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Master's Degree in Advanced Mathematics

Responsible Center: Official Masters School  Location: Móstoles
Modality: in-person or   Title code: 6350 Orientation: Researcher
Number of ECTS Credits: 60 ECTS  Duration of the Master: an academic year
Price: See table
Academic Calendar    Opening hours    Examinations    Teaching Guides     Faculty
Director of the Master: Mr. Alejandro Garcia del Amo Jimenez
Official master information: Phone: 91 488 8508   Inquiries Mailbox

Basic Information

What knowledge will I acquire with this Master?


Is this degree official according to the regulations required by the European Higher Education Area?

Yes, (final verification report is attached) the implementation of the degree will be done progressively, starting the first year in the academic year 2022-23.

Final verification report turned out FAVORABLE

Is it necessary to pass an access test?

It is not necessary.

What is the minimum number of credits for which I can enroll?

You can see it in the rules of permanence in this link

Recommended income profile

This Master is aimed at graduates in Mathematics, Statistics, Physics, Engineering or other scientific and technological disciplines with a high mathematical content with an interest in deepening their knowledge and with the vocation to develop a research career in Universities, Research Institutes or Departments. of R+D+i of the private sector.

On the other hand, qualities such as the capacity for abstraction, analysis, synthesis and logical reasoning, taste for problem solving, interest in the applications of mathematics and familiarity with performing mathematical calculations, are suitable as a personal profile of the student of this Master's degree.

In terms of personal skills and attitudes, it is highly recommended that applicants for this master's degree have the ability to study, curiosity, imagination, creativity and an entrepreneurial spirit.

The English language will be used regularly in the Master, mainly at the level of recommended bibliography and information search. In this sense, it is recommended that the student has at least a level of linguistic skills with respect to the English language equivalent to B1 of the Common European Framework of Reference for Languages.


The Master's Degree in Advanced Mathematics allows graduates to complete their academic training for access to doctoral programs with a view to starting a teaching and research career in Universities and Research Institutes or in R&D Departments in the private sector, especially in companies in the technological, financial and computer sectors, with the following fundamental objectives:

  • Complete the mathematical training of graduates in Mathematics, Statistics, Physics and Engineering, both in relation to new concepts and their application to different fields.
  • Train versatile specialists, capable of joining academic research in different areas of Mathematics and writing a doctoral thesis.
  • Train researchers capable of solving problems of a very diverse nature in the world of industry, business and administration using the language and tools provided by Mathematics.




Possess and understand knowledge that provides a basis or opportunity to be original in the development and/or application of

ideas, often in a research context


That students know how to apply the knowledge acquired and their ability to solve problems in environments

new or little known within broader (or multidisciplinary) contexts related to their area of ​​study


That students are able to integrate knowledge and face the complexity of formulating judgments based on

information that, being incomplete or limited, includes reflections on the social and ethical responsibilities linked to the

application of their knowledge and judgment


That students know how to communicate their conclusions and the knowledge and ultimate reasons that support them to the public

specialized and non-specialized in a clear and unambiguous way


That students know how to communicate their conclusions and the knowledge and ultimate reasons that support them to the public

specialized and non-specialized in a clear and unambiguous way


CG01 - Be able to communicate orally and in writing the results of the activities, readings and work carried out.

CG02 - Be able to document on specific topics and become familiar with the main bibliography of the subject

CG03 - Being able to promote new scientific-technological developments in their work environment

CG04 - Have advanced knowledge in various areas of Mathematics and its applications

CG05 - Be able to use appropriate computer tools, and, in particular, mathematical, statistical and optimization software, to address problems related to Mathematics

CG06 - Know the applications of Mathematics and be able to solve problems in the field of engineering, industry, science, technology and society through modeling skills, numerical calculation, simulation and optimization


CT01 - Be able to work in groups and in multidisciplinary teams


CE01 - Be able to propose, analyze, validate and interpret advanced mathematical models that simulate complex real situations, using the most appropriate mathematical tools for the purposes pursued.

