Study programme competencies |
Code
|
Study programme competences / results
|
A1 |
CE1 - Capacidade para utilizar con destreza conceptos e métodos propios da matemática discreta, a álxebra lineal, o cálculo diferencial e integral, e a estatística e probabilidade, na resolución dos problemas propios da ciencia e enxeñaría de datos. |
A2 |
CE2 - Capacidade para resolver problemas matemáticos, planificando a súa resolución en función das ferramentas dispoñibles e das restricións de tempo e recursos. |
B1 |
CB1 - Que os estudantes demostrasen posuír e comprender coñecementos nunha área de estudo que parte da base da educación secundaria xeral, e adóitase atopar a un nivel que, aínda que se apoia en libros de texto avanzados, inclúe tamén algúns aspectos que implican coñecementos procedentes da vangarda do seu campo de estudo |
B5 |
CB5 - Que os estudantes desenvolvesen aquelas habilidades de aprendizaxe necesarias para emprender estudos posteriores cun alto grao de autonomía |
B6 |
CG1 - Ser capaz de buscar e seleccionar a información útil necesaria para resolver problemas complexos, manexando con soltura as fontes bibliográficas do campo. |
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. |
Learning aims |
Learning outcomes |
Study programme competences / results |
Know and handle the symbolic language, formalize logical arguments and prove the validity of them |
A1 A2
|
|
|
Know the basic concepts of the theory of sets and applications |
A1 A2
|
B1 B6
|
C1
|
Know the counting techniques and their applications |
A1 A2
|
B1 B5 B6
|
C1
|
Know the fundamental concepts of graph theory and its application to problem solving. |
A1 A2
|
B1 B5 B6
|
C1
|
Contents |
Topic |
Sub-topic |
1-. Logic Reasoning |
Propositional logic: propositions and logical operators
Implications and Logical Equivalences
Proof methods: Semantic tables, induction principle
Normal forms
Predicate Logic |
2.- Sets, functions and relations
|
Basic theory of sets: elements, subsets
Some sets of numbers: the integers and the complexes
Functions, types of functions, composition
Binary relations, properties
Equivalence relations, equivalence classes and quotient set
Order relations, distinguished elements, Hasse diagrams |
3.- Combinatorics and Recurrence |
Basic counting principles
Variations, permutations and combinations
Binomial and multinomial coefficients
Inclusion-exclusion principle
Successions and series
Recurrent relations
Resolution of some recurrence equations. Applications |
4.-Graphs |
Directed graphs: basic concepts
Non directed graphs: basic concepts
Connectivity
Trees. Rooted Trees
Search trees
Weighted graphs: the problem of the minimal spanning tree |
Planning |
Methodologies / tests |
Competencies / Results |
Teaching hours (in-person & virtual) |
Student’s personal work hours |
Total hours |
Guest lecture / keynote speech |
A2 A1 B3 B6 B8 C1 |
30 |
45 |
75 |
Seminar |
A2 A1 B1 B3 B6 B8 C1 |
8 |
12 |
20 |
Objective test |
A1 A2 B1 B3 B6 B8 C1 |
3 |
0 |
3 |
Laboratory practice |
A1 A2 B5 C1 |
20 |
30 |
50 |
|
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 |
Through the virtual platform of the university, students will be provided detailed information on the contents of each topic so that each student can configure, according to their criteria and needs, the appropriate material for monitoring and understanding the matter; You can make use of the recommended bibliography and / or material available in the network.
