Bachelor in Mathematics and Computing

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.

Movilidad europea

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

Graduates in 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.

1. Knowledge of Titles

K1 - To know the principles and values of democracy and sustainable development, in particular respect for human rights and fundamental rights, gender equality and non-discrimination, the principles of universal accessibility and climate change.

K2 - To know basic humanistic contents, oral and written expression, following ethical principles and completing a multidisciplinary training profile.

K3 - Know the fundamental results of real, complex and functional mathematical analysis and how to apply them in solving theoretical and applied problems..

K4 - Know the principles of probability calculus and statistical inference and how to apply them in solving real-life problems.

K5 - Know the fundamental results of linear algebra, linear geometry and discrete mathematics and how to apply them in applied contexts.

K6 - Know the fundamental results of the theory of ordinary, partial differential and stochastic differential equations and their applications in mathematical models.

K7 - To know the structure and architecture of computers, as well as the basic components that make them up.

K8 - To know the declarative paradigm of programming in general and logic programming in particular, as an alternative to other types of programming.

K9 - Know the principles of the relational model and database design, as well as software verification strategies, including the definition of tests in different development processes.

K10 - Conocer las técnicas de representación en inteligencia artificial y las estrategias heurísticas de optimización, pudiendo seleccionar y aplicar las más adecuadas según el tipo de problema y utilizar herramientas informáticas para su implementación.

K-OPT1 - Know discretisation and approximation techniques for modelling physical phenomena and dynamic processes by means of differential equations, evaluating the suitability of each method according to the problem, understanding its precision, stability and convergence.

K-OPT2 - Know advanced mathematical models to represent real-world phenomena, assessing their validity in different contexts.

K-OPT3 - To know mathematical algorithms for portfolio optimisation, financial product valuation and market risk modelling.

K-OPT4 - Relate non-linear modelling techniques and stochastic processes describing spatially and temporally complex dynamical systems.

K-OPT5 - Know algorithms for concurrent and parallel execution environments, taking advantage of multiprocessor and distributed architectures.

K-OPT6 - Know interactive data analysis and visualisation tools to facilitate the interpretation of large volumes of information and decision-making.

K-OPT7 - Relate different bio-inspired computing techniques, such as genetic algorithms and neural networks, to the resolution of optimisation and learning problems.

K-OPT8 - Determine machine learning models for pattern identification and data-driven decision making.

K-OPT9 - Relate the theoretical and practical techniques acquired in the degree, in a professional context, solving real problems and developing teamwork skills and experience in the workplace.

2. Skills of Titles

S1 - To plan and organize team work making the right decisions based on available information and gathering data in digital environments.

S2 - To use information interpreting relevant data avoiding plagiarism, and in accordance with the academic and professional conventions of the area of study, being able to assess the reliability and quality of such information.

S3 - Apply mathematical language and abstract-rigorous reasoning in the enunciation and demonstration of results in various areas of mathematics.

S4 - Identify programming paradigms (imperative, generic, object-oriented and functional) evaluating their impact on the performance of algorithms and applications.

S5 - Analyse the operation of the computer and its impact on the performance of programs, considering its physical limitations.

S6 - Apply the theory of grammars, languages and automata in the design of parsers for programming languages and domain-specific languages.

S7 - Apply the mathematical foundations of cryptography to evaluate the advantages and limitations of different cryptographic algorithms.

S8 - Develop programs that make use of the features, functionalities and structures of the operating system.

S9 - Apply software verification techniques to assess compliance with specifications and detect errors in software components.

S10 - Apply the fundamentals of Bayesian statistics and computationally intensive techniques to implement Bayesian inference and prediction in machine learning.

S11 - Analyse the influence of mathematical foundations in functional programming languages and their impact on practical applications.

S12 - Develop numerical calculation techniques, selecting suitable algorithms and programming them on a computer to solve mathematical problems.

S13 - Formulate realworld problems by means of mathematical models for their subsequent analysis and resolution.

S14 - Apply appropriate analytical or numerical techniques to solve mathematical models associated with real-world problems and interpret the results obtained.

3. Competences of Titles

C1 - To Know and be able to handle interpersonal skills on initiative, responsibility, conflict resolution, negotiation, etc., required in the professional environment.

C2 - Design programs that solve mathematical problems, applying algorithmic procedures with special attention to performance.

C3- Design data structures, determining their computational and storage complexity.

C4 - Evaluate database storage and management systems, designing efficient storage and access structures.

C5 - Utilise multiprocessor architectures, multicore processors and computational accelerators to improve the performance of mathematical algorithms with parallelisation.

C6 - Model real-world processes using stochastic processes and queuing theory, and simulate them on a computer.

C7 - Establish the definition of a new mathematical object, in terms of others already known for solving problems in different contexts.

C8 - Solve mathematical problems arising from new developments in computer science using advanced mathematical tools and techniques.

C9 - Individually elaborate, present and defend before a university panel, a project or original work in the field of Mathematics and Computer Science in which the learning results acquired in the courses are synthesised and integrated.

C-OPT9 - Apply the theoretical and practical techniques acquired in the degree, in a professional context, solving real problems and developing teamwork skills and experience in the workplace.

External Internships

This is a selection of places where students of this degree can do their internships:

• Innova Next S.L.U.
• Banco Santander
• mscope
• Sngular
• MrByte
• 12_GRUPO GENERALI ESPAÑA, A.I.E.
• Hologic
• EY
• Avanade
• Banco de España
• PHILOTECH IBÉRICA SISTEMAS Y LOGÍSTICA, S.L
• AGROAEROSPACE SL
• INDIZEN TECHNOLOGIES, S.L.
• BBVA
• Byevolution Creative Factory S.L.
• SAMSUNG ZHILABS SLU
• SimplAI SL

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.

Schedules and calendars

Schedule in bachelor's degree

Academic calendar

Exams calendar (first semester)

Exams calendar (second semester)

Exams calendar (recovery tests)

Schedules and Calendar

Schedule in bachelor's degree

Academic calendar

Exams calendar (first semester)

Exams calendar (second semester)

Exams calendar (recovery tests)