| Study programme competencies |
| Code | Study programme competences |
| A2 | CE2 - Capacidade para resolver problemas matemáticos, planificando a súa resolución en función das ferramentas dispoñibles e das restricións de tempo e recursos. |
| B2 | CB2 - Que os estudantes saiban aplicar os seus coñecementos ao seu traballo ou vocación dunha forma profesional e posúan as competencias que adoitan demostrarse por medio da elaboración e defensa de argumentos e a resolución de problemas dentro da súa área de estudo |
| B3 | CB3 - Que os estudantes teñan a capacidade de reunir e interpretar datos relevantes (normalmente dentro da súa área de estudo) para emitir xuízos que inclúan unha reflexión sobre temas relevantes de índole social, científica ou ética |
| B4 | CB4 - Que os estudantes poidan transmitir información, ideas, problemas e solucións a un público tanto especializado como non especializado |
| B7 | CG2 - Elaborar adecuadamente e con certa orixinalidade composicións escritas ou argumentos motivados, redactar plans, proxectos de traballo, artigos científicos e formular hipóteses razoables. |
| B8 | CG3 - Ser capaz de manter e estender formulacións teóricas fundadas para permitir a introdución e explotación de tecnoloxías novas e avanzadas no campo. |
| B9 | CG4 - Capacidade para abordar con éxito todas as etapas dun proxecto de datos: exploración previa dos datos, preprocesado, análise, visualización e comunicación de resultados. |
| B10 | CG5 - Ser capaz de traballar en equipo, especialmente de carácter multidisciplinar, e ser hábiles na xestión do tempo, persoas e toma de decisións. |
| C1 | CT1 - Utilizar as ferramentas básicas das tecnoloxías da información e as comunicacións (TIC) necesarias para o exercicio da súa profesión e para a aprendizaxe ao longo da súa vida. |
| C4 | CT4 - Valorar a importancia que ten a investigación, a innovación e o desenvolvemento tecnolóxico no avance socioeconómico e cultural da sociedade. |
| Learning aims | |||
| Learning outcomes | Study programme competences | ||
| Identify the potential of numerical methods in the solution of problems from data science. | A2 |
B2 B3 B4 B8 B9 |
C1 C4 |
| Understand the basis of numerical methods to be able to apply them with criteria, not being a mere user of the options of a software package as a black box. | A2 |
B2 B3 B4 B7 B8 B9 |
C1 C4 |
| Be able to decide which numerical methods can be applied to solve each problem and which ones are the most efficient. Have the basis to learn more advanced methods. | A2 |
B2 B3 B4 B7 B8 B9 |
C1 C4 |
| Manage software tools that implement the numerical methods studied and acquire the ability to implement them and make extensions. | A2 |
B2 B4 B9 B10 |
C1 C4 |
| Contents |
| Topic | Sub-topic |
| Basic concepts in numerical methods: convergence, errors and order. | |
| Numerical methods for nonlinear equations | Bisection, secant method, Regula Falsilla, fixed point method and Newton-Raphson |
| Numerical methods for the solution of large linear systems | Direct and iterative methods |
| Numerical methods for approximating eigenvalues and eigenvectors | Power methods. QR method. |
| Methods for storing large matrices in the computer | |
| Numerical methods for solving nonlinear systems of equations | Fixed point methods. Newton's method. |
| Numerical methods for optimization | Gradient and Conjugate gradient methods. Line-search methods. Newton and quasi-Newton methods. Global optimization methods and two-phase methods. |
| Numerical interpolation in one and several variables. |
| Planning | ||||
| Methodologies / tests | Competencies | Ordinary class hours | Student’s personal work hours | Total hours |
| ICT practicals | A2 B2 B3 B4 B9 B10 C1 C4 | 14 | 35 | 49 |
| Supervised projects | A2 B2 B3 B4 B7 B8 B9 B10 C1 C4 | 1.5 | 6 | 7.5 |
| Problem solving | A2 B2 B4 B9 B10 | 7 | 14 | 21 |
| Objective test | A2 B2 B3 B4 B7 B8 C1 | 2 | 4 | 6 |
| Collaborative learning | A2 B2 B3 B4 B7 B9 B10 C1 | 0.5 | 5 | 5.5 |
| Guest lecture / keynote speech | A2 B2 B3 B4 B8 B9 | 20 | 40 | 60 |
| Personalized attention | 1 | 0 | 1 | |
| (*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. | ||||
| Methodologies |
| Methodologies | Description |
| ICT practicals | The teacher will help students deepen the concepts and numerical methods presented during the guest lectures using Python. |
