Students will be assessed through
“continuous assessment” consisting of two parts or “stages”.

FIRST
STAGE:

Several
exams will be done by students throughout the course.

Active attendance in the class will be taken
into account for assessment (1 point at most).

In this stage, students could pass the
subject by passing the established exams.

SECOND STAGE:

Students failing the subject in the “first
stage”, will be able to pass the subject by doing a final exam consisting of
theoretical and practical questions.

The final mark will be the sum of 80% of the
final exam and 20% of the continuous assessment.

Students participating in some of the
scheduled assignments throughout the course will be assessed at
the end of the course. They will not be marked as not-presented.

SECOND OPORTUNITY: In this oportunity (July)
the same criteria as those of the second part will be considered.

Students with recognition of part-time dedication
and academic exemption from attendance will be graded under the same conditions
than other students, as explained above.

In special cases, such as,
SICUE or Erasmus students, specific exams could be established.

Learning outcomes	Study programme competences
To consolidate student’s knowledge of algebra, geometry and differential geometry and cover gaps in relation to some basic contents, by encouraging the relationship between theory and practice.	A1	B1 B2 B3 B5 B6 B7 B12	C1 C3 C4 C5 C6 C7 C8
To know basic concepts about systems and computer programs used in construction sector.	A2
To know and to connect the basic concepts and fundamental tools of calculus, and to be fluent in mathematical language appearing in the subject.	A1 A8	B1 B2 B3 B4 B5 B6 B7 B12	C1 C2 C3 C4 C5 C6 C7 C8
To know some mathematical models required for the formulation and solving of problems in construction sector.	A1 A8	B1 B2 B3 B4 B5 B6 B7 B12	C1 C2 C3 C4 C5 C6 C7 C8
To design, compute and execute building installations.	A9	B16 B27 B28

Topic	Sub-topic
TEMA I.- CONCEPTOS BÁSICOS DE ÁLXEBRA LINEAR	I.1.- Espazos vectoriais. Definicións e propiedades básicas. Subespazos. I.2.- Combinación linear de vectores. Bases, dimensión. I.3.- Ecuacións dun subespazo. Intersección e suma de subespazos. I.4.- Aplicacións lineares. Definicións e conceptos básicos. Núcleo, imaxe, propiedades.
TEMA II.- MATRICES E DETERMINANTES	II.1.- Matrices. Definicións. Matriz asociada a unha aplicación. Operacións con matrices. Matriz de cambio de base. II.2.- Determinantes. Definicións e propiedades básicas. Cálculo da inversa dunha matriz. Rango dunha matriz.
TEMA III.- SISTEMAS DE ECUACIÓNS LINEARES.	III.1.- Sistemas de ecuacións lineares. Definicións e conceptos básicos. Condicións de compatibilidade. Teorema de Rouché-Frobenius. Resolución de sistemas: regra de Cramer. Método de Gauss. III.2.- Solución de sistemas, métodos iterativos. Métodos de Jacobi e de Gauss-Seidel. Norma dunha matriz. Converxencia dos métodos iterativos. Acoutamento do erro.
TEMA IV.- DIAGONALIZACIÓN	IV.1. Vectores propios e valores propios IV. 2. Diagonalización dunha matriz
TEMA V.- XEOMETRÍA AFÍN E EUCLÍDEANA NO ESPACIO	V.1.- Xeometría afín. Sistemas de referencia, coordenadas. Cambio de coordenadas no plano e no espazo. V.2.- Ecuacións da recta. Posicións relativas de rectas. V.3.- Ecuacións do plano. Posicións relativas de planos. Posicións relativas de rectas e planos. Feixes de rectas e de planos. V.4.- Xeometría euclidiana. Produto escalar. Ortonormalización. Produto vectorial. Produto mixto. V.5.- Aplicacións á xeometría. Distancias: entre puntos, dun punto a unha recta, dun punto a un plano. Entre rectas. Dunha recta a un plano. Entre planos.
TEMA VI.- TRANSFORMACIÓNS ORTOGONAIS E SIMETRÍAS	VI.1.- Transformacións ortogonais.Definicións e propiedades básicas. VI.2.- Clasificación de transformacións en R2 e en R3. VI.3.- Formas cuadráticas. Definicións e propiedades básicas. Variedades cuadráticas. VI.4.- Cónicas. Clasificación. VI.5.- Cuádricas. Ecuación reducida. Clasificación.
TEMA VII.- XEOMETRÍA DIFERENCIAL DE CURVAS E SUPERFICIES. TENSORES	VII.1.- Curvas no espazo euclidiano. Recta tanxente, lonxitude dunha curva. VII.2.- Triedro de Frenet, curvatura e torsion. Caracterización de curvas planas. VII.3.- Noción de superficie. Plano tanxente. Primeira Forma Fundamental. Área dunha superficie. VII.4.- Segunda Forma Fundamental. Curvatura Total. Aplicacións multilineares. Tensores nunha superficie
Anexo:	Se existe dispoñibilidade horaria e material faranse prácticas nalgúns dos temas usando o programa Maxima

