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

The subject Discrete Mathematic is part of the Mathematics matter which in turn is part of the Basic Training Module of the Degree in Computer Engineering, 2010. This subject is compulsory and consists of 6 ECTS credits which are divided into 3 theory credits (Wednesday, room 15 and Friday, room 11 in the building B5) and 3 practical (solving problems on the blackboard and with the computer, using the Mathematica software) (room I23 in the building A4).

Syllabus - Full version (in Spanish)

2024/2025 Course schedule ( pdf)

Course presentation (11-09-2024) ( 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 13th to October 2nd)

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 October 4th to October 25th)

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 25th to November 8th)

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 13th to December 4th)

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 4th to December 20th)

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

Qualification continuous assessment of theory

If you want to review the exercise of unit 1 and 2, it will be next --- in a tutorial time.

It is essential to reserve a time on the teacher`s website or if it is not possible during the tutorial hours proposed by the teacher, please make an appointment in other date by sending an email to the teacher.

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 practice 0, the Mathematica program from this LINK

SESSIONS	CONTENTS	EXERCISES TO CORRECT ON THE BOARD	PROPOSED EXERCISES TO DO WITH MATHEMATICA
SESSION 1 17-september	The working environment: Mathematica Multimedia material in the following link	Exercise 1 from the list of problems in unit 1.	IN PLATEA
SESSION 2 24-september	Basic arithmetic. Variables and functions Multimedia material in the following link	Exercises 3, 5 and 8 from the list of problems in unit 1.	IN PLATEA
SESSION 3 1-october	Lists: Tables, matrices and vectors Multimedia material in the following link	Exercises 8, 9 and 12 from the list of problems in unit 1.	IN PLATEA
SESSION 4 8-october	Programming in Mathematica Multimedia material in the following link	Exercise 1 b) from the exam in ordinary 1 call year 2023/24 and exercises 15 and 20 from the list of problems in unit 1.	IN PLATEA
SESSION 5 15-october	Propositional logic: Connectives and truth tables Multimedia material in the following link	Exercises 1 and 3 from the list of problems in unit 2.	IN PLATEA
SESSION 6 22-october	Propositional logic: Tautologies, contradictions, normal forms. Logical equivalences and implications. Arguments Multimedia material in the following link	Exercises 4, 6 and 7 (graph G₄) from the list of problems in unit 2.	IN PLATEA
SESSION 7 29-october	Sets and functions Multimedia material in the following link	Second part of exercise 7 (graph G₄ ) Exercise 17 of the list of problems of unit 2.	IN PLATEA
SESSION 8 5-november	Binary relations. Ordered sets Multimedia material in the following link	Exercise 2 of the extraordinary 2 call exam year 23/24 and exercise 24 of the list of problems of unit 2.	IN PLATEA
SESSION 9 12-november	Practice continuous assessment (sessions 1 to 8 both included) Files you can use in the exercise ( zip) Theory continuous assessment unit 1 and 2	Delivery of practice exercise will take place in PLATEA	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 10 19-november	Lattices and finite Boole algebras Multimedia material in the following link	Exercise 3 of the ordinary 1 call exam year 23/24 and exercise 6 (optional exercise 9 as a complement of the first with the order relation a £ b if and only if b \| a) of the list of problems of unit 3.	IN PLATEA
SESSION 11 26-november	Boolean functions Multimedia material in the following link	Exercises 13 and 14 from the list of problems in unit 3.	IN PLATEA
SESSION 12 3-december	Natural and integer numbers. Divisibility Multimedia material in the following link	Exercises 4 from the list of problems in unit 4 and exercise 11.9 from the practice manual (in PLATEA)	IN PLATEA
SESSION 13 10-december	Natural and integer numbers. Congruences and numeral systems Multimedia material in the following link	Exercises 6, 25, 26 and 27 from the list of problems in unit 4, exercise 11.9 (using system of congruences) from the practice manual (in PLATEA) and exercise 4 of the ordinary 1 call exam year 23/24.	IN PLATEA
SESSION 14 17-december	Practice continuous assessment (75%) Files you can use in the exercise ( zip)	Delivery of practice exercise will take place in PLATEA	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):

Thursday, January 23^th, 2025

Classroom: 23,24 y E3 Building: B-4

Hour: 9:00

Extraordinary call 2 (June-July):

Thursday, July 10^th, 2025

Classroom: E-1, 13, 14 Building: B-4

Hour: 9:00

PREVIOUS YEARS EXAMS (before course 2015/16 in Spanish)
2025/26		2024/25	Extraordinary call 2 (JUNE/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