Universidad de Jaén

Unit 1. The ring of polynomials.

The ring of polynomials. Divisibility. Division algorithm. Factorization of polynomials. Greatest common divisor and least common multiple.

Unit 2. Symmetric group.

Group and subgroups. Permutations, cycles and transpositions. Cycle decomposition for permutations. Signature of a transposition. The alternating subgroup.

Unit 3. Systems of linear equations. Matrices and determinants.

Systems of linear equations. Gauss-Jordan elimination method. Matrices and systems of linear equations. Hermite normal form. Rank of a matrix. Rouché-Fröbenius theorem. Elementary matrices. Inverse matrices. Determinants and some applications.

Unit 4. Vector spaces and inner product space.

Vector spaces. Linearly independet and dependet sets. Bases and dimension. Vector subspaces and operations with subspaces. Inner product and length. Orthogonal vectors. 

Unit 5. Linear maps. Diagonalization.

Linear maps. Null space and range. Matrix expression of a homomorphism. Classification of a linear map. Diagonalization of an endomorphism. Applications.

Unit 6. Introduction to the graph theory.

Basics of graphs. Subgraphs. Isomorphic graphs. Connected graphs. Geodesic. Euler and Hamilton graphs. Trees. Bipartite graphs. Planar graphs. Coloring of planar graphs. Directed graphs.

PRACTICAL CONTENTS

Practice 1. The polynomial ring.

Practice 2. Groups and subgroups.

Practice 3. The symmetric group.

Practice 4. Graphs I. Definition, implementation and representation.

Practice 5. Graphs II. Regular graphs, complete graphs, subgraphs and bipartite graphs.

Practice 6. Graph III. Paths and cycles.

Practice 7. Graphs IV. Graph coloring, planar graphs and trees.

Practice 8. Elementary matrices. Hermite normal form.

Practice 9. Systems of linear equations. Matrices and determinants.

Practice 10. Vector spaces.

Practice 11. Inner product space.

Practice 12. Linear maps.

Practice 13. Diagonalization.

Lecture (Theory): there will be two one-hour-long sessions each week during all the semester. These sessions will be devoted to regular lectures and problem solving, using a video projector and computer-generated slides. The lecturer makes their notes available online after a lecture through his institutional web which can help to supplement the notes you take during the class. You have to attend lectures in order to make better use of the course.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

To pass the course is necessary to obtain a score of 5 out of 10 points between the weighted average of theory and practical part of the course; In order to calculate such average, it will also be essential to have obtained a minimum of 4 out of 10 points in each block (theoretical and practical part). When a student will not reach the minimum in a block, the rating which it will reflect in the minutes will be less than 4 out of 10. The positive evaluation will mean that the student has sufficiently achieved the learning results: 1, 2 y 4.

The block "Theoretical concepts of the subject" (S2) will be evaluated by means of a final exam with 60% of the weight of that block, and another 40% by continuous evaluation.

The block "Computer practices" (S3) will be evaluated 100% by continuous evaluation.

The block "Attendance and participation" (S1) will be evaluated through active participation and the delivery of theoretical and practical exercises.

In relation to the overall weight of the course, the continuous evaluation of the three blocks (S1, S2 and S3), represents 52% of the subject.

Students who have done some test belong to continuous assessment will appear in the academic record of the ordinary call 1as presented, even if they do not done the final exam.

In the face-to-face exams of each call or in any class exercise which is qualifying, except for special and particular circumstances that will be specified by your teacher, electronic devices, notes, books or any other medium that allows the storage or transmission of data will not be allowed. In the event of non-compliance, it will act according to current regulations.

Competences assessed in the theoretical part: CB1R, CB5R, CBB1R and CBB3R.

Competences assessed in the practical part: CB1R and CB1R y CB5R.

Face-to-face teaching:

Taking into account different parameters (number of students enrolled per group, capacity of the assigned classroom and distance between students), the minimum number of subgroups will be determined in which each group of theory or practice must be subdivided to guarantee that the classroom attendance is carried out with the sanitary guarantees established by the competent authority.

The face-to-face teaching in the multimodal or mixed scenario will be: non-rotating, for 100% of the students, whenever possible, and rotating when it is not possible.

