Titular Professors
Professors
Basic Algebra
Learning Outcomes of this subject are:
M02.K01 Recognize mathematical problems linked to building projects. based on examples of formulating mathematical models in architecture.
M02.H01 Apply numerical calculation, mathematical analysis, analytical and differential geometry and algebraic methods to solve practical problems that allow the understanding of physical phenomena that concern the systems, equipment and services of the building and the town planning.
Students will acquire the knowledge and skills described below, linked to essential mathematical tools, in particular to be able to: - understand - classify - solve problems of differential calculus in one variable, integral calculus, linear algebra and geometry, as well as such as: - identify - examine - reorganize the mathematical concepts and objects used in the disciplinary fields provided in the training itinerary, such as matrices, vectors, geometric entities in the plane, calculation of areas, functional relationships and their classifications (M02.K01) . Special attention will also be paid to spatial visualization and the associated mathematical description, so they will be able to: - recognize the properties of a function from a graphical representation, as well as: - represent elementary geometric entities and functions of a real variable in graphic form. The subject will allow them to analyze, formalize using a mathematical model and solve simple problems of various kinds that arise in their profession, recognizing the most appropriate analytical and geometric tools (M02.H01).
BLOCK 1. LOGIC OF SPACE. SPACE REPRESENTATION
1.1 Systems of linear equations
1.2 Linear combination and linear independence of vectors
1.3 Vector spaces and subspaces
1.4 System of generators and bases
1.5 Operations of vector sub spaces
1.6 Inner vector spaces
BLOCK 2. ANALYTIC GEOMETRY
2.1 Types of transformations
2.2 Characterization
2.3 Change of basis
2.4 Eigenvectors and eigenvalues of an endomorphism
BLOCK 3. QUADRIC SURFACES
3.1 Quadratic forms in geometry
3.2 Classification of conics and quadrics
BLOCK 4. BIG DATA
4.1 Data
4.2 Measures of centrality and dispersion
4.3 Quantiles and measures of form
4.4 Statistics in more dimensions
4.5 Linear regression models
BLOCK 5. ENERGY_ PARAMETRIZATION
5.1 Mathematical models
5.2 Elementary functions
The subject has a weekly operation with two class sessions.
Each session is divided into three parts: a first is dedicated to solving problems carried out by the students at home, a second part in which the teacher explains the new content (seminar, flipped classroom, peer instructions) and a third in which students work on new exercises to consolidate the matter.
Every two or three sessions, individual or group evaluation activities are carried out through written tests, online questionnaires, collection of exercises carried out at home, etc.
There are also gamification activities (Socrative, Kahoot) where students get bonuses that they can use during official assessments.
In order to assess whether the student has achieved the learning outcomes pursued in the subject to an adequate degree, different evaluation activities are used (with a frequency approx. weekly).
Minimum requirements for the student to benefit from continuous evaluation:
- participation in evaluation activities ≥ 90%
- minimum grade of the average of the written tests (5x12%) ≥ 4
- deliver all the exercises of each block to be able to attend the written tests
If the student cannot carry out an activity for justified reasons, depending on the % of the activity:
- <5% will not be taken into account for the evaluation (it will not be recovered) distributing the % in the other activities
- 5% or 12% (written test) will be recovered at the end of the course
In the case of students who do not participate in Aula Barcelona (because it has already been completed) the % of this activity will be distributed among the others.
Objectives of continuous evaluation:
- The main objective is to help students keep up to date with the subject and achieve a good working method, so that it helps them assimilate the subject, taught progressively, and obtain good academic results.
- It also allows the student's work to be assessed day by day, without their grade depending solely on the exams taken during the semesters of the academic year.
- For the teacher, it helps to have more information about the work done by the students and a better knowledge of them, both on an academic and personal level.
After the completion of each block, students will be able to review them (specific day and time). Reviewing evaluation activities is as important as attending them. In this session, all doubts about the proposed exercises will be resolved. No review will be conducted outside of this date. If a student cannot attend, she may delegate to a classmate with written authorization.
Campus evaluation regulations:
https://www.salleurl.edu/es/estudios/grados/informacion-academica/normat...
Students who do not pass the continuous evaluation will have to take a single written test in July of the entire course.
General evaluation criteria in written tests: maximum points are awarded to the exercise when it is complete, correct, logically coherent and clearly presented. An exercise not performed is scored zero. The written is passed with a minimum score of 5/10. The final grade is made up of the evaluation of the written text and, by the teacher's free decision (if further study is appropriate), the grade of a possible oral exam, which can vary the grade both positively and negatively. The oral exam will focus on the discussion and in-depth analysis of the topics proposed in the written test, and may require the completion of exercises of a similar type, and basic theoretical notions may be requested that justify the use of the most commonly used solution methods.
Students who do not take the July written test will have a final grade for the subject NP (Not Presented) in the extraordinary call.
The minimum grade to pass the subject is 5.
The categorization of the subject evaluation activities is:
Final evaluative activities: Highly significant.
Final written tests: Highly significant.
Evaluative activities/Tests in class: Moderately significant.
The use of AI tools will be limited to some course activities. Teachers will communicate this in the statement of the corresponding activity.
Use of AI tools: If AI tools are used in any activity, a paragraph must be indicated indicating what AI has been used for and what indications have been used to obtain the results. Failure to do so is a violation of academic honesty policies.
CONTINUOUS EVALUATION SYSTEM:
BLOCK 1 5% ACTIVIDADES EN CLASE (TRABAJO EN EQUIPO, CUESTIONARIO, ETC.)
12% PRUEBA ESCRITA
BLOCK 2 5% ACTIVIDADES EN CLASE (TRABAJO EN EQUIPO, CUESTIONARIO, ETC.)
12% PRUEBA ESCRITA
BLOCK 3 5% ACTIVIDADES EN CLASE (TRABAJO EN EQUIPO, CUESTIONARIO, ETC.)
12% PRUEBA ESCRITA
BLOQUE 45% ACTIVIDADES EN CLASE (TRABAJO EN EQUIPO, CUESTIONARIO, ETC.)
12% PRUEBA ESCRITA
BLOCK 5 5% ACTIVIDADES EN CLASE (TRABAJO EN EQUIPO, CUESTIONARIO, ETC.)
12% PRUEBA ESCRITA
TRANSVERSAL ACTIVITIES
5% Aula Barcelona
5% Ruled surfaces model
5% Data Analysis Poster
Alsina C., Jacas J., Belenguer T., Geometria a larquitectura, Edicions UPC, 2007.
Anton H., Elementary Linear Algebra, Wiley, 2014.
Giralt-Miracle, D., Gaudí. La búsqueda de la forma. Lunwerg Ediciones, 2002.
Gujiarro P., Crueles P, Màtematiques per a larquitectura. Problems resolts. Edicions UPC, 2002.
Alsina C., Casabó J., Jacas J., Monreal A., Belenguer T., Càlcul per a larquitectura, Edicions UPC, 2008.
Larson R., Hostetler R., Edwards B., Calculus, Brooks Cole, 2010.
Bowerman B., OConnel T., Murphree E., Business Statistics in Practice, McGrw-Hill, 2014
H. Pottmann, A. Asperl, M. Hofer, A. Kilian: Architectural Geometry, Bentley Institute Press, 2007
Burry, M. Burry: The new mathematics of architecture, Thames and Hudson, 2010
Hahn: Mathematical excursions to the world's great buildings, Princeton University Press, 2012