Identifying Data 2024/25
Subject (*) Numerical and Statistical Methods Code 610G04013
Study programme
Grao en Nanociencia e Nanotecnoloxía
Descriptors Cycle Period Year Type Credits
Graduate 1st four-month period
 Second Obligatory 6
Language
Spanish
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Ferreiro Ferreiro, Ana María
 E-mail
ana.fferreiro@udc.es
Lecturers
Ferreiro Ferreiro, Ana María
López Igrexas, Macías
López Salas, José Germán
 E-mail
ana.fferreiro@udc.es
macias.lopez@udc.es
jose.lsalas@udc.es
Web http://https://campusvirtual.udc.gal/
General description Nesta asignatura preténdese o desenvolvemento de competencias que permitan ao alumnado desenvolver un coñecemento critico dos métodos numéricos e estadísticos.

Competencies / Study results
Code Study programme competences / results
A3 CE3 - Reconocer y analizar problemas físicos, químicos, matemáticos, biológicos en el ámbito de la Nanociencia y Nanotecnología, así como plantear respuestas o trabajos adecuados para su resolución, incluyendo el uso de fuentes bibliográficas.
A7 CE7 - Interpretar los datos obtenidos mediante medidas experimentales y simulaciones, incluyendo el uso de herramientas informáticas, identificar su significado y relacionarlos con las teorías químicas, físicas o biológicas apropiadas.
B2 CB2 - Que los estudiantes sepan aplicar sus conocimientos a su trabajo o vocación de una forma profesional y posean las competencias que suelen demostrarse por medio de la elaboración y defensa de argumentos y la resolución de problemas dentro de su área de estudio
B4 CB4 - Que los estudiantes puedan transmitir información, ideas, problemas y soluciones a un público tanto especializado como no especializado
B5 CB5 - Que los estudiantes hayan desarrollado aquellas habilidades de aprendizaje necesarias para emprender estudios posteriores con un alto grado de autonomía
B6 CG1 - Aprender a aprender
B7 CG2 - Resolver problemas de forma efectiva.
B8 CG3 - Aplicar un pensamiento crítico, lógico y creativo.
B9 CG4 - Trabajar de forma autónoma con iniciativa.
B10 CG5 - Trabajar de forma colaborativa.
B11 CG6 - Comportarse con ética y responsabilidad social como ciudadano/a y como profesional.
B12 CG7 - Comunicarse de manera efectiva en un entorno de trabajo.
C3 CT3 - Utilizar las herramientas básicas de las tecnologías de la información y las comunicaciones (TIC) necesarias para el ejercicio de su profesión y para el aprendizaje a lo largo de su vida
C7 CT7 - Desarrollar la capacidad de trabajar en equipos interdisciplinares o transdisciplinares, para ofrecer propuestas que contribuyan a un desarrollo sostenible ambiental, económico, político y social.
C8 CT8 - Valorar la importancia que tiene la investigación, la innovación y el desarrollo tecnológico en el avance socioeconómico y cultural de la sociedad
C9 CT9 - Tener la capacidad de gestionar tiempos y recursos: desarrollar planes, priorizar actividades, identificar las críticas, establecer plazos y cumplirlos

Learning aims
Learning outcomes Study programme competences / results
Identify the need for the use of numerical and statistical methods in solving models of real problems, especially originated in nanoscience and nanotechnology A3
A7
 B2
B4
B5
B7
B8
B9
B10
 C7
Know and acquire fluency in the handling of numerical methods for the solution of different problems, as well as knowing the conditions to approximate the solution A3
A7
 B2
B4
B5
B6
B7
B8
B9
B10
Have criteria to select the most efficient numerical methods in different problems, especially those related to nanoscience and nanotechnology A3
A7
 B2
B4
B5
B6
B7
B8
B9
B10
B11
B12
 C7
C8
Acquire knowledge about probability and statistical methods of modeling, data analysis, diagnosis and interpretation of results A3
 B2
B4
B5
B6
B7
B8
B9
B10
B11
B12
 C3
C7
C8
C9
Manage software tools that implement the studied methodology and know how to analyze the results A3
A7
 B2
B4
B5
B6
B7
B8
B9
B10
B11
B12
 C3
C7