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
Short answer questions	A2 B1 B12 C1 C3	1	0	1
Directed discussion	A1 A8 A9 B1 B2 B3 B4 B5 B6 B7 B12 C1 C3 C4 C5 C6 C7 C8	30	45	75
Guest lecture / keynote speech	A1 A2 B3 B5 B12 C2 C6 C7	30	33	63
Objective test	A1 B1 B16 B27 B28 C1	3	0	3
Problem solving	A1 A8 A9 B1 B2 B3 B4 B5 B6 B7 B12 C1 C3 C7 C8	3	0	3

Personalized attention		5	0	5

(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies	Description
Short answer questions	It will be a final exam consisting of questions with alternative or short answers.
Directed discussion	Solving exercises during regular classes in a participatory way.
Guest lecture / keynote speech	In the regular classes, the professor will explain the main concepts and results of the subject.
Objective test	For the continuous assessment option, several exams must be done by students throughout the course.
Problem solving	In the final exam, several exercises related to what was explained during the course must be solved by students.

Methodologies	Competencies	Description	Qualification
Short answer questions	A2 B1 B12 C1 C3	It will be an exam with several short questions.	30
Problem solving	A1 A8 A9 B1 B2 B3 B4 B5 B6 B7 B12 C1 C3 C7 C8	It will be a final exam including several problems (practical exercises).	50
Objective test	A1 B1 B16 B27 B28 C1	These consist of several exams for students with regular attendance choosing continuous assessment.	20

Assessment comments
Students will be assessed through “continuous assessment” consisting of two parts or “stages”. FIRST STAGE: Several exams will be done by students throughout the course. Active attendance in the class will be taken into account for assessment (1 point at most). In this stage, students could pass the subject by passing the established exams. SECOND STAGE: Students failing the subject in the “first stage”, will be able to pass the subject by doing a final exam consisting of theoretical and practical questions. The final mark will be the sum of 80% of the final exam and 20% of the continuous assessment. Students participating in some of the scheduled assignments throughout the course will be assessed at the end of the course. They will not be marked as not-presented. SECOND OPORTUNITY: In this oportunity (July) the same criteria as those of the second part will be considered. Students with recognition of part-time dedication and academic exemption from attendance will be graded under the same conditions than other students, as explained above. In special cases, such as, SICUE or Erasmus students, specific exams could be established.

Basic	Díaz Hernández, Ana María; Hernández García, Elvira; Tejero Escribano, Luis (2012). Ejercicios de álgebra para Ingenieros. Madrid: Sanz y Torres Bartoll Arnau, S. y otros (2009). Fundamentos Matemáticos en Arquitectura. Editorial de la U. P. V. (Universidad Politécnica de Valencia) García Abel, Marta; Tarrío Tobar, Ana Dorotea (2019). Leccións de Álxebra Linear e Xeometría (orientadas ao alumnado do Grao en Arquitectura Técnica e outras Enxeñarías). Reprografía Noroeste S.L. De la Villa, Agustín (2010). Problemas de Álgebra [con esquemas teóricos]. Madrid: CLAGSA

Complementary	Grossman, Stanley I. (2007). Álgebra Lineal. McGraw-Hill J. García Cabello (2006). Álgebra Lineal: sus aplicaciones en Economía, Ingeniería y otras Ciencias. Delta publicaciones Díaz Hernández, Ana María; Hernández García, Elvira; Tejero Escribano, Luis (1994). Álgebra para Ingenieros. Madrid: Sanz y Torres Burgos Román, Juan de (2011). Álgebra y su introducción. Madrid: García-Maroto Gómez Bermúdez, Carlos (2015). Problemas de Alxebra Linear. Ed. Andavira Danielson, D. A. (2003). Vectors and tensors in engineering and phisics. Westview Press

Other comments
To study this subject, it is important that students have mathematical knowledge corresponding to the science area and have passed the subject Mathematics I. To understand and pass other subjects in the career, it is positive to master this subject.