Applied Mathematics
Applied Mathematics bridges the gap between the real world and the ideal realm of Mathematics. This is achieved through mathematical models that translate concrete problems into terms amenable to sophisticated tools like differential equations, simulation, estimation, and approximation, among others. Nearly every branch of science relies on mathematics in one way or another. Below, we give a brief description of some of the most exciting areas of study related to Applied Mathematics here at IE. Check our researchers’ profile for more information.
When designing mathematical models, there is a tradeoff between their ability to resemble reality and their simplicity. Highly accurate models whose complexity prevents practical analysis are often rendered ineffective. Thus, approximation and simulation become pivotal, providing surrogates of the original system that are easier to work with. These ideas have a profound impact in our life. For instance, Fourier set the bases for the approximation theory that inspired the mp3 format!
Mathematics is also used to optimise and make informed decisions in daily life and to build autonomous systems in control theory. This may include finding the best route for a ship to reach its destination, determining the optimal path for a set of drones or robots to achieve a specific formation, or managing traffic flows efficiently. Mathematics describes the evolution of complex systems over time through the theory of dynamical systems, allowing for predictions of system behaviour and informed planning.
Mathematics provides a solid foundation for AI and machine learning (ML), which are used to create systems that can learn from data, make predictions, and automate tasks. Many of today’s fascinating algorithms have their roots in clever mathematical observations. For instance, the ubiquitous Gradient Descent Algorithm has its origins in Cauchy’s work in mathematical analysis.
Lines of Research
- Orthogonal polynomials and approximation theory
- Control theory and dynamical systems
- Geometrical integrators
- Distributed algorithms
- Optimization algorithms and mathematical programming
- Learning of dynamical systems and temporal series
Applications
- Numerical methods (e.g. for navigation problems)
- Robotics (e.g. robot formation)
- Optimization of traffic flows
- Drone control
Faculty
David Gómez-Ullate
Full Professor
Alexandre Anahory
Assistant Professor
Miguel Vaquero
Assistant Professor
Publications
External Collaborators
- Robert Milson (Dalhousie University)
- Mª Angeles García-Ferrero (ICMAT)
- David Martín de Diego (ICMAT)
- Anthony Bloch (University of Michigan)
- Leonardo Colombo (CAR)