Master's & PhD

Ph.D. in Mathematical Modelling

Course duration
4 years
Applications period
27/06 to 15/07/2022

Presentation

The Doctorate in Mathematical Modeling provides cutting-edge academic training, aligned with the needs of modern society, in all applications of mathematics for the solution of concrete problems. In addition, it trains professionals with specific skills in the various areas of mathematics and its applications, the field of scientific research that represents the distinguishing feature of the program.


GOAL

To enable the doctoral student to analyze scenarios and support decision making in situations of intensive use of data and information, in addition to the objective of training excellent researchers in the area.


TARGET AUDIENCE

Masters in mathematics, statistics, applied mathematics, computing, engineering, physics, economics and related fields, who wish to work with academic, scientific and technological research in public or private institutions, supporting the decision-making process in any spheres.

About the course

Research lines

This line of research began worldwide with the development of Probability and the formal construction of the Brownian Movement in the early 20th century. This is probably one of the areas of mathematics with the most applications in the real world. From a theoretical point of view, we are interested in the study of Stochastic Differential Equations and the incorporation of path-dependence in several aspects of the theory.

In addition, another aspect of this line is the numerical resolution of differential equations, in particular random (RDEs) and stochastic (EDEs). The theory of EDEs and RDEs are themes, at the crossroads of differential equations and stochastic processes, with a wide variety of applications in the modeling of phenomena and practical situations in which the quantities of interest are subject to random disturbances. Since obtaining solutions to these equations is rarely possible, much attention is paid to the construction and study of approximation methods, with good qualitative properties, for their integration and simulation.

The Optimal Control Theory studies Optimization problems whose state variables are subject to differential equations (ordinary or partial) whose dynamics depend on a control variable, while Stochastic Optimization is focused on the study of optimization problems involving uncertainties modeled by a stochastic process. A stochastic optimization problem is usually formulated using conditional risk measures.

In this line of research, mathematical models and methods are studied with a focus on applications in problems of Finance, Economics and Actuarial Sciences. For applications in Finance and Economics, research projects are usually based on techniques involving Stochastic Calculation and/or Partial Differential Equations, whereas applications in Actuarial Sciences, such as Reserves calculation, tend to use statistical regression models or time series.

Mathematical epidemiology is an applied mathematics subject with more than a century of tradition, which incorporates ideas and methods from different branches of mathematics in the representation and analysis of its objects of study.   
At EMAp, the Mathematical Epidemiology group studies how information on how communicable diseases can be treated from a quantitative point of view, differently from the classic statistical techniques well known in the medical field. In addition, the projects require a basic understanding of biological assumptions and the mathematical models that underlie infection models and the tools available today to extract biological information from these models.

In general, this line of research is divided into theoretical, methodological and applied aspects involving data analysis. In particular, EMAp researchers are interested in the following areas of Statistics: Estimation of time series in high dimension; Modeling of non-linear time series; Non-parametric tests; Monte Carlo simulation for Bayesian inference; Statistical inference for stochastic optimization problems averse to risk or neutral risk (central limit theorems, hypothesis tests, non-asymptotic confidence intervals); Nonparametric hypothesis testing using convex optimization techniques.

The objective of this line of research is the exploration and development of objects and research problems through methods originated from the statistical learning of machines (Machine Learning) and its applications in the analysis of structured and unstructured data. This range of empirical objects encompasses numerical, categorical and textual data, images, graphs, time series, among others. It also includes the development of algorithms, languages and methodologies for manipulating these complex databases, in tasks such as classification, regression, learning, identification of clusters, recommendation systems, optimization, extraction and representation of knowledge, modeling knowledge domains, data mining, text mining, visualization, sentiment analysis, high-dimensional data analysis, cryptography.

FGV Main Office

Praia de Botafogo, 190 Rio de Janeiro - RJ. Zip Code: 22250-900 Tel: +55 21 3799-5917 E-mail: ri@fgv.br

Ombudsman FGV

Ph.D. in Mathematical Modelling

Curriculum Grid

The PhD in Mathematical Modeling at FGV EMAp has as its disciplinary axes Applied Mathematics and Computer and Information Sciences.

