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

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Course: Discrete Mathematics

Degree in Computer Engineering

 Program            Bibliography           Problems               Practices             Evaluation

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 (room 31 in the building A4) and 3 practical (solving problems on the blackboard and with the computer, using the Mathematica software) (room I14 in the building A4). 

 Syllabus  -  Full version (in Spanish)

2022/2023 Course schedule ( pdf)

Course presentation (12-09-2022) ( pdf) 

The following link leads to a web page created for the development of the PIMED51_201921 teaching innovation project with the title “Edición y publicación de recursos audiovisuales para las asignaturas del área de Álgebra de la Universidad de Jaén" granted within The Teaching Innovation and Improvement Plan of the University of Jaén 2019-2023 (PIMED-UJA 2019). The objetive is to create and publish audiovisual material related to the courses of the Algebra area that serves as tool to complement the teaching-learning process of these courses:

Audiovisual resources for courses of the Algebra area (This link takes us to a page that is under construction, if you find an error in any of its pages you can notify us by clicking on "FORM" in the upper right corner of the previous web)

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 4th)

            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 November 7th)

            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 November 7th to November 15th)

            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 21st to December 12th)

            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 13th 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.

 

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BIBLIOGRAFY

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

MAIN BOOKLIST:

  1. Discrete and Combinatorial Mathematics. Edition: 5ª. Author: Grimaldi, Ralph P.. Publisher: Pearson Education.

  2. 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.

  3. Métodos computacionales en álgebra para informáticos: matemática discreta lógica. Edition: -. Author: García Muñoz, Miguel A.. Publisher: [Jaén]: Área de Álgebra, Universidad de Jaén, 2006.

  4. Discrete mathematics. Edition: -. Author: Norman L. Biggs

  5. Logic for mathematicians. Edition: Rev. ed.. Author: Hamilton, Alan G.. Publisher: Cambridge [etc] : University Press, cop. 2000.

  6. Discrete mathematics and its applications. Edition: 6th ed. Author: Rosen, Kenneth H.. Publisher: Boston [etc.]: McGraw-Hill, cop.2007.

ADDITIONAL BOOKLIST:

  1. Mathematica: quick reference, version 2. Edition: [2nd printing]. Author: Blachman, Nancy. Publisher: Massachusetss [etc.]: Addison-Wesley, 1992.

  2. Mathematica a practical approach. Edition: 2nd. ed. Author: Blachman, Nancy. Publisher: Upper Saddle River: Prentice Hall, 1999.

  3. Classic algebra. Edition: -. Author: Cohn, P. M.. Publisher: Chichester [etc.]: John Wiley & Sons, impr. 2001.

  4. Discrete mathematics. Edition: 4th ed. Author: Johnsonbaugh, Richard. Publisher: Upper Saddle River (New Jersey): Prentice Hall, 1997.

  5. Mathematica: a system for doing mathematics by computer. Edition: 2nd. ed. Author: Wolfram, Stephen. Publisher: Reading: Addison-Wesley Publishing Company, cop. 1991.

  6. 2000 solved problems in discrete mathematics. Edition: -. Author: Lipschutz, Seymour. Publisher: New York [etc.] : Mac Graw-Hill, 2000.

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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

 

Practice 1: The working environment: Mathematica (15-09-22). (.nb) Mathematica file  

 

 

Practice 2: Basic arithmetic. Variables and functions. (22-09-22).   (.nb) Mathematica file  

                   We are going to solve on the blackboard the following exercises: 1, 2, 3, 4 and 5 from the list of problems in unit 1. 

                   (Try to work them at home in advance).

 

Practice 3: Lists: Tables, matrices and vectors (29-09-22). (.nb) Mathematica file

                   We are going to solve on the blackboard the following exercises:  8, 9 y 12 from the list of problems in unit 1.

                   (Try to work them at home in advance).              

 

Practice 4: Programming in Mathematica (6-10-22). (.nb) Mathematica file

                   We are going to solve on the blackboard the following exercises:  12, 13, 20 y 21,  from the list of problems in unit 1.

                   (Try to work them at home in advance).                  

 

Practice 5: Propositional logic: Connectives and truth tables (13-10-22). (.nb) Mathematica

                   We are going to solve on the blackboard the following exercises: doutbs in list of problems unit 1 and 1, 2, 3 and 4 list of problem unit 2.

                   (Try to work them at home in advance).

                

Practice 6: Propositional logic: Tautologies, contradictions, normal forms. Logical equivalences and implications. Arguments (20-10-22) (.nb) Mathematica

                   We are going to solve on the blackboard the following exercises:  theory of unit 2.

                   (Try to work them at home in advance).

                

Practice 7: Sets and functions (27-10-22). (.nb) Mathematica

                   We are going to solve on the blackboard the following exercises: 6, 8 and 13 from list of problem unit 2.

                   (Try to work them at home in advance).

 

Practice 8: Binary relations. Ordered sets (10-11-22). (.nb) Mathematica

                   We are going to solve on the blackboard the following exercises: 16, 17 and 22 from list of problem unit 2.                                                                                                        

                   (Try to work them at home in advance).

 

Practice 9: Lattices and finite Boole algebras (10 and 17-11-22). (.nb) Mathematica

                   We are going to solve on the blackboard the following exercises:  6 and 8 from list of problem unit 3.

                   (Try to work them at home in advance).

 

Practice 10: Boolean functions (17-11-22) (.nb) Mathematica

                   We are going to solve on the blackboard the following exercises: 13 and 14 from list of problem unit 4.

                   (Try to work them at home in advance).

 

Practice A: Practice continuous assessment (25%) (24-11-22).      

                      Files you can use in the exercise (.zip)             

                   

                      Theory continuous assessment (Unit 1 and 2)

    First practice exercise qualifications  

           If you want to review the exercise, it will be in a tutoring hour next Monday, December 5th.

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.

 

                         

Practice 11: Natural and integer numbers. Divisibility (1-12-22). (.nb) Mathematica   

                    We are going to solve on the blackboard the following exercises:  3, 4 and 12 from list of problem unit 4.

                    (Try to work them at home in advance).

                     

Practice 12: Natural and integer numbers. Congruences and numeral systems (15-12-22). (.nb) Mathematica   

                    We are going to solve on the blackboard the following exercises:  6, 17, 26 and 27 from list of problem unit 4.

                   (Try to work them at home in advance).

 

Practice B: Practice continuous assessment (75%)   (22-12-22)

                    Files you can use in the exercise (.zip)   

Score after continuous assessment of practice

 

 

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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):

Friday, January 27th, 2023    

Classroom: 10   Building: B-4   

Hour: 9:00

 

 

Extraordinary call 2 (June-July):

Monday, July 3rd, 2023        

Classroom: E1, 13, 14 y 20  Building: B4

Hour: 9:00

 

 

 

 

PREVIOUS YEARS EXAMS (before course 2015/16 in Spanish)     
2023/24   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) ( pdf)  (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)

 

 

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Miguel Ángel García Muñoz

Universidad de Jaén

Departamento de Matemáticas

magarcia ujaen.es

Tfn: +34 953212935