilbert y Gödel: dos perspectivas de la matemática" and another unpublished boo of his on Godel's incompleteness theorems (please let me know if it has been published already). We also relied on Smullyan's amazing book "Gödel's Incompleteness Theorems".
• Computability Theory (UNAM, 2022)
• Lecturer: Prof. Dr. Omar Antolín Camarena
. This was one of the lectures that heavily influenced my future direction of study.
• The course was entirely based the book "Computability Theory" by Rebeca Weber.
• Gemeotry and Dynamical Systems (UNAM, 2022)
• Lecturer: Prof. Dr. Renato Leriche Vázquez
. I learned to code in Julia for this course and totally fell in love with the language.
• Probably the best reference book I've used in any course: "Indra's Pearls: The vision of Felix Klein" by David Mumford.
• Combinatorial Optimization (Bonn, wintersemester 2023)
• Lecturer: Prof. Dr. Stephan Held
• Outline of topics: Matching in graphs, T-joins and b-matchings, Polyhedra for TSP, Matroids and Generalizations, Splitting Off Lemma and Connectivity in graphs, Subomdular flows, Graph Orientation, Directed Cuts, Survivable Network Design.
• Mostly taken from the book "Combinatorial Optimization. Theory and Algorithms" by Bernhard Korte Jens Vygen.
• Scientific Computing I (Bonn, wintersemester 2023)
• Lecturer: Prof. Dr. Jürgen Dölz
• Outline of topics: PDE Theory, Finite Differences, Variational Formulations and Sobolev Spaces, The Galerkin Method, The Finite Element Method, Error Analysis for Elliptic PDEs, Implementation and Adaptivity, Multigrid Methods, Parabolic PDEs.
• As far as I know no specific book was followed, but a general reference is "Finite Elements" by D. Braess.
• Approximation Algorithms (Bonn, sommersemester 2024)
• Lecturer: Prof. Dr. Vera Traub
• Outline of topics: Bin packing, Set covering, Scheduling, MAX-SAT, TSP, Knapsack, LP Formulations, Randomized Algorithms, Steiner Trees, k-Steiner Trees, Prize-Collecting Steiner Forests, PTAS, FPTAS, Hardness of Approximation.
• A great reference book is "Approximation Algorithms" by Vijay Vazirani (whom I had the enormous privilege of meeting in Bonn).
• Inverse Problems and Convex Optimization (Bonn, sommersemester 2024)
• Lecturer: Prof. Dr. Alexander Effland and Prof. Dr.-Ing. Jan Hasenauer
• Outline of topics: Convex Functions, Subdifferentials, Subgradient Methods, Proximal Operators, Convex Conjugates, Min-Max Theorems, Primal Dual methods, Optimal Transport, Identifiablity and Uncertainty Analysis, Quality of Fit, Frequentist Methods for Uncertainty Analysis, Bayesian Uncertainty Analysis, Metropolis Hasthings Algorithm.
• Reference: "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe.
• Seminar on Probabilistic Algorithms (Bonn, sommersemester 2024)
• Lecturer: Prof. Dr. Thomas Kesselheim
• I gave a talk on the paper "Controlling Tail Risk in Online Ski-Rental" by Michael Dinitz, Sungjin Im, Thomas Lavastida, Benjamin Moseley, Sergei Vassilvitskii.
• Seminar on Uncertainty Quantification (Bonn, sommersemester 2024)
• Lecturer: Prof. Dr. Jürgen Dölz
• I gave a talk on the paper "Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates" by I.M. Sobol.
• Continous Methods in Discrete Mathematics (Bonn, wintersemester 2024)
• This was an amazing lecture by Prof. Dr. Lazlo Vegh which I inmensely enjoyed (it was also his first lecture in Bonn).
• Outline of topics: Semidefinite Programming and Graph Coloring, The Lovasz Theta Number, Shannon Capacity and Sums of Squares, The Multiplicative Weights Update Method, Solving Linear programs Approximately, Semidefinite Programming and Multicommodity Flows, Eletrical Flows, The Matrix Tree Theorem and Spectral Sparsification, Cheeger's Inequality, Solving Laplacian Systems.
• These notes by Dr. David Williamson give a good overview of the course.
• Modelling of Disease Dynamics (Bonn, wintersemester 2024)
• Lecturer: Dr. Martin Joachim Kühn
• Outline of topics: Generation-based Models, Compartment Models, Steady States of ODE systems, Generalizations of the Reproduction Number, Integro-Differential equation-based Models, Stochastic Models, Agent-based Models.
• The course was mostly based on the book "Mathematical Models in Epidemiology" by Carlos Castillo-Chávez and Zhilan Feng.

