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Doctorate in Sciences, Specialization in Mathematics




8 Semestres


General Description

The Doctoral Program in Sciences with a Specialization in Mathematics at UCN is an academic program which began in 2003. The program aims to prepare and train researchers capable of carrying out independent research and developing original projects to resolve problems in their field. The program is constantly developed and strengthened through the execution of projects including work with visiting professors, study visits for students and faculty, research projects and joint publications.

Lines of Research

The scientific activity of the program is based on study carried out by research groups at the Department of Mathematics in the areas of Matrix Algebra, Linear Numeric Algebra, Differential Equations, Dynamic Systems, Control Theory, Actions and Foliations.


The objective of the program is to prepare professional researchers in the field of Mathematics who are capable of carrying out high-level original scientific research on a permanent basis, as well as generating research and development projects. Graduates of the program are expected to be capable of contributing to the development of Mathematics and its applications in other disciplines, as well as raising the quality of teaching in the field.

Candidate Profile

Candidates for the program will be graduates of a Master’s program in Mathematics or a similar area, from universities in Chile or abroad. Students who have shown outstanding performance in the first year of the Master’s of Science with a Specialization in Mathematics at UCN may also be admitted to the program.

Plan of Studies

The program has a duration of four years, on a full time basis. Classes take place during the daytime and students should give the course their full dedication.

The Plan of Studies consists of five elective courses, one obligatory subject, a thesis project and paper, four seminars and a final examination. At the end of the first year of the Plan of Studies, the student should take a qualification test.


Elective courses:

MAE01 Numerical Analysis
MAE03 Differential Equations
MAE04 Matrix Analysis
MAE07 Foliations and Geometry
MAE08 Lie Groups and Algebras
MAE09 Dynamic Systems
MAE12 System Dynamics Topics
MAE14 Theory of Foliated Spaces
MAE15 Ergodic Theory
MAE16 Inverse Eigenvalue Problems
MAE17 Actions of Locally Free Groups
MAE19 Invariant Systems around Lie Groups
MAE20 Non-Negative Matrices
MAE21 Hyperbolic Dynamics
MAE24 Linear Numerical Algebra and Applications
MAE25 Optimum Control of Distributed Systems
MAE26 Theory of Extreme Problems
MAE27 Navier-Stokes Equations
MAE28 Spectral Graph Theory Topics
MAE29 Partial Differential Equations
MAE30 Inverse Eigenvalue Problems and Elementary Dividers
MAE36 Elements of Operator Theory
MAE37 Linear Systems around Lie Groups and Equivalence Theorems


Candidates for the Doctorate in Sciences with a Specialization in Mathematics will have a master’s degree in Mathematics or an equivalent qualification, from a university in Chile or abroad. In exceptional cases, students with an undergraduate degree in Mathematics will be considered.

Applicants should submit the following information via email or ordinary mail by October 30th of each year at the latest, for entry during the following year.

The documents needed to apply are:
• Program application form (form available at www.mat.ucn.cl)
• Photocopy of undergraduate degree or professional title
• Photocopy of Chilean national ID card or passport
• Transcript of grades from undergraduate degree
• Transcript of grades from postgraduate degree
• Curriculum vitae (documented)
• Two academic letters of recommendation, to be sent directly to the Program Director (format available at www.mat.ucn.cl)


General Fee $267.000.- (CLP)
1st Year Enrollment Fee $3.000.000 (CLP)
Total Program Fee $12.000.000 (CLP)
Observations Program fee does not include general fees or cost of academic diploma.

* 2018 Admission Fees


Director: Elva Ortega Torres
Telephone: (56-55) 2355576
Email: postgrado.matematica@ucn.cl

Secretary: Dániza Ramírez
Telephone: (56-55) 2355573
Email: daramirez@ucn.cl

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