To obtain the title of Doctor, the student must obtain at least 42 credits, distributed as follows: six central subjects, totaling 18 credits, and eight elective subjects, totaling 24 credits. The eight electives must belong to two different lines of research, five of which must be in the main line and three in another (note that the same subject can belong to more than one line of research)

Admissions

In the application form, in addition to personal data and information about academic qualifications, applicants must submit a letter describing their reasons for applying for the program and how they intend to use the knowledge acquired (it is suggested to prepare the text in advance and paste it in the appropriate field of the form).

Enrollment will be formalized by uploading the documentation below, on the registration page of the Selection Process, available on the School's page:

  1. ID;
  2. CPF (Brazilian Social Security Number);
  3. Passport (foreign applicants);
  4. Lattes / CNPq Curriculum (http://lattes.cnpq.br) attaching copies of the most relevant works, when available (optional) or Curriculum Vitae;
  5. Social Name requirement form;
  6. Medical Report (People with Disabilities).
  7. School Records for Graduation. In the case of a course taken abroad, the document must be consularized by the Brazilian representative at the Embassie/Consulates in the country of origin of the Diploma or booklet, according to the Hague Convention, and presented with a sworn translation;
  8. Master's Degree (holders of a Master's degree). In the case of a course taken abroad, the document must be consularized by the Brazilian representative at the Embassie/Consulates in the country of origin of the Diploma or booklet, according to the Hague Convention, and presented with a sworn translation;
  9. Candidates in the process of completing their Undergraduate course may submit, for registration to the Selection Process, a statement with the expected completion of the course (issued less than 60 days ago). For the effective enrollment, it will be mandatory to present the Diploma or Declaration containing the date of graduation;
  10. Classification and grade in one of the following exams (optional) valid for 2 years: POSCOMP, GRE, ANPAD, ANPEC.  
  11. English language proficiency certificate from one of the following tests (optional): IELTS, TOEFL, Cambridge ESOL: FCE, CAE or CPE.

Guidelines:

  • Documents must be scanned, saved in "PDF" format and attached to the Registration Form;
  • Photos of documents will not be accepted;
  • The maximum size allowed for uploading each document is 1.5MB;
  • Documents that have front and back or more than 1 (one) page, must be scanned in a single file (ID, passport, Diploma etc);
  • Candidates should consult the status of the documentation sent through the website www.fgv.br/processoseletivo/dmm, in the Overview menu, in the link Follow-up your Registration. Documents will be verified within 3 (three) business days after confirmation of payment of the registration fee.

Selection Criteria

Candidates for the Doctorate Program in Mathematical Modeling will be selected by a Selection Committee made up of teachers from the Program, according to the criteria specified below, all phases being of an eliminatory nature:

  1. Document analysis;
  2. Interview;
  3. Research proposal.

A single score will be assigned, from 0 (zero) to 10 (ten) points for each item that is part of the selection phases.

PHASE 1 Document analysis:

  1. Analysis of the Curriculum Vitae or Lattes;
  2. Research proposal.

PHASE 2 – Interview:

  1. The selection interviews will take place in the period provided for in the Calendar.
  2. Candidates residing in other states will be able to conduct the interview via Skype.
  3. The Course Coordination will schedule the interviews. Contact will be held by e-mail or telephone.

Guidelines for the interview

  1. The candidate must arrive at the interview site at least 30 (thirty) minutes in advance, carrying an original ID with photo or passport;
  2. The candidate who does not attend the interview on the dates, times and places determined will be automatically eliminated from the Selection Process;
  3. Under no circumstances will there be rescheduling of the interview as a result of non-compliance with any item of the notice;
  4. FGV is not responsible for the custody of objects and will not be responsible for the loss of IDs and/or other objects during the interview, nor for damages caused to them;
  5. When entering the premises of the interview, the candidate must turn off and store cell phones and all electronic equipment, in addition to other objects, under the penalty of being eliminated from the selection process;
  6. It will not be allowed to access FGV facilities wearing shorts, flip-flops, tank tops, miniskirts, tops or cropped blouses.

CRITERIA FOR APPROVAL OF CANDIDATES

The criteria will be judged by the selection committee that will assess the candidates' ability to analyze scenarios and support decision-making in situations of intensive data use, in addition to significant contributions to research in the area. The final average will be composed of the arithmetic average achieved by analyzing the selection criteria, with 7.0 (seven) being the minimum approval average.

