Course guide of Mathematics (2351111)

Mathematics at pre-university learning levels. In the case of using AI tools for the development of the subject, the student must adopt an ethical and responsible use of such tools. The recommendations outlined in the document "Recommendations for the Use of Artificial Intelligence at the UGR," published at the following location, must be followed:
https://ceprud.ugr.es/formacion-tic/inteligencia-artificial/recomendaciones-ia#contenido0

The contents covered in the program are the typical topics of Mathematical Analysis and Linear Algebra:

Numerical series. Geometric series.
Differential and integral calculus of functions of one variable.
Optimization of functions of one variable.
Matrices and determinants. Application to the solution of systems of linear equations.

C01 – Possesses basic knowledge related to the field of study (Computer Science, Statistics, Mathematics, Finance, Accounting, Business Organization and Management, Marketing, Economics), allowing for its integration toward a common goal.

C03 – Analyzes and understands economic reality, identifies the role of companies and the State within the economy, and applies instrumental techniques and tools to solve economic problems and real-life situations.

C07 – Has knowledge of basic mathematical and statistical techniques applied to the economic-business field, quantitatively analyzes the economic-business reality, and interrelates the knowledge acquired in various subjects of the degree program within the mathematical, statistical, and economic theory domains.

1. Basic concepts of single-variable functions

   1. Intervals. Domain and range of a function.

   2. Elementary functions. Properties.

   3. Functions in Economics: supply, demand, revenue, cost, profit, utility.

   4. Limit of a function at a point. Continuity.

   5. Bolzano's Theorem. Applications.

2. Differential calculus of single-variable functions

   1. Differentiability: interpretations and applications.

   2. Derivatives of elementary functions. Differentiation rules.

3. Optimization of single-variable functions

   1. Increasing and decreasing behavior. Concavity and convexity.

   2. Relative and absolute extrema. Weierstrass Theorem.

4. Integral calculus of single-variable functions

   1. Finding antiderivatives.

   2. Definite integral. Barrow's Rule.

5. Basic concepts of matrices and vectors

   1. General overview of vectors: notation, operations, and properties.

   2. General overview of matrices: notation, operations, and properties.

   3. Calculation of determinants.

   4. Inverse matrices.

6. Systems of linear equations

   1. Matrix reduction. Rank of a matrix.

   2. Gauss method.

   3. Rouché–Fröbenius Theorem.

   4. Homogeneous systems.

7. Matrix diagonalization by similarity

   1. Determining eigenvalues and eigenvectors of a matrix.

   2. Equivalent matrices and change-of-basis matrices. Diagonalization.

   3. Economic interpretations and applications.

8. Sequences and series of real numbers

   1. Sequences of real numbers, operators on sequences, arithmetic and geometric sequences.

   2. Series of real numbers, convergence and convergence criteria.

   3. Sums of geometric series.

Seminars/Workshops: Seminars to be chosen by the instructor as reinforcement (when necessary in borderline cases), selected from the following:

1. Supply and demand equations. Profit regions.

2. Approximation of functions using Taylor polynomials (recommended).

3. Optimization of typical economic functions.

4. Matrix equations.

Laboratory Sessions: Computer-based practical sessions as reinforcement (when necessary in borderline cases, i.e., applicable to those students whose grades are between 4.5 and just below 5):

1. Graphing single-variable functions. Differentiation and integration. Computer-assisted methods for solving optimization problems.

2. Matrix operations. Systems of equations. Diagonalization.

M. Álvarez de Morales Mercado y M.A. Fortes Escalona. Matemáticas para Economía y Administración y Dirección de Empresas.

Julia García Cabello, Matemáticas Imprescindibles en la Administración de Empresas: ejemplos prácticos y aplicaciones, Monografías Matemáticas Editorial Avicam Fleming (2016).

J.R. Haeussler. Matemáticas para Administración, Economía, Ciencias Sociales y de la Vida. Ed. Prentice Hall.

