# Double Degree in Mathematics and Telematics (2013)

360
credits
- Higher Polytechnic School

*This study programme*

**will not be continued**; new students will not be admitted. You can refer to

**the corresponding current study programme.**.

Title

Official

Start Year

2013-14

Minimum number of credits to be taken in the first year

- 48 first-year subject credits for full-time students.
- 24 credits for part-time students.
- After the first year of registration, there is no minimum number of credits to take.

Attendance requirements

Other information

Public tuition prices per credit
.
Academic Year
2019-20

- 1st registration : 18,50¤
- 2nd registration : 41,12¤
- 3rd registration : 89,02¤
- 4th registration : 123,35¤

## Skills

### Mathematical Skills. General and Cross-cutting Skills

- Developing interpersonal skills and commitments to fundamental ethical and legal values, especially in terms of equality and ability.
- Developing analytical and summary, organisation and planning, and decision making skills.
- Being able to communicate orally and in writing with people who have different knowledge levels in maths.
- Having the ability to understand, speak and write English at intermediate level.
- Developing leadership skills, initiative, an entrepreneurial spirit and effectiveness in a demanding environment, based on creativity, quality and adaptation to new situations.
- Having an ability for teamwork, both in maths and in a multidisciplinary field.
- Having the ability to speedily acquire new knowledge through self-managed and independent work.
- Having the ability to understand and use mathematical language and setting out proposals in different mathematical fields.
- Having the ability to take in the definition of a new mathematical object, in other known terms, and being able to use this object in different contexts.
- Having the ability to apply acquired knowledge to building demonstrations, detecting errors in incorrect reasoning and problem solving.
- Having the ability to abstract the structural properties of mathematical objects, observed reality and other fields, and knowing how to prove them through simple demonstrations or refute them through counterexamples.
- Having the ability to propose, analyse, validate and interpret simple real situation models.
- Having the ability to search for resources and manage information in the mathematics field.
- Knowing how to develop computer programs and use applications to experiment in mathematics and solve problems, deciding in each instance on the most suitable computational environment.

### Mathematical Skills. Specific Skills

- Working with vectors, bases, sub-spaces, matrices, linear applications, endomorphism and multi-linear forms. Solving linear geometry problems.
- Working with points, vectors, linear variations, distances, angles, affine, orthogonal and isometric transformations. Solving affine and metric geometry problems.
- Knowing the foundations of Euclid's axiomatic geometry and other non-Euclidean geometries.
- Putting forward and solving problems linked to basic plane and spatial geometry figures with synthetic methods.
- Classifying conics and quadrics, and solving problems related to them.
- Knowing some matrices calculation applications and, generally, linear methods in different areas of knowledge: science, social sciences and economics, engineering and architecture.
- Knowing and using basic logic language. Working with sets, ratios and applications.
- Knowing the basic methods and principles of combinatorics. Solving calculation problems.
- Knowing and applying the arithmetical properties of whole numbers. Working with congruence relations. Knowing some applications of modular arithmetic.
- Recognising the properties of an algebraic structure. Using substructures, product structures and quotient morphisms. Solving problems linked to groups and rings.
- Knowing the structure of some simple groups and working with them. Knowing some applications of group theory in mathematics and in other areas of knowledge.
- Knowing the arithmetical properties of polynomials on a field. Working with ideals of polynomial rings.
- Constructing fields from polynomials. Knowing some applications of finite fields in information theory.
- Knowing the basic concept of field extensions and working with algebraic and transcendental extensions.
- Knowing the basic concepts of graph theory, as well as problem solving algorithms in graphs and some of their applications.
- Knowing and using basic concepts linked to the notions of normed, metric and topological spaces.
- Building examples of topological spaces using the notions of subspace topology, product space and quotient space.
- Knowing the basic concepts of homotopy paths and their basic applications.
- Knowing and determining local geometry of curves in R3.
- Knowing the intrinsic and extrinsic geometry of surfaces in R3, and knowing how to determine some aspects.
- Recognising some global properties of curves and surfaces.
- Knowing how to work formally, intuitively and geometrically with the fundamental notions of infinitesimal calculus.
- Knowing how to use elementary functions and their applications in modelling both continuous and discrete phenomena.
- Knowing how to use and knowing the fundamental concepts and results of differential and integral calculus for functions with a real variable and multi-variables, as well as classic vector calculus.
- Knowing how to set out and analytically solve optimisation problems linked to fields that are not necessarily mathematical, applying the methods studied to solve them.
- Knowing the fundaments of the theory of functions with a complex variable and knowing some of their applications.
- Knowing the historical development of the main mathematical concepts, placing them in the context of their evolution.
- Knowing the basic aspects of the Fourier series and some of its applications.
- Knowing and being able to use the basic concepts and results linked to differential equations, with particular emphasis on the linear side.
- Understanding the need to use numerical methods and qualitative focuses to solve differential equations, and knowing some of them.
- Knowing and applying the main methods for solving some ordinary differential equations and simple partial derivatives.
- Solving linear systems of ordinary differential equations.
- Extracting qualitative information on an ordinary differential equation solution, without having to solve it.
- The ability to use mathematical formalism to design and test computer programs.
- Knowing the environment and elements of a computer system and using basic IT tools.
- Having the ability to efficiently design, analyse and implement symbolic and numerical algorithms in a high-level programming language.
- Having the ability to assess and compare different methods based on the problems to be solved, the computational cost, performance time and the existence and propagation of errors, amongst other features.
- Assessing results obtained and reaching conclusions after a computing process.
- Developing the ability to identify and mathematically describe a problem, structure available information and select a suitable mathematical model to solve it.
- Having the ability to carry out different stages in the mathematical modelling process: set out the problem, experiment/test, the mathematical model, simulation/program, debate results and adjust/overhaul the model.
- Knowing the basic principles and results of mathematical programming.
- Setting out and solving linear and simple programming problems.
- Having the ability to use, synthesise, display and interpret data sets from a descriptive statistical standpoint.
- Knowing the basic concepts and results of probability theory and some of its applications, and being able to recognise that the most common probability distributions appear in real situations.
- Knowing the basic properties of estimators and using basic methods to construct them.
- Being able to make inference about the parameters of a population or two through confidence intervals and contrasting hypotheses.
- Solving and analysing basic linear model problems by using regression analysis.

