Degree in Mathematical Engineering + Computer Engineering

Objectives

This module, together with Algebra II, forms the subject of Algebra. This module, which forms part of the degree programme’s Core Curriculum, aims not only to ensure that students are familiar with the main fundamental theorems of linear algebra, but also to enable them to understand matrix calculus from a conceptual perspective and to apply it to solving problems typical of mathematical engineering; it is, therefore, the foundation for other modules and subjects within the degree programme, such as Numerical Calculus, Operational Research, Stochastic Calculus and Artificial Intelligence.

Prerequisites

No prerequisites have been set.

Learning Outcomes

Not applicable.

Learning outcomes

RK4 – To be familiar with rigorous proofs of some classical theorems in different areas of mathematics. TYPE: Knowledge or content.

RS1 - To use mathematical language to formulate propositions in various fields and construct proofs for the problems posed. TYPE: Skills or abilities.

Description of the content

1. SYSTEMS OF LINEAR EQUATIONS.

1.1 Systems of linear equations. Types. Gauss-Jordan method. Discussion of solutions.

1.2 Matrices. Classification. Elementary transformations, Hermitian normal form and rank. Operations: addition, scalar multiplication and matrix multiplication; trace; transposition; inversion. Properties. Regular matrices. Equivalence.

1.3 Matrix notation for systems of linear equations. Rouché–Frobenius theorem.

1.4 Determinants. Properties. The determinant-rank-inversion relationship. Determinants and systems of linear equations: Cramer’s rule.

2. VECTOR SPACES.

2.1 Vector spaces. Further properties of addition and scalar multiplication.

2.2 Linear dependence and independence. Properties. Systems of generators. Bases. Dimension. Coordinates of a vector in a given basis. Change of coordinates.

2.3 Vector subspaces. Vector subspaces of interest: intersection, linear envelope, row and column spaces of a matrix, solutions to a homogeneous system of linear equations. Equations and dimension of a vector subspace. Sum of vector subspaces. Dimension formula. Direct sum. Quotient vector space.

3. CLASSIFICATION OF ENDOMORPHISMS.

3.1 Linear mappings. Properties. Types. Kernel and image.

3.2 Matrix associated with a linear map. Relationship with the kernel and image; dimension formula. Changes of basis.

3.3 Operations on linear mappings. Properties.

3.4 Linear forms and dual space. Dual basis. Nullator of a vector subspace. Transposed linear map.

4. DIAGONALISATION OF ENDOMORPHISMS.

4.1 Eigenvectors and eigenvalues of an endomorphism. Characteristic and minimal polynomials. Algebraic and geometric multiplicities.

4.2 Diagonalizable matrices. Eigen subspaces. Diagonal form and basis of eigenvectors. Symmetric matrices.

4.3 Non-diagonalisable matrices. Generalised eigenspaces. Maximum subspaces. Canonical form and Jordan basis.

4.4 Complex eigenvalues and eigenvectors. Real canonical form and Jordan basis.

Training activities

AP1. Lectures.

AP2. Interactive classes.

AP3.1 Project work and problem-solving.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutoring.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be specified in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University will be the sole assessment criterion, with the weighting specified in the course syllabus.

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The assessment process will consist of evaluating the extent to which the student has achieved the learning outcomes associated with the subject.

ASSESSMENT SYSTEMS

The assessment methods for this module are:

 AS1 Practical activities.

 AS1 Final knowledge assessments.

 AS3 Portfolio.

These systems contribute to a greater or lesser extent to the assessment of the learning outcomes assigned to this subject.

ASSESSMENT CRITERIA

The assessment systems described above are set out in the following assessment criteria:

- There are two official examination sessions: the ordinary and the supplementary.

+++REGULAR EXAMINATION PERIOD+++

The final mark for this sitting is the weighted average of a set of assessment tasks detailed below:

-- a case study (SE1), accounting for 30 per cent of the final mark for the ordinary assessment period, to be carried out during the teaching term in small groups (designated by the course coordinator); this will require both the submission of exercises whilst the case study is in progress and the submission of a report and its public defence at the end of the teaching period.

-- a non-exemption exam (SE3), to be taken individually during the teaching term, which will account for 20 per cent of the final mark for the standard examination session.

-- a final examination (SE2) to be taken individually during the ordinary examination period in January (for further information, please consult the virtual campus), which assesses the entirety of the course content and will account for 50 per cent of the final mark for the standard examination session.

***** The weighted average of all these assessment components will be calculated only if the mark obtained in the final exam is 4.0 out of 10 or higher.

Furthermore, only the examinations will be subject to re-marking.

***** A student will have passed the module in the ordinary examination period if, and only if, they obtain a final mark (weighted average of all assessment tests) of 5.0 out of 10 or higher.

Otherwise, the student may pass the module in the supplementary assessment period.

********** If a student loses their right to continuous assessment, they must achieve a mark of 10.0 out of 10.0 in the regular examination session in order to pass the module.

+++SESSION EXTRAORDINARY+++

If a student fails to pass the module in the ordinary examination session, they may do so in the supplementary examination session.

This consists of a single examination which will take place during the supplementary examination period, June–July (for further information, please consult the online learning platform), and which assesses the entire syllabus covered in the module.

*** The module is considered to have been passed in the supplementary sitting if the final mark is 5.0 or higher.

GRADES

Article 5 of Royal Decree 1125/2003 of 5 September establishes the grading system applicable to modules within degree programmes falling within the scope of the European Higher Education Area. This system is as follows:

The award of the corresponding credits is conditional upon passing the associated examinations or assessment tests.

The level of learning achieved by students will be expressed as numerical marks on a scale of 0 to 10, to one decimal place, to which the corresponding qualitative grade may be added:

- 0–4.9: Fail (SS).

- 5.0–6.9: Pass (AP).

- 7.0–8.9: Good (NT).

- 9.0–10: Distinction (SB).

The distinction of ‘Honours’ shall be awarded to students who have obtained a mark of 9.0 or higher. The number of students awarded this distinction may not exceed five per cent of those enrolled on the course in the relevant academic year, unless the number of enrolled students is fewer than 20, in which case only one ‘First Class Honours’ may be awarded.

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Basic:

1. Juan De Burgos Román

Algebra and Geometry. Definitions, Theorems and Results

García Maroto Editores. 2010.

ISBN: 9788492976942

2. Luis Merino and Evangelina Santos

Linear Algebra using elementary methods

Paraninfo. 2010.

ISBN: 978-84-9732-4

Supplementary:

3. Gilbert Strang

Introduction to Linear Algebra

Wellesley Cambridge Press. 2008.

ISBN: 8175968117

4.- Juan De Burgos Román

Linear Algebra. 80 Useful Problems

García Maroto Editores. 2007.

ISBN: 9788493601805

Others:

5. Eugenio Hernández

Linear Algebra and Geometry

3rd ed. ADDISON WESLEY. 2012.

ISBN: 9788478291298

6. Jesús Rojo

Linear Algebra

McGraw-Hill. 2001.

ISBN: 8448130162

7. Jesús Rojo

Exercises and Problems in Linear Algebra

2nd ed. McGraw-Hill. 2005.

ISBN: 8448198581

8. Stanley I. Grossman and José Job Flores

Linear Algebra

McGraw-Hill. 2012.

