ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 114 Hours of tutorials: 6 Expository Class: 12 Interactive Classroom: 18 Total: 150
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Quantitative Economy
Areas: Quantitative Economics (USC-specific)
Center Faculty of Economics and Business Studies
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Economics deals with quantitative concepts. That is why mathematics and statistics play an important role in the field of economic science, serving as essential tools for analysis, quantification, and economic modeling.
This subject aims to provide students with a set of essential techniques for other courses in the master's program. In fact, advancing in the understanding of economic reality heavily relies on the analysts' ability to gather relevant information, describe it, and study it using appropriate indicators and techniques. This facilitates prediction and enhances decision-making accuracy. Therefore, the objective is for students to acquire proficiency in using specific indicators, techniques, and methodologies that are highly valuable in this field.
More specifically, the following objectives are pursued:
- Understand the fundamental mathematical and statistical tools required for formalizing economic behavior.
- Develop skills in searching, identifying, and interpreting relevant sources of economic information and their content.
- Acquire the capacity to formulate simple models that establish relationships among economic variables, employing technical instruments.
- Evaluate the consequences of different courses of action through empirical techniques and select the most suitable ones.
- Foster a critical and self-critical attitude.
- Manage the formulation and resolution of various static and dynamic optimization problems.
- Gain familiarity with statistical methods.
MATHEMATICS
1. Convexity and optimization
1.1. Eigenvalues, eigenvectors, matrix diagonalization.
1.2. Convex sets and functions.
1.3. Convexity and differentiation.
1.4. Optimisation with the equality constraints.
1.5. Optimisation with inequality constraints.
2. Differential equations
2.1. Concept of differential equation.
2.2. First-order differential equations.
2.3. Systems of differential equations
2.4. Equilibrium, stability, phase diagram.
3. Dynamic optimization
3.1. Problem formulation
3.2. First-order conditions
3.3. Transversality condition.
3.4. Sufficiency condition
3.5. Infinite horizon
STATISTICS
1. Data analysis with R
1.1. Introduction to R.
1.2. Data preparation.
1.3. Exploratory data analysis.
2. Random variables and parameter estimation
2.1. Types of random variables, characterization, notable examples.
2.2. Simulation of random variables
2.3. Parameter estimation
2.4. Properties of estimators.
3. Statistical inference: confidence intervals and hypothesis testing.
3.1. Introduction to statistical inference
3.2. Point estimation.
3.3. Confidence interval estimation.
3.4. Hypothesis testing.
MATHEMATICS
• Adams, R. (2009). Cálculo. Pearson.
• Barro, R., Sala-i-Martin, X. (2004). Economic Growth. (Anexo matemático). MIT Press.
• Cerdá, E. (2011). Optimización Dinámica. Garceta.
• Kamien, M., Schwartz, N. (2012). Dynamic Optimization, Second Edition: The Calculus of Variations and Optimal Control in Economics and Management. Dover Publications, Inc.
• Sydsaeter, K., Hammond, P. Seierstad, A., Strom, A. (2008). Further Mathematics for Economic Analysis. Prentice-Hall.
STATISTICS
Basic
• Dalgaard, P. (2008). Introductory Statistics with R
• Lind, D.A.; Marchal, W.G. e Wathen, S.A. (2015): Estadística Aplicada a los Negocios y a la Economía. Ed. McGrawHill.
• Newbold, P. et al. (2008). Estadística para los Negocios y la Economía. Prentice-Hall.
• Ruiz-Maya Pérez, L., Martín Pliego, F.J. (2005). Fundamentos de Inferencia Estadística. Ed. Thomson
• Sarrión Gavilán, Mª Dolores (2013). Estadística Descriptiva. España, Mc Graw Hill
• Triola, M.F. (2018). Estadística. Pearson.
• Wasserman, L. (2003). All of Statistics. A Concise Course in Statistical Inference. Springer
Complementary
• Cabrero Ortega, Yolanda y García Pérez, Alfonso (2015). Análisis estadístico de datos espaciales con QGIS y R. España,
UNED
• Wickham, H, Grolemund, G. (2016). R for Data Science. O’Reilly
Exercise books
• Martín Pliego, F.J., Montero Lorenzo, J.M. e Ruiz-Maya L. (1998): Problemas de probabilidad. Ed. AC.
• Martín Pliego, F.J., Montero Lorenzo, J.M. e Ruiz-Maya L. (2000): Problemas de inferencia estadística. Ed. AC
Basic and General:
- Apply acquired knowledge and enhance problem-solving skills in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study.
