# Degree in Mathematics

240 credits - Higher Polytechnic School

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 | 144 | 24 | - | 12 | 240 |

## Subject list by year and semester

## Subjects

### First Year

#### First Semester

Mathematical Analysis I*

Linear Algebra I*

Fundamentals of Mathematics*

Software and Problems Laboratory I*

#### Second Semester

Mathematical Analysis II*

Discrete Mathematics*

Programming (Computer Science I)*

Software and Problems Laboratory II*

### Second Year

#### First Semester

Mathematical Analysis III

Linear Algebra II

Differential Calculus with Diverse Variables

Topology

Introduction to Geometry

#### Second Semester

Abstract Algebra I

Numerical Methods I

Integral Calculus with Diverse Variables

Affine and Metric Geometry

Mathematic Models of Technology

### Third Year

#### First Semester

Probability

Ordinary Differential Equations

Differential Geometry

Algorithmics

Abstract Algebra II

#### Second Semester

Numerical Methods II

Statistics

Equations in Partial Derivatives

Complex Variable Functions

Introduction to Optimisation

### Fourth Year

#### First Semester

Data Analysis

Geometry and Topology of Varieties

Mathematical Models of Physics

History of Mathematics

#### Second Semester

Final Degree Project - Mathematics

*Elective 1 Elective 2 Elective 3 Elective 4*

* Core Training

## Skills

### Cross-cutting and General 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.
- 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.
- 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.

### 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 apply the fundamental concepts and results of differential and integral calculus for functions with a real variable and multi-varaiables, as well as classic vector calculus, in both mathematics and other areas of knowledge.
- 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.