ISBN: 978-607-15-07

Objectives

To provide students with the basic knowledge and tools of statistical analysis, covering both data representation and, above all, statistical inference, which will be essential for tackling related topics in subsequent courses.

Prerequisites

No prior requirements have been set.

Competencies

Not applicable.

Learning outcomes

RC2 – Identify the different phases of the mathematical modelling process, distinguishing between formulation, analysis, solution and interpretation of results. TYPE: Competencies.

RC3 – Apply software to solve mathematical and engineering problems, using the appropriate computational environment for each case. TYPE: Competencies.

RC7 – Develop work and projects related to mathematical engineering that have an impact on interdisciplinary teams or in multicultural contexts. TYPE: Competencies.

RS3 – Propose, analyse, validate and interpret the most appropriate mathematical models and tools in real-world situations, in accordance with the objectives being pursued. TYPE: Skills or competences.

RS5 – Use computer applications for statistical analysis, numerical and symbolic computation, graphical visualisation, optimisation or other purposes to solve problems. TYPE: Skills or competences.

Description of the content

1. Elements of data analysis

2. Descriptive statistics: samples and distribution of sample characteristics

3. Probability distributions

4. Random variables

5. Statistical inference models. Statistics and their basic properties

6. Frequentist approach: point estimation, interval estimation and hypothesis testing

7. Bayesian approach: posterior distribution, credible intervals and Bayesian tests

Training activities

AP1. Lectures.

AP2. Interactive classes.

AP3.1. Project work and problem-solving.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutoring.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be specified in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities requiring physical attendance will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University will be the sole assessment criterion, with the corresponding weighting as specified in the course syllabus.

----

ASSESSMENT SYSTEMS

The assessment methods for this module are:

- AS1: Practical activities

- AS1: Final knowledge assessments

- AS3: Portfolio

ASSESSMENT CRITERIA

The assessment methods described above are set out in the following assessment criteria:

- There are two official examination sessions: the ordinary and the supplementary.

+++REGULAR SESSION+++

The final mark for this examination period is the weighted average of a set of assessment tasks detailed below:

-- Assignment submissions (SE3), accounting for 20 per cent of the final mark for the ordinary examination period, to be completed individually or in small groups during class time.

-- Mid-term exam (SE1), to be taken individually during term time, accounting for 25 per cent of the final mark for the ordinary assessment period.

-- Skill School (SE1), accounting for 5% of the final mark for the standard assessment period.

-- Final exam (SE2), to be taken individually during the official ordinary examination period, covering the entire syllabus, and accounting for 50% of the final mark for the ordinary examination period, provided that the minimum mark is above 4 out of 10. If this mark is not achieved, the final mark for the module will be a fail in the ordinary examination period.

*** The module is considered passed in the ordinary examination period if the final mark is 5.0 or higher.

+++EXTRAORDINARY EXAMINATION PERIOD+++

If a student fails the module in the ordinary examination period, they may retake it in the extraordinary examination period, which accounts for 100 per cent of the mark and covers the entire syllabus.

The supplementary examination will take place during the July examination period (for further information, please consult the virtual campus). It consists of a single examination covering the entire syllabus of the module.

*** The module is considered passed in the extraordinary examination session if the final mark is 5.0 or above.

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Core:

1. A. García Pérez

Solved Problems in Basic Statistics.

National University of Distance Education. 1998.

ISBN: 978-84-362-37

2. J. Gorgas García, N. Cardiel López, and J. Zamorano Calvo.

Basic Statistics for Science Students.

UCM Publishing. 2011.

ISBN: 978-84-691-89

3. R. Mullor Ibañez

Basic Statistics I. An Introduction to Statistics.

Published by the University of Alicante. 2017.

ISBN: 978-84-9717-4

4. R. Mullor Ibañez

Basic Statistics II. Probability: random variables.

Published by the University of Alicante. 2023.

ISBN: 978-84-9717-8

Supplementary:

5. González Rosales, Alfredo

Applied Statistics:

Madrid: García-Maroto, D.L. 2009. 2009.

ISBN: 9788492976416

6. Murray Spiegel

PROBABILITY AND STATISTICS

4th ed. McGraw-Hill Interamericana de España S.L. 2014.

ISBN: 9786071511881

7. Neuhauser, Claudia

Mathematics for Science

2nd ed. Madrid: Pearson-Prentice Hall, 2004. 2004.

ISBN: 9788420542539

Objectives

This module has a twofold objective: on the one hand, students must learn to recognise that different mathematical tools share a common algebraic structure and therefore function in essentially the same way.

On the other hand, students must learn to prove theorems and properties of mathematical objects using abstract reasoning. In this module, although some numerical calculations will be carried out, the focus is entirely on the use of symbols and their properties.

Prerequisites

No prerequisites have been set.

Competencies

Not applicable.

Learning outcomes

RC9 – Formulate problems from a professional context in mathematical language in such a way as to facilitate their analysis and resolution. TYPE: Competences.

RK2 - Master the basic concepts of discrete mathematics, logic, algorithms, coding, operations research and artificial intelligence, and their application to solving engineering problems. TYPE: Knowledge or content.

RK4 – Be familiar with rigorous proofs of certain classical theorems in various areas of mathematics. TYPE: Knowledge or content.

RS1 – Use mathematical language to formulate propositions in various fields and construct proofs for the problems posed. TYPE: Skills or competences.

Description of the content

Groups:

1) Definition of a group and its properties

2) Examples: congruences, permutations, matrices, dihedral groups, the direct product

3) Subgroups

4) Lagrange’s theorem

5) Normal subgroups. Quotient group

6) Group homomorphisms

7) Isomorphism theorems

Rings

1) Definition of a ring and its properties

2) Subrings and ideals

3) Ring homomorphisms

4) The ring of polynomials in one variable, with coefficients in a field

Learning activities

AP1. Lectures.

AP2. Interactive classes.

AP3.1. Project work and problem-solving.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutorials.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be specified in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University shall be the sole assessment criterion, with the weighting assigned to it in accordance with the course syllabus.

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Continuous assessment consists of the following marks:

1) A set of exercises based on the syllabus will be set, or a written assignment will be set in which a topic from the course is explored in greater depth.

These will account for 10 per cent

2) A written test will be held halfway through the course

This mark will account for 40 per cent

3) The official course examination will be held during the regular examination period; it will be written and cover the course content.

This mark will account for 50 per cent. Under no circumstances will passing the tests exempt students from any part of this final exam.

Continuous assessment may be forfeited in two circumstances:

1) if class attendance is less than or equal to 70 per cent

2) if the mark in the official examination is less than or equal to 4

Students who, for any reason, forfeit their continuous assessment will sit the official examination, which will count for 100% of the final mark

For clarity, please note that even if you do not lose your continuous assessment due to attendance, scoring less than a 4 in the official exam will result in a fail for the module

In the resit period, no previous marks will be taken into account. A single examination covering the entire course content will be held.

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Core:

1. E. Bujalance, J. Etayo, J.M. Gamboa

Commutative Rings and Fields

UNED. 2002.

ISBN: 8436244486

2. E. Bujalance, J. Etayo, J.M. Gamboa

Elementary Group Theory

UNED. 2002.

