Posgrado
Doctorate degree in Mathematical Engineering
SNIES 103604, Medellin
A Doctor of Mathematical Engineering combines mathematics and engineering to create innovative solutions in areas such as artificial intelligence, resource optimization, and the modeling of complex phenomena. These advances address challenges in sectors such as banking, energy, technology, industry, and academia.
The doctorate program focuses on areas such as optimization, modeling and simulation, control of dynamic systems, and advanced computational methods. It attracts those who wish to research and apply complex mathematical theories to practical problems, driving developments in sectors like energy, healthcare, finance, and technology.
Registro calificado
Resolution 023028 of November 30, 2021.
Ver resolución
Sobre el programa
Calidad y excelencia
We Are Among the World’s Top
Our professors María Eugenia Puerta Yepes and Olga Lucía Quintero Montoya received recognition in 2020 for being among the 25 most influential women mathematicians in Colombia.
This year, we are celebrating 10 years of excellence and impact of our doctoral program, which began in 2015 and renewed its official registration in 2020.
Given that our program has consistently received positive evaluations, since 2023 we have been conducting an internal self-assessment process with the goal of applying for program accreditation before the Ministry of Education.
International Partnerships
We have international agreements across Europe and the Americas, including:
Europe: TU Delft (Delft, Netherlands); University of Angers (France); Universidad Carlos III de Madrid (Spain); German Cancer Research Center (DKFZ, Heidelberg, Germany); INRIA (Grenoble, France); and VICOMTECH Technology Center (Spain).
Americas: National University of San Juan (Argentina); National Autonomous University of Mexico (Institute of Mathematics, Mexico); University of Louisiana at Lafayette (United States); and Cornell University (Ithaca, NY, United States).
Innovación y liderazgo
Somos innovación en educación
La investigación en este programa está estrechamente vinculada con procesos de innovación y creación. Los estudiantes son motivados a generar nuevas ideas y soluciones que puedan tener un impacto significativo en su campo de estudio.
Generalidades
Somos innovación en educación
La investigación en este programa está estrechamente vinculada con procesos de innovación y creación. Los estudiantes son motivados a generar nuevas ideas y soluciones que puedan tener un impacto significativo en su campo de estudio.
Intended for applicants with undergraduate and/or graduate studies in mathematics, engineering, or related fields, who possess critical thinking skills, respect for diversity, a sense of responsibility and commitment to society, and the ability to work independently. Candidates should have a strong interest in pursuing research training, where they will face challenges related to continuous and lifelong learning.
Graduates will be able to analyze problems in interdisciplinary fields that require mathematics and engineering, design academic and research processes using engineering tools with mathematical rigor, and address problems and needs that contribute to scientific, technological, and business development in a critical, comprehensive, and ethical manner. In addition, they will be capable of communicating and disseminating their knowledge to a variety of audiences and engaging effectively in teamwork and research groups across different contexts.
Our graduates will be able to work as professors, sharing their advanced knowledge in mathematics and engineering; as researchers, leading innovation and the application of new mathematical theories and their uses across different fields of knowledge; and as consultants, providing advanced mathematical solutions to business and organizational challenges.
Líneas de investigación
Our PhD program includes research lines that integrate the knowledge, interests, and capabilities of the School of Applied Sciences and Engineering to strengthen our students’ research and the training of our PhDs in Mathematical Engineering, contributing to the solution of problems relevant to society.
Since its development in the 1950s, control theory—grounded in mathematical foundations—has played a crucial role in the design and implementation of major global advances, particularly in the fields of engineering, defense, economics, finance, and healthcare, among others. In parallel, the study of nonlinear and non-Gaussian dynamic systems, as well as the exploration of their complexities and possible simplifications, has driven theoretical progress in the estimation of states and/or system parameters for analysis, control, or intervention purposes.