| Supervised projects | Students will develop a supervised project in which they will combine the use of the different learning outcomes acquired in the subject. |
| Problem solving | Students will solve problems that help them to understand how the studied numerical methods work. |
| Objective test | There will be an exam on the dates decided by the Faculty Board. The exam will focus essentially on the solution of practical problems. |
| Collaborative learning | Students will have the opportunity to participate in a COIL project. |
| Guest lecture / keynote speech | During guest lectures, the teacher will present the different contents. She will motivate the need of the different numerical methods using real problems, and she will present the necessary concepts and different numerical methods, discussing their main features. |
| Personalized attention |
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| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| ICT practicals | A2 B2 B3 B4 B9 B10 C1 C4 | Several practical small projects will be proposed and evaluated along the course. | 30 |
| Supervised projects | A2 B2 B3 B4 B7 B8 B9 B10 C1 C4 | Teachers will propose a supervised project to each student that he/she will have to defend at the end of the subject. | 20 |
| Problem solving | A2 B2 B4 B9 B10 | During the course there will be some small tests. They will consist on solving problems of the same type as those studied during the classes. | 20 |
| Objective test | A2 B2 B3 B4 B7 B8 C1 | There will be a written exam on the dates set by the Faculty Board. | 30 |
| Collaborative learning | A2 B2 B3 B4 B7 B9 B10 C1 | The teacher will propose a supervised project that students will have to defend during the course. This project is optional and can be seen as an alternative to the supervised project. Therefore, it will count up to 20% of the final mark. | 0 |
| Assessment comments | |||
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In order to pass the subject, it is mandatory to attain at least a qualification of 50%. In the extraordinary call there will be an objective test. It will not be possible to recover the part of the final mark corresponding to continuous assessment. Part-time students and those with academic dispensation of attendance exemption that have not been evaluated of ICT practicals can do a specific exam to recover 30% of the final mark; they can obtain 50% of the final mark with the objective test. Fraudulent performance of the tests or evaluation activities, once verified, will directly imply a mark of "0" in the subject, invalidating any grade obtained in all the evaluation activities. |
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| Sources of information |
| Basic |
R.L. Burden, D.J. Faires & A.M. Burden (2017). Análisis Numérico. CENCAGE Learning
A. Quarteroni & F. Saleri (2006). Calculo cientifico con Matlab y Octave. . Springer
J. Nocedal & S.J. Wright (2006). Numerical Optimization. Springer
S. Linge & H.P. Langtangen (2020). Programming for Computations - Python. Soringer
C.T: Kelley (2003). Solving Nonlinear Equations with Newton's Method. SIAM
R. Barrett, M. Berry, T.F. Chan, J. Demmel, J.M. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romin (1994). Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM |
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| Complementary |
J.W. Demmel (1997). Applied Numerical Linear Algebra. SIAM
M. Locatelli & F. Schoen (2013). Global Optimization. Theory, Algorithms and Applications. SIAM
C.T. Kelley (1995). Iterative Methods for Linear and Nonlinear Equations. SIAM
C.T. Kelley (1999). Iterative Methods for Optimization. SIAM
G. Strang (2019). Linear Algebra and Learning from Data. Wellesley Cambridge Press
D.R. Kincaid & E.W. Cheney (2022). Numerical Analysis: Mathematics of Scientific Computing. AMS
J Kiusalaas (2013). Numerical Methods in Engineering with Python 3. Cambridge University Press |
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| Recommendations | |||
| Subjects that it is recommended to have taken before | |||
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| Subjects that are recommended to be taken simultaneously |
| Subjects that continue the syllabus |
| Other comments | |
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Students are recommended to take the subject up to date and consult with the teachers any doubts that may arise. |