Contents
Topic Sub-topic
Unit 0: Introduction to numerical methods Introduction to numerical methods. Erros.
Unit 1: Numerical resolution of linear systems and numerical approximation fo eigenvalues
 - Direct methods (LU, Cholesky)
- Iterative methods (Jacobi, Gauss-Seidel)
- Aproximation of eigenvalues:: QR
- Aplications
Unit 2: Numerical resolution of non-linear equations
 - Non-linear equations (bisection, Newton and variant, functional iteration)
- Non-linear systems (functional iteration, Newton)
- Aplications
Unit 3: Interpolation, numerical derivation and integration - Interpolation (Lagrange, Chebyshev, Splines)
- Numerical derivation
- Numerical integration (middle point, trapezoid, Simpson, gaussian quadrature)
- Aplications
Unit 4. Basic concepts on probability theory

 - Probability formulas
- Conditional probability and independent events
- Bayes' theorem
Unit 5. Random variables - Discrete and continuos variables
- Normal distribution and Central Limit Theorem
- Applications in Nanoscience and Nanotechnology
Unit 6. Introduction to Statistical Inference
- Estimators and sampling distributions
- Linear regression
- Statistical analysis software tools

Planning
Methodologies / tests Competencies / Results Teaching hours (in-person & virtual) Student’s personal work hours Total hours
Guest lecture / keynote speech A3 B2 B4 B5 B6 B7 B11 C8 28 56 84
Problem solving A7 B8 B12 8 16 24
ICT practicals A3 A7 B2 B4 B10 C3 C7 C9 12 25 37
Mixed objective/subjective test B7 B9 C9 3 0 3
 
Personalized attention 2 0 2
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies Description
Guest lecture / keynote speech Exhibition of the contents specified in the program of the subject, for which audiovisual media or blackboard will be used.
Problem solving Sessions where relevant problems in the field of Science and Engineering will be presented, which will be solved both analytically and numerically: the student must be able to reach the solution of any problem using pencil and paper or alternatively using computer tools, and compare the results.
ICT practicals Interactive practices in which relevant problems in the field of Science and Engineering will be solved.
In the part corresponding to Numerical Methods Units 0 - 3) we will programate in Python, and in the Statistical Methods part (Units 4-6) we will work with R using Rcmdr.
Mixed objective/subjective test Development of issues and problems of the subject.

Personalized attention
Methodologies
ICT practicals
Problem solving
Description
- Due to the diversity of the students and their training, a personalized orientation is recommended, which could be carried out through tutorials.

- Practices with ICT tools in problem solving, or teachers will help students in the development of two stated problems, as well as applications to problems in the field of Science and Engineering.

- The specific personalized attention measures for "Students with recognition of part-time dedication and academic waiver of attendance exemption" for the study of the subject, the continuous evaluation of the practices through ITC and the resolution of problems carried out attending, as far as possible, to your particular circumstances.

- In the part of Numerical Methods: With the aim of preparing students for the different continuous assessment tests, as well as for the final test; Group defenses will be made, of the problems raised. Its implementation will be determined jointly between the teacher and the students. They will take place in the teachers' office. The defenses will be distributed in groups, in four sessions of 10 minutes (for each group).


Assessment
Methodologies Competencies / Results Description Qualification
ICT practicals A3 A7 B2 B4 B10 C3 C7 C9 Resolución de problemas de carácter práctico empregando o lenguaxe de programación Python ou R. 30
Problem solving A7 B8 B12 Resolución de problemas de carácter práctico.
20
Mixed objective/subjective test B7 B9 C9 Proba que inclúe a resolución de cuestións e problemas da materia 50
 
Assessment comments

The subject is organized into tow parts: Numerical Methods (MNum) and Stadistic Methods (MEst). 

The contents corresponding to the MNum part are those indicated in topics 0- 3, and the contents corresponding to MEst are indicated in topics 4-6. Each part will bed graded out of 10 points: 

  • The MNum (CNum) grade will be between 0 and 10 points. 
  • The MEst (CEst) grade will be between 0 and 10 points.

The final grade for the subject will be the average of the grades obtained in each of the two parte: Final grade= (CNum + CEst)/2

The breakdown of the grade for each of the two parts of the subject is indicated below:

  1. The qualification corresponding to the MNum part consist of three parts:
    • Quatlification of practices through TIC (CP_1): between 0 and 3.5 points
    • Problem solving resolution (CR_1): between 0 and 1.5 points
    • Mixed test qualification (CE_1): between 0 and 5 points.

    The final grade of MNum (CNUm) will be the sum of the three partes CP_1 + CR_1 + CE_1, as long as the grade of the mixed test is greater than 1.5 (out of 5 points). Otherwise, the final grade will be the grade obtained in the objective test, CE_1.