• Discrete Random Matrices (Bonn, wintersemester 2024)
• Lecturer: Prof. Dr. Lisa Sauermann. She's one of the best lecturers I've had in my life!
• Outline of topics: Given an nxn matrix with independent identically distributed random {-1,1}-valued entries, what is the probability that the matrix is invertible?
• The course was a great an detailed exposition of the paper "Singularity of random Bernoulli matrices" by Konstantin Tikhomirov.

Calisthenics

I've formally practiced calisthenics since the beginning of 2022, but I've been practicing it informally since I was about 16 years old, so I decided it would be a nice idea to upload some of my favorite routines and my best times. My favorite type of training is EMOM (Every Minute on the Minute) and I've been doing it more often especially since I moved to Germany where I don't have a proper coach or training group.
I was very lucky to have attended FIBO 2025 in Cologne where I met some of the best calisthenics athletes in the world. Here are the routines for male and female resistance qualification rounds:

Resistance Qualification Rounds

Male	Female
Round of 16: - 30-second L Sit hold on dip bars (unbroken) - 30 dips - 30 pull ups - 30 push ups - 5 muscle ups - 20 squats with 20 kg vest - 20 dips - 20 pull ups - 20 push ups - 5 muscle ups - 20 squats with 20 kg vest - 30-second chin over the bar hold (unbroken)
Quarter-finals: - 10 pull ups | 10 muscle ups | 10 straight bar dips - 15 squats with 20 kg weight vest - 8 pull ups | 8 muscle ups | 8 straight bar dips - 15 squats with 20 kg weight vest - 6 pull ups | 6 muscle ups | 6 straight bar dips - 15 squats with 20 kg weight vest - 4 pull ups | 4 muscle ups | 4 straight bar dips - 15 squats with 20 kg weight vest - 2 pull ups | 2 muscle ups | 2 straight bar dips	Quarter-finals: - 5 muscle ups - 20 dips - 20 pull ups - 20 push ups - 20 squats with 10 kg weight vest - 10 dips - 10 pull ups - 10 push ups - 10 squats with 10 kg weight vest - 20-second chin over the bar hold (unbroken)
Semi-finals: - Bodyweight: 20 pull ups | 20 dips - With 10 kg: 5 muscle ups | 5 straight bar dips | 5 pull ups (unbroken) - With 10 kg: 20 pull ups | 20 dips - With 5 kg: 5 muscle ups | 5 straight bar dips | 5 pull ups (unbroken) - With 20 kg: 20 pull ups | 20 dips - Bodyweight: 5 muscle ups | 5 straight bar dips | 5 pull ups (unbroken) - 30 deadstop push ups - 30 squats with 20 kg weight vest - 5 muscle ups	Semi-finals: - Bodyweight: 5 muscle ups | 5 straight bar dips | 5 pull ups (unbroken) - 20 squats with 10 kg weight vest - 20 second L-sit hold on dip bars (unbroken) - Bodyweight: 3 muscle ups | 3 straight bar dips | 3 pull ups (unbroken) - 20 squats with 10 kg weight vest - 20 second L-sit hold on dip bars (unbroken) - Bodyweight: 1 muscle up | 1 straight bar dip | 1 pull up (unbroken)

Leg Day

Exercise	Details
8 pistol squats (each leg)	3 circuits (each per column)
20 explosive lunges
30 squats + jump
15 push ups
10 diamond push ups
4 sets + 1.5 min rest	Under 15 mins

Push Day

Exercise	Details
15 push ups (different types)	EMOM
15 sec L-sit
10 diamond push ups
20 dips
4 rounds + 2 min rest	10 mins exercise + 10 mins rest

Pull Day

Exercise	Details
5 muscle ups	Everything without letting go of the bar
10 bar dips	4 times
5 pull ups	5 min break between sets

Bar Barian Requirements

Exercise	Details
5 muscle ups
45 dips	Everything in under 6 minutes
25 pull ups
55 push ups
5 muscle ups

Halloween Special (100 muscle ups)

Exercise	Details
2 muscle ups every minute	50 minutes

Two Fun Circuits

Circuit 1 (maximum 20 minutes)

Push Ups	Pull Ups	Squats
30 push ups	10 pull ups	30 squats
25 push ups	10 pull ups	35 squats
20 push ups	10 pull ups	40 squats
15 push ups	10 pull ups	45 squats
10 push ups	10 pull ups	50 squats

Circuit 2 (maximum 15 minutes)

Pull Ups	Handstand (seconds)	Push Ups
2 pull ups	10 sec	5 push ups
4 pull ups	15 sec	10 push ups
6 pull ups	20 sec	15 push ups
8 pull ups	25 sec	20 push ups
10 pull ups	30 sec	25 push ups