Field Notes: EMALCA 2023 at UES
EMALCA 2023 just wrapped up at the University of El Salvador (UES). Coming from engineering at UCA, it was an interesting change of environment. Most attendees were Pure Mathematics and Physics students from various countries in the region (Mexico, Colombia, Brazil), so the approach was considerably more theoretical than what I'm used to.
The event took place in the auditorium of the Faculty of Natural Sciences. A visually modern space, though the combination of tropical weather (heavy rain) and the humid heat inside the auditorium made the sessions physically demanding.
The Logistics
Transportation was no small detail. Since I wasn't staying with the international group, I had to drive home every afternoon. Due to the constant rains these past days, traffic in San Salvador would collapse, resulting in commutes of up to two hours. It was the most tedious part of the two weeks, but the course content made up for the effort.
Course Summary
The school offered a varied "menu" of applied mathematics. Here are my main notes from each track:
1. Differential Geometry
Dr. Guillermo Lobos
The course started very intuitively, defining fundamental concepts like Curvature (), Torsion (), and the Frenet-Serret formulas.
It was interesting to see the mathematical construction behind 3D curves. However, midway through, the level of abstraction increased considerably. Although I lost track during the more complex proofs, the final evaluation was accessible and allowed me to apply the basic concepts that did stick.
2. Partial Differential Equations
Dr. Cuminato
This module was much more practical, using MATLAB for simulations.
- We worked with the Convection-Diffusion equation
- We implemented Euler's method — for someone used to Finite Element Methods (FEM), this approach felt more direct and intuitive
- A key point was using Fourier analysis to determine stability and convergence conditions for the simulation
3. Data Science
Dr. Thomas Peron
The focus here was methodological: treating data science with the rigor of a laboratory experiment. We focused heavily on analyzing error averages and the behavior of average models, seeking to understand result reliability beyond standard metrics.
4. Optimization
We covered several mathematical models, but the practical application was the most entertaining: solving a Sudoku using integer programming in Python. The challenge was translating the game rules into linear mathematical constraints. Watching the solver crack the puzzle in milliseconds was a good demonstration of the power of these algorithms.
Interdisciplinary Collaboration
In the Coding Theory course, I worked with Denis, a Pure Mathematics student. It was a good opportunity to combine different skill sets.
We studied how QR codes use redundancy for error correction. For the final project, we implemented a simplified version using Lagrange interpolation polynomials. The combination of his theoretical foundation with my implementation experience allowed us to present a functional demo of the encoding and decoding algorithm.
Visit to the Historic Center
The organization included a visit to the Historic Center. I hadn't been there in years (since the days when you'd only go for pirated movies). Walking through the renovated plazas with the international group was a pleasant experience and a good break from the academic workload.
Conclusion
EMALCA 2023 was a demanding experience due to the weather and traffic, but academically valuable. It served to validate that, although my background is in systems engineering, there's a very fertile meeting point with pure mathematics. Tools like R, PCA, and the optimization methods we covered are resources I actually plan to integrate into my future projects.
Recommended for engineering students who want to see what lies beyond standard calculus. Just check the weather forecast before heading out.