ISBN: 8436244362

3. J. Dorronsoro, E. Hernández

Numbers, Groups and Rings

Addison Wesley, UAM. 1996.

ISBN: 0201653958

Objectives

- Understanding the basics of programming: Students will be able to understand the fundamentals of programming, including algorithmic logic and the use of control structures.

- Develop skills in Python: Students are expected to learn to programme effectively in Python, applying the principles of object-oriented programming and other key techniques.

- Solve problems using programming: Students should be able to design algorithms and write code to solve a variety of computational problems.

- Apply good coding practices: Students will acquire knowledge of writing clean, efficient and modular code, following industry standards and best practices.

- Foster logical and analytical thinking: Throughout the course, students will develop the ability to tackle complex problems in a structured and efficient manner.

- Develop projects applying programming concepts: Students will be able to integrate the knowledge they have acquired into programming projects that solve real or simulated problems, using software design and development techniques.

- Understand and evaluate the different types of storage systems and how they affect the performance of a computer system.

- Introduction to computer architecture and microprocessors.

Prerequisites

No prerequisites have been set.

Competencies

Not applicable.

Learning outcomes

RC2 – Identify the different phases of the mathematical modelling process, distinguishing between formulation, analysis, solution and interpretation of results. TYPE: Competencies.

RC3 – Apply software to solve mathematical and engineering problems, using the appropriate computing environment for each case. TYPE: Competencies.

RS5 - Use computer applications for statistical analysis, numerical and symbolic computation, graphical visualisation, optimisation or other purposes to solve problems. TYPE: Skills or competences.

Course description

This course is designed to introduce students to the fundamental concepts of programming and computational logic, with a specific focus on the Python programming language and SQL. Python and SQL are widely used in industry due to their simple syntax and readability, making them an excellent choice for beginners. Throughout the course, students will learn essential concepts such as control structures, data types, functions and file management. Principles of algorithmic design and good coding practices will also be covered.

Learning activities

AP1. Lectures.

AP2. Interactive classes.

AP3.2 Workshops and practical sessions.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutoring.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be specified in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University shall be the sole assessment criterion, with the corresponding weighting as specified in the course syllabus.

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Ordinary Examination Period:

1) Participation and attendance + completion of case studies (50 per cent):

a) Regular attendance at classes and scheduled activities.

b) Active participation in discussions and debates.

c) Correct and complete completion of case studies.

d) If a ULAB is held, it is assessed as a mid-term exam.

2) Final examination (50%): an examination held during the standard examination period, comprising 50% theoretical questions and 50% case studies.

The calculation of the final mark in the standard examination period will be conditional upon achieving a minimum mark of 4.0 out of 10 in the final exam. Once this requirement has been met, a weighted average of all activities and assessment tests will be calculated, even if any of them have been failed.

If the mark obtained in the final exam is less than 4.0 out of 10, the final mark will be the mark obtained in that exam.

Extraordinary Examination Period (100% Exam):

- In the supplementary assessment, the mark will be based solely on an exam covering the entire course content.

- The exam will account for 100 per cent of the final mark.

Timetable

Click on this link to view the detailed timetable in Excel

Reading list

Core:

1. Al Sweigart

Automate the Boring Stuff with Python, 3rd Edition: Practical Programming for Total Beginners

No Starch Press. 2025.

ISBN: 1718503407

2. Charles Russell Severance

Python for Everyone: Exploring Data with Python 3

Self-published. 2020.

ISBN: 9798633985566

3. Eric Matthes

Python Crash Course, 3rd Edition: A Hands-On, Project-Based Introduction to Programming

No Starch Press. 2023.

ISBN: 1718502702

4. F. Cuesta

Introduction to Programming with Python

Marcombo. 2019.

ISBN: 978-842673616

5. John M. Zelle

Python Programming: An Introduction to Computer Science

Franklin, Beedle & Associates. 2024.

ISBN: 1590282973

6. John V. Guttag

Introduction to Computation and Programming Using Python, third edition: With Application to Computational Modelling and Understanding Data

The MIT Press. 2021.

ISBN: 0262542366

7. Mark Lutz

Learning Python

O’Reilly Media. 2013.

ISBN: 1449355730

Objectives

This module, which together with Mathematical Foundations of Engineering II forms part of the Mathematical Analysis I course within the degree programme’s Basic Training module, aims to provide the mathematical foundations necessary to understand, interpret and apply various concepts and theories, which are fundamental aspects for a graduate in mathematics.

Prerequisites

No prerequisites have been set.

Competencies

Not applicable.

Learning outcomes

RK4 – To be familiar with rigorous proofs of some classical theorems in different areas of mathematics. TYPE: Knowledge or content.

RS1 – To use mathematical language to formulate propositions in different fields and construct proofs for the problems posed. TYPE: Skills or competences.

RS3 - To propose, analyse, validate and interpret the most appropriate mathematical models and tools in real-world situations, in accordance with the objectives being pursued. TYPE: Skills or competences.

Description of the content

The content to be covered in this module is as follows:

Topic 1: Real numbers

Topic 2: Complex numbers

Topic 3: Numerical sequences

Topic 4: Numerical series

Topic 5: Limits and continuity

Topic 6: Derivatives

Topic 7: Applications of the derivative

Topic 8: Graphing functions

Training activities

AP1. Lectures.

AP2. Interactive classes.

AP3.1 Project work and problem-solving.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutoring.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be specified in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard assessment period. In this case, the examination to be held during the official period set by the University shall be the sole assessment criterion, with the weighting specified in the course syllabus.

----

The assessment process will consist of verifying and evaluating the student’s acquisition of the required competences.

There are two official examination sessions: the ordinary and the supplementary.

+++REGULAR EXAMINATION PERIOD+++

The final mark for this sitting is the weighted average of a set of assessment tasks detailed below:

- Assignment submissions (SE1), accounting for 20% of the final mark, to be completed individually or in small groups during the term.

- Submission of a project (SE2), accounting for 20 per cent of the final mark, to be carried out individually or in small groups at the end of the term.

- Two mid-term examinations (SE3), to be taken individually during the term. Each will account for 30 per cent of the final mark.

*** The module is considered passed in the ordinary assessment period through continuous assessment if the final mark is 5.0 or above.

*** Otherwise, the student must sit the final exam in the ordinary examination period. Their mark in the ordinary examination period will correspond to the mark obtained in the final exam.

+++EXTRAORDINARY EXAMINATION PERIOD+++

If a student has not passed the module during the ordinary examination period, they may sit the examination during the extraordinary examination period.

The supplementary examination period will take place during the July examination period (for further information, please consult the Academic Calendar). It consists of a single examination covering the entire syllabus of the course.

*** The module is considered passed in the supplementary sitting if the final mark is 5.0 or above.

GRADES

Article 5 of Royal Decree 1125/2003 of 5 September establishes the grading system applicable to modules in degree programmes within the European Higher Education Area. This system is as follows:

The award of the corresponding credits is conditional upon passing the associated examinations or assessment tests.

The level of learning achieved by students will be expressed as numerical marks on a scale of 0 to 10, to one decimal place, to which the corresponding qualitative mark may be added:

- 0–4.9: Fail (SS).

- 5.0–6.9: Pass (AP).

- 7.0–8.9: Good (NT).

- 9.0–10: Distinction (SB).

