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 (room 22 in the building A4) and 3 practical (solving problems on the blackboard and with the computer, using the Mathematica software) (room I34 in the building A4). 

 Syllabus  -  Full version (in Spanish)

2023/2024 Course schedule ( pdf)

Course presentation (14-09-2023) ( 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 15th to September 29th)

            List of vocabulary

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

The continuous assessment of this unit will be on Thursday, 26th of October from 14.20 to 15:30 in the building B4, classroom 25 (second floor).

Unit 2. Sets and order relations. (material for the lectures from September 29th to October 27th)

            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 2nd to November 10th)

            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 16th to December 7th)

            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 7th to December 22nd)

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

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 19-september-2023 The working environment: Mathematica     Multimedia material in the following link   Exercise 1 from the list of problems in unit 1.     IN PLATEA   SESSION 2 19-september-2023 Basic arithmetic. Variables and functions Multimedia material in the following link SESSION 3 26-september-2023 Lists: Tables, matrices and vectors Multimedia material in the following link Exercises 2, 3, 5 and 8 from the list of problems in unit 1. IN PLATEA   SESSION 4 3-october-2023 Programming in Mathematica Multimedia material in the following link Exercises 8, 9 and 12 from the list of problems in unit 1. IN PLATEA   SESSION 5 10-october-2023 Propositional logic: Connectives and truth tables Multimedia material in the following link Exercises 15, 19 and 20 from the list of problems in unit 1. IN PLATEA SESSION 6 17-october-2023 Propositional logic: Tautologies, contradictions, normal forms. Logical equivalences and implications. Arguments Multimedia material in the following link Exercises 1 and 3 from the list of problems in unit 2.   IN PLATEA   SESSION 7 24-october-2023  Sets and functions  Multimedia material in the following link Exercises 4, 6 and 13 from the list of problems in unit 2.   IN PLATEA   SESSION 8 31-october-2023 Binary relations. Ordered sets   Multimedia material in the following link Exercises 16, 17 and 22 from the list of problems in unit 2.    IN PLATEA   SESSION 9 7-november-2023 Lattices and finite Boole algebras   Multimedia material in the following link       Exercises 6 and 8 from the list of problems in unit 3.     IN PLATEA SESSION 10 14-november-2023 Practice continuous assessment     Files you can use in the exercise (.zip)      It is essential to have ALL the assistance and have the practice notebook printed (exercises in PLATEA sessions 1 to 8)   Exercise 10 from the list of problems in unit 3. Delivery of practice exercise will take place in PLATEA   SESSION 11 21-november-2023 Boolean functions   Multimedia material in the following link Exercises 13 and 15 from the list of problems in unit 3.     EN PLATEA   SESSION 12 28-november-2023 Natural and integer numbers. Divisibility   Multimedia material in the following link Exercises 4 and 12 from the list of problems in unit 4.     IN PLATEA   SESSION 13 5-december-2023 Natural and integer numbers. Congruences and numeral systems   Multimedia material in the following link Exercises 6, 17, 26 and 27 from the list of problems in unit 4.       IN PLATEA SESSION 14 12-december-2023 Practice continuous assessment (75%)   Files you can use in the exercise (.zip)      Delivery of practice exercise will take place in PLATEA SESSION 15 19-december-2023 Solve exercise from unit 4 and 5 Exercises 16 and 21 from the list of problems in unit 4.      Analyze the algorithm in the following exercises a) Exer. 5 of Ordinary 1 of 2022/23. b) Exer. 5 of the Ordinary 1 exam of 2014/15. c) Exer. September 3A, 2011/12. Analyze and count the number of iterations produced by the loops of programs 7.2, 7.3 and function 12.5. Do it with several examples in each program.        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

Ordinary call 1 (January):

Thursday, January 11^th, 2024    

Classroom:  10   Building:  B4  

Hour: 9:00 

Extraordinary call 2 (June-July):

Friday, July 8^th, 2024        

Classroom:   Building: 

Hour:

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

Miguel Ángel García Muñoz

Universidad de Jaén

Departamento de Matemáticas

magarcia ujaen.es

Tfn: +34 953212935