Professor: Miguel Ángel García Muñoz

Department of Mathematics (Algebra)

Campus Universitario, Paraje de Las Lagunillas S/N. 23071 - Jaén
Ed. B3, dep. 016. Tlfno.: 953212935

Course: Discrete Mathematics

Degree in Computer Engineering /Degree in Artificial Intelligence and Cybersecurity

The subject Discrete Mathematics is part of the Mathematics matter which in turn is part of the Basic Training Module of the Degree in Computer Engineering, 2010 and Degree in Artificial Intelligence and Cybersecurity, 2026. This subject is compulsory and consists of 6 ECTS credits which are divided into 3 theory credits (Monday 8:30 and Tuesday 8:30, classroom 23 (building A4) and 3 practical (solving problems on the blackboard and with the computer, using the Mathematica software) (Wednesday 10:30, classroom I13 in the building A4).

Syllabus - Full version (in Spanish)

2026/2027 Course schedule ( pdf)

Course presentation (07-09-2026) ( pdf)

Audiovisual resources for mathematics courses ( This link leads to a web page resulting from the teaching innovation project PIMED29_102224 entitled "Recursos audiovisuales para el aprendizaje de las matemáticas" directed by Professor Miguel Ángel García Muñoz. This web resource is under construction. If any error is observed, we would appreciate it if anyone finds it, please notify us by clicking on "FORM" in the upper right corner of the web page).

PROGRAM

Our goal in this course is to build skills and give you experience in areas such as Mathematical Reasoning (ability used by a computer engineer in constructing proofs and in writing programs), Discrete Structures (abstrac mathematical structures used to represent discrete objects and relationships between them) and Algorithmic Thinking (some problems are solved by the specification of an algorithm that can be implemented in a program). Topics covered in the course include:

Unit 1. Fundamentals of logic. (material for lectures from September 9th to September 28th)

List of vocabulary

Statements, connectives and truth tables. Normal forms. Adequate sets of connectives. Proof techniques. Arguments and validity.

Unit 2. Sets and order relations. (material for the lectures from September 29th to October 20th)

List of vocabulary

Basic concepts. The power set of a set. Functions. Equivalence relations. Order relations.

Unit 3. Boole algebras. Boolean functions. (material for the lectures from October 26th to November 3th)

List of vocabulary

Lattices. Types of lattices. Boole algebra. Boolean functions: canonical forms. Applications: boolean circuits.

Unit 4. Introduction to number theory: modular arithmetic. (material for the lectures from November 9th to November 30th)

List of vocabulary

Natural number: induction and first properties. Integers. Divisibility and congruences. Bezout theorem applications. Conguences and numeral systems.

Unit 5. Notions of computational complexity. (material for the lectures from December 1st to December 16th)

Algorithms. Growth functions. Complexity of an algorithm. The classes P and NP.

BIBLIOGRAFY

All these titles can find them in the Library of the University of Jaen

MAIN BOOKLIST:

Discrete and Combinatorial Mathematics. Edition: 5ª. Author: Grimaldi, Ralph P.. Publisher: Pearson Education.
Matemática discreta para la computación: nociones teóricas y problemas resueltos . Edition: -. Author: García Muñoz, Miguel Ángel. Publisher: Jaén: Universidad de Jaén, Servicio de Publicaciones, 2010.
Métodos computacionales en álgebra para informáticos: matemática discreta lógica. Edition: -. Author: García Muñoz, Miguel A.. Publisher: [Jaén]: Área de Álgebra, Universidad de Jaén, 2006.
Discrete mathematics. Edition: -. Author: Norman L. Biggs
Logic for mathematicians. Edition: Rev. ed.. Author: Hamilton, Alan G.. Publisher: Cambridge [etc] : University Press, cop. 2000.
Discrete mathematics and its applications. Edition: 6th ed. Author: Rosen, Kenneth H.. Publisher: Boston [etc.]: McGraw-Hill, cop.2007.

ADDITIONAL BOOKLIST:

Mathematica: quick reference, version 2. Edition: [2nd printing]. Author: Blachman, Nancy. Publisher: Massachusetss [etc.]: Addison-Wesley, 1992.
Mathematica a practical approach. Edition: 2nd. ed. Author: Blachman, Nancy. Publisher: Upper Saddle River: Prentice Hall, 1999.
Classic algebra. Edition: -. Author: Cohn, P. M.. Publisher: Chichester [etc.]: John Wiley & Sons, impr. 2001.
Discrete mathematics. Edition: 4th ed. Author: Johnsonbaugh, Richard. Publisher: Upper Saddle River (New Jersey): Prentice Hall, 1997.
Mathematica: a system for doing mathematics by computer. Edition: 2nd. ed. Author: Wolfram, Stephen. Publisher: Reading: Addison-Wesley Publishing Company, cop. 1991.
2000 solved problems in discrete mathematics. Edition: -. Author: Lipschutz, Seymour. Publisher: New York [etc.] : Mac Graw-Hill, 2000.

PRACTICES

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

(A) Solving the proposal relationships problems:

Problem lists
1.-	Unit 1: Logic
2.-	Unit 2: Set and relations
3.-	Unit 3: Boole algebras
4.-	Unit 4: Number theory
5.-	Unit 5: computational complexity

(B) Solving problems with the help of computer using the Mathematica software.

Computer practice classes

In practical classes we solve exercises in the blackboard and we use the software Mathematica in order to solve problems related to all the topics previously develops in the course.