The distinction of ‘Honours’ shall be awarded to students who have obtained a mark of 9.0 or higher. The number of students awarded this distinction may not exceed five per cent of those enrolled on the course in the relevant academic year, unless the number of enrolled students is fewer than 20, in which case only one ‘First Class Honours’ may be awarded.

Timetable

Click on this link to view the detailed timetable in Excel

Reading list

Core reading:

1. Michael Spivak

Infinitesimal Calculus

2nd ed. Reverté. 1988.

ISBN: 8429151362

Supplementary:

2.- Roland E. Larson, Robert P. Hostetler, Bruce H. Edwards

Calculus and Analytic Geometry (Volume 1)

McGraw-Hill. 2010.

ISBN: 8448122291

Objectives

• To build a foundation of knowledge and skills based on the optimised use of IT resources and tools designed for academic, educational and professional purposes.

• To foster information and knowledge management skills.

• To provide a useful foundation for management and learning based on independent research using user-centred IT tools.

• The ability to apply general knowledge of office automation and new information technologies in current practice and in future professional contexts.

Prerequisites

No prerequisites have been established

Learning outcomes

RK4 Basic knowledge of the use and programming of computers, operating systems, databases and software applications in engineering.

RK5 Knowledge of the structure, organisation, operation and interconnection of computer systems, the fundamentals of their programming, and their application to solving engineering problems.

RC5 Knowledge and application of the tools required for the storage, processing and access to information systems, including web-based ones.

Description of the content

General content covered by the module:

Concepts of information and communications technology. Basic structure and operation of computers. Computer applications for engineering. Advanced use of spreadsheets. Introduction to programming. The Web and web services. Web application development. Client-side (front-end) development. Server-side (back-end) development

Course content:

Computers and their use; File management; Word processing; Spreadsheets; Use of databases; Presentations; The Internet; Email; Instant messaging; Other Internet services; Creating content for the Internet; Blogs.

Learning activities

V1. – Lecture sessions: viewing and presentation of content

V2.- Interactive synchronous classes

V3.- Workshop and/or laboratory activities in virtual environments

V4.- Guided exercises on the platform

V5. – Independent study

V6. Completing knowledge tests

Assessment system and criteria

For competences involving practical problem-solving skills, assessment will be based on the submission and presentation of case studies, as well as on students’ performance in the classroom during practical sessions.

For competencies relating to the use of tools, students will undertake practical case studies in the laboratories or carry out group-based fieldwork.

Submission of practical assignments and reports on their progress.

For competences involving knowledge of subject content, a series of written examinations will be set to cover the full range of learning activities carried out in the classroom.

Ordinary and supplementary examination sessions

The assessment of the module consists of two parts (a mark of at least 4 in the final examination is required for the following percentages to apply):

- Continuous assessment mark on campus (exercises, tests, etc.): 40%

* Exercises and tests for the units: 40%

* Final course assignment: 60%

- Final exam: 60%

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Core:

1. Peña Pérez, Rosario

Office 2016:

Ediciones Altaria, 2015.

ISBN: 9788494404979

2. VALENTIN, HANDZ

OFFICE 2016 PRACTICAL COURSE

Ra-Ma. 2016.

ISBN: 9788499646343

Supplementary:

3.- CLAUDIA VALDES-MIRANDA

EXCEL 2016 (ESSENTIAL HANDBOOK)

Anaya Multimedia. 2016.

ISBN: 9788441538023

4.- Lambert, Joan.

MOS 2016 Study Guide for Microsoft Excel:

Microsoft Press. 2016.

ISBN: 9780735699434

5. VALENTIN, HANDZ

EXCEL 2016 STEP BY STEP, 2nd UPDATED EDITION

Ra-Ma. 2016.

ISBN: 9788499646619

Objectives

To equip students with the skills to:

1. Develop oral and written communication skills in Spanish and improve their interpersonal communication.

2. Develop linguistic and textual skills (comprehension and production) and pragmatic skills in Spanish.

3. Improve their lexical competence and use appropriate terminology.

4. Use expressive, textual, contextual and documentary resources effectively.

5. Develop persuasive rhetoric and professional communication skills: reports, minutes, notices, etc.

6. Adopt responsible attitudes towards written culture and the written language.

7. Appreciate the role and value of linguistic communication in business and society.

8. Master the discourse of negotiation: verbal courtesy, argumentation.

9. Protocol

Prerequisites

No prerequisites have been set.

Learning outcomes

RC16 Ability to enter and integrate into a real professional environment within the field of the degree programme, adapting to its dynamics and working procedures, as well as its internal organisation, with the aim of carrying out tasks and/or performing specific roles that may or may not require participation in work teams

RODS Develops effective communication, teamwork, analytical thinking, creativity and ethical leadership from a cross-disciplinary perspective, clearly inspired by democratic principles and values, as well as the Sustainable Development Goals, in order to operate with integrity within the professional sphere.

Description of the content

General content covered by the module:

Human communication, Business communication, General writing. Processes and methods, Professional texts in ICT engineering, Grammar correction, Vocabulary, Summarising, Oral communication.

Course content:

Introduction to human communication.

Communication in the workplace.

General writing: processes and methods.

Professional texts.

Oral communication.

The desire for a positive image.

Acts that threaten one’s image (AAIP).

Verbal courtesy.

Qualitative studies of the main strategies of verbal politeness in various types of contexts: conversations, interviews, speeches, etc.

Conflict management.

Negotiation discourse.

A qualitative study of the main agreements and conventions.

Etiquette and social interaction.

Business etiquette.

Official state protocol.

Training activities

V1. – Lectures: Viewing and presentation of content

V2.- Interactive synchronous classes

V4.- Guided exercises on the platform

V5. – Self-study

V6. – Completing knowledge tests

Assessment system and criteria

Regular and supplementary assessment periods

Assessment of the module consists of two parts:

* Continuous assessment mark on campus (exercises, tests, etc.): 40%

* Final exam: 60%

Timetable

Click on this link to view the detailed timetable in Excel

Reading list

Core:

1. ALCARAZ VARÓ, E.; J. MATEO MARTÍNEZ

Professional and Academic Languages.

Ariel. 2007.

ISBN: 9788434481220

2. Aranzadi Tellería, Dionisio

The Art of Being a Business Leader Today

Deusto. 2000.

ISBN: 8474856728

3. Borrell i Carrió, F.

How to work as part of a team: and build good relationships with managers and colleagues

Gestión 2000. 2004.

ISBN: 8480889705

4. Borrell, Francesc

Communicate Well, Lead Better

Barcelona: Gestión 2000, 2002. 2002.

ISBN: 8480887249

5. Cardona Soriano, Pablo and García Lombardía, Pilar

How to Develop Leadership Skills

EUNSA. 2007.

ISBN: 8431323094

6. Cordón, José Antonio, et al.

A Handbook on Document Search and Bibliographic Practice

Pirámide. 1999.

ISBN: 8436812026

7. David V. Feliciano

Rules and Correct Usage of Modern Spanish

Tirant Humanidades. 2011.

ISBN: 9788493931605

8. Felipe Portocarrero

Profitable Writing

SM. 2001.

ISBN: 9788434876026

9. Fernando Martínez

Written Communication

Centre for Financial Studies. 2012.