In this context, the Ph.D. in Mathematical Engineering directs one of its research lines toward theoretical development in areas such as signal analysis, nonlinear systems, and estimation in low- and high-dimensional spaces. The objective is to generate solutions with direct application potential to real-world problems in both industry and science.
Among the research topics addressed by faculty and students are inverse problems through wavelet analysis, integral transforms, Bayesian estimation, and data assimilation. These tools have applications in various sectors, including applied computational mechanics, atmospheric modeling, seismic migration, epidemiological modeling, industrial automation, and fluid mechanics with health applications, among others.
Members: Olga Lucia Quintero Montoya, Cristhian David Montoya Zambrano y Carlos Mario de Jesús Vélez Sánchez. (enlazar al perfil web
The formulation of mathematical models for disease transmission, together with the estimation of biologically coherent parameters through optimization techniques, represents a strategic research line to address current epidemiological challenges. Although numerous models exist in the literature, many fail to adequately capture the specific dynamics of diseases in local contexts, even when data are available.
In response to this limitation, the PhD in Mathematical Engineering promotes interdisciplinary research on interval-valued optimization, network modeling, sensitivity analysis, parameter estimation with biological constraints, and inverse problems. Additionally, this line extends to sectors such as mass transportation, focusing on the design of multi-objective models for routes, frequencies, and transfer points, integrating data mining, heuristics, fuzzy methods, and metaheuristics in highly uncertain environments.
Members: María Eugenia Puerta Yepes, Cristhian David Montoya Zambrano, Paula Alejandra Escudero Marín, and Juan Carlos Rivera Agudelo.
The numerical solution of differential equations constitutes a fundamental line of research within the PhD in Mathematical Engineering. It is focused on the development, analysis, and application of efficient and robust computational methods to solve problems modeled by ordinary and partial differential equations. This line addresses both theoretical aspects—such as the stability, convergence, and accuracy of numerical schemes—and practical applications in physical, biological, engineering, and financial phenomena.
It emphasizes the design of adaptive algorithms, advanced discretization techniques (such as finite elements, finite differences, or finite volumes), as well as the treatment of problems with complex geometries, nonstandard boundary conditions, or nonlinear behaviors. Furthermore, it promotes the implementation of these methods on high-performance computing platforms, enabling their integration into large-scale simulations that contribute to solving real-world problems in various areas of science and industry.
Members: José Manuel Escorcia Tafur, Cristhian David Montoya Zambrano, Nicolás Guarín Zapata, Juan Manuel Rodríguez Prieto, and Carlos Alberto Cadavid Moreno.
This line of research seeks to provide new evidence of the power that diffusion processes have to simplify, in informational terms, functionals defined on a differentiable manifold
𝑀
M, and thus obtain those that are optimal in some sense—whether determined by mathematical characteristics or by interpretative advantages within a context where the diffusion process serves as a model.
Members: Carlos Alberto Cadavid Moreno, Gabriel Ignacio Loaiza Ossa, Andrés Ramírez Hassan, John Jairo García, Jorge León David Caro, and Luis Alejandro Gómez Ramírez.
This line of research focuses on building computability models and establishing their relationships with existing ones, as well as exploring the various possibilities offered by quantum physics—and modern physics in general—for the development of new models of computation and programming. Likewise, the group’s work is oriented toward the construction of deductive systems based on classical propositional calculus, using alternative affirmation operators (in contrast to the usual or classical affirmation), alternative negation operators (in contrast to the usual or classical negation), and operators of incompatibility and determinability between pairs of operators (negations versus affirmations).
Within this line, methods are developed for the correction, debugging, writing, transformation, and verification of logical and/or functional programs through the use of formal techniques.
Members: Andrés Sicard Ramírez, Sergio Steven Ramírez Rico, and Juan Guillermo Lalinde Pulido.
Our students will have access to the EAFIT University Laboratory Center for the development of their research projects. Depending on the focus areas of their dissertation, they will have access to specific infrastructure capabilities and technological resources.