CE02 - Being able to know and understand quantum mechanics, the theories, laws and advanced models that govern it, including its application domain and its formulation in mathematical language

CE03 - Being able to abstract the structural properties (of mathematical objects, of observed reality and of the world of applications) distinguishing them from those that are purely occasional and being able to verify or refute them.

CE04 - Being able to propose, interpret, analyze and validate advanced mathematical models that simulate real situations.

CE05 - Be able to prepare, present and publicly defend an original work-project, synthesis of the skills acquired in the degree, communicate the conclusions to a specialized court, and discuss with its members any aspect related to them.

CE06 - Know the scientific policy in the regional, national and international sphere in the area of ​​Mathematics.

CE07 - Being able to understand the most relevant open problems in some areas of Mathematics.

CE08 - Being able to apply the Theory of Numbers to current computational scenarios.

CE09 - Being able to understand and synthesize the content of seminars and colloquiums on current topics in Mathematics.

CE10 - Being able to develop, adjust, interpret and validate advanced statistical and optimization models that represent real situations.

CE11 - Be able to apply advanced procedures of operations research in decision making.

CE12 - Being able to model real problems using advanced algebraic tools.

CE13 - Be able to know and understand advanced results of measurement theory and functional analysis, as well as their applications to real and complex problems.

Admission and enrollment


The requirements for access to the proposed title are according to article 18, of Royal Decree 822/2021, of September 28:

  1. Possession of an official Spanish Graduate or Graduate university degree or equivalent is a condition for accessing a Master's Degree, or, where appropriate, having another University Master's degree, or titles of the same level as the Spanish Bachelor's or Master's degree issued by universities and higher education institutions in an EHEA country that in that country allow access to Master's degrees.
  2. In the same way, people in possession of titles from educational systems that are not part of the EHEA, which are equivalent to a Bachelor's degree, will be able to access a Master's Degree in the Spanish university system, without the need for homologation of the title, but verification by of the university of the level of training that they imply, as long as in the country where said title was issued it allows access to university postgraduate level studies. In no case will access through this route imply the homologation of the previous degree held by the person concerned or its recognition for other purposes than that of carrying out the Master's degree.

Recommended requirements:

The specific qualifications that will facilitate access to the Master are the following:

  • Mathematics (Grade)
  • Mathematical Engineering (Bachelor)
  • Mathematics and Computer Science (Undergraduate)
  • Mathematics and Statistics (Undergraduate)
  • Applied Mathematics and Computing (Undergraduate)
  • Engineering in Mathematics Applied to Data Analysis (Bachelor's Degree)
  • Physics (Grade)
  • Engineering Physics (Bachelor)
  • Statistics (Grade)
  • Applied Statistics (Grade)
  • Statistics and Business (Undergraduate)
  • Mathematics + Physics (Double Degree)
  • Computer Engineering + Mathematics (Double Degree)
  • Software Engineering + Mathematics (Double Degree)
  • Primary Education + Mathematics (Double Degree)
  • Economics + Mathematics (Double Degree)
  • Economics + Mathematics and Statistics (Double Degree)

Applicants who have advanced degrees in scientific and technological disciplines may also be admitted, provided that they prove, in the opinion of the Master's Academic Committee, sufficient mathematical knowledge to be able to take the master's degree successfully.

Selection of applicants:

Where appropriate, if necessary, assessment of the student's curriculum, its projection in relation to the objectives of the master's degree, as well as their academic record.

In the event that the demand exceeds the places offered, the following scale will be followed:

  1. Academic record: 70%
  2. Research experience related to the master's degree (publication of articles or monographs, participation in research groups, etc.): 10%
  3. Personal interview (the student's personal motivation and attitude and aptitude towards the contents of the master's degree will be assessed): 10%
  4. Other merits (awards, scholarships, attendance at scientific meetings related to the master's degree, professional experience related to the master's degree, level of English accredited by official bodies, etc.): 10%

Offer of places: 15 seats. If the minimum number of students envisaged is not reached in a course, the University may choose not to open the teaching group.

