Program Objective:

The program's objective is to train high-level researchers in Applied Mathematics who can formulate mathematical models to address significant problems in the productive sector and society. Through a theoretical study of model properties and available mathematical methods, researchers will be able to propose new numerical and computational methodologies for efficient solutions, which, in turn, can be used to develop decision-support computer tools.

Professional Profile:

1. Design and implementation of mathematical models to provide creative solutions to scientific and industrial problems, including weather prediction, simulation, and optimization of fluids (industrial, biological), public transportation optimization, industrial process optimization (logistics, scheduling, production design), computational medicine, etc.
2. Research and university teaching based on academic excellence.
3. Academic and scientific leadership of public and private research institutions (institutes, universities, etc.).
4. Leadership of national and international research groups and centers.
5. Formulation, direction, and execution of scientific research projects.

5 Key Reasons to Join Our Program:

1. We have highly academically accomplished professors who are personally dedicated to their research teams.
2. We have accredited 60 impactful scientific publications produced by our professors in the last 5 years.
3. We have direct collaboration with the Mathematical Modeling Center and the National Laboratory of Scientific Computing.
4. We are part of an extensive scientific network with national institutes and international research centers.
5. We form an active group with a strong international presence, rooted in excellence and characterized by a respectful and collaborative scientific environment.

Research Areas:

The priority areas of the Doctoral Program are:

• Mathematical Optimization and Control.
• Mathematical Modeling of Complex Systems.
• Numerical Analysis and Scientific Computing.
• Optimization in Transportation and Logistics.
• Inverse Problems and Image Processing.
• Mathematical Statistics and Statistical Models.
• Mathematical Analysis and Differential Equations.
• Operations Research.
• Biomathematics and Bioinformatics.

Education

Candidates must successfully complete courses that will provide a strong theoretical foundation for their doctoral thesis preparation. In addition, research seminars will be offered, where candidates can present and discuss their research progress with program professors.

As per Article 23 of the Academic Regime Regulation of the Council of Higher Education - CES, the educational stage varies depending on whether the applicant has a master's degree with a research trajectory in mathematics or related sciences (MA with RI), or a master's degree with a professional trajectory or a master's degree with a research trajectory in a field different from the program's (MA with PT or MA with RI in another field). The Doctoral Committee will make the decision regarding the compatibility of the master's degree title presented by each applicant.

The program's credit and hour details are as follows:

PAO: Academic Period or Semester (in the case of EPN, each PAO is an academic semester).

The Doctoral Program in Applied Mathematics will consist of, at most, 8 courses divided into core courses, elective courses, and research seminars:

Core Courses:

These courses are required for all students in the program who hold a Master's degree with a professional trajectory or a Master's degree with a research trajectory in a field different from the program. These courses include: Advanced Topics in Mathematical Analysis, Advanced Topics in Linear Algebra, Advanced Topics in Computational Mathematics, Advanced Topics in Mathematical Optimization, and Advanced Topics in Mathematical Modeling.

Elective Courses:

All students in the program must take 4 credits of an elective course, based on their tutor's recommendation. This course will be offered during the second academic period (PAO) of the program and can be chosen from a menu of subjects permanently offered by the Department of Mathematics at EPN. Additionally, elective courses proposed by program-affiliated professors or invited professors may be opened, subject to approval by the Doctoral Committee of the Program.

Research Seminars:

During the first two academic periods (PAOs), students are required to participate in separate research seminars led by program professors.

The curriculum for each possible pathway in the doctoral program can be downloaded here: MA con TI y MA con TP.

Requirements:

• Master's degree in related areas to the doctoral program (sciences or engineering).
• Two letters of recommendation from professors and/or researchers who hold a Ph.D. in Applied Mathematics or related sciences.
• Updated Curriculum Vitae.
• Proficiency in the English language.
• An essay of up to 10 pages on a mathematical problem of interest.
• Interview with the Doctoral Committee of the Program.
• Admission exam approval with at least 80% of the maximum score.

NOTE:
The requested documentation can be submitted digitally to the email: posgrados.matematica@epn.edu.ec or delivered physically to the Department of Mathematics' secretary's office (Ladrón de Guevara E11-253, Building No. 12, 7th floor).

Application Schedule for the 2023 Period:

• Application Period: January 18, 2023 - March 10, 2023
• Review of Applications: March 13, 2023 - March 14, 2023
• Publication of the list of applicants eligible to take the admission exam: March 14, 2023
• Admission Exam: April 1, 2023
• Interviews with the Doctoral Committee: April 3, 2023 - April 4, 2023
• Official notification of admitted candidates: April 5, 2023
• Start of activities: May 8, 2023

Admission Exam Syllabus:

1. Vector Analysis
   • Continuity of functions of several variables.
   • Differentiability of functions of several variables. Gradient vector.
   • Critical points and extrema of functions of several variables.
2. Linear Algebra
   • Vector spaces. Definitions and fundamental properties.
   • Linear mappings. Basic properties. Kernel and range space.
   • Eigenvalues and eigenvectors.
3. Linear Programming
   • Modeling optimization problems using linear programs.
   • Duality Theorem of Linear Programming.
4. Differential Equations
   • Solution of first-order equations by separation of variables.
   • Solution of homogeneous linear equations of order N.
   • Solution of non-homogeneous linear equations: annihilator method.
   • Numerical solution of ODEs: one-step methods.

