PD:Matemàtiques I

Teaching plan for the course unit

(Short version)

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General information

Course unit name: Mathematics I

Course unit code: 366710

Academic year: 2025-2026

Coordinator: David Ceballos Hornero

Department: Department of Economic, Financial and Actuarial Mathematics

Credits: 6

Single program: S

Estimated learning time

Total number of hours 150

Face-to-face and/or online activities

	- Lecture with practical component	Face-to-face		50
	- Problem-solving class	Face-to-face		10

Supervised project

Independent learning

Learning objectives

Referring to knowledge

Mathematics I plays a central role in providing students with the scientific foundation required for this degree course.

Any discipline that relies on formal modelling depends on the methodological rigour and instrumental approach afforded by mathematical language. Accordingly, students must acquire familiarity with the fundamentals of this language, which forms an integral component of the degree’s scientific content.

The primary objective of the subject is to equip students with the basic mathematical knowledge and techniques necessary to understand mathematical formalism and to express themselves accurately in mathematical language.

A further objective is to develop their capacity to formulate and solve economic problems using mathematical methods, with a gradual progression in the complexity of the problems addressed.

The subject is also designed with a strong instrumental focus, supporting the study of other modules across the degree programme. In particular, it provides the mathematical tools and methods that students will require in subsequent stages of their studies.

Upon successful completion of this subject, students will:

Demonstrate a solid grounding in the core concepts and properties underpinning mathematical formalism.

Show mastery in the use of mathematical tools and procedures and apply mathematical concepts and techniques to the formal representation of economic principles, employing these tools effectively to enhance their understanding of the specific content of Mathematics I and related subjects within the programme.

Referring to abilities, skills

Develop an understanding of the fundamental objects of linear algebra, enabling students to represent relationships involving multiple variables and to express them systematically through vectors.

Acquire analytical skills for studying optimisation problems.

Gain knowledge of the fundamental concepts of real functions and their properties, and use these properties to understand the relationships between economic variables.

Learn to formulate problems in mathematical language, identify the relevant mathematical concepts, determine the most appropriate methods of solution, and interpret the results both from both a mathematical and economics perspective.

Teaching blocks

1. Algebra

1.1. Vector space Rⁿ

1.1.1 Concept
1.1.2 Linear combination of vectors
1.1.3 Linear dependence and independence of vectors
1.1.4 Generating set
1.1.5 Basis of a vector space; components of a vector relative to a basis
1.1.6 Vector subspace

1.2. 1.2 Euclidean space. Quadratic forms

1.2.1 Scalar product: definition and properties
1.2.2 Vector norm: definition and properties
1.2.3 Distance: definition and properties
1.2.4 Basic topological concepts
Quadratic forms: definition and classification

2. Calculus

2.1. Real-valued functions of n variables

2.1.1 Concept, domain and level curves
2.1.2 Partial and directional derivatives. Gradient vector. Marginal concepts
2.1.3 Differentiable functions. Tangent hyperplane
2.1.4 Differentiation of implicit functions
2.1.5 Higher-order derivatives. Hessian matrix
2.1.6 Homogeneous functions

2.2. Unconstrained optimisation

2.2.1 Concept of local and global optima. Weierstrass theorem
2.2.2 Necessary condition for local optimality
2.2.3 Sufficient condition for local optimality
2.2.4 Convex optimisation
2.2.5 Economic applications: optimisation problems

Official assessment of learning outcomes

Assessment procedures are the same for all groups in this subject.

In both the continuous and single modes of assessment, all tasks aim at consolidating the competencies that the course seeks to develop.

All problems and exercises set require the ability to analyse and interpret data, and, where possible, exercises are based on practical applications of the concepts introduced on the course.

Where appropriate, ICT tools are included in the presentation, resolution or interpretation of these exercises.

Continuous assessment

The continuous assessment grade is derived from two components:

— Coursework (CW).

— Final examination (FE).

The coursework mark corresponds to two tests (the first on Block 1 of the course, the second on block 2), both carrying equal weight. Students who fail to sit either of these two tests are automatically transferred to the single mode of assessment. The dates of these tests, which coincide with the completion of the corresponding teaching blocks, are announced at the beginning of the course.

Students are also required to sit a final examination on a date determined by the Academic Board. Students who fail to sit this examination appear as a ’no show’ (no presentat) on the official grade record.

The final grade (FG) for students who complete all the activities is calculated as follows:

1. If the mark obtained on the FE is 3 out of 10 or higher, then the mean of the marks awarded for the FE and the CW is calculated (with both weighted at 50%). The FG awarded is then either this mean or the mark obtained on the final exam, whichever is higher:

FG = Maximum {FE, (CW + FE)/2}

2. If the mark obtained on FE is lower than 3 out of 10, the student fails the course:

FG = FE

Students must obtain at least 5 out of 10 to pass the course.

Repeat assessment

Students who do not pass the subject are entitled to sit the repeat assessment exam on the date set by the Academic Board. This examination covers the whole syllabus. The mark obtained on this examination is the final grade for the course. Students must obtain at least 5 out of 10 to pass the course.

Examination-based assessment

Students who fail to sit either of the two coursework tests are automatically transferred to the single mode of assessment.

Students who opt for the single mode of assessment are examined on the entire syllabus in a single examination, held on the date determined by the Academic Board. The mark obtained on this examination is the student’s final course grade. Students must obtain at least 5 out of 10 to pass the course.

Repeat assessment

Students who do not pass the subject are entitled to sit the repeat assessment exam on the date set by the Academic Board. The repeat assessment exam takes the same format as that of the single mode of assessment.

Reading and study resources

Check availability in Cercabib

Book

ADILLON, R.; JORBA, L. (2011): Matemàtiques per a l’economia i l’empresa. Barcelona: Servei de Publicacions de la Facultat d’Economia i Empresa, DL.

Catàleg UB

ADILLON, R.; JORBA, L. (2010): Matemáticas para los grados de Economía y Empresa. Barcelona: Servei de Publicacions de la Facultat d’Economia i Empresa, DL.

Catàleg UB

ALEGRE, P. [et al.] (1995): Matemáticas Empresariales. Madrid: AC.

Catàleg UB

SYDSAETER, K.; HAMMOND, P.J. (2012): Matemáticas para el análisis económico. 2a ed. Madrid: Prentice Hall.

Catàleg UB