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Bachelor in Applied Mathematics and Computing

4 years (240 ECTS credits)


The Bachelor’s Degree in Applied Mathematics and Computing seeks to train professionals who are capable of applying mathematics in those areas of science, engineering, economics, and other social sciences where computation plays a key role. 

Students will be prepared in the design and use of algorithms and numerical methods for modelling and for solving real problems.  This degree, in great demand by companies and research institutions, enables future professionals to undertake their professional activity in all the business sectors and in research and development where this mixed profile combining competencies in mathematics and computer science is required.  

Students will acquire sound mathematical knowledge and a robust command of programming and software development, enabling them to focus on the implementation of mathematical computer methods and statistics. In addition, they will learn the theoretical fundamentals of computing and its practical applications; furthermore, students will acquire a solid understanding of the operation of computers which will endow them with the ability to make the most adequate design decisions.

Employability and profesional internships

UC3M has agreements with over 3000 companies and institutions in which students can undertake internships and access job openings.

A total of 93.4 % of graduates from this University enter the job market the first year after finishing their studies, according to the 2019 XXIV Estudio de Inserción Profesional (Professional Placement Study).


International Excellence

QS Top 50 Under 50
Times Higher Education (THE)


  • In year 2020/21 only 1st. and 2nd. year will be offered.

Course 1 - Semester 2

General subjects
Integral CalculusFB6English
Vector CalculusO6English
Linear GeometryFB6English
Discrete MathematicsO6English
Programming TechniquesFB6English

Course 2 - Semester 1

General subjects
Numerical MethodsO6English
Computer StructureFB6English
Integration and MeasureO6English
Automata and formal languages theoryO6English

Course 2 - Semester 2

General subjects
Data structures and algorithmsFB6English
Artificial IntelligenceO6English
Operating SystemsFB6English
Complex AnalysisO6English

** At the end of your studies you must have obtained a total of 12 credits of electivity in Computing and a total of 12 credits of electivity in Maths. 6 credits on each specialization (12 in total) in case you course Professional Internships.

At the end of you studies you must have obtained a total of 24 credits of electivity, 12 of them must be of Electives of type I.






BC: Basic Core
C: Compulsory
E: Electives
BT: Bachelor Thesis








  • Exchange programs

    Exchange programs

    The Erasmus programme permits UC3M first degree and post graduate students to spend one or several terms at one of the European universities with which UC3M has special agreements or take up an Erasmus Placement, that is a work placement or internship at an EU company. These exchanges are funded with Erasmus Grants which are provided by the EU and the Spanish Ministry of Education.

    The non-european mobility program enables UC3M degree students to study one or several terms in one of the international universities with which the university has special agreements. It also has funding from the Banco Santander and the UC3M.

    These places are offered in a public competition and are awarded to students with the best academic record and who have passed the language threshold  (English, French, German etc..) requested by the university of destination.

  • European Mobility

    Movilidad europea

  • Non-European Mobility

Student Profile

  • Incoming students profile

    Incoming students profile

    It is highly advisable that students pursuing this Bachelor's Degree have completed a Science modality during high school (or equivalent modalities in terms of subjects when students come from other non Spanish education systems).

    If some contents need to be higlighted, the student should have a good previous education in Physics and Mathematics. Personal attitudes that are highly appreciated include initiative, work team, personal organization of work, abstraction ability, critical thinking and responsibility and interest towards the practical application of knowledge for real problem solving.

    Last, but not least, the University offers this Bachelor's Degree only in the English option. Consequently, students must complete their 240 credtis in this language. For this reason, students must show a good level in English language skills, equivalent to level B2 in the Common European Framework of Reference for Languages, as all the teaching will be given int that language and all texts, materials, exercises etc will be in English.


    Application for a place in the degree

  • Graduate Profile

    Graduate Profile

    Graduates in Applied Mathematics and Computing must be able to make use of the application of mathematics in those areas of science, engineering, economy and other social sciences where computing plays a central role with a focus in the use of algorithms, and numerical methods to model and solve real world problems that emerge in those disciplines.

