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Department of Mathematics (Algebra)
Campus Universitario, Paraje de Las
Lagunillas S/N. 23071 - Jaén |
Professor:
Miguel Ángel García MuñozCourse: 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 (
Monday 11:30,
classroom 03
(building B5)
and Tuesday 10:30, classroom 02 (building B5) and 3 practical
(solving problems on
the blackboard and with the computer, using the Mathematica software) (Thursday
8:30, classroom
I3 in the building A4).
Syllabus - Full version (in Spanish)
2025/2026 Course schedule (
pdf)
Course presentation (08-09-2025) ( 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).
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 9th to September 29th)
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
September 30th to October 21st)
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 27th to November 4th)
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 10th to December 1st)
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 2nd to December 16th)
Algorithms. Growth functions. Complexity of an algorithm. The classes P and NP.
All these titles can find them in the Library of the University of Jaen
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Discrete and Combinatorial Mathematics. Edition: 5ª. Author: Grimaldi, Ralph P.. Publisher: Pearson Education.
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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.
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Métodos computacionales en álgebra para informáticos: matemática discreta lógica. Edition: -. Author: García Muñoz, Miguel A.. Publisher: [Jaén]: Área de Álgebra, Universidad de Jaén, 2006.
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Discrete mathematics. Edition: -. Author: Norman L. Biggs
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Logic for mathematicians. Edition: Rev. ed.. Author: Hamilton, Alan G.. Publisher: Cambridge [etc] : University Press, cop. 2000.
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Discrete mathematics and its applications. Edition: 6th ed. Author: Rosen, Kenneth H.. Publisher: Boston [etc.]: McGraw-Hill, cop.2007.
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Mathematica: quick reference, version 2. Edition: [2nd printing]. Author: Blachman, Nancy. Publisher: Massachusetss [etc.]: Addison-Wesley, 1992.
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Mathematica a practical approach. Edition: 2nd. ed. Author: Blachman, Nancy. Publisher: Upper Saddle River: Prentice Hall, 1999.
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Classic algebra. Edition: -. Author: Cohn, P. M.. Publisher: Chichester [etc.]: John Wiley & Sons, impr. 2001.
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Discrete mathematics. Edition: 4th ed. Author: Johnsonbaugh, Richard. Publisher: Upper Saddle River (New Jersey): Prentice Hall, 1997.
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Mathematica: a system for doing mathematics by computer. Edition: 2nd. ed. Author: Wolfram, Stephen. Publisher: Reading: Addison-Wesley Publishing Company, cop. 1991.
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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 |
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Unit 4: Number theory |
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(B) Solving problems with the help of computer using the Mathematica software.
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Exam dates and qualifications
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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):
Monday, January 26th, 2026
Classroom: Building:
Hour:
Extraordinary call 2 (June-July):
Monday,
July 13th, 2026
Classroom: Building:
Hour: