## Differential Geometry

Fundamental Theorem of Space Curves Visualization

In differential geometry, the fundamental theorem of space curves states that every regular curve in three-dimensional space, with non-zero curvature, has its shape (and size) completely determined by its curvature and torsion.

Given curvature and torsion , the Frenet equation relates the tangent, normal, and binormal vector of the curve at each position. ## Linear Programming

Simplex Algorithm

I have coded recently the simplex algorithm. It is an algorithm that solves the optimizations of a problem of linear programming. It gives a function to minimize and constrains the variables with an inequality form. It can be proven that the simplex algorithm solves this problem in Non-Polynomial time.

## Pathfinding Algorithms

We usually want to know the shortest/fastest route between two points. This is a well-known problem in graph theory. There are several algorithms that solve this problem: A*, Dijkstra, etc.

I have implemented in C++ those algorithms and a graph of the roads in California.

## Connect 4 AI Solver

Recurrent algorithms C++ and Python

I have been working on recurrent algorithms. They’re a bunch of examples in which you can implement these algorithms. However, we usually see that they are efficient.

Connect 4 is a simple game that can be easily programmed and solved to win every time. I have made in Python an AI that solves and wins. It is not programmed in C++ because I wanted a GUI.

## Computational Neuroscience

Computational neuroscience: neuron and network simulation

# Neuron

The neuron is the most common component in our brain,  we have nearly 86 billion neurons and 1000 trillion synaptic connections, estimates to a computer with a 1 trillion bit per seconds processor # Computational Neuroscience

Is the field of study in which we measure and simulate the neurons process. Our brain is a complex machine and its behavior is non-linear.

We need previous knowledge of electronics, ODE’s, neurobiology, chemistry, and programming.