The attendance percentage, taking into account the aforementioned parameters, will be established and specified by the Center. In general, and when dealing with estimates, we will take as reference the one provided in July 2020 by the Center: 50% for the theory groups (2 subgroups) and 50% for the practice groups (2 subgroups). These percentages will be set by the Center before the start of classes. If the percentage estimates improved for any circumstance (reduction of the minimum distance between people, use of adjoining teaching spaces, etc.) and allowed higher percentages of attendance, they would always opt for these, and would take the fewest possible subgroups, understanding as the most optimal case 100% attendance.

Temporal planning:

The temporal planning and schedule will be the same in any scenario: if the attendance is 100%, a rotating system or an exclusively online teaching system. The only thing that will vary will be the teaching methodology.

  Methodology:

• In the event of establishing a weekly rotation system for face-to-face teaching, each subgroup will receive face-to-face teaching for a full week, alternating with the rest of the subgroups. The subgroup of assinged students in a week will attend to face-to-face class, while the rest of the students attend the class, (according to the instructions the Center has given), by means of videoconference retransmission ⁽¹⁾.
• Expository classes in large groups, face-to-face / online ⁽¹⁾ rotating 50% (or a different percentage according to the Center indications), where a large part of the contents of the subject will be exposed, as well as standard examples.
• Classes in practice groups, face-to-face / online ⁽¹⁾ rotating 50% (or a different percentage according to the Center indications), in which problems related to the contents exposed in the classes in large groups will be solved with the help of the computer. At the same time, in these classes, the theoretical contents of the subject not exposed in the expository classes will be exposed in a more practical way. Finally, they will be solved on the blackboard, and whenever it is possible to use the computer, exercises of the subject that previously has been proposed to the student so that he works them at home.

Evaluation:

To pass the course, on any situation, is necessary to obtain a score of 5 out of 10 points between the weighted average of theory and practical part of the course; In order to calculate such average, it will also be essential to have obtained a minimum of 4 out of 10 points in each block (theoretical and practical part). When a student will not reach the minimum in a block, the rating which it will reflect in the minutes will be less than 4 out of 10. The positive evaluation will mean that the student has sufficiently achieved the learning results: 1, 2 y 4.

The block "Theoretical concepts of the subject" (S2) will be evaluated by means of a final exam with 60% of the weight of that block, and another 40% by continuous evaluation.

The block "Computer practices" (S3) will be evaluated 100% by continuous evaluation.

The block "Attendance and participation" (S1) will be evaluated through active participation and the delivery of theoretical and practical exercises.

In relation to the overall weight of the course, the continuous evaluation of the three blocks (S1, S2 and S3), represents 52% of the subject.

The qualification of blocks S2 and S3, which exceed 5 out of 10 points, if the subject has not been approved, will be maintained in each of the official calls for the academic year.

Students who have done some test belong to continuous assessment will appear in the academic record of the ordinary call 1as presented, even if they do not done the final exam.

The blocks, percentages and evaluation will be the same in any situation, exclusively varying the evaluation methodology, and in particular the exercises or exams, which will be in-person or online. Whenever possible, efforts will be made to carry out the exercises or exams in person.

In the face-to-face exams of each call or in any class exercise which is qualifying, except for special and particular circumstances that will be specified by your teacher, electronic devices, notes, books or any other medium that allows the storage or transmission of data will not be allowed. In the event of non-compliance, it will act according to current regulations.

Evaluation tests will be carried out online according to the recommendations provided by the University of Jaén.

An oral online evaluation will be used for those students who have technical or other difficulties (duly justified) that occur during the evaluation process, or when the teachers of the subject cannot verify the authorship of the tests carried out.

The mandatory instructions for conducting online exams of official calls will be published in advance in the course space at the Intranet site Docencia Virtual. These will consider the compatibility of carrying out all the tests online, with the use of webcam, recordings, etc. according to the guidelines given by this university.

Each student must have the technical means necessary to carry out the exams online, such as a computer, a webcam, a microphone and the necessary software in each case. In this sense, according to instructions received from the Secretaria General of the University of Jaén, teachers must comply with the duty of information contained in article 13 of the Reglamento General sobre Protección de Datos (Reglamento (UE) 2016/679 del Parlamento Europeo y del Consejo of April 27, 2016) and report to the students about the recording of the exam via video call, through the Google Hangouts Meet platform ⁽²⁾, as an essential instrument to guarantee the transparency of the process.

