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Bachelor in Applied Mathematics and Computing

Duration
4 years (240 ECTS credits)
Centre
Language
English

Presentation

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)
Erasmus+

Program

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

Course 1 - Semester 2

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

Course 2 - Semester 1

General subjects
SubjectsECTSTYPELanguage
Numerical MethodsO6English
CryptographyO6English
Computer StructureFB6English
Integration and MeasureO6English
Automata and formal languages theoryO6English

Course 2 - Semester 2

General subjects
SubjectsECTSTYPELanguage
Data structures and algorithmsFB6English
Artificial IntelligenceO6English
ProbabilityFB6English
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.

 

 

 

 

TYPES OF SUBJECTS

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

 

 

 

 

 

 

Mobility

  • 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 of the Bachelor’s Degree in Applied Mathematics and Computing

    RA1 Students must have acquired advanced cutting-edge knowledge and demonstrated indepth understanding of the theoretical and practical aspects of working methodology in the area of applied mathematics and computing.

    RA2 Through sustained and well prepared argument and procedures, students will be able to apply their knowledge, their understanding and the capabilities to resolve problems in complex specialized professional and work areas requiring the use of creative and innovative ideas"

    RA3 Students must have the capacity to gather and interpret data and information on which they base their conclusions, including where relevant and necessary, reflections on matters of a social, scientific, and ethical nature in their field of study.

    RA4 Students must be able to perform in complex situations that require developing novel solutions in the academic as well as in the professional realm, within their field of study.

    RA5 Students must know how to communication with all types of audiences (specialized or not) their knowledge, methodology, ideas, problems and solutions in the area of their field of study in a clear and precise way.

    RA6 Students must be capable of identifying their own education and training needs in their field of study and the work or professional environment and organize their own learning with a high degree of autonomy in all types of contexts (structured or not).

    RA7 Students must possess the professional maturity necessary to choose and evaluate their work objectives in a reflexive, creative, self-determined and responsible way, for the betterment of society.

    General skills of the Bachelor’s Degree in Applied Mathematics and Computing

    Basic Skills

    CB1        Que los estudiantes hayan demostrado poseer y comprender conocimientos en un área de estudio que parte de la base de la educación secundaria general, y se suele encontrar a un nivel que, si bien se apoya en libros de texto avanzados, incluye también algunos aspectos que implican conocimientos procedentes de la vanguardia de su campo de estudio

    CB2        Que los estudiantes sepan aplicar sus conocimientos a su trabajo o vocación de una forma profesional y posean las competencias que suelen demostrarse por medio de la elaboración y defensa de argumentos y la resolución de problemas dentro de su área de estudio

    CB3        Que los estudiantes tengan la capacidad de reunir e interpretar datos relevantes (normalmente dentro de su área de estudio) para emitir juicios que incluyan una reflexión sobre temas relevantes de índole social, científica o ética

    CB4        Que los estudiantes puedan transmitir información, ideas, problemas y soluciones a un público tanto especializado como no especializado

    CB5        Que los estudiantes hayan desarrollado aquellas habilidades de aprendizaje necesarias para emprender estudios posteriores con un alto grado de autonomía

     

    General Skills

    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       Students 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.

    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.

     

    Transversal Skills

    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 Skills

    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 phenmena, 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.

  • Career opportunities

    Career opportunities

    This degree, highly demanded in this industry, allows future professionals to work in all business and research and development sectors where this mixed profile combining mathematics and computer science skills is in demand.

    • Researcher in R&D centers and universities.
    • Expert in scientific computing applied to industry.
    • Research and Development Manager.
    • Project engineer.
    • Developer of scientific applications.
    • Designer of computer-based models and simulations.
    • Quantitative analyst in financial institutions.
    • Videogame and computer animation developer.
    • Technological and business consultant.
    • Expert in logistics and distribution solutions.
    • Software developer.
    • Data analyst.
    • Development engineer in industrial sectors such as energy, aerospace, naval, manufacturing, ...
    • Teacher.

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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