ISBN: 9788445421468

10. Flora Davis

Non-verbal Communication

Alianza Editorial. 2010.

ISBN: 9788420664248

11. Gómez Torrego, Leonardo

Speaking and Writing Correctly

Madrid, Arco Libros. 2006.

ISBN: 8476356536

12. Jesús Mesanza

How to Write Well: Spelling and Related Topics

Editorial Esceual Española. 1995.

ISBN: 9788433106582

13. Jesús Sánchez Lobato

How to Write

Madrid: Aguilar, 2006. 2006.

ISBN: 8403097239

14. Josefa Gómez de Enterría

Business Correspondence in Spanish

SGEL. 2002.

ISBN: 9788471434265

15. Josefa Gómez de Enterría y Sánchez

Communication in the workplace

Arco Libros. 2002.

ISBN: 978847635508

16. Montolío, Estrella

A Practical Guide to Academic Writing

Barcelona: Ariel, 2000. 2000.

ISBN: 8434428695

17. Royal Spanish Academy

Dictionary of the Spanish Language

[Madrid]: Royal Spanish Academy, 2001. 2001.

ISBN: 8423968146

18. Royal Spanish Academy

Spelling of the Spanish Language

Espasa-Calpe. 2010.

ISBN: 9788467034264

19. Torres, Isabel

Sources of Information: Theoretical and Practical Studies

Madrid: Síntesis, 1999. 1999.

ISBN: 8477384606

20. Trujillo, José Ramón

Negotiation, Communication and Verbal Courtesy: Theory and Techniques

Madrid: Ediciones 2010, 2004. 2004.

ISBN: 8495058537

21. Various authors

The Art of Speaking

Aguilar. 2008.

ISBN: 9788403098060

Supplementary:

22. Beatriz Lucía

Communication Skills. Training Programme

Autonomous University of Madrid. 2008.

ISBN: 9788483441190

23. Gómez de Enterría y Sánchez, Josefa

Oral Communication in the Workplace

Madrid: Arco Libros, [2008]. 2008.

ISBN: 9788476357095

24. Jesús Mesanza

Speaking and Writing Correctly: Errors, Incorrect Usage and Uncertainties in Spoken and Written Spanish

WOLTERS KLUWER EDUCACION. 2009.

ISBN: 9788471979100

25. Miles Paterson

More than just words: the power of verbal communication

UOC. 2011.

ISBN: 9788497889179

26. Various authors

Non-verbal communication and leadership

Netbiblo. 2010.

ISBN: 9788497454971

Others:

27. Gaspar González

Techniques for Telephone Conversations

Edelsa. 2008.

ISBN: 9788477115595

28. Manuel Campo Vidal

Why Don’t Professionals Communicate Better?

RBA Books. 2011.

ISBN: 9788490061244

29. Manuel Campo Vidal

Why don’t professionals communicate better?

Plaza. 2008.

ISBN: 9788401379857

30. Manuel Cifo

Oral and Written Communication in the Spanish Language

Diego Marin. 2012.

ISBN: 9788415429326

31. Marcus Tullius Cicero

The Perfect Orator

Autonomous University of Mexico. 1991.

ISBN: 9789683669841

32. Margarita Recasens

Oral Comprehension and Expression

CEAC. 2003.

ISBN: 9788432986598

Objectives

This module, together with Algebra I, forms the subject Algebra. This module, which forms part of the degree programme’s Basic Training module, aims not only to ensure that students are familiar with the main fundamental theorems of linear algebra, but also to enable them to understand matrix calculus from a conceptual perspective and to apply it to solving problems typical of mathematical engineering; it is, therefore, the foundation for other subjects within the degree programme, such as Numerical Calculus, Operational Research, Stochastic Calculus and Artificial Intelligence.

Prerequisites

Although no prerequisites have been set, it is advisable to have previously taken the course Algebra I or another course with similar learning outcomes.

Competencies

Not applicable.

Learning outcomes

RK4 – To be familiar with rigorous proofs of some classical theorems in different areas of Mathematics. TYPE: Knowledge or content.

RS1 - Use mathematical language to formulate propositions in various fields and construct proofs for the problems posed. TYPE: Skills or abilities.

Description of the content

1. QUADRATIC FORMS: CONCEPT AND CLASSIFICATION.

1.1 Bilinear forms. Properties. Associated matrix. Change of basis. Symmetric and antisymmetric bilinear forms. Degeneration and positive definition.

1.2 Quadratic forms. Polar form of a quadratic form. Associated matrix. Conjugation. Signature. Classification. Diagonalisation by congruence. Sylvester’s criterion.

2. EUCLIDEAN VECTOR SPACES.

2.1 Scalar product. Properties. Associated matrix (Gram matrix). Change of basis.

2.2 Angle between two vectors. Orthogonality. Distance between two vectors. Orthogonal projection. Orthogonal complement of a vector subspace.

2.3 Orthogonal and orthonormal bases. Gram–Schmidt algorithm. Change of coordinates between orthonormal bases: orthogonal matrices.

2.4 Vector product.

3. AFFINE SPACES AND EUCLIDEAN AFFINE SPACES.

3.1 Affine spaces. Reference systems and coordinates. Change of reference system.

3.2 Affine varieties. Affine varieties of interest: affine variety generated by a set of points, intersection. Equations and dimension of an affine variety. Sum of affine varieties.

3.3 Relative positions between affine varieties. Orthogonal projection of a point onto an affine variety. Distance from a point to an affine variety. Distance between affine varieties. Metric problems in two- and three-dimensional Euclidean affine spaces.

4. CONICS, QUADRICS AND MOTIONS.

4.1 Conic sections. General and reduced equations of a conic. Associated matrix: classification. Calculation of geometric elements. Metric invariants and the reduced equation of conics.

4.2 Quadric surfaces. General and reduced equations of a quadric. Associated matrix: classification. Metric invariants and classification of quadric surfaces by invariants.

4.3 Affine transformations and movements. Examples. Matrix representation. Rigid movements. Fixed points and invariant manifolds. Classification of rigid movements in two- and three-dimensional Euclidean affine spaces.

Training activities

AP1. Lectures.

AP2. Interactive classes.

AP3.1 Project work and problem-solving.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutoring.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be specified in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University shall be the sole assessment criterion, carrying the weighting specified in the course syllabus.

----

The assessment process will consist of evaluating the extent to which the student has achieved the learning outcomes associated with the subject.

ASSESSMENT SYSTEMS

The assessment methods for this module are:

 AS1 Practical activities.

 AS1 Final knowledge assessments.

 AS3 Portfolio.

These systems contribute to a greater or lesser extent to the assessment of the learning outcomes assigned to this subject.

ASSESSMENT CRITERIA

The assessment systems described above are set out in the following assessment criteria:

- There are two official examination sessions: the ordinary and the supplementary.

+++REGULAR EXAMINATION PERIOD+++

The final mark for this sitting is the weighted average of a set of assessment tasks detailed below:

-- a case study (SE1), accounting for 30 per cent of the final mark for the ordinary assessment period, to be carried out during the term in small groups (designated by the course coordinator) and which will require both the submission of exercises whilst the case study is being carried out and the submission of a report and its public defence at the end of the teaching term.

-- a non-exemption exam (SE3), to be taken individually during the teaching term, accounting for 20 per cent of the final mark for the ordinary examination period.

