Academic Year/course:
2023/24
634 - Joint Programme in Computer Engineering - Business Administration
39810 - Discrete mathematics
Syllabus Information
Academic year:
2023/24
Subject:
39810 - Discrete mathematics
Faculty / School:
326 - Escuela Universitaria Politécnica de Teruel
Degree:
634 - Joint Programme in Computer Engineering - Business Administration
ECTS:
6.0
Year:
1
Semester:
Second semester
Subject type:
Basic Education
Module:
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1. General information
The objective of the subject is that the students acquire a series of knowledge in different topics of discrete mathematics that will be useful for their training as computer engineers.
In terms of the approach of the subject, special emphasis will be placed on mathematical rigor as a means to enhance the student's reasoning capacity, and on the correct use of mathematical language as a means to enhance their ability to communicate accurately.
This is a subject whose evaluable contents alone do not yet provide the student with direct capabilities to contribute to the achievement of the 2030 Agenda, however, they are essential to base the subsequent knowledge of the rest of the degree that is more directly related to the SDGs and therefore to the 2030 Agenda.
2. Learning results
Upon passing the subject, the student will be more competent to...
Define and solve mathematical problems that may arise in Computer Engineering.
Understand and master the basic concepts of Discrete Mathematics.
Apply knowledge of Discrete Mathematics to computer science.
Continuous learning and development of autonomous learning strategies.
Thus, in order to pass this subject, students must demonstrate the following results......
Manage the basic concepts of symbolic logic to be able to apply them in computing.
Know how to use the knowledge acquired about congruences in its application to computer science.
Know how to apply the basic concepts of combinatorics, particularly the principles of enumeration.
Be able to pose some enumeration problems by means of recurrences. Know how to solve recurrences by means of generating functions.
Know how to model problems in terms of graphs. Recognize the different types of graphs. Apply some algorithms on graphs and know how to handle the representation of graphs by means of matrices.
3. Syllabus
1. Logic : Connectives, truth tables, logical equivalence, tautologies, valid and invalid arguments, introduction to the logic of predicates.
2. Number theory : Principle of induction, Euclidean division, Euclid's algorithm, Bézout's identity, fundamental theorem of arithmetic, congruences, Chinese remainder theorem, modular binary exponentiation,Fermat' s little theorem , Euler's theorem, RSA.
3. Combinatorial : Permutations, combinations, binomial coefficients, pigeon hole principle, binclusion principle- exclusion, recurrence relations.
4. Graph theory : Basic concepts, Eulerian graphs, Hamiltonian graphs, matrix representations of graphs, isomorphism of graphs, trees, Kruskal's algorithm, Prim's algorithm, Dijkstra's algorithm.
4. Academic activities
The student dedication to achieve the learning results is estimated at 150 hours, distributed as follows:
45 hours of theory and problems classes (3 hours per week)
12 hours of computer practice (6 sessions of 2 hours each)
90 hours of effective self-study
3 hours of final written exam
The face-to-face sessions, both theory and problems classes as well as computer practice, are scheduled for the following days by the center and can be consulted on the website. The dates of the intermediate and final tests will be announced well in advance.
5. Assessment system
The student must demonstrate achievement of the intended learning results through the following assessment activities:
1. Partial written test (35%, minimum grade 4.5): theoretical-practical questions, problems and practical exercises.
2. Academic Work (10%): Assignments with theoretical-practical exercises.
3. Computer practice (20%): Work developed during the practical sessions and final practice exam.
4. Final Exam (35%, minimum grade 4.5): Written test (in 1st call) on the theoretical-practical contents of the subject, with exercises and questions of similar difficulty to those worked on in the term.
In addition to the continuous assessment, students are entitled to a global assessment with a single exam in the two official exams.