• 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.

• Analysis of data
• Databases
• Multivariate Statistical Analysis
• Computational Statistics
• Data mining
• Data visualization

Data Science is a new paradigm, potentially one of the most significant advances of the early 21st century. The field of Data Science has emerged due to the intersection of several Sciences, including: mathematics, statistics, data engineering, pattern recognition and learning, advanced computing, uncertainty modeling and visualization, data storage and the high-performance computation with the goal of extracting insights from data and creating new products from the data. In today’s world, there is no doubt that a data scientist is among the most sought after experts due to the nature of their jobs.

• Artificial intelligence
• Machine Learning
• Deep Learning
• Computer Vision
• Reinforcement Learning
• Agents

The branch of computational intelligence encompasses the creation or replication of intelligence by computational means. The goal is to create innovative algorithms and agents, capable of learning complex problems on their own, such as driving a car, playing chess, administering exact doses of medicine or a bipedal robot that starts crawling and ends up upright.

This is unsupervised learning because the programmer only creates the conditions and access to an environment and the machine has to figure things out for itself. The intellectual capacities of humans remain as a frontier of human knowledge. For this reason, it is of interest to be able to replicate human and collective intelligences in such a way that we can understand, replicate and extend these intelligences. This development has great repercussions on the societies and economic activities of the immediate future.

• Modeling and Simulation
• High Performance Computing
• Algorithms
• Numerical analysis
• Computing Theory
• Discrete Structures
• Scientific Visualization
• Internet of things (loT)

Scientific Computing is the science of computer problem solving, and from this point of view, it is undoubtedly the most widespread scientific area that establishes precise, efficient and realistic algorithms, methods and models that model our world, store its data, and establish and process their sets.

These data can be geospatial and scientific, and their applications touch each citizen in all their activities: from natural and man-made disaster prevention, monitoring and warning systems coupled with physical, chemical or biological gauges and sensors. Topics covered include self-driving cars, drones with visual auto-return, and smart homes that protect themselves from dangerous chemical intruders and flooding.

These elements are unified through web platforms that allow communication and taking data from common things (loT) such as refrigerators, plants, etc. Scientific computing provides tools that allow molecular elements to be modeled, which allows solving problems such as protein folding, which in turn leads to the production of drugs and the possible control of viral epidemics such as COVID-19 and other diseases.

• Computational Agriculture
• Intelligent Transportation Systems
• Information security
• Communication & Networking
• Software

Information Technologies are found transversally in the daily lives of societies. Information technologies have revolutionized social, economic, political and industrial processes, being catalysts for the knowledge society and Industry 4.0. Modern society has seen its reality transformed by digitization processes in all its areas, which include: communication, education, social behavior, transportation, industry, commerce.

The use of a wide range of technologies allows us to be agents of change in all these sectors, increasing productivity and reducing risks. This line of research aims to propose transformative changes for Ecuador.