Learn more about the capabilities of our Laboratory Center, here
Admission Requirements
Applicants to our PhD in Mathematical Engineering must:
- Attend an admission interview with the Program Director or the Graduate Studies Coordinator of the School of Applied Sciences and Engineering.
- Prepare their résumé, two (2) letters of recommendation, and one (1) research proposal.
- Meet the second language requirement: English at level B1 of the Common European Framework of Reference for Languages (CEFR).
Evaluation Procedures
Applicants to our PhD in Mathematical Engineering must:
- Attend an admission interview with the Program Director or the Graduate Studies Coordinator of the School of Applied Sciences and Engineering.
- Prepare their résumé, two (2) letters of recommendation, and one (1) research proposal.
- Meet the second language requirement: English at level B1 of the Common European Framework of Reference for Languages (CEFR).
The qualifying exams consist of two knowledge assessments, which may be written (problems proposed by the evaluating professors) or project-based (solution to a proposed problem) with an oral defense. Calls for the qualifying exams will be made at the end of each academic semester, with at least four working days between the two tests.
Evaluation procedure for the qualifying exams:
The Doctoral Committee is responsible for overseeing the administration of the two qualifying exams. The exams will be designed by at least two professors (at least one external to EAFIT) who work in the area of the doctoral training and are appointed by the Doctoral Committee. The thesis advisor may recommend the evaluators —approved by the Doctoral Committee— as well as the basic and supplementary bibliography covering the specific topics of the qualifying exams.
Exam 1. Disciplinary Training:
This exam evaluates the student’s competencies in one or more areas of mathematical training necessary for the development of their research topic, in alignment with the program’s focus and defined profile. It assesses the student’s conceptual knowledge in coherence with the areas and research activities around which the doctoral work is structured.
Exam 2. Specific Training:
This exam aims to validate the soundness, feasibility, relevance, and scope of the research the doctoral student has conducted since joining the program. This specific training assessment refers to the impact of the ongoing research in the areas that enable the student to transfer their theoretical developments to practical applications.
The student must pass both qualifying exams before submitting the Doctoral Thesis Proposal to the Graduate Office and the Program Director. Every doctoral student must individually prepare a Thesis Proposal with the approval of their Thesis Advisor. The Doctoral Thesis Proposal outlines the research activities related to the Advanced Research Training component completed up to that point in the curriculum. The proposal must include at least the contents established in the current structure of the INVESTIGA research management system at Universidad EAFIT.
Notes:
The approval of both qualifying exams, the submission of the doctoral thesis proposal, and the successful completion of all required and elective courses constitute the candidacy for the Doctorate in Mathematical Engineering.
Once the student attains doctoral candidacy and is therefore authorized to register for thesis development, they are also required to submit a progress report, endorsed by their Thesis Advisor, at the end of each academic semester.
Every student in the Doctorate in Mathematical Engineering program must individually prepare and defend a doctoral thesis on the topic approved upon attaining doctoral candidacy. The research underlying the doctoral thesis is the central component of the student’s work in the program, where they present the results obtained during their research activity, highlighting their original and significant contributions to mathematical knowledge or its applications.
The thesis must advance the state of the art and expand the frontiers of knowledge. The scientific level of its contributions should be of sufficient quality to merit publication in indexed journals of recognized scientific standing.
Contact Us
Head of the Doctorate in Mathematical Engineering
Cristhian David Montoya Zambrano
Email: dim@eafit.edu.co
Head of Master's and Doctoral Programs – School of Applied Sciences and Engineering
Gloria María Doria Herrera
Email: jefatura.pos.ecaei@eafit.edu.co
Commercial Executive
Stiven López Fernández
Email: slopez7@eafit.edu.co
Escuela de Ciencias Aplicadas e Ingeniería
Becas y financiación
Guía de aspirantes posgrados
Registration
Register and make the payment
Registration dates: August 26 to November 29, 2024.
a. Registration process
Any professional who has completed bachelor level studies or a program at a national or foreign university recognized by competent state educational authorities may apply for admission to postgraduate programs, while technicians, technologists or specialized technologists are not eligible. If you have been enrolled in a higher education institution, other than EAFIT, in a postgraduate program, you must apply for External Transfer admission, regardless of whether you wish to request subject recognition. First time applicants should select First time studies in type of applicant box, in EPIK self-service, module "Undergraduate and Postgraduate Registration".
