Teaching plan for the course unit

 

 

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General information

 

Course unit name: Mathematics I

Course unit code: 363645

Academic year: 2025-2026

Coordinator: Laura Maria González-Vila Puchades

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

60

 

-  Lecture with practical component

Face-to-face

 

50

 

-  Problem-solving class

Face-to-face

 

10

Supervised project

40

Independent learning

50

 

 

Recommendations

 

Students are expected to have prior knowledge of:
— Calculation of the rank of a matrix using determinants.
— Discussion and solution of linear equation systems.
— Calculation of derivatives.

To this end, an introductory mathematics seminar is offered in early September for new students. This seminar covers the required foundational topics. This seminar takes place before the start of teaching.

 

 

Competences / Learning outcomes to be gained during study

 

   -

Capacity for learning and responsibility (capacity for analysis and synthesis, to adopt global perspectives and to apply the knowledge acquired/capacity to take decisions and adapt to new situations).

   -

To be able to use ICT in professional practice.

Learning objectives

 

Referring to knowledge

Mathematics I is important for ensuring the adequate scientific training of students.

Any discipline that requires the application of formal models needs the instrumental approach and methodological rigour provided by mathematical language. In this subject, students learn the basic outlines of mathematical language, which enable them to handle the scientific content of the rest of the degree.

The first goal of this subject, therefore, is that students acquire the basic mathematical tools to facilitate their scientific training and ensure they can understand mathematical formalism and, at the same time, express themselves in this language.

The second goal is to ensure that students are able to identify and solve, by means of mathematics, problems of an economic nature appropriate to their level of training, with the idea that this level is subject to progressive improvement.

This subject also includes an appreciable instrumental component that can be applied in other subjects. Therefore, an additional objective is that students acquire a solid understanding of instrumental mathematics that they will be able to apply throughout the rest of their studies.

This subject seeks to fulfil two basic aims: students who successfully complete the subject should have acquired a satisfactory basic level of mathematical training and the ability to implement mathematical tools and procedures when required. In other words, the subject covers the concepts required to understand the formal representation of an economic phenomenon and the application of these concepts to the more specific topics of the different teaching blocks.

 

Referring to abilities, skills

Students learn to perform basic linear algebra operations. This enables them to represent and solve equations with multiple variables and arrange them into vector functions. Students also acquire the analytical skills to study optimization problems.

Know the fundamental concepts of real functions and their properties. Use the properties of functions to understand the relationships between economic variables.

Pose problems in mathematical language, detect which mathematical concepts are involved in a problem, know how best to resolve the problem and how to interpret the result, distinguishing between mathematical and economic interpretation.

 

 

Teaching blocks

 

1. Algebra

1.1. Vector space R n

1.1.1. Concept
1.1.2. Linear combination of vectors
1.1.3. Dependence and linear independence of vectors
1.1.4. Generator system
1.1.5. Base of vector space. Components of a vector in a base
1.1.6. Vector subspace

1.2. Euclidean space. Quadratic forms

1.2.1. Scalar product: definition and properties
1.2.2. Rule of a vector: definition and properties
1.2.3. Distance: definition and properties
1.2.4. Basic topological notions
1.2.5. Quadratic forms: definition and classification

2. Calculus

2.1. Real functions of n variables

2.1.1. Concept, domain and contours
2.1.2. Partial and directional derivatives. Gradient vector. Marginality
2.1.3. Differentiable function. Tangent hyperplane
2.1.4. Derivation of compound functions
2.1.5. Derivation of implicit functions
2.1.6. Successive derivation. Hessian matrix
2.1.7. Homogeneous functions

2.2. Unconstrained optimization

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

 

 

Teaching methods and general organization

 

In total, students are expected to dedicate 150 hours to this course (with the exception of GIE groups), distributed as follows:

  • Contact hours: 60 hours, divided between three activities:
    • 48 core lecture hours, where the teaching staff deliver sessions to the whole student cohort. During these classes, students are introduced to the theoretical and practical concepts needed to engage with the course content and achieve the intended learning outcomes.
    • 10 supplementary contact hours. The student cohort is divided into two subgroups. Each subgroup is assigned a lecturer for the discussion and resolution of problems. These sessions are also used to complete the written assessment tests.
    • 2 additional contact hours. Presentation of the subject. Methodology.
  • Tutorials: 40 hours. Students are expected to dedicate these non-contact hours to completing the tasks assigned by the teaching staff.

  • Independent learning: 50 hours. Students are expected to devote these non-contact hours to studying the course material and preparing for the assessment tasks.

NB: GIE groups follow a specific teaching methodology. They comprise students who have already taken the subject. Face-to-face learning consists of one 2-hour session per week. These groups make intensive use of the Virtual Campus.

 

 

Official assessment of learning outcomes

 

The assignments and exercises designed for both types of assessment train students in the specific competences that the course seeks to promote.

Problem sets and exercises require analytical and interpretative skills, and, where possible, tasks are based on practical applications of the concepts studied within the field of economics and business. Where relevant, ICT tools are incorporated into the design, solution, or interpretation of the proposed exercises.

 

Continuous assessment

The final continuous assessment grade is based on two components:

  • Coursework mark (CM);
  • Final examination mark (FEM) obtained during the official assessment period.

The coursework mark (CM) is calculated on the basis of two tests (one on block 1 of the course and the second on block 2), each with the same weighting. Students who fail to sit either of these two tests are automatically transferred to the single mode of assessment. The dates of these two examinations, coinciding 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 (FE) on a date specified by the Academic Board. Students who fail to sit this examination appear as ’no show’ (no presentat) on the final grade record.

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

1. If students obtain a final examination mark (FEM) of 3 out of 10 or higher, the average of the FEM and the CM is calculated (each representing 50%). Once the average has been calculated, the FG is the higher of the two: the average mark or the FEM.

                                                       FG = Maximum {FEM, (CM + FEM) / 2}.

2. If students obtain a FEM lower than 3 out of 10, the student fails the course:

                                                       FG = FEM.

A minimum final grade (FG) of 5 out of 10 is required to pass the subject.

 

Repeat assessment

Students who do not pass the subject are entitled to repeat assessment on the date set by the Academic Board. This examination covers the entire course syllabus. The mark obtained on this examination is the final grade for the subject. Students must obtain a grade of 5 (out of 10) or higher to pass.

 

Examination-based assessment

Students who request single assessment sit a single examination on all of the course content on the date set by the Academic Board. The mark obtained for this examination is the final grade for the subject. Students must obtain a grade of 5 (out of 10) or higher to pass.

Repeat assessment

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

 

 

Reading and study resources

Check availability in Cercabib

Book

ADILLÓN, R.; JORBA, L.. Matemàtiques per a l’economia i l’empresa. Barcelona: Publicacions UB, 2011

Catāleg UB  Enllaç
Catāleg UB. Versiķ en castellā (2010)  Enllaç

SYDSAETER, K.; HAMMOND, P.J.;CARVAJAL, A.M. Matemáticas para el análisis económico. Madrid: Prentice Hall, 2012

Catāleg UB  Enllaç

ALEGRE, P. et al. Matemáticas Empresariales. Madrid: AC, 1995.

Catāleg UB  Enllaç