Competences assessed in the theoretical part: CB1R, CB5R, CBB1R and CBB3R. 

Competences assessed in the practical part: CB1R and CB5R.

Resources and facilities ⁽²⁾:

-Those necessary, for online following of classes, online tutoring, online exercises, etc. (Google Meet, Google Form, YouTube, Virtual Teaching, etc.)

-Tablets or tablet PCs, to replace the blackboard, to teach online and tutoring.

-Different types of videos made for theory and practice by the teachers of the subject.

-Programs for self-assessment exercises carried out by the teachers of the subject.

- Own design software for the generation and proposition of a unique, different and random exam for each student from a wide question bank, randomly, and online.

⁽¹⁾ In the multimodal and / or non-face-to-face situation, when appropriate, the teaching staff involved in teaching, reserves the right not to consent to the capture, publication, retransmission or reproduction of their speech, image, voice and explanations of chair, in the exercise of his teaching functions, in the field of the University of Jaén.

⁽²⁾ The software or hardware that will be used to carry out the exams or exercises, classes or online tutoring, will be the specified or any other equivalent or updated that is provided or recommended at the University of Jaén.

Face-to-face teaching:

Teaching will be exclusively online.

Temporal planning:

The temporal planning and schedule will be the same in any scenario: if the attendance is 100%, a rotating system or an exclusively online teaching system. The only thing that will vary will be the teaching methodology.

Methodology:

• Expository classes in large online groups (1), where a large part of the contents of the subject will be exposed, as well as standard examples.
• Classes in online practice groups (1), in which problems related to the contents exposed in the expository classes in large groups will be solved with the help of the computer. At the same time, in these classes, the theoretical contents of the subject not exposed in the expository classes will be exposed in a more practical way. Finally, they will be solved on the blackboard, and whenever it is possible to use the computer, exercises of the subject that previously has been proposed to the student so that he works them at home.

Evaluation:

To pass the course, on any situation, is necessary to obtain a score of 5 out of 10 points between the weighted average of theory and practical part of the course; In order to calculate such average, it will also be essential to have obtained a minimum of 4 out of 10 points in each block (theoretical and practical part). When a student will not reach the minimum in a block, the rating which it will reflect in the minutes will be less than 4 out of 10. The positive evaluation will mean that the student has sufficiently achieved the learning results: 1, 2 y 4.

The block "Theoretical concepts of the subject" (S2) will be evaluated by means of a final exam with 60% of the weight of that block, and another 40% by continuous evaluation.

The block "Computer practices" (S3) will be evaluated 100% by continuous evaluation.

The block "Attendance and participation" (S1) will be evaluated through active participation and the delivery of theoretical and practical exercises.

In relation to the overall weight of the course, the continuous evaluation of the three blocks (S1, S2 and S3), represents 52% of the subject.

The qualification of blocks S2 and S3, which exceed 5 out of 10 points, if the subject has not been approved, will be maintained in each of the official calls for the academic year.

Students who have done some test belong to continuous assessment will appear in the academic record of the ordinary call 1as presented, even if they do not done the final exam.

The blocks, percentages and evaluation will be the same in any situation, exclusively varying the evaluation methodology, and in particular the exercises or exams, which will be in-person or online. Whenever possible, efforts will be made to carry out the exercises or exams in person.

In the exams of each call or in any class exercise which is qualifying, except for special and particular circumstances that will be specified by your teacher, electronic devices, notes, books or any other medium that allows the storage or transmission of data will not be allowed. In the event of non-compliance, it will act according to current regulations.

Evaluation tests will be carried out online according to the recommendations provided by the University of Jaén.

An oral online evaluation will be used for those students who have technical or other difficulties (duly justified) that occur during the evaluation process, or when the teachers of the subject cannot verify the authorship of the tests carried out.

The mandatory instructions for conducting online exams of official calls will be published in advance in the course space at the Intranet site Docencia Virtual. These will consider the compatibility of carrying out all the tests online, with the use of webcam, recordings, etc. according to the guidelines given by this university.

