FALL SEMESTER: MATHEMATICAL TOOLS FOR MODELING
MOTIVATION 
The last forty years have seen an accelerating trend toward the applicability of mathematics. To such a degree that, today, they flood and permeate our whole life: finance, climate, electronic commerce, communication and new materials, to name but a few. Many of the groundbreaking technologies that have become available in recent years are mathematical in nature. A strong background in the basic aspects of these mathematical tools is fundamental to understanding their effectiveness and for developing new technologies. This success cannot be explained without the equally accelerated power of computation available to us. By combining mathematical techniques and computational power, we can tackle problems that were unthinkable a few years ago. The complexity of today's challenges requires the participation of multidisciplinary teams in which mathematicians play a central role. Successful participation in this process requires not only a solid foundation in some mathematical disciplines, but also the ability to manage the computer implementations that facilitate their application to specific problems. During this semester, we focus on six areas of Mathematics which have had a huge impact on applications: Algebra, Linear Algebra, Differential Equations, Differential Geometry, Dynamics Modeling, and Probability. The courses combine an overview of the basic aspects of each area with interesting applications based on stateoftheart software. The ability to use mathematical techniques to model reallife situations gives participants in this semester a definite advantage in a world with problems that become more challenging and complex every day. In this semester, we provide the basic tools to tackle a variety of dynamic problems. 
SEMESTER GOALS AND OBJECTIVES 
The aim of this semester is to learn and master the mathematical and computational foundations necessary for students majoring in Math to deepen their knowledge and practical skills in areas related to modeling. The aim is for students to develop the following skills by the end of the semester:

GENERAL REQUIREMENTS 
Successful applicants will:

Click on the tiles below to see details of each of the courses in the program*
*Minimum course load = three per semester
Other courses might be offered depending on the academic background of the students admitted to the program
Extra: Workshop on Computational Tools for Modeling [2 weeks]
 Introduction to programming in Python: variables, conditionals, loops, functions, introduction to classes.
 Introduction to programming in R.
 Introduction to SageMath.
CLASS SCHEDULE FALL 2019  
TIME  MONDAY  TUESDAY  WEDNESDAY  THURSDAY 
8.00 AM 9.20 AM 
Discrete Probability and Simulation Christen Gracia, José Andrés 
Núñez Betancourt, Luis 
Discrete Probability and Simulation Christen Gracia, José Andrés 
Núñez Betancourt, Luis 
11.00 AM 12.20 PM 
González Villa, Manuel 
Arizmendi Echegaray, Octavio 
González Villa, Manuel 
Arizmendi Echegaray, Octavio 
FACULTY FALL 2019 
Arizmendi Echegaray, Octavio CIMAT, Probability and Statistics Ph.D. Universität des Saarlandes, Germany (2012) Master’s degree: Mathematics and Statistics, Queen’s University, Canada (2010) Research interests: Combinatorics, Free Probability, Random Matrices, Graph Theory, Functional Analysis and Operator Theory.
Christen Gracia, José Andrés CIMAT, Probability and Statistics Ph.D. University of Nottingham, UK (1994) Research interests: Applied Statistics and Bayesian Inference.
Postdoctoral research: Universität Heidelberg, Germany; Centro de Investigación en Matemáticas (CIMAT), Mexico; University of WisconsinMadison, USA Ph.D. Universidad Complutense de Madrid, Spain (2010) Research interests: Algebraic Geometry, Singularity Theory.
Postdoctoral research: University of Virginia, USA Ph.D. University of Michigan, Ann Arbor, USA (2013) Research interests: Commutative and Algebraic Geometry. 