Double degree in Mathematics and Informatics Engineering

360 credits - Higher Polytechnic School

  If you cannot find all of the information on the course that you are taking, check the old Double degree in Mathematics and Informatics Engineering study programme.
Title
Official
Implementation year of this curriculum version
2025-26

The Double Degree in Mathematics and Informatics Engineering enables students to attain all the skills and abilities on both degree programmes. This double degree provides Balearic society with highly qualified graduates in mathematics and informatics engineering thanks to their useful double professional profile and a mutually reinforced global overview.

The Degree in Mathematics at the UIB is characterised by its applied aspects related to specific real-life problems. The modelling subjects with their mathematical aspects provide students with the chance to acquire the typical skills of mathematicians from a more applied approach. This enables them to deal with a far wider spectrum in their professional development.

The Degree in Informatics Engineering trains students with the knowledge to design and handle computer hardware, or design and develop computer networks. It also provides training in conceptualising and developing all types of apps. In turn, it trains them in project management, as well as how to effectively manage and allocate human and computing resources at any organisation.

Thanks to a solid foundation in mathematical theory, the learning on both degrees enables students to apply modelling tools to analyse and solve computing problems. In turn, thanks to the computing knowledge provided, mathematical training is complemented in its most applied aspect. This double programme trains future graduates to undertake the inherent professional tasks of mathematicians and computer engineers from a new multifaceted interdisciplinary approach that is in ever greater demand in today's society.

Finally, one of the programme's goals is to provide students with the skills to understand, speak and write in English.

Credit Summary

Core Training Mandatory Elective Subjects External Practicum Final Degree Project Total
  78   210   42   -   30 360

Subject list by year and semester

Subjects

First Year

First Semester

Mathematical Analysis I*
Linear Algebra I*
Programming - Computer Studies I*
Computer Engineering, Business and Society*
Fundamentals of Mathematics*

Second Semester

Mathematical Analysis II*
Programming II*
Linear Algebra II*
Physical Foundations of Computers*
Software Engineering

Second Year

First Semester

Digital Systems
Algorithmics and Data Structures I
Discrete Mathematics
Differential Calculus with Diverse Variables
Topology
Mathematical Analysis III

Second Semester

Databases I
Integral Calculus with Diverse Variables
Fundations of Probability and Statistics
Computer Structure I*
Abstract Algebra I
Algorithmics and Data Structures II
English for Engineering (Elective)

Third Year

First Semester

Affine and Metric Geometry
Operating Systems I
Computer Structure II
Probability
Ordinary Differential Equations
Data Communication and Networks

Second Semester

Numerical Methods I*
Statistics
Operating Systems II
Performance Evaluation of Information Systems
Programming Languages
Theory of Computation*

Fourth Year

First Semester

Differential Geometry
Abstract Algebra II
Compilers**
Project Management
Artificial Intelligence
Databases II**

Second Semester

Partial Differential Equations
Abstract Algebra III
Numerical Methods II
Multivariate Data Analysis**
Computer Graphics**
Advanced Algorithms**

Fifth Year

First Semester

Functions of Complex Variable
Optimisation
Concurrent Programming
Internet Distributed Applications and User Interfaces
Numerical Methods III
Machine Learning**

Second Semester

Software Project Lab**

Annual

Final Degree Project in Mathematics
Final Degree Project in Informatics Engineering

 * Core Training
** Majors Electives

  Learning Outcomes

Mathematical Capabilities

  • RA01- Supporting equality, liberty, tolerance and respect for diversity; universal accessibility; social integration; justice; peace; participation; gender equality; equal treatment and non-discrimination, and respecting the needs and rights of current and future generations, other species and nature.
  • RA02- Understanding how elements in systems interact from a systemic approach; questioning the status quo through critical thinking, and contextualising social and environmental issues in terms of space, time and glocalisation, in order to identify approaches to prevent and anticipate problems, as well as mitigate and adapt to existing problems.
  • RA03- Identifying the required steps for a sustainable future and managing transitions in light of uncertainty and risk; creating and experimenting with new approaches from an inter- and intra-disciplinary approach.
  • RA04- Identifying political responsibilities and advocating for accountability for unsustainable activities through personal and professional conduct, as well as demanding effective sustainability policies.
  • RA05- Developing interpersonal skills and commitments to fundamental ethical and legal values, especially in terms of equality and ability.
  • RA06- Developing skills for analysis, summaries, organisation, planning and decision-making.
  • RA07- Being able to communicate orally and in writing with people who have different knowledge levels in maths.
  • RA08- Knowing how to develop computer programs and use applications to experiment in mathematics and solve problems, deciding in each instance on the most suitable computing environment.
  • RA09- Developing leadership skills, initiative, an entrepreneurial spirit and effectiveness in a demanding environment, based on creativity, quality and adapting to new scenarios.
  • RA10- Having an ability for teamwork in maths and multidisciplinary fields.
  • RA11- Having the ability to acquire new knowledge quickly through self-directed and independent learning.
  • RA12- Having the ability to understand and use mathematical language and setting out proposals in different mathematical fields.
  • RA13- 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.
  • RA14- Having the ability to apply acquired knowledge to building demonstrations, detecting errors in incorrect reasoning and problem solving.
  • RA15- 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.
  • RA16- Having the ability to propose, analyse, validate and interpret simple real situation models.
  • RA17- Having the ability to search for resources and manage information in the mathematics field.
  • RA21- Framing and solving elemental geometric shape problems (plane and space) via synthetic methods.
  • RA39- Knowing how to work formally, intuitively and geometrically with the fundamental notions of infinitesimal calculus.
  • RA40- Knowing how to use elementary functions and their applications in modelling both continuous and discrete phenomena.
  • RA42- Knowing how to use the fundamental concepts and results of differential and integral calculus for functions with one and several real variables, as well as classic vector calculus.
  • RA43- Knowing how to set out and analytically solve optimisation problems not necessarily linked to mathematics by applying the studied methods.
  • RA51- Extracting qualitative information on an ordinary differential equation solution, without having to solve it.
  • RA52- The ability to use mathematical formalism to design and test computer programs.
  • RA54- Having the ability to efficiently design, analyse and implement symbolic and numerical algorithms in a high-level programming language.
  • RA55- 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, in addition to other features.
  • RA57- Developing the ability to identify and mathematically describe a problem, structure available information and select a suitable mathematical model to solve it.
  • RA58- 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.
  • RA61- Having the ability to use, synthesise, display and interpret datasets from a descriptive statistical standpoint.

