Mathematical Tools for Modeling

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, Complex Variables, 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 problems.

Click on the tiles below to see details of each course of the Fall Program

Modeling with Differential Geometry  Discrete Probability and Simulation  Modeling with Linear Algebra  Tools for Modeling Dynamics  Algebra and its Applications  Functions of a Complex Variable

Other courses, including an Independent Research Project, might be offered depending on the academic background of the students admitted to the program. The minimum course load is three mathematics courses per semester.  A one-week workshop on computational tools for data science is organized at the beginning of the Semester.

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 semester's learning outcomes are:

• To master the core results in the mathematical areas covered during the semester needed to develop mathematical models for concrete problems.
• To gain experience utilizing the main software tools related to these fields and be able to solve relevant modeling problems.
• To participate in projects that solve or explore problems with modeling tools and in cocurricular activities that showcase how mathematicians are currently collaborating with multiple sectors to solve problems.
• To discover aspects of the Mexican culture by immersing themselves in one of its most vibrant historical cities in the heartland of Mexico.

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, and limits.
  • In linear algebra, the student should be familiar with the concepts of vector spaces, bases, dimensions, matrices, linear transformations, determinants, and kernels.
  • In multivariate calculus, the student should be familiar with the concepts of derivative of a map from R^d to R^k for d and k up to three, chain rule, Hessian, maxima and minima, gradient, cross and dot products.
  • Have taken a course on, or have had prior experience with proof writing.