If you have been enrolled in an undergraduate or graduate program at EAFIT, the system will provide you with a list of the types of admission that will apply, depending on the program selected. If the system does not show you any type of admission, please contact us via email (posgrados@eafit.edu.co) with your full name, identification document type and number, and indicate the program of interest, the city where you are going to study and the name of the program you will be taking at EAFIT.
To register, enter the Registration module by clicking here, press the P.I button. Start your registration here, and proceed to fill out the form. Enter all the required data.
Enter here, click on the button Learn about our Postgraduate offering and learn about our programs available for the 2025-1 semester.
b. Registration payment
Registration fee: $341.700 (approximately $82 USD).
After successfully submitting your registration request, go to the end of the form and proceed to make your payment. If you filled out the form and are going to make the registration payment later, enter the EPIK self-service, "My Finances" module, "Payment Center" option, where the system shows the payment document. Select it and activate the Pay Online button.
You can pay the registration fee online, with a credit or debit card through one of the banks registered in PSE. Do not close the page until the bank reports that your transaction was successful. Afterwards, look for the return option.
If you cannot pay online, click on Download PDF, print receipt on a laser printer and and make an in-person payment at any authorized bank nationwide: Bancolombia, Davivienda, Banco de Bogotá, AV Villas and Banco de Occidente.
If you have difficulty generating the payment document, send an email to posgrados@eafit.edu.co
If you have trouble making the payment, send an email to apoyofinanciero@eafit.edu.co
Payments abroad can be made through bank transfer; to obtain the University account information, contact the Support area, contact the finance department at tesoreria@eafit.edu.co.
Once the payment is made, the system will send it to the email registered to the dilig. Send your registration form, a notification informing you of the confirmation of registration and the procedures you must follow to continue with your admission process.
Requirements
Attach your documents with your registration form
a. List of documents
If you have made your registration payment, attach your documents online through the EPIK self-service, in the "Document Annex" module. The system will show you the documents that you must attach, depending on the program and type of admission; files should be JPG, TIF or PDF type, with a size is between 1 Kb and 12 Mb.
| Document | First time applicant
| External Transfer
| EAFIT University Graduate |
Original or scanned Undergraduate degree certificate issued by the University with the corresponding signatures. If your degree is from abroad, attach your diploma as well, and its translation into Spanish.
| Yes. It is required for admission. | Yes. It is required for admission. | No. |
Photocopy of both sides of identification document amended vertically at 150% on the same page or sides or on the digital document.
| Yes. It is required for admission. | Yes. It is required for admission. | Only if you do not already have it updated in Admissions and Records. |
| For external transfer request: Personal letter addressed to Admissions and Records that clearly states the reasons why you wish to make the external transfer and indicates if you are requesting subject recognition. In case of recognition, list the subjects you wish to be recognized. | No. | Yes. It can be attached online in the module Annex of documents. Required for admission. | No |
b. Additional requirements
Click here, click on the button Learn about our Graduate Programs and learn about the available programs for the 2025-1 semester, schedules and additional requirements if applicable.
c. External transfers with subject recognition
For the recognition of subjects, applicants for external transfer must bring the certificates listed below to the interview; and attach the following to the registration form:
| Document | External Transfer
|
Certificate from the university of origin, with letterhead and corresponding signatures, indicating the subjects taken with their grade and time intensity.