    To achieve this, graduates will have a strong command of programming and software development with special attention to the implementation in computers of mathematical methods. Additionally, they will know the theoretical fundamentals of computation theory and their practical applications, include those used by programming languages compilers and interpreters. They will also have a sound understanding of operation of computers that will allow them to take the adequate design decisions to ensure the best performance of the solutions they may conceive. They will know the main techniques in artificial intelligence and how they can be used to solve real world probelms. They will have knowledge in probability, statistics, stochastic methods, and simulation methods that they will be able to use to solve problems. All these aspects will be supported by a strong base in different aspects of mathematics.

    With all these, they will have the ability to carry out their professional career in all domains of the economic activity as well as in research where there is demand for professionals with a profile of application of mathematics with a strong use of computers as a fundamental tool.


    Learning Outcomes

    RA1. To have acquired adavanced knowledge and to have shown understanding of the theoretical and practical aspects and work methodology in the field of applied mathematics and computing with a depth that leads to cutting-edge knowledge.


    RA2. To be able to apply, through arguments or procedures carried out or supported by them, their knowledge, the understanding of them and their problem solving skills in professional and specialized complex work environments where the use of creative or innovative ideas are required.


    RA3. To have the ability to gather and interpret data and information to be used to base their conclusions including, when it is needed, reflection on social, scientific or ethical aspects in the scope of their subject matter.


    RA4. To be able to deal with complex situations or requiring the development of new situations both in academic and professional environments within their field of study.


    RA5. To know how to communicate to all kind of audiences (specialized or no) in a clear and precise way knowledge, methodologies, ideas, problems and solutions in the scope of their field of study.


    RA6. To be able to identify their own training needs in their field of study and their work or professional environment as well as to organize their own learning with a high degree of autonomy in all kinds of contexts (either structured or not).


    RA7. To have the needed professional maturity to select and evaluate their work goals in a reflexive, creative, self-determined and responsible way, for the benefit of society.


    General competencies:


    CB1. Students have shown to have and to understand knowledge in a subject area built from the general secondary education background, and is usually at a level that is supported by advanced textbooks, but also includes some aspects implying knowledge coming from the state of the art in their subject matter.

    CB2. Students are able to apply their knowledge to their job or vocation in a professional way and have the competences that are usually shown by elaboration and defense of arguments and problem solving within their subject matter.

    CB3. Students have the ability to gather and interpret relevant data (usually  within their subject matter) to make judgements, including a reflection on relevant social, scientific or ethical topics.

    CB4. Students can communicate information, ideas, problems and solutions to specialized and non-specialized public.

    CB5. Students have developed those learning abilities that are needed to take later studies with a high degree of autonomy.


    Basic competencies:


    CG1. Students are able to demonstrate knowledge and understanding of concepts in mathematics, statistics and computation and to apply them to solve problems in science and engineering with an ability for analysis and synthesis.

    CG2. Students are able to formulate in mathematical language problems that arise in science, engineering, economy and other social sciences.

    CG3. Students can solve computationally with the help of the most advanced computing tools mathematical models coming from applications in science, engineering, economy and other social sciences.

    CG4. Students are able to show that they can analyze and interpret, with help of computer science, the solutions obtained from problems associated to real world mathematical models, discriminating the most relevant behaviours for each application.

    CG5. Students can synthesize conclusions obtained from analysis of mathematical models coming from real world applications and they can communicate in verbal and written form in English language, in an clear and convincing way and with a language that is accessible to the general public.

    CG6. tudents can search and use bibliographic resources, in physical or digital support, as they are needed to state and solve mathematically and computationally applied problems arising in new or unknown environments or with insufficient information.


    Transversal competencies


    CT1. Students  are able to work in teams that are multidisciplinary and international, as well as to organize and plan work taking the right decisions based on the available information, gathering and interpreting relevant data to emit judgments and critical thoughts within their subject matter.

    CT2. Students are able to state and write correctly on a topic and to compose their discourse following a logical order, providing precise information and according to the established grammar and lexical rules.

    CT3. Students are able to evaluate reliability and quality of information and their sources, using that information in an ethical way, avoiding plagiarism, and following academic and professional conventions in the subject matter.

    CT4. Students can demonstrate that they have acquired humanistic basic knowledge that allows them to complete their cross-cutting educational profile.

