PhD in Applied and Computational Mathematics

Alumni from Argentine or foreign universities in disciplines such as: mathematics, physics, engineering, economics and related fields.

• To train professionals with high capacity for research in applied and computational mathematics, and participate in interdisciplinary scientific groups that allow them to formulate, solve and analyze mathematical models derived from problems in basic sciences, engineering, and other areas of knowledge, which contribute to the improvement of processes, technologies, services, environment and quality of life.

Graduates of the PhD program in Applied and Computational Mathematics will possess rigorous scientific training, enabling them to make original contributions to the field of exact sciences. They will be able to conduct research in interdisciplinary groups focused on development, innovation, and technology transfer, and will have the capacity to understand and interact with other scientific disciplines (physics, computer science, chemistry, engineering, economics, finance, etc.). Essentially academics, they will be capable of teaching at all levels of applied and computational mathematics education, disseminating cutting-edge knowledge in their specialty.

Applications to: Biomathematics, Data Science, Engineering Science, Management Science, Economics, Solar Energy, Finance, Soil Physics, Mathematical Physics, Continuum Mechanics, Phase Change Processes, Industrial Processes, Thermodynamics, Food Technology.

1. Ordinary and partial differential equations
2. Problems of mobile and free border
3. Differential equations with fractional derivatives
4. Integral equations
5. Numerical analysis of differential equations
6. Optimal control of systems governed by differential equations
7. Optimization and variation calculation
8. Heat and mass transfer with phase change
9. Inverse problems
10. Quantitative Finance
11. Mathematical economics
12. Bio-mathematics
13. Systems of dinosaurs

Content of the compulsory subjects of the Basic Training Cycle (260 hours)

• Research Methodology
• Applied functional analysis
• Partial Differential Equations and Applications
• Professional ethics

Content of the eligible subjects of the Higher Education Cycle (320 hours)

• Moving and free boundary problems for the one-dimensional heat equation
• Elliptic variational inequalities. The one-dimensional heat equation.
• Numerical analysis of variational equations and inequalities
• Free boundary problems for the multidimensional heat equation
• Nonlinear Volterra integral equations
• Optimal control of systems governed by partial differential equations
• Calculation and numerical analysis of free boundary problems for the Stefan-type heat equation
• Convex analysis
• Nonlinear elliptic partial differential equations
• Differential equations with fractional derivatives
• Inverse problems
• Mathematical methods of classical mechanics
• Mathematical methods of continuum mechanics
• Optimal control theory
• Numerical analysis: optimization algorithms and linear algebra problems
• Control of dynamic systems
• Advanced Topics in Control Theory
• Probability and stochastic processes
• Optimal stochastic control
• Advanced topics in game theory
• Relationship between dynamic systems and stochastic processes
• The mathematics of financial options
• The Black-Scholes partial differential equation and the calculation of European and American financial options
• Applied Mathematics Seminar
• Seminar on computational mathematics
• Advanced seminar in analysis
• Advanced seminar on partial differential equations

Thesis (4000 hours)

• The Governing Council of the Faculty of Business Sciences-Headquarters Rosario You may pass other courses annually, valid for the Doctorate in Applied and Computational Mathematics, which will be incorporated into the Higher Education Cycle.

• Director: Dr. Domingo A. Tarzia. Retired Senior Researcher ad-honorem of CONICET and Full Professor of the Universidad Austral
• Co-director: Dr. Adriana C. Briozzo. Independent Researcher at CONICET and Full Professor at the Universidad Austral