Subject: 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 (lectures in large groups) and 3 practical (solving problems on the blackboard and computer, using the Mathematica software).
 

 Syllabus  ( pdf)

2017/2018 Course schedule ( pdf)

Course presentation (18-09-2017) ( pdf) 

Facebook group: Discrete Mathematics (Degree in Computer Engineering, year 17-18

Este grupo cerrado de Facebook está creado para el desarrollo del proyecto de innovación docente PID43_201617 con título “Facebook como instrumento motivador y de apoyo a la docencia de las matemáticas en el grado de Ingeniería Informática” concedido dentro del Plan de Innovación e Incentivación de las Buenas Prácticas Docentes de la Universidad de Jaén 2016-2019 de la Universidad de Jaén. El objetivo es usar la red social Facebook como una herramienta que complemente el proceso de enseñanza-aprendizaje y acerque la asignatura a los estudiantes del Grado en Ingeniería Informática. A su vez, con el uso de esta red social en la docencia se intentará resolver la desconexión entre parte del alumnado con la asignaturas de matemáticas y dinamizar la acción tutorial manteniendo una mejor interacción profesor-alumno, alumno-alumno fuera del ámbito del aula.

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 25th to October 11th)

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 9th to November 6th)

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 6th to November 20th)

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 22nd to December 11th)

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.

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 with the help of computer problems related to content of the subject. 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:

Relationships problems
1.-	Unit 1: Logic It includes individual assigment for this unit. Due: Thursday, October 26th (at the beginning of the class)
2.-	Unit 2: Set and relations It includes individual assigment for this unit. Due: Monday, November 13th (at the beginning of the class)
3.-	Unit 3: Boole algebras It includes individual assigment for this unit. Due: Thursday, November 30th (at the beginning of the class)
4.-	Unit 4: Number theory It includes individual assigment for this unit. Due: Monday, December 18th (at the beginning of the class) The delivery of exercises of the unit is advanced so that the teacher has time to correct them before Thursday, December 21th
5.-	Unit 5: computational complexity It doesn't include individual assigment for this unit.

 

If you do not deliver an assignment or you do not do the academically supervised activities, the corresponding qualification increases the weight of the final exam of the course. For instance: you know that the weight of the final theory exam is the 35%, but if you do not do one academically supervised activities whose weight is 15%, the weight of your theory final exam is 50%.

Quick guide to use JMathWiki ( pdf)

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

ASSESSMENT METHODOLOGY                    

• To pass the course is necessary to obtain a score of 5 out of 10 points between the weighted average of theory and practical part of the course; It will also be essential to have obtained a minimum of 4 out of 10 points in each block (theoretical and practical part). When someone will not reach the minimum in a block, the rating which it will reflect in the minutes will be less than 4 out of 10.

• The block "Theoretical concepts of the matter" will be assessed through a final exam in each call, the weight of the block of 70%. However, students who would attend class actively will have the opportunity to take part in a system of continuous assessment, which will be held in period class and will be complemented by the final exam, in which will be essential to obtain a minimum of 4 out of 10 on average between questions that will be answered in the examination.

• The block "Computer practices" will be assessed through a final exam for each call. However, students who actively attend all practical classes of the course, optionally and voluntarily, could assess this block through a system of continuous assessment, which will take place in the class period. The total weight of this block will be 20%.The students must be submitted to each practical exam with all proposed activities during the practical classes well resolved and printed in paper.

• In the exams no electronic devices, notes, books or any other medium that allows the storage or transmission of data will be allowed. In case of default we will act in accordance with regulations.

• The scores for the practice or the theory exam, exceeding 5 out of 10 points, if the subject has not been approved, will remain in each of the official announcements of the academic year.

• If the percentage allocated to the final exam, depending on attendance, continuous assessment and earlier work by each student, is equal to or greater than 70%. The grades obtained by students who exceed 5 out of 10, in the process of continuous assessment in paragraphs "Theoretical concepts of matter" and "Computer practices" will be kept in each of the official announcements of the academic year. However, since the maximum score that students can get in the sum of these items does not exceed 30% of the total grade, students who do not present the final exam of theory and also the practices appear as absent in corresponding to this call record. If the percentage allocated to the final exam, depending on attendance, continuous assessment and earlier work by each student, is less than 70%. The grades obtained by students who exceed 5 out of 10, in the process of continuous assessment in paragraphs "Theoretical concepts of matter" and "Computer practices" will be kept in each of the official announcements of the academic year. But according to Article 18 of the Rules of Academic System and Student Assessment at the University of Jaen, is considered out a call, this call is understood to be the ordinary call of course, considering calls for the same criteria as other in the previous section, that is, the final grade for the course will be "not attend" for all students who do not make the final exam of theory and also the practices in that call, although it has done some previous work, continuous assessment or attended some lectures or practices.

Exam dates and qualifications

Qualification of the practical part of the course

To review the last practical exam you can go through the teacher's office during tutoring hours on Monday 15th or

Tuesday 16th January. If possible, reserve tutorials on the web: TUTORIALS RESERVE

If you have not obtained a mark greater or equal to 5, you must do the practice part of the exam in the final exam of the course.

Do not forget that to carry out the evaluation of practices; you must take printed the notebook with the exercises proposed during the course.

Important information: In order to qualify all assignments that you had to do during the course before the final exam of January 25th, it is necessary that you deliver before January, 20th the exercises that you want to be evaluated by me.

If you do not deliver an assignment or you do not do the academically supervised activities, the corresponding qualification increases the weight of the final exam of the course. For instance: you know that the weight of the final theory exam is the 35%, but if you do not do one academically supervised activities whose weight is 15%, the weight of your theory final exam is 50%.

Qualification obtain during the continuous assessment of the theory part of the course

Ordinary call 1 (january):

Thursday, January 25, 2018

Classroom:  1, 2, 3  Building:   B-4

Hour: 9:00

Extraordinary call 2 (june-july):

Monday, July 2, 2018

Classroom: 20, 21, 22 / I-1, I-2   Building: B4 / A4 

Hour: 9:00 / 12:00

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