J. Stewart. Cálculo Diferencial e integral. Ed. Thomson. H. Sydsaeter. Matemáticas para el Análisis Económico. Ed. Prentice Hall.

P. Alegre. Matemáticas Empresariales. Ed. AC. A. Balbás.

Análisis Matemático para la Economía (I y II). Ed. AC. R. Caballero.

Matemáticas Aplicadas a la Economía y la Empresa. Ed. Pirámide.

https://prado.ugr.es/

https://mateapli.ugr.es/

• MD01. Docencia presencial en el aula 
• MD02. Estudio individualizado del alumno, búsqueda, consulta y tratamiento de información, resolución de problemas y casos prácticos, y realización de trabajos y exposiciones. 
• MD03. Tutorías individuales y/o colectivas y evaluación  

The evaluation will preferably be continuous. However, a single final evaluation may be requested in accordance with the “Evaluation and Grading Regulations for UGR Students” (see the corresponding section below). If the single final evaluation is not requested within the established deadline and form, it will be understood that the student waives this possibility.

Continuous evaluation will be divided into 2 blocks. The score for each block will be obtained from one or more partial exams plus other activities such as practicals, class exercises, virtual exams, seminars/workshops, blackboard presentations, assignments, etc. The breakdown of these scores will be as follows:

• Block I, covering topics 1, 2, 3, and 4, with a maximum score of 5 points, representing 50% of the final grade. Each instructor will inform students of the percentage distribution between problems, theory, computer practices, and other activities included in this block.

• Block II, covering topics 5, 6, 7, and 8, with a maximum score of 5 points, representing 50% of the final grade. Each instructor will inform students of the percentage distribution between problems, theory, computer practices, and other activities included in this block.

The final grade will be the sum of all partial grades obtained.

If the sum is less than 5 points, the student must take the final exam for the block(s) not passed, on the date and place established by the Faculty.

If the sum is equal to or greater than 5 points and one of the blocks is not passed, the student may take the final exam for that block on the date and place established by the Faculty; the definitive exam schedule can be consulted on the Faculty’s website.

The final exam will be a comprehensive written test covering both blocks described, with the same scoring: Block I out of 5 points and Block II out of 5 points.

If a student takes the final exam for a block, they waive the score previously obtained in that block; that is, the score obtained in each block on the final exam will replace the score obtained during the course.

The grade recorded will be the sum of the grades obtained in each block. Otherwise, the grade will appear as “not presented.”

In extraordinary exam sessions, a single written exam will be held, and its score will account for 100% of the final grade (10 points).

The single final evaluation exam, which the student may opt for in the cases indicated in the UGR Student Evaluation and Grading Regulations, last amended by the Governing Council on October 26, 2016, and published in BOUGR No. 112 on November 9, 2016 (see Article 8), will consist of:

A written final exam that will account for 100% of the final grade (10 points). The date and location will be set by the Faculty and will coincide with those of the continuous evaluation.

Students who do not attend this final exam will receive a grade of “Not Presented.”

Both for continuous evaluation and the single final evaluation, all aspects related to assessment will be governed by the current regulations of the University of Granada.
The Student Evaluation and Grading Regulations of the UGR, last amended by the Governing Council on October 26, 2016, and published in BOUGR No. 112 on November 9, 2016, apply.

Inclusion and Diversity:
For students with disabilities or other specific educational support needs (NEAE), the tutoring system will be adapted to these needs, following the recommendations of the university’s inclusion competence area. Departments and faculties will implement appropriate measures to ensure that tutoring sessions take place in accessible locations. Additionally, upon faculty request, support may be requested from the competent UGR unit for special methodological adaptations.

Information of interest for students with disabilities and/or Specific Educational Support Needs (NEAE):
Management of services and support: https://ve.ugr.es/servicios/atencionsocial/estudiantes-con-discapacidad.