See admission and enrollment

Training itinerary

Master's Teaching Guides


Training Itinerary

Custom code






Advanced Algebra





Advanced Mathematical Analysis





Algebraic and Analytic Methods in Geometry and Topology





Advanced Methods of Equations in Partial Derivatives





Advanced Numerical Methods





Advanced Methods in Statistics and Operations Research





Quantum mechanics





Research Methodology in Mathematics





Mathematics Research Seminar





Master's thesis





External Internships

The External Practices subject is a curricular subject whose main objective is to promote a comprehensive training of the student through the practical application of the knowledge acquired during the Master's degree, which facilitates direct contact with the professional activity and the opportunity to join the professional world with a minimum of experience. All practices are designed so that the students who participate in them acquire professional experience in real situations and conditions, applying the knowledge, skills and attitudes that are acquired in the training processes throughout the degree. The internships represent a decisive opportunity for the personal development and professional future of the students.

Internships are activities carried out by the student in companies, institutions and organizations; that is, in centers outside the university premises, which aim to enrich and complement their university education, while providing them with a deeper knowledge about the skills they will need in the future.

The External Practices subject will consist of two phases.

First. Completion of the internship period that offers professional experience related to any of the profiles that are expressed in the Verification Report of the degree.

Second. Preparation of memory.


Degree Training Project

For more information:  External Internship Unit

Social Security contributions for interns starting January 1, 2024

Mobility programs

University Master's degrees, due to their duration and characteristics, in general do not specifically contemplate the mobility of their students. However, the Rey Juan Carlos University has different mobility programs for both students and University workers (PDI and PAS) and has procedures for collecting and analyzing information on these mobility programs.

URJC Mobility







  • Article 6.1.2. The favorable resolution of the request for total cancellation of registration does not necessarily imply the refund of the amount paid by the student. To do this, the requirements established in the Article 10.3 of the present regulations.
  • Article 11.3.  The extension of the period of permanence will be requested through the procedure established for this purpose by the Rey Juan Carlos University in the electronic office, within the established period. The Rector may authorize the continuation of studies in those cases in which exceptional causes, duly documented, have affected the academic performance of the students., valid for that academic year (up to a maximum of one year)
  • Article 11.4.  In accordance with what is established by the Article 4 of these regulations, those students whose request to remain is resolved favorably will have to enroll in all the remaining subjects to complete their studies.
  • Article 11.5.  For subjects with an indefinite call, once the extension of the permanence period is granted, the fees corresponding to the second and successive registrations will be paid according to the corresponding Public Price Decree as long as they have been previously enrolled in that subject.
  • Article 12.4.  Once this is granted, the student must enroll in accordance with the provisions of the Article 4 of the present regulations.
  • Article 12.5.  For subjects with an indefinite call, once continuity in the University Master's studies is granted, the fees corresponding to the second and successive registrations will be paid according to the corresponding Public Price Decree as long as they have been previously enrolled in that subject.


Quality guarantee

RUCT link


Results report

Once the monitoring of the Master's Degree has been carried out, the most relevant quantitative information on the results obtained in the monitoring of said Degree is displayed, differentiated by academic year.

Report by course:    


General information collection plan

Within the quality assurance system of the Rey Juan Carlos University, the following surveys are planned:

- Student profile

- Teacher evaluation

- Degree of satisfaction:

  • Of the students
  • of the graduates
  • From the Faculty
  • Administration and Services Staff

- Labor insertion

- External internships:

  • Satisfaction of interns
  • External tutor satisfaction
  • Employer satisfaction

Survey results:

Improvement actions

The Quality Assurance System of the Rey Juan Carlos University establishes that the degree's Quality Assurance Commission will annually analyze the information derived from the degree's indicators and prepare a report that will include improvement plans if the results so indicate.

Renewal of accreditation

The renewal of the accreditation represents the culmination of the implementation process of the official Bachelor's and Master's degrees registered in the Register of Universities, Centers and Degrees (RUCT). The renewal of the accreditation of official bachelor's and master's degrees is organized in three phases: self-assessment report, external visit and final assessment.

In the first phase, the university describes and assesses the status of the degree with respect to the established criteria and guidelines. The result is the Self-Assessment Report (IA) that is presented. The second and third phases are carried out by a group of evaluators external to the evaluated title.”