Each student must have the technical means necessary to carry out the exams online, such as a computer, a webcam, a microphone and the necessary software in each case. In this sense, according to instructions received from the Secretaria General of the University of Jaén, teachers must comply with the duty of information contained in article 13 of the Reglamento General sobre Protección de Datos (Reglamento (UE) 2016/679 del Parlamento Europeo y del Consejo of April 27, 2016) and report to the students about the recording of the exam via video call, through the Google Hangouts Meet platform ⁽²⁾, as an essential instrument to guarantee the transparency of the process.

Competences assessed in the theoretical part: CB1R, CB5R, CBB1R and CBB3R. 

Competences assessed in the practical part: CB1R and CB5R.

  Resources and facilities ⁽²⁾:

- Those necessary, for online following of classes, online tutoring, online exercises, etc. (Google Meet, Google Form, YouTube, Virtual Teaching, etc.)

- Tablets or tablet PCs, to replace the blackboard, to teach online and tutoring.

- Different types of videos made for theory and practice by the teachers of the subject.

- Programs for self-assessment exercises carried out by the teachers of the subject.

• Own design software for the generation and proposition of a unique, different and random exam for each student from a wide question bank, randomly, and online.

⁽¹⁾  In the multimodal and / or non-face-to-face situation, when appropriate, the teaching staff involved in teaching, reserves the right not to consent to the capture, publication, retransmission or reproduction of their speech, image, voice and explanations of chair, in the exercise of his teaching functions, in the field of the University of Jaén.

⁽²⁾  The software or hardware that will be used to carry out the exams or exercises, classes or online tutoring, will be the specified or any other equivalent or updated that is provided or recommended at the University of Jaén.

Institution in charge of data processing: Universidad de Jaén, Campus Las Lagunillas, s/n, 23071 Jaén

Data Protection Delegate: dpo@ujaen.es

Purpose: In accordance with the Universities Law and other national and regional regulations in force, carrying out exams and assessment tests corresponding to the courses students are registered in. In order to avoid frauds while sitting the exam, the exam will be answered using a videoconference system, being able the academic staff of the University of Jaén to compare and contrast the image of the person who is answering the exam with the student's photographic files. Likewise, in order to provide the exam with evidential content for revisions or claims, in accordance with current regulation frameworks, the exam will be recorded and stored.

Legitimacy: compliance with legal obligations (Universities Law) and other national and regional regulations currently in force.

Addressees: service providers who are the owners of the platforms where the exams are carried out and with whom the University of Jaén has signed the corresponding data access contracts.

Storage periods: those established in current in force regulations. In the specific case of exam videoconference recordings, not before the examination records and transcripts are closed or the exam can still be reviewed or challenged.

Rights: you can exercise your right of access, amendment, cancellation, opposition, suppression, limitation and portability by sending a letter to the postal or electronic address indicated above. In the event that you consider that your rights have been violated, you may submit a complaint to the Andalusian Council for Transparency and Data Protection www.ctpdandalucia.es

Person in charge: Universidad de Jaén, Paraje Las Lagunillas, s/n; Tel.953 212121; www.ujaen.es

Data protection delegate (DPO): TELEFÓNICA, S.A.U. ; Email: dpo@ujaen.es

Procedure aim: To manage proper recordings of teaching sessions with the aim of facilitating learning process under a multimodal and/or online teaching

Period for record storage: Images will be kept during legal term according to regulations in force

Legitimacy: Data will be managed according to legal regulations (Organic Law 6/2001, December 21, on Universities) and given consent provided by selecting corresponding box in legal admission documents

Data recipients (transfers or assignments): Any person allowed to get access to every teaching modality

Rights: You may exercise your rights of access, rectification, cancellation, portability, limitation of processing, deletion or, where appropriate, opposition. To exercise these rights, you must submit a written request to the Information, Registration and Electronic Administration Service of the University of Jaen at the address above, or by e-mail to the address above. You must specify which of these rights you are requesting to be satisfied and, at the same time, you must attach a photocopy of your ID card or equivalent identification document. In case you act through a representative, legal or voluntary, you must also provide a document that proves this representation and identification. Likewise, if you consider that your right to personal data protection has been violated, you may file a complaint with the Andalusian Data Protection and Transparency Council www.ctpdandalucia.es