Guías Docentes Electrónicas
1. General information
ECTS credits:
Academic year:
23  20  21  22 
Main language:
Second language:
Use of additional languages:
English Friendly:
Web site:
Lecturer: JOSE LUIS ESPINOSA ARANDA - Group(s): 23  20  21  22 
Phone number
Office hours
Laboratorio 1.09.2 (Edificio Politécnico)
Mondays anf Wednesday at 17:00-20:00

Lecturer: RICARDO GARCIA RODENAS - Group(s): 23  20  21  22 
Phone number
Office hours
926295300 EXT 6222
Wednesday and Thursdays at 10:00-13.00

Lecturer: MARIA LUZ LOPEZ GARCIA - Group(s): 23  20  21  22 
Phone number
Office hours
926295300 EXT 6222
Wednesday and Thursdays at 10:00-13.00

2. Pre-Requisites

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.

3. Justification in the curriculum, relation to other subjects and to the profession

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.

4. Degree competences achieved in this course
Course competences
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.
5. Objectives or Learning Outcomes
Course learning outcomes
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.
6. Units / Contents
  • Unit 1: Sets, Functions and Relations
  • Unit 2: Counting
  • Unit 3: Arithmetic
  • Unit 4: Graphs
  • Unit 5: Introduction to linear algebra

MATLAB is used in the laboratory sessions.

7. Activities, Units/Modules and Methodology
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).

8. Evaluation criteria and Grading System
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%  
According to art. 6 of the UCLM Student Evaluation Regulations, it must be provided to students who cannot regularly attend face-to-face training activities the passing of the subject, having the right (art. 13.2) to be globally graded, in 2 annual calls per subject , an ordinary and an extraordinary one (evaluating 100% of the competences).

Evaluation criteria for the final exam:
  • Continuous assessment:
    IIn compulsory activities, a minimum mark of 40% is required in order to pass that activity and have the possibility to therefore pass the entire subject. The evaluation of the activities will be global and therefore must be quantified by means of a single mark. In the case of the activities that may be retaken (i.e., rescheduling), an alternative activity or test will be offered in the resit/retake exam call (convocatoria extraordinaria).

    The final exam will be common for all the theory/laboratory groups of the subject and will be evaluated by the lecturers of the subject in a serial way, i.e., each part of the final exam will be evaluated by the same lecturer for all the students.

    A student is considered to pass the subject if she/he obtains a minimum of 50 points out of 100, taking into account the points obtained in all the evaluable activities, and also has passed all the compulsory activities.

    For students who do not pass the subject in the final exam call (convocatoria ordinaria), the marks of activities already passed will be conserved for the resit/retake exam call (convocatoria extraordinaria). If an activity is not recoverable, its assessment will be preserved for the resit/retake exam call (convocatoria extraordinaria) even if it has not been passed. In the case of the passed recoverable activities, the student will have the opportunity to receive an alternative evaluation of those activities in the resit/retake exam call and, in that case, the final grade of the activity will correspond to the latter grade obtained.

    The mark of the passed activities in any call, except for the final exam, will be conserved for the subsequent academic year at the request of the student, provided that mark is equal or greater than 50% and that the activities and evaluation criteria of the subject remain unchanged prior to the beginning of that academic year.

    The failure of a student to attend the final exam will automatically result in her/him receiving a "Failure to attend"(no presentado). If the student has not passed any compulsory evaluation activity, the maximum final grade will be 40%.
  • Non-continuous evaluation:
    Students may apply at the beginning of the semester for the non-continuous assessment mode.
    In the same way, the student may change to the non-continuous evaluation mode as long as she/he has not participated during the teaching period in evaluable activities that together account for at least 50% of the total mark of the subject. If a student has reached this 50% of the total obtainable mark or the teaching period is over, she/he will be considered in continuous assessment without the possibility of changing to non-continuous evaluation mode.

    Students who take the non-continuous evaluation mode will be globally graded, in 2 annual calls per subject, an ordinary and an extraordinary one (evaluating 100% of the competences), through the assessment systems indicated in the column "Non-continuous evaluation".

    In the "non-continuous evaluation" mode, it is not compulsory to keep the mark obtained by the student in the activities or tests (progress test or partial test) taken in the continuous assessment mode.

Specifications for the resit/retake exam:
Evaluation tests will be conducted for all recoverable activities.
Specifications for the second resit / retake exam:
Same characteristics as the resit/retake exam call.
9. Assignments, course calendar and important dates
Not related to the syllabus/contents
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
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
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
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
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
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 4.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 3

Global activity
Activities hours
10. Bibliography and Sources
Author(s) Title Book/Journal Citv Publishing house ISBN Year Description Link Catálogo biblioteca
K.H. Rosen Matemática Discreta y sus Aplicaciones. Madrid McGRaw-Hill 8448140737 2004  
K.H. Rosen Discrete Mathematics and its Applications Mc Graw-Hill 978-1-259-67651-2 2019 8th edition.  
N.L. Biggs. Matemática Discreta. Barcelona Vicens Vives. 9788431633110 1998  
R. Johnsonbaugh Matemáticas Discretas México Pearson Educación 9701702530 2005 Ficha de la biblioteca
R.P. Grimaldi Matemática Discreta y Combinatoria. México Prentice Hall 9701702530 1999 Ficha de la biblioteca

Web mantenido y actualizado por el Servicio de informática