Attention: It would be advisable to download, before session 1 the Mathematica program from this LINK

SESSIONS	CONTENTS	EXERCISES TO CORRECT ON THE BOARD	PROPOSED EXERCISES TO DO WITH MATHEMATICA
SESSION 1 September 9th	The working environment: Mathematica. Basic arithmetic. Variables and functions Multimedia material in the following link1 y link2	Exercise 1 from the list of problems in unit 1.	IN PLATEA
SESSION 2 September 23th	Lists: Tables, matrices and vectors Multimedia material in the following link	Exercise 5, 8 and 12 from the list of problems in unit 1.	IN PLATEA
SESSION 3 September 30th	Programming in Mathematica Multimedia material in the following link		IN PLATEA
SESSION 4 October 7th	Propositional logic: Connectives and truth tables Multimedia material in the following link		IN PLATEA
SESSION 5 October 14th	Propositional logic: Tautologies, contradictions, normal forms. Logical equivalences and implications. Arguments Multimedia material in the following link		IN PLATEA
SESSION 6 October 21st	Sets and functions Multimedia material in the following link		IN PLATEA
SESSION 7 October 28th	Practice continuous assessment (sessions 1 to 7 both included) Files you can use in the exercise ( zip)		It is essential to have ALL the attendance and bring the practice notebook printed (exercises proposed in Platea, sessions 1 to 8 both included)
SESSION 8 November 4th	Binary relations. Ordered sets Multimedia material in the following link		IN PLATEA
SESSION 9 November 11st	Lattices and finite Boole algebras Multimedia material in the following link		IN PLATEA
SESSION 10 November 18th	Boolean functions Multimedia material in the following link		IN PLATEA
SESSION 11 December 2nd	Natural and integer numbers. Divisibility Multimedia material in the following link		IN PLATEA
SESSION 12 December 9th	Natural and integer numbers. Congruences and numeral systems Multimedia material in the following link		IN PLATEA
SESSION 13 December 16th	Practice continuous assessment (75%) Files you can use in the exercise ( zip) Computational complexity Multimedia material in the following		It is essential to have ALL the attendance and bring the practice notebook printed (exercises proposed in Platea, sessions 1 to 7 and 9 to 13)

First practice exercise qualifications

If you want to review the exercise, it will be in a tutoring hour ----.

It is essential to reserve time on the teacher's website or if it is not possible during the teacher's tutoring hours, make an appointment with the teacher by email.

Score after continuous assessment of practice

ASSESSMENT METHODOLOGY

Exam dates and qualifications

IMPORTANT NOTE: Any student who want assist to any call of this subject must carry some document accrediting (ID, passport, driving license, etc.). Otherwise you will not be allowed to do the exam.

Ordinary call 1 (January):

Monday, January 20^th, 2027

Classroom: Building:

Hour:

Extraordinary call 2 (June-July):

Monday, July 7^th, 2027

Classroom: Building:

Hour:

PREVIOUS YEARS EXAMS (before course 2015/16 in Spanish)
2025/26	Extraordinary call 2 (JULY 2026) ( pdf) Ordinary call 1 (JANUARY 2026) ( pdf)	2024/25	Extraordinary call 2 (JULY 2025) ( pdf) Ordinary call 1 (JANUARY 2025) ( pdf)
2023/24	Extraordinary call 2 (JUNE/JULY 2024) ( pdf) Ordinary call 1 (JANUARY 2024) ( pdf)	2022/23	Extraordinary call 2 (JUNE/JULY 2023) ( pdf) Ordinary call 1 (JANUARY 2023) ( pdf)
2021/22	Extraordinary call 2 (JUNE/JULY 2022) ( pdf) Ordinary call 1 (JANUARY 2022) ( pdf)	2020/21	Extraordinary call 2 (JUNE/JULY 2021) ( pdf) Ordinary call 1 (JANUARY 2021) ( pdf)
2019/20	Extraordinary call 2 (JUNE/JULY 2020) (Online) Ordinary call 1 (JANUARY 2020) ( pdf)	2018/19	Extraordinary call 2 (JUNE/JULY 2019) ( pdf) Ordinary call 1 (JANUARY 2019) ( pdf)
2017/18	Extraordinary call 2 (JUNE/JULY 2018) ( pdf) Ordinary call 1 (JANUARY 2018) ( pdf)	2016/17	Extraordinary call 2 (JUNE/JULY 2017) ( pdf) Ordinary call 1 (JANUARY 2017) ( pdf)
2015/16	Extraordinary call 2 (JUNE/JULY 2016) ( pdf) Ordinary call 1 (JANUARY 2016) ( pdf)	2014/15	Examen Extraordinaria 2 (JUNIO/JULIO 2015) ( pdf) Examen Ordinaria 1 (ENERO 2015) ( pdf)
2013/14	Examen Extraordinaria 2 (JUNIO/JULIO 2014) ( pdf) Examen Ordinaria 2 (MAYO/JUNIO 2014) ( pdf) Examen Ordinaria 1 (ENERO 2014) ( pdf)	2012/13	Examen Extraordinaria 2 (JUNIO/JULIO 2013) ( pdf) Examen Ordinaria 2 (MAYO/JUNIO 2013) ( pdf) Examen Ordinaria 1 (ENERO 2013) ( pdf)
2011/12	Examen SEPTIEMBRE 2012 ( pdf) Examen JUNIO 2012 ( pdf) Examen FEBRERO 2012 ( pdf)	2010/11	Examen SEPTIEMBRE 2011 ( pdf) Examen JUNIO 2011 ( pdf) Examen FEBRERO 2011 ( pdf)

Course: Discrete Mathematics

Problem lists