- Possess learning skills that enable them to continue studying in a largely self-directed or autonomous manner.
- Develop the ability to conceive, design, and implement substantial research processes in the field of economics in general, and particularly in their areas of specialization, with academic rigor.
- Acquire the capacity to present and defend new ideas rigorously, clearly, and precisely in both typical work settings and national or international scientific meetings.
Specific:
- Understand the mathematical, statistical, and econometric tools necessary for rigorously handling economic models.
- Master current econometric techniques.
- Develop the ability to model specific economic situations and obtain numerical results by applying relevant econometric techniques.
- Analyze and propose changes in the design of organizations and incentive systems to enhance their performance and efficiency.
- Contribute to interdisciplinary workgroups focused on studying long-term socioeconomic trends.
- Analyze the advantages and disadvantages of regulations and economic policies and propose alternatives.
Transversal:
- Develop the ability to interact and defend works, proposals, new ideas, etc., with rigor, clarity, and precision when communicating with other specialists.
- Foster oral and written communication skills.
- Develop the ability to analyze and synthesize information.
Expository and interactive teaching will be conducted entirely in a face-to-face format. During interactive classes, students will have the opportunity to work individually or in groups. Tutoring will primarily be held in person, but remote options such as email, the virtual classroom, or the USC virtual platform (Teams) may also be utilized.
The course combines both expository and interactive teaching methods, which are further enhanced through individual and/or small group tutorials.
A virtual classroom will be available on the USC platform for the subject, providing access to classroom presentations and supplementary materials to support course learning and preparation.
Lecture sessions involve oral presentations supported by audiovisual media, encompassing both theoretical concepts and practical examples.
Objective tests will be administered to assess students' ability to comprehend and establish connections between concepts.
ICT-based practices and supervised assignments will be implemented, enabling students to apply empirical applications under the guidance and support of the professors.
The subject is divided into two independent modules: Mathematics and Statistics.
The final grade for the subject is the sum of the grades from both modules, each valued on a scale of 5 points. The assessment system for each module is disaggregated as follows:
- Objective test (written exam) 40%.
- Continuous assessment (exercises and practical work) 60%.
It is necessary to obtain a minimum of 50% on the exams in order for the remaining continuous assessment activities to be considered. To pass the subject, it is required to pass both modules.
The evaluation system in the extraordinary opportunity is the same as in the ordinary opportunity.
Repeating students will be evaluated in the same way as non-repeating students.
Students who have been granted dispensation from class attendance based on current regulations may choose to take the final exam, which will be assessed with 100% of the grade.
As a general guideline, it is understood that students require 120 hours of independent work to assimilate the content of the lectures, complete the ICT-based practices, prepare for the objective test, and carry out supervised assignments.
Continued use of bibliographic resources, the supporting materials used in class, and maintaining regular communication with the professor are highly recommended.
Maria Luisa Chas Amil
- Department
- Quantitative Economy
- Area
- Quantitative Economics (USC-specific)
- Phone
- 881811549
- marisa.chas [at] usc.es
- Category
- Professor: University Lecturer
Xesus Pereira Lopez
Coordinador/a- Department
- Quantitative Economy
- Area
- Quantitative Economics (USC-specific)
- Phone
- 881811708
- xesus.pereira [at] usc.es
- Category
- Professor: University Lecturer
| Tuesday | |||
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| 11:30-13:00 | Grupo /CLE_01 | Galician | Computer room 5 |
| Wednesday | |||
| 11:30-13:00 | Grupo /CLIS_01 | Galician | Computer room 5 |
| 12.09.2024 16:00-19:00 | Grupo /CLE_01 | Computer room 5 |
| 12.09.2024 16:00-19:00 | Grupo /CLIS_01 | Computer room 5 |
| 12.16.2024 16:00-19:00 | Grupo /CLIS_01 | Computer room 5 |
| 12.16.2024 16:00-19:00 | Grupo /CLE_01 | Computer room 5 |
| 05.05.2025 10:00-13:00 | Grupo /CLE_01 | Computer room 5 |
| 05.05.2025 10:00-13:00 | Grupo /CLIS_01 | Computer room 5 |
| 05.09.2025 16:00-19:00 | Grupo /CLE_01 | Computer room 5 |
| 05.09.2025 16:00-19:00 | Grupo /CLIS_01 | Computer room 5 |