    The continuous evaluation qualification fo MNum, CP_1 + CR_1, will be carried out through two small mixed test where the student will have to solve problems analytically and numerically (vía Python).

    With the aim of preparing students for the different continuous assessment test, as well as for the final test; throughout the course, group defenses will be carried out on the problem raised. These defense will be allow to recover up to one point of the grade (if grade of mixed test is greater than 1.5-over 5 points). The score corresponding to these works will only be taken into account in the first and second opportunity.

    The final grade of Num will be: CNum= CP_1 + CR_1 + CE_1

    In the middle of the semester there will be an eliminatory partial, corresponding to the numerical methods part. This eliminatory partial corresponds to the mixed test CE_1. If a student does not pass this eliminatory partial, they will have the option of taking the exam again on the official dates included in the Faculty's exam schedule.

  2. The qualification corresponding to MEst consist of three parts:
    • Qualification of practices through TIC (CP_2): between 0 and 2.5 points
    • Problem solving score (CR_2): between 0 and 2.5 points
    • Mixed test qualificaton (CE_2): between 0 and 5 points.

    The final grade of MEst (CEst) will be the sum of the three parts CP_2 + CR_2 + CE_2, as long as the grade of the mixed test is greater than  1.5 (out of 5 points). Otherwise, the final grade will be the grade obtained in the objective test, CE_2.

    The qualification of the continuous evaluation of MNum, CP_1 + CR_1, will be carried out through one small test and a delivery of work. 

    The final note of the part MEst será: CEst= CP_2 + CR_2 + CE_2

The final grade for the subject will be the avarage of CNum and CEst: NotaFinal = (CEst + CNum)/2

On the second opportunity of the evaluation:

  • The student who has to go to the second opportunity of the subject will only have to appear for the failed part:
    • From the MNum part, practices through TIC (CR_1) and problem solving (CP_1) are preserved.
    • From the MEst  part, continuous evaluation (CR_2 and CP_2) are preserved.

A Not Presented will be given to those students who don not appear to the final mixed test.

All previous observations are applied to students who request the early December call.

All aspects related to “academic dispensation”, “dedicaton to study”, “permanence” and “academic fraud” are governed in accordance with the current academic regulations of the UDC.

Sources of information
Basic James F. Epperson (2021). An Introduction to Numerical Methods and Analysis (3rd Ed.). Wiley
F. Rius Díaz, F.J. Barón López (2005). Bioestadística. Thomson.
A.J. Arriaza Gómeza (2008). Estadística básica con R y R-Commander. Servicio Publicaciones UCA.
R. Cao Abad y otros (2001). Introducción a la estadística y sus aplicaciones. Ed. Pirámide
J. Douglas Faires, R. Burden (2014). Métodos Numéricos (7ª ed). Thomson
Steven C. Chapra, Raymond P. Canale (2019). Métodos Numéricos para ingenieros (7º ed). McGrawHill

Complementary Jeffrey J. Heys (2017). Chemical and Biomedical Engineering Calculations Using Python. Wiley
J. Baró LLinas, (1998). Estadística Descriptiva, Cálculo de probabilidades e Inferencia estadística (tres volúmenes). Ed. Parramón
W. Navidi (2006). Estadística para ingenieros y científicos (1ª Ed) . Mc Graw-Hill
Jaan Kiusalaas (2013). Numerical Methods in Engineering with Python 3. Cambridge University Press
Alicia Cordero Barbero, José Luís Hueso Pagoaga, Eulalia Martínez Molada, Juan Ramón Torregrosa Sanc (). Problemas resueltos de métodos numéricos. Paso a paso. Paraninfo


Recommendations
Subjects that it is recommended to have taken before
Fundamentals of Mathematics/610G04001
Advanced Calculus /610G04009
Fundamentals of Computing Science/610G04010

Subjects that are recommended to be taken simultaneously

Subjects that continue the syllabus
Differential Equations/610G04016

Other comments

  • Daily study of the contents treated in the classroom, complementing them with the recommended bibliography.

  • To help achieve an immediate sustainable environment and comply with point 6 of the "Environmental Declaration of the Faculty of Science (2020)", the documentary work carried out in this area: Most will be requested in virtual format and computer support.

  • Gender perspective: as stated in the transversal competences of the title (C4), the development of a critical, open and respectful citizenship with diversity in our society will me promoted, highlighting the equal rights of students without discrimination based on gender or sexual condition. An inclusive language will be used in the material and during the development of the lessons.


(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.