| Yes. Attached to the Registration. |
Syllabus with detailed contents of the subjects to be recognized by EAFIT, duly certified with the signature and seal of the university of origin.
| Yes. To be handed in person to the interviewer. |
| For recognition of subjects currently being studied, a duly certified letter from the university of origin, on letterhead with the corresponding signatures must be attached, indicating hour intensity, syllabus with detailed contents. Recognition is conditional on the final grade obtained in the course, which must be attached with the certificate of qualifications. | Yes. Attached to the registration form To. be submitted by January 10, 2025. |
Si no deseas homologación, debes adjuntar desde el formulario o desde el módulo Anexo de documentos, la carta personal dirigida a Registro Académico, en la que indiques si tu transferencia externa es sin reconocimiento de asignaturas, y finalmente informar a tu entrevistador.
Importante: la información suministrada en la inscripción debe coincidir con los documentos entregados, de lo contrario, se anulará cualquier proceso adelantado en la Universidad.
Interview
Select your interview appointment (if applicable for the program)
Once we receive your registration payment, schedule your interview. To do this, enter the Self-service here, go to the "Services and certificates" module, enter the "Request for services" option, and in the "Requests Made" section, access the "Admission interview appointment" service, select it and request your interview appointment.
Important: please check both in-person and online availability.
If no appointments are available, select the option "I did not find an appointment", so we can proceed to create new spaces for you to later come and select one.
If the program does not require an interview, the system will not present you with the "Admission Interview Appointment" service for selection.
Admission
Check your admission result
The admission process begins on September 19, 2024, after which you will be notified regarding your admission status to the email provided in registration form.
You can also check your status by entering the EPIK Self-service, "Undergraduate Graduate Registration" module and clicking on the "Status" field.
To be admitted, it is an essential requirement to have submitted all the required documentation and, if applicable, to have submitted your admission interview.
Note: foreign applicants who are admitted, must present their student visa that is valid for the academic period to which they will enroll.
Credit recognition
Credit recognition(if applicable for your type of admission)
For information regarding recognition of subjects in graduate programs, consult here the Graduate Academic Regulations of EAFIT University or with the director of the program to which you are applying.
Class Schedule
Check your class schedule and receipt
Once you are admitted and submit the required documentation, you will be registered based on the information provided by the program to which you were admitted.
Check your schedule through the EPIK Self-Service, by clicking here and entering the "My Registration" module and then entering the "My Certificates" option.
Schedules will be assigned beginning May, based on the syllabus of each postgraduate program.
Tuition
Pay your tuition
Once you have registered for classes and generated the payment document, verify payment dates.
Check your payment document
Enter the EPIK Self-Service by clicking here, select the "My Finances" module, go to "Payment Center" option and select the document under registration payment document.
If you have any difficulty with the payment, write to email apoyofinanciero@eafit.edu.co
Online payment
Verify in your bank if your debit or credit cards are authorized for online transactions as well the amounts allowed to prevent the transaction from being rejected.
To make the payment of your registration, enter through the EPIK Self-service with username and password; in the "My finances" module, go to the "Payment Center" option and in the "Online payment" button, go directly to the PlacetoPay platform which allows payment with multiple credit and/or debit cards.
Full payment must be made to conclude the process successfully and be registered as an active student.
Do not close the page after the bank confirms your transaction, and return to the University website to confirm your payment, otherwise, the information will not be recorded in our database.
Payment in banks
In person payment can be made at the following authorized banks nationwide: Bancolombia, Davivienda, Banco de Bogotá, AV Villas and Banco de Occidente.
A laser printed copy of the payment document that allows barcodes to be scanned must be presented at Banco de Bogotá offices, or a digital registration copy on your cell phone or tablet.
Banks receive payment in cash and/or checks made payable to EAFIT University.
If payments are made with checks, student identification number, phone number and the amount to be payed must be written on the reverse side of the check.
