TecnoCampus Foundation
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General information

Subject type: Basic

Coordinator: Vladimir Bellavista Parent

Trimester: Third term

Credits: 6

Teaching staff: 

Alfonso Palacios González
Carles Bonet Papell 

Academic year: 2025

Teaching course: 2

Languages ​​of instruction

  • Catalan

This subject is taught in Catalan, but the bibliography and documentation is mostly in English. 

Competencies / Learning Outcomes

Basic skills

  • B1_That students have demonstrated knowledge and understanding in a field of study that is based on general secondary education, and is accustomed to finding at a level that, although with the support of advanced textbooks, also include some aspects that involve knowledge from the forefront of your field of study

  • B3_Students have the ability to gather and interpret relevant data (usually within their area of ​​study), to make judgments that include reflection on relevant social, scientific or ethical issues

Specific skills

  • EFB1_Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge about: linear algebra, differential and integral calculus, numerical methods, numerical algorithms, statistics and optimization

  • EFB3_Ability to understand and master the basic concepts of discrete mathematics, logic, algorithms and computational complexity, and their application for solving engineering problems

Transversal competences

  • T1_That students know a third language, which will be preferably English, with an adequate level of oral and written form, according to the needs of the graduates in each degree

Presentation of the subject

Discrete mathematics studies mathematical structures that are intrinsically discrete, that is, they are not continuous. For example, the real number line is continuous because the numbers vary smoothly (it is not known and cannot be said which real number comes after another, for example we do not know which number comes after 1,0), on the other hand, the integer number line is discrete because we can clearly distinguish their values (after 1 comes 2). In this subject we will study propositional logic and graph theory which are two disciplines widely used in the field of computing. Logic is used in programming, in fact there is the logical programming paradigm in the same way as there is imperative and functional, in databases, in the design and verification of systems and in artificial intelligence among others. In the case of graphs, they are a mathematical structure widely used in computing (and other disciplines) to represent problems, data, concepts and their interrelationships. They are easily programmable structures of which many mathematical properties are known that can be used to validate the correctness of the proposed solution to computational problems. 

The classroom (physical or virtual) is a safe space, free of sexist, racist, homophobic, transphobic and discriminatory attitudes, either towards students or towards teachers. We trust that together we can create a safe space where we can make mistakes and learn without having to suffer prejudice from others. 

Contents

  1. Propositional logic
    1. Reasoning, natural language and propositional language
    2. The language of propositional logic, CP0
    3. Formalization of sentences and interpretation of statements
    4. Theory of models (tautologies, contradictions and contingencies)
    5. Demonstration theory
    6. Valid and invalid reasoning, consistency and inconsistency, counterexamples
    7. Normal forms
    8. The method of resolution
    9. Linear Resolution
  2. Graph theory
    1. Basic definitions: paths, connectivity and distance, Isomorphism between graphs
    2. Representation of graphs
    3. Algorithms on graphs: paths in depth and width (DFS, BFS)
    4. Digraphs and DAGs
    5. Topological arrangement
    6. Minimal expansion trees: Prim and Kruskal algorithms
    7. Shorter paths: Dijkstra's algorithm

Activities and evaluation system

The final grade is the average grade of the two parts of the subject

ACTIVITY and WEIGHT

  1. PL: Attendance and participation in seminars and solving Logic problems 5% (Under continuous evaluation)
  2. PG: Attendance and participation in Graphs seminars and problem solving 5% (Under continuous evaluation)
  3. EL: Logic Exam 45% (Under continuous evaluation)
  4. EG: Graphs Exam 45% (Under continuous evaluation)

Conditions for passing the subject:

  • (PL 0,1 + EL 0,9) >= 5 (You must pass the Logic thematic block with a grade equal to or higher than 5)
  • (PG 0,1 + EG 0,9) >= 5  (You must pass the thematic block of Graph Theory with a grade equal to or higher than 5)

Recovery

  • Each thematic block can be retaken separately. Only the EL and EG retake exams are retaken and repeated. 
  • The result of the recovery, if the recovery of EL>=5 and the recovery of EG>=5 will be PASS(5), otherwise, it will be FAIL.
  • In the retake, the continuous assessment mark -attendance and participation- is not taken into account, each exam represents 50%.

Any form of academic fraud will be sanctioned in accordance with the center's assessment regulations. If signs of fraud are detected, including the improper use of generative artificial intelligence tools, the subject's teaching staff may call the student for an individual interview with the aim of verifying their authorship.

Bibliography

Basic

K. Erciyes, "Discrete Mathematics and Graph Theory, a concise study companion and guide (Undergrate Topics in Computer Science)". Springer, 2021. ISBN 978-3-030-61114-9

Kenneth H. Rosen, "Discrete Mathematics and its Applications." Eighth Edition. McGraw-Hill-Education, 2019. ISBN 978-1-260-09199-1.

Complementary

Gabriel Valiente, "Algorithms on Trees and Graphs: With Python Code (Texts in Computer Science)". Second Edition. Springer, 2021. ISBN 

978-3030818845

K. Erciyes, "Algebraic Graph Algorithms, a practical guide using Python (Undergrate Topics in Computer Science)". Springer, 2021. ISBN 978-3-030-87885-6

Robert Sedgewick and Kevin Wayne, "Algorithms", Fourth Edition, Addison-Wesley, 2011. ISBN 978-0321573513.