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## Syllabus 2015-16 - 13311008 - Discrete Mathematics (Matemática discreta)

- Level 1: Tutorial support sessions, materials and exams in this language
- Level 2: Tutorial support sessions, materials, exams and seminars in this language
- Level 3: Tutorial support sessions, materials, exams, seminars and regular lectures in this language

DEGREE: | Grado en Ingeniería informática |

FACULTY: | SCHOOL OF ENGINEERING OF JAÉN |

ACADEMIC YEAR: | 2015-16 |

COURSE: | Discrete Mathematics |

NAME: Discrete Mathematics | |||||

CODE: 13311008 | ACADEMIC YEAR: 2015-16 | ||||

LANGUAGE: English | LEVEL: 3 | ||||

ECTS CREDITS: 6.0 | YEAR: 1 | SEMESTER: PC |

NAME: GARCÍA MUÑOZ, MIGUEL ÁNGEL | ||

DEPARTMENT: U124 - MATEMÁTICAS | ||

FIELD OF STUDY: 005 - ÁLGEBRA | ||

OFFICE NO.: B3 - 016 | E-MAIL: magarcia@ujaen.es | P: 953212935 |

WEBSITE: www4.ujaen.es/~magarcia | ||

ORCID: https://orcid.org/0000-0002-6252-0592 | ||

LANGUAGE: English | LEVEL: 3 |

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.

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

Unit 2. Sets and order relations.

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

Unit 3. Boole algebras. Boolean functions.

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

Unit 4. Introduction to number theory: modular arithmetic.

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

Unit 5. Notions of computational complexity.

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

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

Practice 1: The working environment: Mathematica.

Practice 2: Basic arithmetic. Variables and functions.

Practice 3: Lists: Tables, matrices and vectors.

Practice 4: Programming in Mathematica

Practice 5: Propositional logic: Connectives and truth tables.

Practice 6: Propositional logic: Tautologies, contradictions, normal forms. Logical equivalences and implications. Arguments.

Practice 7: Sets and functions.

Practice 8: Binary relations and ordered sets.

Practice 9: Lattices and finite Boole algebras.

Practice 10: Boolean functions.

Practice 11: Natural and integer numbers. Divisibility.

Practice 12: Natural and integer numbers. Congruences and numbering systems.

Lecture (Theory): there will be two one-hour-long sessions each week during all the semester. These sessions will be devoted to regular lectures and problem solving, using a video projector and computer-generated slides. The lecturer makes their notes available online after a lecture through his institutional web which can help to supplement the notes you take during the class. You have to attend lectures in order to make better use of the course.

Lecture (Practice)- 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.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

- 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 80%. 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%.
- 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.

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

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