Banks will only accept payments for the total tuition fee stipulated on the document.
Tuition must be paid in full in order to acquire the status of active student.
Dirigirte al campus principal bloque 29 primer piso, taquilla de Tesorería – Caja en horario de 8:00 am a 5:00 pm de lunes a viernes. En caso de que no puedas desplazarte a la Universidad escribe al correo electrónico pagos@eafit.edu.co, informando que vas a realizar un pago mixto.
En cualquier caso, se debe pagar el 100% del valor generado en el documento de pago de matrícula, para que puedas adquirir la calidad de estudiante activo.
For additional information, call our service line (604) 2619500 or write to: apoyofinanciero@eafit.edu.co
Payment of invoices by a Company
If payment is made a Company that requires an invoice in its name, keep in mind the types of invoices that can be issued to a Company:
Cash: in this case, the Company must make the payment immediately.
Credit: the company requires a 30-day term to pay prior to a credit approval.
The company invoicing process must be carried out here.
Los documentos que se deben de anexar son:
- Letter on company stationery with letterhead in which the Company authorizes EAFIT University to send them an invoice for tuition, readjustments, additional enrollment, inter-semestral course or internship validation signed by the Legal Representative or the head of Human Resources, and in no case, by the student.
- RUT (Tax Registración Number).
- Certificate of existence of the Company issued by the Chamber of Commerce.
- The letter must contain information such as Tax identification number (NIT), Company name, address, email where they receive electronic invoice, amount to be billed, and indicate if invoice is to be paid by cash or credit.
Under no circumstances, should payments be made in a personal capacity, that is, in the name of the student, In such cases we will not be able to issue a receipt or register the payment in the name of the Company.
To learn about other payment methods, click here.
If you need support with any payment method, please write to apoyofianciero@eafit.edu.co.
Payment at the cash teller - EAFIT Treasury
Mixed Payments that include cards and checks can be made at the Treasury Offices as follows:
- Credit Card + Check.
- Credit Card + Cash.
Educational financial aid 'EAFIT at your fingertips'
Applicants admitted who financial aid may apply for short and long-term loans.
This initiative also contemplates a semester quota in which priority will be given to those with the best academic merits.
For more information on financial aid, write to financiacion@eafit.edu.co, contact our customer service line (604) 2619500 or consult the following website here.
Student ID
Tramita tu carné de estudiante
Para nosotros eres muy importante y nos alegra que seas parte de nuestros Eafitenses.
Te informamos el paso a paso para que solicites tu carné y puedas disfrutar de nuestro campus.
- Asegúrate que tu documento de identidad este actualizado en el sistema EPIK, de lo contrario debes tráelo al bloque 29, 1 piso, ¡En Registro Académico!
- Presenta el documento de identidad en la oficina de Carnetización, ubicada en el bloque 3, oficina 106. el día que te corresponda.
- ¡Prepárate para la foto! No debes traer prendas blancas.
Horarios de atención de Carnetización: lunes a viernes de 8:00 a.m. a 12:00 m. y de 2:00 p.m. a 6:00 p.m. y los sábados de 8:00 a.m. a 12:00 p.m.
El carné se puede reclamar, a los 4 días de haberlo tramitado, en las taquillas de Registro Académico.
Horarios de atención de Registro: lunes a viernes de 8:00 a.m. a 6:00 p.m. jornada continua.
¡Te esperamos!
Nota: Recuerda que para realizar el trámite de tu carné primero debes realizar el pago de tu matrícula. Para más información da clic aquí.
Begin your registration process
The process has a cost of $341.700 COP.
Register here
Líneas de atención
También te puede interesar
Doctorate degree in Earth Sciences
Más información
Doctorate degree in Engineering
Noticias
La excelencia de cuatro eafitenses fue reconocida en los Premios Medellín Investiga 2025
Llegó el momento de conocer a los ganadores del premio Inspiradores EAFIT 2025
