- Ordinary and/or partial Differential Equations
- Mathematical and Numerical Analysis
- Control and/or Synchronization Theory
- Dynamic systems
- Probability and statistics
- Algebra and Geometry
- Topology
- Discrete Mathematics and Logic
- Complex Analysis
- Didactics of Mathematics
Assumptions about a system often involve the rate of change of one or more variables. This leads to the fact that the mathematical statement of all these hypotheses can be one or more equations where derivatives intervene. Thus, a deterministic mathematical model is an equation or a system of differential equations, which can be ordinary or partial, depending on the number of variables present in the phenomenon studied.
In most of these models, the existence of solutions is established by means of some theorem from Mathematical Analysis, which deals with the study of the favorable conditioning factors to be able to establish these results in both finite and infinite dimensional spaces. However, obtaining the solution is reduced, in the vast majority of cases, to approximations using computational algorithms.
Hence, both the theoretical and computational study of the problem addressed is important.
Also, many phenomena that occur in the real world, such as biological systems, weather, economics, and finance, behave randomly; and the dynamic nature of these processes cannot be determined using deterministic models because there are variables that cannot be included in the modeling, whereas this uncertainty can be quantified by incorporating a stochastic structure.
In both cases, deterministic or non-deterministic, when favorable conditions are considered, it is important to take into account algebraic and geometric structures inherent to the problem. On the other hand, Mathematical Logic and Discrete Mathematics tools are useful for modeling and solving problems coming from different important domains. Included here are challenging problems in Artificial Intelligence, Symbolic Models, Decision Theory, Social Choice Theory, Axiomatic Set Theory and Functional Systems.
Additionally, modern university mathematics teaching, particularly the use of textbooks, requires an intelligent balance between 1) the obviously important purely mathematical concepts, 2) the possibility of using the ever-increasing computational resources in potential, and 3) the use of interesting application examples. This puts the didactics of mathematics in tune with the elements that make up the line of research.
Definitively, the line focuses on a multidisciplinary spirit, thus promoting the relationship with other schools of our university and abroad, both nationally and internationally.