• On the Quicksort algorithm
• π+e and π·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

• Number Theory I (UNAM, 2019)
  • Lecturer: Prof. Julio César Guevara
  • Relevant references include "An Introduction to the Theory of Numbers" by I. Niven and "The Book of Prime 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 Algebra" by Friedberg.
• 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 univariate 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course was entirely based on his extraordinary book "Hilbert y Gödel: dos perspectivas de la matemática" and another unpublished book of his on Gödel's incompleteness theorems (please let me know if it has been published already).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 on the book "Computability Theory" by Rebecca Weber.
• Geometry 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, Submodular flows, Graph Orientation, Directed Cuts, Survivable Network Design.
  • Mostly taken from the book "Combinatorial Optimization. Theory and Algorithms" by Bernhard Korte and 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)
  • Lecturers: 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, Identifiability and Uncertainty Analysis, Quality of Fit, Frequentist Methods for Uncertainty Analysis, Bayesian Uncertainty Analysis, Metropolis-Hastings 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.
• Continuous Methods in Discrete Mathematics (Bonn, Wintersemester 2024)
  • This was an amazing lecture by Prof. Dr. László Végh, which I immensely enjoyed (it was also his first lecture in Bonn).
  • Outline of topics: Semidefinite Programming and Graph Coloring, The Lovász Theta Number, Shannon Capacity and Sums of Squares, The Multiplicative Weights Update Method, Solving Linear Programs Approximately, Semidefinite Programming and Multicommodity Flows, Electrical 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 n×n matrix with independent identically distributed random {-1,1}-valued entries, what is the probability that the matrix is invertible?
  • The course was a great and detailed exposition of the paper "Singularity of random Bernoulli matrices" by Konstantin Tikhomirov.

Resistance Qualification Rounds

Leg Day

Push Day

Pull Day

Bar Barian Requirements

Halloween Special (100 muscle ups)

Two Fun Circuits

Circuit 1 (maximum 20 minutes)

Circuit 2 (maximum 15 minutes)