    CT5. Students can demonstrate that they know and are able to manage interpersonal skills about initiative and responsibility, negotiation, emotional intelligence, etc, as well as computational tools that allow to consolidate basic technical skills as required in every professional area.


    Specific competencies


    CE1. Students have shown that they know and understand the mathematical language and abstract-rigorous reasoning as well as to apply them to state and prove precise results in several areas in mathematics.
    CE2. Students have shown that they understand the fundamental results from real, complex and functional mathematical analysis.
    CE3. Students have shown that they understand the fundamental results from linear algebra, linear geometry and discrete mathematics.

    CE4. Students have shown that they understand the fundamental results from the theory of ordinary differential equations as well as the theory of partial derivative and stochastic equations.

    CE5. Students have shown that they understand basic techniques from numerical calculus, and that they are able to select adequate algorithms for every situation and to program them in a computer.

    CE6. Students have shown that they know the fundamental mathematical results supporting the theory and the development of programming languages and intelligent systems.

    CE7. Students are able to construct mathematical models of both discrete and continuous processes that appear in real world applications emphasizing the use of deterministic and stochastic difference and differential equations.

    CE8. Students are able to discretize mathematical models associated to real world problems using interpolation and approximation techniques, in order to solve them numerically  by means of direct or iterative methods and to interpret the obtained solutions.

    CE9. Students have shown that they can solve mathematical problems derived from new developments in computer science.

    CE10. Students have shown that they know and understand the algorithmic procedures to design and build programs that solve mathematical problems paying special attention to performance.

    CE11. Students have shown that they know the concepts of imperative, generic, object oriented and functional programming and distinguish interpreted, virtual machine based and native programming languages as well as the impact that they have on performance of algorithms and applications.

    CE12. Students have shown that they know the main data structures, being able to use, design, and implement them determining its computational and storage complexity.

    CE13. Students have shown that they understand how computers work,  and the impact of their structure and operation on programs’ performance as well as their physical limitations.

    CE14. Students have shown that they know the theory of grammars, languages and automatas and they can apply it to programming languages and domain specific languages analyzers as well as that they understand the translation process for high-level languages and most common optimizations.

    CE15. Students have shown that they know the mathematical foundations of cryptography and that they understand the advantages and limitations of different cryptographic algorithms.

    CE16. Students have shown that they understand the characteristics, functionalities and structure of the operating system, and that they can develop programs that make use of their services.

    CE17. Students know how to apply software verification techniques to determine if a software component fulfills its specifications, and that they are able to detect faults in those components.

    CE18. Students know how to evaluate and select in an adequate way storage systems and database management systems and to adequately design storage and access structures, as well as applications that make use of them, including data visualization tools.

    CE19. Students have shown that they know multiprocessor architectures as well as multi-core processors and computing accelerators and that they can use such knowledge to improve performance of mathematical algorithms with special attention to parallelization of those algorithms.

    CE20. Students have shown that they understand the fundamentals of bayesian statistics and that they have learnt the different computational intensive techniques to implement inference and bayesian prediction, as well as techniques used in machine learning.

    CE21. Students have shown that they understand the influence and usefulness of the mathematical foundations used in functional programming languages and the impact of the practical applications of those languages.

    CE22. Students have shown that they understand the concept of random phenomenon, and that they can apply the basic principles of probability calculus and the statistic inference, recognizing their applicability to real problems.

    CE23. Students have shown that they understand the concepts of stochastic processes and queuing theory to model real world processes as well as to simulate them in a computer.

    CE24. Students have shown that they are able to carry out an original exercise individually defended and consisting of a project in the scope of the specific technologies of the Degree, of professional nature, in which the acquired competencies during their studies are synthesized and integrated.

Study in English

Studies in English only

This degree courses completely in English. No groups available in Spanish in any subject. You must take into mind that:

  • In groups in English, all work (classes, drills, exercises, tests, etc.) shall be conducted in English.
  • Along the first year, it must be established an English B2 level, passing a test, providing one of the supported official certificates or any way determined by the university. 
  • After completing the studies, the DS mention of having carried out the studies in English will appear.

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