## Syllabus 2022-23 - 11711001 - Algebra (Álgebra)

Caption
• Level 1: Tutorial support sessions, materials and exams in this language
• Level 2: Tutorial support sessions, materials, exams and seminars in this language
• Level 3: Tutorial support sessions, materials, exams, seminars and regular lectures in this language
 DEGREE: Grado en Estadística y empresa FACULTY: FACULTY OF LAW AND SOCIAL SCIENCES ACADEMIC YEAR: 2022-23 COURSE: Algebra
SYLLABUS
1. COURSE BASIC INFORMATION
 NAME: Algebra CODE: 11711001 ACADEMIC YEAR: 2022-23 LANGUAGE: English LEVEL: 1 ECTS CREDITS: 6.0 YEAR: 2 SEMESTER: PC
2. LECTURER BASIC INFORMATION
 NAME: GARCÍA MUÑOZ, MIGUEL ÁNGEL DEPARTMENT: U124 - MATEMÁTICAS FIELD OF STUDY: 005 - ÁLGEBRA OFFICE NO.: B3 - 016 E-MAIL: magarcia@ujaen.es P: 953212935 WEBSITE: www4.ujaen.es/~magarcia ORCID: https://orcid.org/0000-0002-6252-0592 LANGUAGE: - LEVEL: 1
3. CONTENT DESCRIPTION

Unit 1. 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 2. Vector spaces and inner product space.

Vector spaces. Linearly independent and dependent sets. Bases and dimension. Vector subspaces. Inner product and norm. Orthogonal vectors.

Unit 3. Linear maps.

Linear maps. Null space and range. Matrix expression of a homomorphism. Classification of a linear map.

Unit 4. Diagonalization.

Eigenvalues and eigenvectors of an endomorphism. Characteristic polynomial. Diagonalization of an endomorphism. Singular values decomposition. Applications.

Unit 5. Generalized inverses.

Left and right inverse matrices. Moore-Penrose generalized inverse. Full rank factorization of a matrix. Minimum quadratic solution of minimum norm.

PRACTICAL CONTENTS

Practice 1. The working environment: Mathematica. Syntax. Basic arithmetic.

Practice 2. Lists: tables, matrices and vectors.

Practice 3. Elementary matrices. Hermite normal form.

Practice 4. Determinants. Range and inverses.

Practice 5. Systems of linear equations.

Practice 6. Vector spaces. Bases.

Practice 7. Vector subspaces.

Practice 8. Euclidean vector spaces.

Practice 9. Linear maps. Matrix expression.

Practice 10. Kernel and range of a linear map.

Practice 11. Diagonalization by similarity. Applications.

Practice 12. Singular values decomposition.

Practice 13. Generalized inverses.

4. COURSE DESCRIPTION AND TEACHING METHODOLOGY

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.

Lecture (Practice): they will be two hours long, and will be held weekly during the semester. In these classes students will solve with the help of computer problems related to content of the subject. In these classes also will be presented in a more practical way, those theoretical contents of the subject which will not be exposed in the lectures. Finally, teacher will solve on the blackboard, and if it is possible, he will be used the computer, exercises of the subject that has previously been proposed to the student for the work at home. You may be asked to work individuals. In most cases, you will be asked to 'write up' your work and this will be assessed with the mark contributing to your overall exam result. You have to attend your practical classes 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

5. ASSESSMENT METHODOLOGY

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: R 11 and R 12.

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, attending to the interest of the student and their circumstances, provided that they are duly accredited in a timely manner. In extraordinary call 2, and as established by the regulations of the University of Jaén, 100% of the block may be evaluated.

The block "Laboratory practices/field practices/use of ICT tools" (S4) will be evaluated 100% by continuous evaluation, with attendance to class, the preparation of a notebook of practice and one or more continuous evaluation tests with which will be determined  the students' grade and  will be verified the authorship of the notebook. In the extraordinary call, only one exam will be carried out with 100% for students who have not passed or do not wish to maintain continuous evaluation. In each continuous assessment test and in all calls, it will be mandatory to bring, to verify its realization, all the exercises in the printed notebook.

In relation to the overall weight of the course, the continuous evaluation of the two blocks (S2 and S4), represents 52% of the subject.

The qualification of blocks S2 and S4, 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.

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: CE5, CG12 y CG2.

Competences assessed in the practical part: CE5, CG16, CG6 y CG8.

6. BOOKLIST
MAIN BOOKLIST:
• Elementary linear algebra [Recurso electrónico]. Edition: 11th edition. Author: Anton, Howard. Publisher: Hoboken, NJ : John Wiley & Sons, [2014]  (Library)
• Linear algebra and its applications. Edition: 5th ed., global ed.. Author: Lay, David C.. Publisher: Boston ; Madrid [etc.] : Pearson, cop. 2016  (Library)
7. VIRTUAL / CLASSROOM TEACHING SCENARIO

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 during the course 2020/21 by the Center: from 25% to 50% for the theory and practice groups. 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 from 25% to 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 from 25% to 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: R 11 y R 12.

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 "Laboratory practice/field practice/use of ICT tools" (S4) will be evaluated 100% by continuous evaluation,  with attendance to class, the preparation of a  notebook of practice and one or more continuous evaluation tests with which will be determined  the students' grade and  will be verified the authorship of the notebook. In the extraordinary call, only one exam will be carried out with 100% for students who have not passed or do not wish to maintain continuous evaluation. In each continuous assessment test and in all calls, it will be mandatory to bring, to verify its realization, all the exercises in the printed notebook.

In relation to the overall weight of the course, the continuous evaluation of the two blocks (S2 and S4), represents 52% of the subject.

The qualification of blocks S2 and S4, 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 1 as 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: CE5,CG12 and CG2.

Competences assessed in the practical part: CE5, CG16, CG6 and CG8.

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.

8. VIRTUAL TEACHING SCENARIO

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: R 11 y R 12.

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 "Laboratory practices/field practices/use of ICT tools" (S4) will be evaluated 100% by continuous evaluation,  with attendance to class, the preparation of a practical notebook and one or more evaluation tests with which will be determined the qualification of the student  and will check the authorship of the notebook. In each exam and in all the calls, all the exercises in the notebook will be delivered by telematics means, to verify its elaboration, obligatorily and as an indispensable requirement.

In relation to the overall weight of the course, the continuous evaluation of the two blocks (S2 and S4), represents 52% of the subject.

The qualification of blocks S2 and S4, 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: CE5, CG12 y CG2.

Competences assessed in the practical part: CE5, CG16, CG6 y CG8.

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.

DATA PROTECTION CLAUSE (on line exams)

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

CLASS RECORDING CLAUSE PERSONAL DATA PROTECTION

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