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#### Data Science

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 noise in Machine Learning

This course seeks to study different types of stochastic noise as well as their interpretations as an error of various algorithms in machine learning.

#### Fourier analysis and Wavelets

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.

#### 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.

#### Parametric and non-parametric algorithms.

To familiarize the student with the ideas and some of the most effective methods in Data Science using two fundamental examples: Deep learning and decision trees.

#### Reinforcement Learning

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.

#### Some computational and statistical aspects of data science

Study the formal mathematical details necessary to continue the systematic study of machine learning and stochastic processes with more computationally efficient solutions

#### 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.

#### 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.

#### Advanced Statistics for Data Science and Finance

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.

#### 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.

#### Machine Learning Notions

This course seeks to help professionals with little experience in mathematics to understand more clearly the limitations and strengths of Machine Learning.

#### Compression theory

You would like to know how audio or video signals are compressed. This course focuses on those mathematical methods used to compress information.

#### 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.

#### Grothendieck inequalities

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.

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