Mathematical Content or Knowledge

  • RA23- Being familiar with certain matrix calculation applications and, generally, linear methods in different areas: science, social sciences, economics, engineering and architecture.
  • RA28- Understanding the structure of some simple groups and working with them. Understanding certain applications of group theory in mathematics and in other knowledge areas.
  • RA30- Constructing fields from polynomials. Understanding certain applications of finite fields in information theory.
  • RA32- Understanding the basic concepts of graph theory, as well as problem-solving algorithms in graphs and some of their applications.
  • RA33- Being aware of and using basic concepts linked to normed, metric and topological spaces.
  • RA35- Understanding core topological concepts linked to connected relation, compact space and separable space.
  • RA38- Recognising some global properties of curves and surfaces.
  • RA41- Using and understanding the fundamental concepts and results of differential and integral calculus for functions with one and several real variables, as well as classic vector calculus.
  • RA44- Understanding the foundations of the theory of functions with a complex variable and their applications.
  • RA45- Understanding the historical development of major mathematical concepts, and contextualising their evolution.
  • RA46- Understanding the basic aspects of the Fourier series and some of its applications.
  • RA48- Understanding the need to use numerical methods and qualitative focuses to solve differential equations, and being familiar with specific examples.
  • RA53- Understanding the environment and elements of a computer system, and using basic IT tools.
  • RA56- Assessing obtained results and reaching conclusions after a computing process.
  • RA59- Understanding the core principles and results of mathematical programming.
  • RA62- Understanding 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.

Mathematical Skills or Abilities

  • RA18- Working with vectors, bases, sub-spaces, matrices, linear applications, endomorphism and multi-linear forms. Solving linear geometry problems.
  • RA19- Working with points, vectors, linear variations, distances, angles, affine, orthogonal and isometric transformations. Solving affine, metric and projective geometry problems.
  • RA20- Understanding and being able to use the fundamental concepts and results from Lebesgue’s Measure and Integral.
  • RA22- Classifying conics and quadrics, and solving problems related to them.
  • RA24- Understanding and using basic logic language. Working with sets, ratios and applications.
  • RA25- Understanding the basic methods and principles of combinatorics. Solving counting problems.
  • RA26- Understanding and applying the arithmetical properties of integers. Operating with congruence. Being aware of certain modular arithmetic applications.
  • RA27- Recognising the properties of an algebraic structure. Using substructures, product structures, quotients and morphisms. Solving problems linked to groups and rings.
  • RA29- Understanding the arithmetical properties of polynomials on a field. Working with ideals of polynomial rings.
  • RA31- Understanding the basic concept of field extensions and working with algebraic and transcendental extensions.
  • RA34- Constructing examples of topological spaces using the concepts of topological subspace, product space and quotient space.
  • RA36- Understanding and determining the local geometry of curves in R3.
  • RA37- Understanding the intrinsic and extrinsic geometry of surfaces in R3, and knowing how to determine certain aspects.
  • RA47- Understanding and being able to use the basic concepts and results linked to differential equations, with particular emphasis on the linear side.
  • RA49- Understanding and applying the main methods for solving certain ordinary differential equations and simple partial derivatives.
  • RA50- Solving linear systems of ordinary differential equations.
  • RA60- Setting out and solving linear and integer programming problems.
  • RA63- Understanding the basic properties of estimators and using core methods to construct them.
  • RA64- Being able to make inference about the parameters of one or two populations through confidence intervals and statistical hypothesis tests.