In the event of a tie, the classification will be defined based on the following criteria:

  1. Highest score in document analysis;
  2. Higher grade in the research proposal;
  3. Highest grade in the interview;
  4. If the tie persists, the age criterion will be used, with the oldest student being selected.

Successful candidates will be listed in descending order, possibly including a waiting list to be determined by the selection committee, which can be used in case of withdrawal or disqualification of selected candidates.

The list of classified candidates and list of alternates will be published, according to the announcement, on the FGV EMAP School of Applied Mathematics website (https://emap.fgv.br), after the completion of all phases. Only the candidate approved in all phases of the selection process will be allowed to enroll.

Final Result

The final result of the Doctorate in Mathematical Modeling Selection will be announced on January 24th, 2020, through an alphabetically ordered list with those selected in the Selection Process. Successful candidates will be contacted by the School of Applied Mathematics - FGV EMAp by phone and/or email and must confirm their intention to enroll with the Academic Records Secretariat - SRA according to the period established in this document.

Registration Confirmation

In order to complete the Registration, the candidate must access the Selective Process website - www.fgv.br/processeletivo> Results> Pre-registration and schedule the appointment at the Academic Records Secretariat, according to the day and time of your preference.

  1. The scheduling period is available in the Calendar;
  2. Scheduling must be done in advance, due to the demand of candidates, availability of dates and times;
  3. Only duly scheduled candidates will be attended;
  4. Candidates who do not comply with the scheduled time or do not present the documentation for registration, as established in the notice, must wait for the availability of the service, in the absence of the next candidate at the time designated for him.

Enrollment will be formalized upon delivery of the following documentation to the SRA – Secretariat of Academic Records:

Brazilian candidate

  1. 2 (two) recent 3x4 photos;
  2. Official ID (passport will not be accepted);
  3. CPF;
  4. Birth or Marriage Certificate, according to marital status;
  5. Social Name inclusion form;
  6. Medical Report (Person with Disabilities);
  7. Undergraduate degree. In the case of a course taken abroad, the document must be consularized by the Brazilian representation (Embassies / Consulates) in the country of origin of the Diploma or booklet, according to the Hague Convention, and presented with a certified translation;
  8. Masters Degree (holders of a Masters degree). In the case of a course taken abroad, the document must be consularized by the representative of Brazil (Embassies / Consulates) in the country of origin of the Diploma or booklet, according to the Hague Convention, and presented with a certified translation.

Foreign candidate

  1. 2 (two) recent 3x4 photos;
  2. Passport;
  3. Temporary Student Visa;
  4. CPF;
  5. National Migration Registry - RNM;
  6. Birth or Marriage Certificate, according to marital status;
  7. Social Name inclusion form;
  8. Medical Report (Person with Disabilities);
  9. Undergraduate degree. In the case of a course taken abroad, the document must be consularized by the Brazilian representation (Embassies / Consulates) in the country of origin of the Diploma or booklet, according to the Hague Convention, and presented with a certified translation;
  10. Masters Degree (holders of a Masters degree). In the case of a course taken abroad, the document must be consularized by the Brazilian representation (Embassies / Consulates) in the country of origin of the Diploma or booklet, according to the Hague Convention, and presented with a certified translation;
  11. Insurance policy with a minimum amount of € 30,000 (thirty thousand euros) or US $ 42,000 (forty-two thousand US dollars) and including transfers to the country of origin.

GENERAL PROVISIONS

The cancellation of enrollment must be made by the contracting party, via a request filed with the SRA - Secretariat for Academic Records. For billing Legal Entities, consult our financial services at the Academic Records Secretariat - SRA.   

Additional Information

FGV HEADQUARTERS Praia de Botafogo, 190 - CEP 22250-900, Rio de Janeiro, RJ

COURSE COORDINATION Praia de Botafogo, 190, 5th floor - CEP 22250-900, Rio de Janeiro, RJ Phone: (21) 3799-5917 / 6262 e-mail: emap@fgv.br Office Hours: Monday to Friday, from 8 am to 5 pm

SECRETARY OF ACADEMIC RECORDS - SRA A / C: Selection Process for the Doctorate in Mathematical Modeling (no site está mestrado na pagina de doutorado) Praia de Botafogo, 190 / office 314 - 3rd floor Zip code 22250-900, Rio de Janeiro, RJ Phone: (21) 3799-5757 e-mail: srarj@fgv.br Office Hours: 9am to 6pm