The pre-requisites for the successful completion of this subject do not go beyond the skills in Linear Algebra acquired at High School. In particular, it is desirable for students to know the basic tools and methods required for matrix calculus and for the resolution of linear equation systems. For students presenting difficulties in these areas, it is recommended they attend the Zero Course organized by the College at the beginning of the first semester.
The subjects Algebra and Discrete Mathematics, Calculus and Numerical Methods, Statistics, and Logic conform the Mathematical Foundations of Computer Science, which is included in the basic training module of the Computer Science curriculum. Algebra and Discrete Mathematics, as its name indicates, dedicates its credits to the formation of the future engineer in these mathematical areas, which serve as a basis for the correct understanding and development of other curriculum subjects. Likewise, the subject contributes to the student's training in transversal competences, but not less important.
In the study of algorithmic processes to analyze information (its theory, design, effectiveness and implementation), the computer scientist needs certain mathematical tools (concepts, results and basic techniques) which are provided in this course. At the same time, the study of these tools provides the student with certain fundamental skills such as rigorousness, the capacity to use a formal language and a logical structure ( which are unambiguous and syntactically coherent), as well as the mastery of deduction and induction processes. To this end, the learning is combined with the acquisition of transversal skills, such as the ability to use mathematical reasoning and logical deduction or the stimulation of intuition when using mathematical concepts, results and methods.
The lessons in Discrete Mathematics, at least those related to Boolean Algebras, Graph Theory and Finite Groups (which are a good part of those developed in the program) are essential because they are linked to the development of computer concepts and technologies. Specifically, computers are finite structures, inherent to Discrete Mathematics, so that their understanding would be impossible without a prior learning of the topics of this area. It is enough to think that internally computers work with lists of zeros and ones (whose basic structure is Boolean algebra), that every time we start a computer session and we open tabs we are using a tree graph, or that modular arithmetic operates on finite groups. Furthermore, the study of abstract data types requires algebraic analysis of the properties of certain operations defined on a certain set. On the other hand, Linear Algebra constitutes an elementary theoretical base in which multiple problems of different sciences are formalized and solved. The applications of Linear Algebra to Computer Science are diverse and highly relevant, such as the use of matrix calculation in coding theory or the identification and classification of transformations in computer graphics.
The course prepares the student to use formal language, an essential aspect of computer science and implicitly present in most of the subjects of the degree. It also provides the student with logical structures of reasoning, which are equally useful in most subjects. Regarding the contents, besides the above mentioned, the course is closely related to Computer Technology (which makes use of the Boolean algebra structure for the study of switching circuits), Physical Foundations, and Calculus and Numerical Methods (which make use of the resolution -algebraic and numerical- of linear equation systems).
Because this is a basic subject in the degree, its contribution is directly focused on the training of the engineer in the aspects previously described. Therefore, It will be implicit in many activities throughout the career development, even if it is not generally explicit.
Course competences | |
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Code | Description |
BA01 | Ability to solve mathematical problems which can occur in engineering. Skills to apply knowledge about: lineal algebra; integral and differential calculus; numerical methods, numerical algorithms, statistics, and optimization. |
BA03 | Ability to understand basic concepts about discrete mathematics, logic, algorithms, computational complexity, and their applications to solve engineering problems. |
INS02 | Organising and planning skills. |
INS03 | Ability to manage information and data. |
INS05 | Argumentative skills to logically justify and explain decisions and opinions. |
SIS09 | Care for quality. |
UCLM03 | Accurate speaking and writing skills. |
Course learning outcomes | |
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Description | |
Use of basic concepts of lineal and combinational algebra. | |
Application of graph theory fundamentals to the modelling and mathematical resolution of real problems. | |
Utilization of programs for symbolic and numerical calculus. | |
Additional outcomes | |
Not established. |
MATLAB is used in the laboratory sessions.
Training Activity | Methodology | Related Competences | ECTS | Hours | As | Com | Description | |
Class Attendance (theory) [ON-SITE] | Lectures | BA01 BA03 | 0.9 | 22.5 | N | N | Lectures about the syllabus. (MAG) | |
Individual tutoring sessions [ON-SITE] | BA01 BA03 | 0.18 | 4.5 | N | N | Individual or small group tutorials in the teacher's office, classroom or laboratory. (TUT) | ||
Study and Exam Preparation [OFF-SITE] | Self-study | BA01 BA03 INS02 INS03 | 2.1 | 52.5 | N | N | Individual study of the student. (EST) | |
Other off-site activity [OFF-SITE] | Practical or hands-on activities | INS02 INS03 | 0.6 | 15 | N | N | Preparation for the subject's practice sessions. (PLAB) | |
Problem solving and/or case studies [ON-SITE] | Problem solving and exercises | BA01 BA03 INS02 INS03 INS05 SIS09 UCLM03 | 0.6 | 15 | Y | N | Resolution of exercises by the teacher and students. (PRO) | |
Writing of reports or projects [OFF-SITE] | Self-study | BA01 BA03 INS02 INS03 INS05 SIS09 | 0.9 | 22.5 | Y | N | Preparation of a report on a topic proposed by the teacher. (RES) | |
Computer room practice [ON-SITE] | Practical or hands-on activities | BA01 BA03 INS02 INS03 INS05 SIS09 UCLM03 | 0.42 | 10.5 | Y | Y | Conducting the scheduled practices in the computer room. (LAB) | |
Final test [ON-SITE] | Assessment tests | BA01 BA03 INS05 SIS09 UCLM03 | 0.3 | 7.5 | Y | Y | Taking a final exam of the entire subject. (EVA) | |
Total: | 6 | 150 | ||||||
Total credits of in-class work: 2.4 | Total class time hours: 60 | |||||||
Total credits of out of class work: 3.6 | Total hours of out of class work: 90 |
As: Assessable training activity
Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).
Evaluation System | Continuous assessment | Non-continuous evaluation * | Description |
Final test | 55.00% | 55.00% | Compulsory activity that can be retaken (rescheduling) to be carried out within the planned exam dates of the final exam call (convocatoria ordinaria). |
Theoretical papers assessment | 20.00% | 20.00% | Non-compulsory activity that can be retaken. To be carried out before end of teaching period. |
Laboratory sessions | 15.00% | 15.00% | Compulsory activity that can be retaken. To be carried out during lab sessions. |
Oral presentations assessment | 10.00% | 10.00% | Non-compulsory activity that can be retaken. |
Total: | 100.00% | 100.00% |
Not related to the syllabus/contents | |
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Hours | hours |
Individual tutoring sessions [PRESENCIAL][] | 4.5 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 52.5 |
Other off-site activity [AUTÓNOMA][Practical or hands-on activities] | 15 |
Writing of reports or projects [AUTÓNOMA][Self-study] | 22.5 |
Computer room practice [PRESENCIAL][Practical or hands-on activities] | 10.5 |
Final test [PRESENCIAL][Assessment tests] | 7.5 |
Unit 1 (de 5): Sets, Functions and Relations | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4.5 |
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 3 |
Unit 2 (de 5): Counting | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4.5 |
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 3 |
Unit 3 (de 5): Arithmetic | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4.5 |
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 3 |
Unit 4 (de 5): Graphs | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4.5 |
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 3 |
Unit 5 (de 5): Introduction to linear algebra | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4.5 |
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 3 |
Global activity | |
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Activities | hours |