### Telematics Skills. General Skills

- Critical reasoning: the ability to analyse and assess different alternatives.
- Problem solving: the ability to find optimum solutions for complex problems and projects.
- Creativity, innovation and a future outlook: the ability to create and innovate products and services.
- The ability to adapt to the rapid development in ICT and markets.
- Writing skills: drafting projects and technical documentation.
- Oral skills: clarity and fluency in presenting results, products and services to specialised and general audiences.
- Knowledge of software and IT support tools to create and present documentation.
- Knowledge of English: the ability to understand, speak and write in English to an intermediate level.
- The ability for multidisciplinary and multilingual teamwork.
- Leadership ability.
- The ability to manage resources and projects.
- The ability to continue independent lifelong learning (continuous vocational training).
- The ability to analyse social, environmental, ethical, economic and commercial dimensions to engineering work.
- The ability to analyse and assess the impact of technological solutions on occupational health, safety and hazards.
- The ability to ensure technical solutions do not discriminate on the grounds of gender or disability.

### Telematics Skills. Core Skills

- The ability to solve mathematical problems that may arise in engineering.
- An aptitude for applying knowledge on: linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial derivatives; numerical methods; numerical algorithms, and statistics and optimisation.
- Basic knowledge on the use and programming of computers, operating systems, databases and computer programs with engineering applications.
- Understanding and mastery of basic concepts of the general laws of motion, thermodynamics, fields and waves, and electromagnetism, and their application to solve inherent engineering problems.
- Understanding and mastery of the basic concepts of linear systems and their related functions and transforms, the theory of electric circuits, electronic circuits, the physical principle of semiconductors and logic families, electronic and photonic devices, materials technology and their application to solve inherent engineering problems.
- Appropriate knowledge on corporate concepts, and corporate institutional and legal frameworks. Business organisation and management.

### Telematics Skills. Common Telecommunications Skills

- The ability to acquire new knowledge and suitable techniques independently to design, develop or operate telecommunications systems and services.
- The ability to use information and communication applications (office automation, databases, advanced spreadsheets, project management, visualisation, etc.) to provide support to telecommunications and electronic network, service and application development and operation.
- The ability to use IT tools to research bibliographic or information resources linked to telecommunications and electronics.
- The ability to analyse and specify the fundamental parameters of a communication system.
- The ability to assess the advantages and disadvantages of different technology alternatives for rolling out and implementing communication systems, from the standpoint of signal space, interference and noise, and analogue and digital modulation systems.
- The ability to design, roll out, organise and manage telecommunications networks, systems, services and infrastructures in residential (home, city and digital communities), business or institutional contexts, taking charge of commissioning and continuous improvement, as well as being aware of their economic and social impact.
- Knowing and using programming fundaments for telecommunications networks, systems and services.
- The ability to understand electromagnetic and sound wave propagation and transmission, and their corresponding emitters and receivers. The ability to analyse and design combinational and sequential, synchronous and asynchronous circuits, and using microprocessors and integrated circuits.
- Knowing and applying hardware description languages.
- The ability to use different energy sources, especially solar and thermal, as well as the fundaments of electrical and electronic power engineering.
- Knowing and using the concepts of network architecture, protocols and communication interfaces.
- The ability to distinguish the concepts of access and transport networks, circuit and packet switching networks, wired and mobile networks, as well as the systems and applications of distributed networking, voice services, data, audio, video, and interactive and multimedia services.
- Knowing network and routing interconnection methods, as well as the fundaments of planning and dimensioning networks based on traffic parameters.
- Knowledge of standards and regulations on telecommunications nationally, in Europe and internationally.

### Telematics Skills. Specific Telematics Skills

- The ability to construct, operate and manage telecommunications networks, services, processes and applications, understood as capture, transport, representation, processing, storage, management and presentation systems for multimedia information, from the standpoint of telematic services.
- The ability to apply techniques based on telematic networks, services and applications, such as management, signalling and switching, routing, security (cryptology protocols, tunnelling, firewalls, payment mechanisms, authentication and content protection), traffic engineering (graph theory, queueing theory and teletraffic), service pricing, reliability and quality systems, in fixed-line and mobile, personal, local and long distance environments, with different bandwidths, including telephony and data.
- The ability to construct, operate and manage telematic services using planning analysis tools, dimensioning and analysis.
- The ability to describe, program, validate and optimise communication protocols and interfaces at different levels of network architecture.
- The ability to follow the technological progress of transmission, switching and processing to improve telematic networks and services.
- The ability to design network architectures and telematic services.
- The ability to program telematic services and applications in networking and distributed networking.

### Skills regarding the Final Degree Project

- An original project to be done individually, and presented and defended before a university panel, comprising a project in the field of specific professional Telecommunications Engineering technologies, where the skills acquired throughout the course are integrated and summarised.