We are convinced that a data analyst both today and in the coming decades will need a deep understanding of the mathematics used in Data Science. The differentiator for being a competitive analyst contains among its qualities the fluency with which mathematical language is spoken. In addition to the above, the capacity for improvement for an analyst with a strong mathematical background provides value with the flavor of an informed investment.
Stochastic calculation and its financial interpretation
The monumental works of both Itô and Black-Scholes are undoubtedly one of the most outstanding achievements of the last century in both mathematics and finance. This program is designed to provide students with the necessary preparation -from different starting points- to understand formalism, intuition and the implications of Stochastic Calculus in Financial mathematics. The courses are designed to start with the details in the discrete world and thus be able to work with concrete examples even when the student does not have a solid mathematical training.
Stochastic approach and algorithms
This course seeks to study some algorithms commonly used in Data Science such as Stochastic Gradient Descent or decision trees from a formal approach using stochastic approximation theory and martingales.
Outliers and anomalous values
Outliers are a phenomenon present in any prediction problem, sometimes related to sampling errors, but sometimes they are a reflection of important and relevant phenomena. In this course we describe some of the most used techniques both for the detection of outliers and for modeling in their presence.
One of the most successful methods in the world of Data Science and Artificial Intelligence is the so-called Reinforcement Learning which is based on very interesting results of dynamic programming. This course studies the Bellman equations that allow learning through reinforcement techniques.
Stability in Machine Learning through its algorithms
The objective of this course is to clarify the fundamental concepts of Machine Learning in various algorithms such as overfitting, regularization and computational cost. We will know the details of three famous and useful algorithms (models) in Machine Learning: Neural Networks, Support Vector Machines and Decision Trees.
Sampling methods, an invitation to Bayesian statistics
Sometimes approximating the probability distribution that guides our databases is not only possible but might be a better idea than approximating a function to predict / classify the data. This course follows the Bayesian approach and focuses on those Monte Carlo-inspired methods for sampling the random variables to approximate the distributions.
Entropy and information theory
Computer scientist C. Shannon drew on some ideas from thermodynamics to devise a sound mathematical theory that could study the difficulties related to information. In the current time when information abounds his work is one of the pillars to be able to solve some of the most complicated problems in the industry and other areas of knowledge. In this course we propose a mathematical study of the phenomenology of the following concepts: transmitter, message and receiver.
Machine learning, game theory and markov chains
This course seeks to study linear programming problems and their dual versions, as well as their applications to data science and signal processing problems. It also seeks to develop the details of game theory by studying the balance of Nash and Markov chains in machine learning.
Graph Theory and Applications
Graph theory was born with the intelligent observation of the mathematician Euler about the impossibility of crossing all the bridges of the city of Königsberg once. In this course we propose the study of complicated problems in industry and network theory using the techniques of graph theory.
Alexander Grothendieck is one of the most influential mathematicians of the 20th century, his work in geometry, topology, and arithmetic revolutionized those areas. However, his professional career as a mathematician did not start in the mentioned areas. He began his career studying Banach spaces and made fundamental contributions, one of which is the so-called Grothendieck inequality. The applications of these inequalities are very powerful and have permeated various areas of knowledge due to their depth and their applications.