The theoretical and practical classes will be developed simultaneously in the classroom, performing exercises after the theoretical explanations. The explanation of formal techniques will begin by means of examples, emphasizing concrete calculations and the algorithmic nature of some of them. It is intended that students are able to draw conclusions from the results obtained, trying to motivate students to participate and be able to infer conclusions. |
Seminar |
During the tutorial sessions, students may raise questions about the concepts, exercises and procedures seen in the theory and problems sessions. |
Objective test |
There will be a written exam that will consist of a collection of theoretical questions and / or problems (of the same type as those proposed in the seminars (TGR) and in the collections of exercises). |
Laboratory practice |
At the beginning of each chapter, students will be given a collection of exercises related to the theoretical contents explained in the guest lecture sessions. In these sessions it is intended:
I) to encourage the student by solving exercises, with the help of the teacher, to reinforce the understanding of the concepts studied,
II)to encourage the reasoned resolution of the exercises, avoiding the use of "recipes".
Depending on the subject and the resources available, work can be done with computer programs that reinforce the concepts worked on in the theoretical and exercise classes. |
Personalized attention |
Methodologies
|
Laboratory practice |
|
Description |
In the sessions in small groups, the doubts raised by the students are solved, especially when they are common to several of them or correspond to cases of special interest for their practical application. If the question is more specific or not fully resolved for any student, it would be treated in the hours of individualized tutoring.
The students will know the evaluation of the tests carried out throughout the course, in order to correct the errors and / or improve the answers to the exercises, with a view to a more solid formation.
Students have also the possibility to review the grade obtained in the final written test, verifying that it meets the established evaluation criteria. |
|
Assessment |
Methodologies
|
Competencies / Results |
Description
|
Qualification
|
Laboratory practice |
A1 A2 B5 C1 |
Ao longo do curso realizarase unha avaliación dos distintos temas onde se exporán definicións dos conceptos introducidos, cuestións e exercicios similares aos do correspondente boletín. Valorarase a resposta correcta ás cuestións e exercicios expostos e, a presentación e a claridade da exposición realizada.
Poderase ter en conta a actitude participativa do alumnado na resolución das cuestións formuladas durante as prácticas. |
20 |
Objective test |
A1 A2 B1 B3 B6 B8 C1 |
Ao final do curso farase unha proba escrita. Esta proba inclúe:
- Preguntas curtas que permiten valorar se o alumno comprendeu os conceptos teóricos básicos.
- Problemas cun grao de dificultade similar aos feitos en clase e os presentados nas coleccións de exercicios propostos.
Valoraranse o dominio dos conceptos teóricos da materia, a súa comprensión e a súa aplicación na resolución de exercicios. Así mesmo, avaliarase a claridade, a orde e a presentación dos resultados expostos.
Para superar a materia é necesario obter máis de 3,2 puntos dos 8 posibles na proba escrita.
A presentación á proba final do curso supón que o alumno completou o proceso de avaliación continua. |
80 |
|
Assessment comments |
The evaluation of the laboratory practices of students with part-time enrollment can be made by attending, as far as possible, to their particular circumstances.
|
Sources of information |
Basic
|
Caballero, R., Hortalá, M.T., Martí, N., Nieva, S., Pareja, A. y Rodríguez, M. (2007). Matemática Discreta para Informáticos. Ejercicios resueltos. Pearson
Rosen, K. H. (2019). Discrete Mathematics and Its Applications. McGraw-Hill
Aguado, F. et al (2018). Problemas resueltos de Combinatoria. Laboratorio con SageMath. Paraninfo
García Merayo, F.; Hernández Peñalver, G. y Nevot Luna, A. (2003). Problemas Resueltos de Matemática Discreta. Thomson
Vieites A. et al (2014). Teoría de grafos. Ejercicios resueltos y propuestos. Laboratorio con SAGE. Paraninfo |
|
Complementary
|
Grimaldi, R. P. (2006). Discrete and Combinatorial Mathematics. Pearson Education
Biggs, N. L. (1994). Matemática Discreta. Vicens Vives
Scheinerman, E. R. (2001). Matemáticas Discretas. Thomson Learning |
|
Recommendations |
Subjects that it is recommended to have taken before |
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Subjects that are recommended to be taken simultaneously |
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Subjects that continue the syllabus |
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Other comments |
<p> It is recommended to have taken the subjects of Mathematics from high school </p> |
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