Degree in Mathematics

240 credits - Higher Polytechnic School

  If you cannot find all of the information on the course that you are taking, check the old Degree in Mathematics study programme.
Title
Official
Implementation year of this curriculum version
2025-26
Report
Fourth official university statement modification ( 07/04/2025 )

The Degree in Mathematics aims to produce graduates for society, given the current difficulty in finding mathematicians to cover job opportunities in this field.

The Mathematics programme at the UIB provides comprehensive training in mathematics to be able to work in any of the fields where graduates may be required. This means that mathematics graduates from the UIB are trained to work in maths teaching and research, as well as in other applied fields.

The Degree in Mathematics programme at the UIB is also known for its training in applied aspects linked to specific problems from everyday life. In this vein, for example, the course offers modelling and computing subjects, especially linked to mathematical aspects. These subjects round out students' learning and enable them to cover a much wider spectrum in their professional career development.

Ensuring that our maths graduates are able to access international postings means a key aspect to the programme at the UIB is the ability to understand, write and speak English. Special emphasis is placed on learning English in the scientific field. This is why the course includes a core English for Science subject, as well as the possibility of writing Final Degree Projects in English. In addition, students also have the possibility of spending time studying on international programmes.

Credit Summary

Core Training Mandatory Elective Subjects External Practicum Final Degree Project Total
  60   132   36   -   12 240

Subject list by year and semester

Subjects

First Year

First Semester

Mathematical Analysis I*
Linear Algebra I*
Fundamentals of Mathematics*
Programming*

Second Semester

Mathematical Analysis II*
Discrete Mathematics*
Linear Algebra II*
Laboratory of Software and Problems*

Second Year

First Semester

Affine and Projective Geometry
Discrete Mathematics
Differential Calculus with Diverse Variables
Topology
Abstract Algebra I

Second Semester

Foundations of Probability and Statistcs
Algorithmics
Integral Calculus with Diverse Variables
Mathematical Analysis III
Numerical Methods II

Third Year

First Semester

Probability
Ordinary Differential Equations
Differential Geometry
Functions of Complex Variable
Abstract Algebra II

Second Semester

Abstract Algebra III
Statistics
Equations in Partial Derivatives
Elective 1
Elective 2

Fourth Year

First Semester

Mathematical Models in Techology
Numerical Methods III
Mathematical Models of Physics
Optimisation

 

Yearlong

Final Degree Project - Mathematics

Second Semester

Elective 2
Elective 3
Elective 4
Elective 5

 * Core Training

  Learning Outcomes

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.

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.

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.