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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
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Estimated learning time |
Total number of hours 150 |
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Face-to-face and/or online activities |
60 |
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- Lecture with practical component |
Face-to-face |
50 |
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- Problem-solving class |
Face-to-face |
10 |
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Supervised project |
40 |
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Independent learning |
50 |
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Recommendations |
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Students are expected to have prior knowledge of: 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. |
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Competences / Learning outcomes to be gained during study |
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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). |
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To be able to use ICT in professional practice. |
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Learning objectives |
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Referring to knowledge Mathematics I is important for ensuring the adequate scientific training of students.
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. |
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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
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Teaching methods and general organization |
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In total, students are expected to dedicate 150 hours to this course (with the exception of GIE groups), distributed as follows:
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. |
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Official assessment of learning outcomes |
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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 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.
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.
2. If students obtain a FEM lower than 3 out of 10, the student fails the course:
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. |
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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
Catāleg UB. Versiķ en castellā (2010)
SYDSAETER, K.; HAMMOND, P.J.;CARVAJAL, A.M. Matemáticas para el análisis económico. Madrid: Prentice Hall, 2012
ALEGRE, P. et al. Matemáticas Empresariales. Madrid: AC, 1995.