Informatics Engineering Skills. Cross-cutting Skills

  1. The ability to analyse and synthesise, organise, plan and take decisions.
  2. The ability for critical analysis and to propose and apply new solutions.
  3. The ability for independent learning.
  4. The ability to search out resources and manage information in the field of computing.
  5. The ability to work in multi-disciplinary and multilingual teams.
  6. Leadership, initiative, entrepreneurial spirit and effectiveness in a demanding environment, based on creativity, quality and adapting to new situations.
  7. The ability to communicate computing concepts orally and in writing in different fields of activity.
  8. The ability to understand, speak and write in English to an intermediate level.
  9. The ability to develop interpersonal skills, with a commitment to the values of social, ethical, environmental and fundamental rights, especially in terms of equality and ability.

Informatics Engineering Skills. Core Module Skills

  1. The ability to solve mathematic problems that may arise in engineering.
  2. The aptitude for applying knowledge on: linear algebra, differential and integral calculus; numerical methods; numerical analysis; statistics and optimisation.
  3. The ability to understand and master core concepts of discrete mathematics, logic, algorithms and computational complexity, and their application for solving engineering problems.
  4. Core knowledge in the use and programming of computers, operating systems, databases and computer programs with engineering applications.
  5. Comprehension of the structure, organisation, functioning and interconnectivity of computer systems, the fundaments of their programming and their applications for solving engineering problems.
  6. Comprehension and mastery of core concepts relating to fields, waves and electromagnetism, the theory of electrical circuits, electronic circuits, the principle of semiconductor and logic family physics, electronic and photonic devices, and their application for solving engineering problems.
  7. Sufficient knowledge of business, and the institutional and legal framework of corporations.
  8. Business organisation and management.

Informatics Engineering Skills. Common Module Skills: IT Branch

  1. The ability to design, develop, select and evaluate computer applications and systems, ensuring reliability, security and quality in line with ethical principles and current legislation and regulations.
  2. The ability to plan, design, roll out and supervise IT projects, services and systems in all areas, leading their commissioning and continuous improvement, and assessing their economic and social impact.
  3. The ability to understand the importance of negotiation, the habits of effective working, leadership and communication skills in all software development environments.
  4. The ability to produce the technical specifications for an IT installation that complies with current standards and regulations.
  5. Knowledge, administration and maintenance of IT systems, services and applications.
  6. Knowledge and application of basic algorithmic procedures in information technology to design solutions for problems, and analysing the suitability and complexity of proposed algorithms
  7. Knowledge, design and efficient use of the most suitable data types and structures for solving a problem.
  8. The ability to analyse, design, build and maintain applications robustly, safely and efficiently, selecting the most suitable paradigm and programming languages.
  9. The ability to discover, understand and assess computer structure and architecture, as well as the basic components therein.
  10. Knowledge of the features, functionalities and structure of operating systems, and designing and implementing applications based on their services.
  11. Knowledge and application of the features, functionalities and structure of distributed systems, computer networks and internet, and designing and implementing applications based on them.
  12. Knowledge and application of the features, functionalities and structure of databases enabling appropriate use, and the design, analysis and implementation of applications based on them.
  13. Knowledge and application of the necessary tools to store, process and access information systems, included web-based services.
  14. Knowledge and application of the main fundaments and core techniques for parallel, concurrent, distributed and real time programming.
  15. Knowledge and application of the main fundaments and core techniques for intelligent systems and their practical application.
  16. Knowledge and application of the principles, methodologies and life cycles in software engineering.
  17. The ability to design and assess user-computer interfaces that guarantee accessibility and usability of computer systems, services and applications.
  18. Knowledge of national, European and international legislation and regulations for computing.

Informatics Engineering Skills. Specific Technology Module Skills: Artificial Intelligence and Computing

  1. The ability to acquire in-depth knowledge on the fundamental principles and models of computation and know how to apply them to interpret, select, assess, model and create new concepts, theories, uses and technological developments linked to IT.
  2. The ability to take on the theoretical fundaments of programming languages and the associated lexical, syntactic and semantic processing techniques, and know how to apply them to create, design and process languages.
  3. The ability to assess the computational complexity of a problem, discover algorithmic strategies that could lead to their solution, and recommend, develop and implement the one that ensures improved performance in accordance with the established requirements.
  4. The ability to take on the fundaments, paradigms and techniques in intelligent systems, and analyse, design and build IT systems, services and applications that use these techniques in any area of application.
  5. The ability to acquire, obtain, formalise and represent human knowledge in a computable format to solve problems through a computer system in any area of application, specifically those linked to computation, perception and action in intelligent environments.
  6. The ability to take on and develop computational learning techniques, and design and implement applications and systems that use them, including those dedicated to automatic data extraction and knowledge from large volumes of data.

Informatics Engineering Skills. Final Degree Project Module Skill

  1. An original and individual piece of work to be presented and defended before a university panel that comprises a project in the area of specific technologies in professional Computer Sciences, and which summarises and integrates the skills acquired on the degree programme.