-- a final examination (SE2) to be taken individually during the ordinary examination period in January (for further information, please consult the virtual campus), which assesses the entirety of the course content and will account for 50 per cent of the final mark for the standard examination session.

***** The weighted average of all these assessment components will be calculated solely and exclusively if the mark obtained in the final exam is 4.0 or above out of 10.

Furthermore, only the examinations will be subject to re-marking.

***** A student will have passed the module in the ordinary examination period if, and only if, they obtain a final mark (weighted average of all assessment tests) of 5.0 out of 10 or higher.

Otherwise, the student may pass the module in the supplementary examination session.

********** If a student loses their right to continuous assessment, they must achieve a mark of 10.0 out of 10.0 in the ordinary examination session in order to pass the module.

+++SESSION EXTRA+++

If a student fails to pass the module in the ordinary examination session, they may do so in the supplementary examination session.

During this session, there will be a single assessment, consisting of an exam to be held during the supplementary exam period in June–July (for further information, please consult the virtual campus), which will cover the entire syllabus of the module.

***** The module will be deemed to have been passed in the supplementary assessment period if the mark obtained in the exam is 5.0 out of 10.0 or higher.

GRADES

Article 5 of Royal Decree 1125/2003, of 5 September, establishes the grading system applicable to modules within degree programmes falling within the scope of the European Higher Education Area. This system is as follows:

The award of the corresponding credits will be contingent upon passing the associated examinations or assessment tests.

The level of learning achieved by students shall be expressed as numerical marks on a scale of 0 to 10, to one decimal place, to which the corresponding qualitative mark may be added:

- 0–4.9: Fail (SS).

- 5.0–6.9: Pass (AP).

- 7.0–8.9: Good (NT).

- 9.0–10: Distinction (SB).

The distinction of ‘Honours’ shall be awarded to students who have achieved a mark of 9.0 or higher. The number of students awarded this distinction may not exceed five per cent of those enrolled on the course in the relevant academic year, unless the number of enrolled students is fewer than 20, in which case only one ‘First Class Honours’ may be awarded.

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Essential:

1. Juan De Burgos Román

Algebra and Geometry. Definitions, Theorems and Results

García Maroto Editores. 2010.

ISBN: 9788492976942

2. Luis Merino and Evangelina Santos

Linear Algebra using Elementary Methods

Paraninfo. 2010.

ISBN: 978-84-9732-4

Supplementary:

3. Gilbert Strang

Introduction to Linear Algebra

Wellesley Cambridge Press. 2008.

ISBN: 8175968117

4.- Juan De Burgos Román

Linear Algebra. 80 Useful Problems

García Maroto Editores. 2007.

ISBN: 9788493601805

Others:

5.- Eugenio Hernández

Linear Algebra and Geometry

3rd ed. ADDISON WESLEY. 2012.

ISBN: 9788478291298

6. Jesús Rojo

Linear Algebra

McGraw-Hill. 2001.

ISBN: 8448130162

7. Jesús Rojo

Exercises and Problems in Linear Algebra

2nd ed. McGraw-Hill. 2005.

ISBN: 8448198581

8. Stanley I. Grossman and José Job Flores

Linear Algebra

McGraw-Hill. 2012.

ISBN: 978-607-15-07

Objectives

The objectives of this module are:

1) To understand the function and importance of data structures:

- To recognise the importance of selecting and designing appropriate data structures to optimise programme performance.

- To distinguish between different categories of structures (linear, non-linear, dynamic, etc.) and their fields of application.

2) To design, implement and manipulate fundamental data structures:

- To understand and work with basic structures such as arrays, lists, stacks, queues, trees and graphs.

- Implement essential operations (insertion, deletion, traversal, search) whilst ensuring robustness and clarity in the code.

3) Analyse the computational complexity of algorithms:

- Calculate and compare the time and space complexity of different operations and algorithms.

- Use Big O notation to estimate the performance of solutions and propose improvements.

4) Apply algorithmic problem-solving methodologies:

- Employ techniques such as recursion, divide and conquer or backtracking when solving problems.

- Select the most appropriate algorithmic strategy based on the type of problem and the available resources.

5) Develop programming skills and best practices:

- Use a clear, modular and well-documented programming style.

- Carry out testing and validation to ensure the correctness and reliability of implementations.

6) Promote critical thinking and decision-making skills:

- Evaluate different approaches to the design of data structures and algorithms to determine the most efficient option.

- Justify the choice of a structure or algorithm based on functional requirements, time and space constraints, and possible use cases.

7) Foster the ability to learn independently and work as part of a team:

- Participate in collaborative project work, exchanging ideas and reviewing code constructively.

- Continue to expand knowledge of data structures and algorithms by consulting literature and external resources.

Prerequisites

It is recommended that students have (previously) taken the module ‘Fundamentals of Programming and Computing’ or another module covering similar skills and learning outcomes.

Competencies

Not applicable.

Learning Outcomes

RC3 – Apply programmes to solve mathematical and engineering problems, using the appropriate computational environment for each case. TYPE: Competencies.

RC6 – Work independently and in an organised manner to develop solutions to the various problems that may arise in the field of mathematical engineering, subject to strict time or budgetary constraints. TYPE: Competencies.

RK2 - Master the basic concepts of discrete mathematics, logic, algorithms, coding, operations research and artificial intelligence, and their application to solving engineering problems. TYPE: Knowledge or content.

Description of the content

1. Introduction to algorithm efficiency

- Basic concepts of computational complexity: Notions of Big O, Big Theta and Big Omega. Evaluation of efficiency in terms of time (operations) and space (memory).

- Case analysis: worst-case, average-case and best-case scenarios. Practical examples of simple algorithms (linear search, binary search) in Python to illustrate the concepts.

- Introduction to optimisation: Identifying bottlenecks in Python code and initial optimisation techniques.

2. Abstract Data Type (ADT)

- Definition of ADTs: Understanding data abstraction through defined operations (creation, insertion, deletion, search, etc.), regardless of the underlying implementation.

- Examples of ADTs in Python: Using classes, methods and encapsulation to create ADTs that represent common entities (e.g. complex numbers, fractions, polynomials).

3. Linear and associative ADTs

- Linear TADs: Lists, stacks and queues. Discussion of their fundamental operations, complexity and application in various engineering contexts.

- Implementation in Python: Lists, queues and stacks using `collections.deque`.

- Associative data structures: Hash tables (dictionaries in Python) and sets. Analysis of collisions, hash functions, and average and worst-case complexity.

- Practical examples: Implementation of custom structures (specific stacks and queues), performance evaluation against predefined Python structures.

4. Tree Data Structures

- Basic concepts: General trees, binary trees, search trees, balanced trees (AVL, Red-Black), etc.

- Fundamental operations: Insertion, deletion, traversal (in-order, pre-order, post-order), search and rebalancing.

- Implementation in Python: Representation of nodes and pointers; use of classes to encapsulate logic. Analysis of common use cases (file systems, hierarchical organisation of data).

5. Graph Data Structures

- Graph representation: Adjacency matrix and adjacency lists. Advantages and disadvantages of each approach.

- Traversals and basic algorithms: Breadth-first search (BFS) and depth-first search (DFS). Applications in networks, maps and route-finding problems.