Basic Bibliography:

• Mardsen and Tromba, Vector Calculus, Freeman Publishing Co.
• Giaquinta and Modica, Mathematical Analysis. An Introduction to Functions of Several Variables, Birkhäuser.
• Quarteroni, Sacco, and Saleri, Numerical Mathematics, Springer.
• Chvatal, Linear Programming.
• Vanderbei, R.J. Linear Programming: Foundations and Extensions.
• J. Hefferon, Linear Algebra (available online).

From the Escuela Politécnica Nacional:

• Almeida Rodríguez, Carlos Almeida. Specialty: Probability Theory and Mathematical Statistics.
• De los Reyes Bueno, Juan Carlos. Specialty: Optimal Control, Nonlinear Optimization, Inverse Problems, and Mathematical Image Processing.
• González Andrade, Sergio Alejandro. Specialty: Numerical Analysis, Scientific Computing, and Nonlinear Optimization.
• Merino Rosero, Pedro Martín. Specialty: Optimal Control, Nonsmooth Optimization, Numerical Analysis, and Scientific Computing.
• Portilla Yandún, Segundo Jesús. Specialty: Data Assimilation.
• Recalde Calahorrano, Diego Fernando. Specialty: Linear and Integer Optimization, Operations Research, and Game Theory.
• Torres Carvajal, Luis Miguel. Specialty: Discrete Geometry, Combinatorial Optimization, and Linear Programming.
• Torres Gordillo, Ramiro Daniel. Specialty: Linear Programming, Combinatorial Optimization, and Logistics and Transportation.
• Vaca Arellano, Wlater Polo. Specialty: Operations Research and Linear Optimization.
• Valkonen, Tuomo Jukka Markus. Specialty: Convex Analysis, Inverse Problems, Mathematical Image Processing, and Nonsmooth Optimization.
• Yangari Sosa, Miguel Angel. Specialty: Mathematical Analysis and Differential Equations.

Invited Professors:

• Borzi, Alfio, University of Würzburg, Germany. Specialty: Numerical Analysis and Scientific Computing.
• Marenco, Javier Leonardo, National University of General Sarmiento, Argentina. Specialty: Computer Science.
• Meyer, Christian, Technical University of Dortmund, Germany. Specialty: Optimal Control, Nonlinear Optimization, and Mathematical Analysis.
• Nasini, Graciela Leonor, National University of Rosario, Argentina. Specialty: Linear and Integer Optimization.
• Neitzel, Ira, University of Bonn, Germany. Specialty: Optimal Control and Numerical Analysis.
• Otárola, Enrique, Federico Santa María Technical University, Chile. Specialty: Differential Equations, Optimal Control, and Numerical Analysis.
• Peypouquet, Juan, University of Groningen, Netherlands. Specialty: Nonlinear Optimization.
• Rapaport, Iván, University of Chile. Specialty: Computer Science and Combinatorial Optimization.
• Schoenlieb, Carola-Bibiane, University of Cambridge, United Kingdom. Specialty: Inverse Problems, Nonlinear Optimization, and Mathematical Image Processing.
• Stadler, Georg, New York University, United States. Specialty: ScientificComputing and Nonlinear Optimization.

What is the student's dedication time?

All students in the program must sign a contract with EPN to ensure their full-time dedication to the execution of their doctoral research. According to Section 1 of Resolution 339 from the Polytechnic Council, it states: "All students in master's and doctoral programs must guarantee, before their registration process, their full-time dedication to the program."

Is the interview evaluated?

The purpose of the interview is to assess the candidate's general aptitudes, predisposition, and level of commitment to the doctoral program, its principles, and its objectives.

Are scholarships maintained for pursuing the doctorate?

To ensure access and integration into fourth-level studies, the Escuela Politécnica Nacional (EPN) will grant up to three contracts to students with the highest GPA who are admitted to the doctoral program.

Section 3 of Resolution 339 from the Polytechnic Council authorizes the hiring of students accepted into doctoral programs offered by the Escuela Politécnica Nacional under the occasional academic personnel category 1 (1,323.00 USD) on a part-time basis, under the following conditions:

1. This academic staff member should dedicate up to 4 hours per week to teaching and up to 4 hours per week to class preparation, exam administration, and grading. Additionally, they should devote 11 hours per week to research activities related to their doctoral program.

The Center for Mathematical Modeling will provide financial assistance, including for applicants, for research work. The amount will be determined by the Doctoral Committee and the project guidelines approved by the Vice-rectorate for Research of the EPN.

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