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 ground-breaking 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 state-of-the-art software. The ability to use mathematical techniques to model real-life 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:

  1. master the basic results in the mathematical areas covered during the semester—linear algebra, differential equations, differential geometry, functions of a complex variable, algebra and probability—needed to develop mathematical models for concrete problems;
  2. master the main software tools related to these fields and be able to solve relevant modeling problems;
  3. form part of multidisciplinary teams to solve modeling problems;
  4. discover aspects of the Mexican culture by immersing themselves in one of its most vibrant historical cities in the heartland of Mexico.

    GENERAL REQUIREMENTS

    Successful applicants will:

    • be currently enrolled in a higher education institution, pursuing a major that includes components involving Mathematics, Statistics, Data Science, or Computer Science.
    • have studied at least one linear algebra course and the standard calculus sequence ending with multivariate calculus.
      • In calculus, the applicant should be familiar with the notions of integration, derivatives, series, limits;
      • in linear algebra, the student should be familiar with the concepts of vector spaces, bases, dimensions, matrices, linear transformations, determinants, kernels;
      • In multivariate calculus, the student should be familiar with the concepts of derivative of a map from Rd to Rk for d and k up to three, chain rule, Hessian, maxima and minima, gradient, cross and dot products.

       

      Click on the tiles below to see details of each of the courses in the program*

        *Minimum course load = four 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

      Algebra and Its Applications

      Núñez Betancourt, Luis

      Discrete Probability and Simulation

      Christen Gracia, José Andrés

      Algebra and Its Applications

      Núñez Betancourt, Luis

      11.00 AM- 12.20 PM

      Modeling with Linear Algebra

      González Villa, Manuel 

      Discrete Mathematics

      Arizmendi Echegaray, Octavio

      Modeling with Linear Algebra

      González Villa, Manuel 

      Discrete Mathematics

      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.

       

      González Villa, Manuel 

      Post-doctoral research: Universität Heidelberg, Germany; Centro de Investigación en Matemáticas (CIMAT), Mexico; University of Wisconsin-Madison, USA

      Ph.D. Universidad Complutense de Madrid, Spain (2010)

      Research interests: Algebraic Geometry, Singularity Theory.

       

      Núñez Betancourt, Luis 

      Post-doctoral research: University of Virginia, USA

      Ph.D. University of Michigan, Ann Arbor, USA (2013)

      Research interests: Commutative and Algebraic Geometry.