The subject is organized in two parts: Numerical Methods (MNum) and Statistical Methods (MEst).

The contents corresponding to part MNum are indicated in Units 0-3, and the contents corresponding to part MEst are indicated in Units 4-6. Each part will be qualified on 10 points:

The quatification of MNum (CNum) will be between 0 and 10 points.
The qualification of MEst (CEst) will be between 0 and 10 points.

The final qualification of the subject will be the mean of the notes achieved in each of the two parts: Nota Final= (CNum + CEst)/2

The qualification for each one of the two parts of the subject is the following:

The MNum qualification is divided into three parts:

Qualificaton of ITC practices (CP_1): between 0 and 3.5 points
Qualification of problems resolution (CR_1): between 0 and 1.5 points
Qualification of the mixed objetive test (CE_1): between 0 and 5 points.

The final qualification of MNum (CNUm) will be the sum of the three parts CP_1 + CR_1 + CE_1, if the qualification of the mixed objetive test is greater than 1.5 (over 5 points). In another case, the final qualification will be the qualification obtained on the objective test, CE_1.

The final qualification of the part will be: CNum= CP_1 + CR_1 + CE_1

The qualification of the part MEst is divided into three parts:

Qualification of ITC practices (CP_2): between 0 and 2.5 points
Qualification of problems resolution (CR_2): between 0 and 2.5 points
Qualification of the mixed objetive test (CE_2): between 0 and 5 points.

The final qualification of MEst (CEst) will be the sum of the three parts CP_2 + CR_2 + CE_2, if the qualification of the mixed objetive test is greater than 1.5 (over 5 points). In another case, the final qualification will be the qualification obtained on the objective test, CE_2.

The final qualification of MEst will be: CEst= CP_2 + CR_2 + CE_2

The final qualifcation of the subject will be the mean of CNum and CEst: NotaFinal = (CEst + CNum)/2

In the second opportunity of the evaluation:

In the second opportunity, the student will only have to attend the part of the exam which he/she failed in the first opportunity:

In the part of MNum, the grades related to the practices through ICT (CR_1) and problem solving (CP_1) will be kept.
In the part of MEst, the grades related to the practices through (CR_2) and problem solving (CP_2) will be kept.

A Non-Attended state will be assigned to those students who do not attend the final mixed test.

-Observations on the “Students with recognition of part-time dedication and academic exemption from attendance exemption”: The specific personalized attention measures for the “Students with recognition of part-time dedication and academic exemption from attendance exemption” for the study of subject, the continuous evaluation of the practices through TIC and of the resolution of problems will realize by means of partial proofs online.

Learning outcomes	Study programme competences
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

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

Methodologies / tests	Competencies	Ordinary class hours	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	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.

Methodologies	Competencies	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 in two parts: Numerical Methods (MNum) and Statistical Methods (MEst). The contents corresponding to part MNum are indicated in Units 0-3, and the contents corresponding to part MEst are indicated in Units 4-6. Each part will be qualified on 10 points: The quatification of MNum (CNum) will be between 0 and 10 points. The qualification of MEst (CEst) will be between 0 and 10 points. The final qualification of the subject will be the mean of the notes achieved in each of the two parts: Nota Final= (CNum + CEst)/2 The qualification for each one of the two parts of the subject is the following: The MNum qualification is divided into three parts: Qualificaton of ITC practices (CP_1): between 0 and 3.5 points Qualification of problems resolution (CR_1): between 0 and 1.5 points Qualification of the mixed objetive test (CE_1): between 0 and 5 points. The final qualification of MNum (CNUm) will be the sum of the three parts CP_1 + CR_1 + CE_1, if the qualification of the mixed objetive test is greater than 1.5 (over 5 points). In another case, the final qualification will be the qualification obtained on the objective test, CE_1. The final qualification of the part will be: CNum= CP_1 + CR_1 + CE_1 The qualification of the part MEst is divided into three parts: Qualification of ITC practices (CP_2): between 0 and 2.5 points Qualification of problems resolution (CR_2): between 0 and 2.5 points Qualification of the mixed objetive test (CE_2): between 0 and 5 points. The final qualification of MEst (CEst) will be the sum of the three parts CP_2 + CR_2 + CE_2, if the qualification of the mixed objetive test is greater than 1.5 (over 5 points). In another case, the final qualification will be the qualification obtained on the objective test, CE_2. The final qualification of MEst will be: CEst= CP_2 + CR_2 + CE_2 The final qualifcation of the subject will be the mean of CNum and CEst: NotaFinal = (CEst + CNum)/2 In the second opportunity of the evaluation: In the second opportunity, the student will only have to attend the part of the exam which he/she failed in the first opportunity: In the part of MNum, the grades related to the practices through ICT (CR_1) and problem solving (CP_1) will be kept. In the part of MEst, the grades related to the practices through (CR_2) and problem solving (CP_2) will be kept. A Non-Attended state will be assigned to those students who do not attend the final mixed test. -Observations on the “Students with recognition of part-time dedication and academic exemption from attendance exemption”: The specific personalized attention measures for the “Students with recognition of part-time dedication and academic exemption from attendance exemption” for the study of subject, the continuous evaluation of the practices through TIC and of the resolution of problems will realize by means of partial proofs online.

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

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.