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.
Fourier's analysis is one of the great achievements of mathematics, his ideas have profoundly influenced almost all areas of mathematics and physics. This course seeks to invite the student to know the details behind these fascinating methods and their applications.
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.
Applications of reguralization in Machine Learning
Sometimes in Data Science, Finance or Engineering problems it is impossible to use traditional methods due to theoretical impossibilities. In this course we will study individual cases of these problems and how to solve them.
This course seeks to provide the student with the statistical foundations to understand the regulators in Machine Learning, as well as to introduce the ideas and uses of Extreme Value Theory and its comparison with other classic results.
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.