- Introduction to more advanced algorithms: Shortest paths (Dijkstra, Floyd-Warshall), minimum spanning trees (Kruskal, Prim), depending on the scope of the course.

- Implementation in Python: Use of dictionaries and lists to represent graph structures, together with functions to perform traversals and calculations.

6. Data structures on disk

- Persistent storage: The concept of secondary storage structures (files, databases, etc.) and their impact on efficiency.

- Introduction to on-disk indexes and trees: B-trees, B+-trees. Differences from main memory structures and the rationale behind their design.

- Practical approach in Python: Use of libraries and storage formats (e.g. sqlite3, pickle) to illustrate how to handle data beyond main memory.

7. Applying data structures to problem-solving

- Integration of content: Development of small projects or case studies requiring the selection and implementation of various data structures, analysing their performance with inputs of different sizes.

- Optimisation and refactoring: Code improvement practices, profiling algorithms in Python (for example, using the cProfile library), and justifying the changes made.

- Collaborative work: Use of version control (Git) and simple agile methodologies (Scrum, Kanban) for carrying out projects.

Training activities

AP1. Lectures.

AP2. Interactive classes.

AP3.1. Project development and problem-solving.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutoring.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be specified in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University shall be the sole assessment criterion, with the weighting corresponding to it as set out in the course syllabus.

----

REGULAR EXAMINATION PERIOD

In the ordinary assessment period, the objective assessment of the student’s learning will be carried out through continuous assessment.

To be eligible for continuous assessment, students must, as indicated above, attend at least 70 per cent of face-to-face sessions (both theoretical and practical).

The weighting of the continuous assessment activities is distributed as follows:

a) Practical 1 (7.5%).

Assessment criteria:

- Correct implementation of the basic data structures (lists, stacks, queues, trees) covered in class.

- Organisation and clarity of the code, including appropriate use of functions and good programming practices.

- Code documentation (docstrings and comments) explaining the logic behind basic operations (insertion, deletion, search) and the chosen data structures.

- Efficiency of operations (basic analysis of time and/or space complexity).

b) Practical 2 (7.5%).

Assessment criteria:

- Use of advanced techniques or more complex structures (balanced trees, hash tables, graphs, etc.), justifying the choice according to the requirements of the proposed problem.

- Correct organisation and modularity of the code (separation of concerns and use of appropriate design patterns).

- Validation of the solution (functionality tests, unit tests) and verification of the correct implementation of the structures.

- Cleanliness, maintainability and readability of the code.

c) Final Assignment (15%).

Assessment criteria:

- Integration of different data structures and algorithms studied throughout the course (e.g. graph search and traversal, sorting algorithms, hierarchical structures).

- Design of an efficient and scalable solution that addresses a more complex problem, applying optimisation strategies and the appropriate selection of structures and algorithms.

- Quality of project documentation (detailed README, user guides, references to theoretical concepts).

- Presentation of results (performance tests, comparison of complexities between different approaches and evaluation of scalability with increasing input sizes).

d) Non-exemption mid-term exam (30%).

Assessment criteria:

- Understanding of the fundamentals of linear and non-linear data structures (lists, stacks, queues, trees, graphs).

- Ability to design and propose basic algorithmic solutions, justifying the choice of the appropriate data structure.

- Theoretical knowledge of the complexity of elementary operations (insertion, deletion, search) and their implications for performance.

- Problem-solving and short exercises focusing on the correct application of structures and algorithms for simple use cases.

e) Final examination covering the entire module (40%).

This is the standard examination session, which assesses all the content taught during the term.

Assessment criteria:

- Comprehensive mastery of the data structures and algorithms covered in the module: theory, application, optimisation and appropriate selection according to context.

- Ability to analyse computational complexity (time and space) and identify potential bottlenecks in the implementation of structures.

- Application of design patterns or best practice in solving more complex problems.

- Both conceptual and practical questions, with an emphasis on identifying and comparing different algorithmic approaches and their optimisation.

IMPORTANT: an average will only be calculated from the practicals, the mid-term exam and the final exam if the mark for each and every one of these assessment activities is 4.0 out of 10.0 or higher.

In the event of failure to achieve continuous assessment due to unexcused attendance of less than 70 per cent, the final mark for the module in the ordinary examination period will be 40 per cent of the mark obtained in the final exam.

SUPPLEMENTARY EXAMINATION PERIOD

In the supplementary examination period, the objective assessment of the student’s learning will be based on a single examination covering the entire course, which will therefore account for 100 per cent of the final mark.

Assessment criteria:

It will consist of theoretical and practical questions covering the entire syllabus, including:

- Fundamental concepts relating to basic and advanced data structures (lists, queues, stacks, trees, graphs, hash tables).

- Algorithm design and analysis techniques (recursion, divide and conquer, greedy algorithms, etc.).

- Use cases for these structures in common problems (sorting, searching, pathfinding in graphs, etc.).

- Complexity analysis and justification of design decisions.

- Assessment will focus on conceptual rigour, the ability to solve complex problems and the clarity of the justification for proposed solutions.

- A minimum mark of 5 out of 10 is required to pass the module.

Timetable

Click on this link to view the detailed timetable in Excel

Reading list

Core:

1. Michael T. Goodrich, Roberto Tamassia, Michael H. Goldwasser

Data Structures and Algorithms in Python

Wiley. 2013.

ISBN: 978-1-118-293

2. Walter Bel

Algorithms and Data Structures in Python

UADER Publishing. 2020.

ISBN: 978-950-9581-

Supplementary:

3. Mariona Nadal

Data Structures and Algorithms

Anaya Multimedia. 2022.

ISBN: 978-84-415-45

Others:

4. Kent D. Lee and Steve Hubbard

Data Structures and Algorithms with Python

Springer. 2015.

ISBN: 978-331913071

Objectives

The design of electrical circuits, and in particular logic circuits, which enable the processing, storage and transmission of information, is key to both classical and quantum computing. Such design is based not only on the practical applications of electromagnetism, but also, and above all, on the use of semiconductor devices – the technological implementation of solid-state physics, a branch of condensed matter physics which, in turn, on other branches of physics such as quantum mechanics.

Through this module, which forms part of the Physics subject within the degree programme’s Basic Training module, a detailed analysis is carried out of the physical fundamentals of computational electronics, as well as basic logic circuits, with the aim of providing students with a better understanding of computing.

Prerequisites

No prerequisites have been set for this module.

Learning Outcomes

Not applicable.

Learning outcomes

RK1 – To understand the basic concepts of electromagnetism and circuit theory for solving engineering problems. TYPE: Knowledge or content.

Description of the content

o Topic 1: Introduction.

o Topic 2: Electrostatic field.

o Topic 3: Magnetostatic field.

o Topic 4: Electromagnetic induction; basic direct current and alternating current circuits.

o Topic 5: Semiconductor devices.

o Topic 6: Logic circuits.

o Topic 7: Fundamentals of integrated circuits.

o Topic 8: Sequential and combinational circuits.

Teaching activities

AP1. Lectures.

AP2. Interactive classes.

AP3.2 Workshops and laboratory sessions.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutoring.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be set out in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University shall be the sole assessment criterion, carrying the weighting specified in the course syllabus.

----

The assessment process will consist of evaluating the extent to which the student has acquired the competences associated with the module.

REGULAR EXAMINATION PERIOD

In the regular examination period, the objective assessment of the student will consist of a continuous assessment process and a final examination.

Continuous assessment will consist of the following components:

• Portfolio: an individual assignment, accounting for 10 per cent of the final mark. It will involve solving various problems throughout the academic term.

• Mid-term exam: this will account for 30% of the final mark. Taking this exam will not reduce or eliminate any content from the final exam. The date will be announced in good time.

As for the final exam, this is the standard exam, and it will assess all the course content. It will account for 60 per cent of the final mark.

A weighted average will only be calculated if the marks for continuous assessment and the final exam are both 4.0 or higher. The mark for continuous assessment will be calculated by weighting the portfolio and the mid-term exam. Furthermore, only the exams may be subject to re-marking."

In order for students to benefit from continuous assessment, a minimum of 70 per cent attendance at scheduled class sessions (SESSION, TRAB) will be required. If attendance falls below 70 per cent without a valid reason, the module must be passed by sitting a final examination in an official examination session (ordinary or supplementary). In the ordinary examination session, the final mark will be 60 per cent of the mark obtained in that examination.

The module is considered passed in the ordinary examination period when the final mark is 5.0 or above.

REGULAR EXAMINATION PERIOD

In the supplementary sitting, the student’s assessment will consist of a single examination covering the entire course content, which will account for 100 % of the final mark.

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Core:

1. Antonio M. Criado and Fabián Frutos

Introduction to the Physical Foundations of Computer Science

Paraninfo. 1999.

ISBN: 8428326061

2. Wolfgang Bauer and Gary D. Westfall

Physics for Engineering and Science (Volume 2)

McGraw-Hill. 2011.

ISBN: 978-607-15-05

Supplementary:

3.- Hugh D. Young and Roger A. Freedman (Francis Sears and Mark Zemansky)

University Physics (Volume 2)

12th ed. Addison-Wesley. 2009.

ISBN: 9780321501219

Objectives

This module, which together with Mathematical Foundations of Engineering I forms the course Mathematical Analysis I, part of the degree programme’s Core Module, aims to provide the fundamentals of Riemann integration in one dimension, as well as to explore in greater depth the study of power series and the concept of polynomial approximation of functions.

Prerequisites

Although no prerequisites have been set, it is advisable to have previously taken the course ‘Mathematical Foundations of Engineering I’ or another course covering similar skills and learning outcomes.

Competencies

Not applicable.

Learning Outcomes

RK4 – To be familiar with rigorous proofs of some classical theorems in different areas of mathematics. TYPE: Knowledge or content.

RS1 – To use mathematical language to formulate propositions in different fields and construct proofs for the problems posed. TYPE: Skills or competences.

RS3 - To propose, analyse, validate and interpret the most appropriate mathematical models and tools in real-world situations, in accordance with the objectives being pursued. TYPE: Skills or competences.

Description of the content

Topic 0. Elementary functions

Topic 1. Riemann integral.

Topic 2. Integration techniques.

Topic 2. Integration techniques.

Topic 4. Polynomial approximation of functions: Taylor’s theorem.

Topic 5. Series and sequences.

Learning activities

AP1. Lectures.

AP2. Interactive classes.

AP3.1 Project work and problem-solving.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutoring.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be specified in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University will be the sole assessment criterion, with the weighting specified in the course syllabus.

----

The assessment system for the REGULAR EXAMINATION PERIOD consists of the following:

- Continuous assessment (50 per cent):

+ Submission of assignments (10%).

+ Group assessments (20 per cent).

+ Non-exemption mid-term exam (20 per cent).

- Final exam (50%): this is the regular assessment exam, which covers the entire course.

A minimum mark of 4.0 out of 10.0 is required in this exam to be included in the average with the continuous assessment. In this case, the average is calculated even if the continuous assessment mark is a fail.

In the event of failure to achieve the continuous assessment mark due to unexcused attendance of less than 70 per cent, the final mark for the module in the standard assessment period will be 50 per cent of the mark obtained in the final exam.

The assessment system for the EXTRAORDINARY EXAMINATION PERIOD consists of the following:

- Exam covering the entire course (100 per cent).

Timetable

Click on this link to view the detailed timetable in Excel

Reading list

Core:

1. Michael Spivak

Infinitesimal Calculus

2nd ed. Reverté. 1988.

ISBN: 8429151362

Supplementary:

2. Roland E. Larson, Robert P. Hostetler, Bruce H. Edwards

Calculus and Analytic Geometry (Volume 1)

McGraw-Hill. 2010.

ISBN: 8448122291

Objectives

Although this course covers several distinct topics, the learning objectives are essentially the same for each topic. These are:

- To be able to prove statements rigorously using logic.

- To be able to use discrete sets such as integers, congruences modulo n or graphs.

Prerequisites

No prerequisites have been set.

Competencies

Not applicable.

Learning outcomes

RC9 – Formulate problems from a professional context in mathematical language in such a way as to facilitate their analysis and resolution. TYPE: Competencies.

RK2 - Master the basic concepts of discrete mathematics, logic, algorithms, coding, operations research and artificial intelligence, and their application to solving engineering problems. TYPE: Knowledge or content.

RK4 – Be familiar with rigorous proofs of certain classical theorems in different areas of mathematics. TYPE: Knowledge or content.

RS1 – Use mathematical language to formulate propositions in different fields and construct proofs for the problems posed. TYPE: Skills or abilities.

Description of the content

To better adapt the content to the duration of the course, it has been divided into four main topics or blocks:

1) Set theory: an introduction to formal logic, Boolean algebra and binary relations.

2) Integers: solving equations involving integers using Euclid’s algorithm and performing operations modulo n.

3) Combinatorics: variations, permutations and combinations with and without repetition.

4) Graph theory: three problems are studied: when are two graphs equal? When is a graph planar? This includes Euler’s formula and, finally, Eulerian and Hamiltonian paths are studied.

Training activities

AP1. Lectures.

AP2. Interactive classes.

AP3.1. Project work and problem-solving.

AP4. Independent study, case studies, problem-solving and literature review.

AP5. Tutoring.

AP6. Knowledge assessments.

Assessment system and criteria

Without prejudice to any other requirements that may be specified in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University will be the sole assessment criterion, with the weighting specified in the course syllabus.

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REGULAR EXAMINATION PERIOD

Continuous assessment will consist of a test following each of the four content blocks, with each test accounting for 10 per cent of the final mark for the module in the ordinary assessment period. Under no circumstances will passing these tests exempt students from further study of the material.

Once the teaching period has ended, the ordinary assessment exam (final exam) will be held, accounting for the remaining 60 per cent. This exam covers the entire course. Furthermore, in order for the mark to be included in the average with the continuous assessment, a minimum mark of 4.0 out of 10.0 must be obtained in this exam. In this case, the average is calculated even if the continuous assessment is failed.

In the event of loss of continuous assessment due to unexcused attendance of less than 70 per cent, the final mark for the module in the ordinary examination period will be 60 per cent of the mark obtained in the final examination.

EXTRAORDINARY EXAMINATION SESSION

In the supplementary examination session, the final mark for the module will be the mark obtained in the examination for that session, which will assess all the content covered.

Timetable

Click on this link to view the detailed timetable in Excel