Educational guide
IDENTIFYING DATA 2024_25
Subject ALGEBRA Code 00709006
Study programme
0709 - GRADO EN INGENIERÍA INFORMÁTICA
Descriptors Credit. Type Year Period
6 Basic Training First Second
Language
Castellano
Prerequisites
Department MATEMATICAS
Coordinador
ARIAS MOSQUERA , DANIEL
E-mail darim@unileon.es
jsusl@unileon.es
Lecturers
ARIAS MOSQUERA , DANIEL
SUSPERREGUI LESACA , JULIÁN
Web http://
General description This subject provides basic theoretical/practical knowledge about the divisibility of integers and polynomials, modular arithmetic, finite fields, as well as those related to linear algebra. Some applications of these contents to Computer Engineering are studied.
Tribunales de Revisión
Tribunal titular
Cargo Departamento Profesor
Presidente MATEMATICAS HERMIDA ALONSO , JOSÉ ÁNGEL
Secretario MATEMATICAS SAEZ SCHWEDT , ANDRES
Vocal MATEMATICAS GARCIA FERNANDEZ , ROSA MARTA
Tribunal suplente
Cargo Departamento Profesor
Presidente MATEMATICAS GOMEZ PEREZ , JAVIER
Secretario MATEMATICAS CASTRO GARCIA , NOEMI DE
Vocal QUIROS CARRETERO , ALICIA

Competencias
Code  
A18096
B5618
B5619
B5623
B5625
C1 CMECES1 That students have demonstrated possession and understanding of knowledge in an area of study that is based on general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study
C4 CMECES4 That students can transmit information, ideas, problems and solutions to both a specialised and non-specialised audience
C5 CMECES5 That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy

Learning aims
Competences
Understand the concepts of Euclidean division, divisibility and congruences in the context of integers and polynomials. Know the basic algorithmic techniques related to these concepts, and apply them in solving engineering problems. A18096
 B5618
B5619
B5623
B5625
 C1
C4
C5
Understand the concepts of vector spaces and linear applications, as well as the basic algorithmic techniques in Linear Algebra, and apply them in solving engineering problems. A18096
 B5618
B5619
B5623
B5625
 C1
C4
C5
Carry out analysis and reasoning through the use of mathematical language. A18096
 B5618
B5619
B5623
B5625
 C1
C4
C5
Apply the mathematical concepts and procedures learned in the elaboration of correct reasoning and arguments, as well as to face situations that involve the use of new mathematical knowledge and techniques, thus promoting autonomous learning. A18096
 B5618
B5619
B5623
B5625
 C1
C4
C5
Communicate orally and/or in writing information, ideas, problems and solutions through mathematical language. A18096
 B5618
B5619
B5623
B5625
 C1
C4
C5

Contents
Topic Sub-topic
Topic I: FINITE FIELDS. Sub-topic 1: INTEGERS.
Divisibility of integers. Bézout Identity and Extended Euclidean Algorithm. Linear diophantine equations. Modular arithmetic. Finite fields of modular integers. Equations in linear congruences. Chinese Remainder Theorem. Euler congruence.

Sub-topic 2: POLYNOMIALS.
Divisibility of polynomials. Irreducible polynomials. Unique factorization of polynomials. Bézout Identity and Extended Euclidean Algorithm for Polynomials. Finite fields of congruence classes of polynomials. Generator of the group of units of a finite field.
Topic II: LINEAR ALGEBRA. Sub-topic 1: GAUSSIAN ELIMINATION.
Vector space of matrices with entries in a field. Ring structure. Gaussian Elimination Algorithm. Gauss-Jordan algorithm. Rank of a matrix. Applications: Calculation of the inverse matrix. Discussion and resolution of systems of linear equations.

Sub-topic 2: VECTOR SPACES.
Vector subspace. Base and dimension of a vector space. Range of a set of vectors. Generating matrix, parametric equations, implicit equations and control matrix of a subspace. Sum and intersection of subspaces. Complementary subspace. Base change matrix.

Sub-topic 3: LINEAR MAPS.
Matrix maps. Kernel and image of a linear map. Injective and surjective linear maps. Isomorphisms. Matrix associated with a linear map.

Sub-topic 4: DIAGONALIZACIÓN.
Diagonalizable matrices. Determinants. Eigenvalues, eigenvectors and characteristic polynomial of a matrix. Matrix diagonalization method. Diagonalizable endomorphisms.

Planning
Methodologies  ::  Tests
  Class hours Hours outside the classroom Total hours
Problem solving, classroom exercises 29 35 64
 
Seminars 6.5 9 15.5
Personal tuition 0.5 0 0.5
 
Lecture 18 26 44
 
Practical tests 6 20 26
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies   ::  
  Description
Problem solving, classroom exercises Sessions aimed at applying the theoretical aspects and algorithmic techniques of each block in solving problems.
Seminars In the seminars, some of the contents of the subject will be discussed in more detail, as well as some practical problems related to Computer Engineering.
Personal tuition The student will have the help of the teacher to resolve any possible doubts regarding the subject.
Lecture Sessions aimed at explaining theoretical aspects and algorithmic techniques in the context of the contents proposed for the subject.

Personalized attention
 
Lecture
Problem solving, classroom exercises
Seminars
Practical tests
Description
It is advisable to use individualized tutoring sessions with the teacher, where the specific learning difficulties of each student can be addressed. To request a tutoring session, the student must send an email to the teacher.

Assessment
  Description Qualification
Practical tests Se llevará a cabo una evaluación continua del trabajo realizado por el alumno a través de la valoración de dos pruebas escritas, cada una con un peso relativo del 50% de la calificación final. 100%
 
Other comments and second call
Primera convocatoria:

Aproximadamente a la mitad del periodo de clases se realizará una primera prueba escrita en la que se evaluarán los conocimientos adquiridos en la primera mitad del semestre. Su peso sobre la calificación final de la asignatura será de un 50%.

Casi al final del periodo de clases se llevará a cabo una segunda prueba escrita en la que se evaluarán los conocimientos adquiridos en la segunda mitad del semestre. Su peso sobre la calificación final de la asignatura será de otro 50%.

Segunda convocatoria:

El alumno podrá optar por repetir en el examen de recuperación una o ambas pruebas escritas (en caso de no repetir la parte correspondiente a uno de los bloques, se conservará la nota obtenida en esa parte en la primera convocatoria).

Convocatoria de diciembre:

La calificación en dicha convocatoria se obtendrá exclusivamente de la evaluación de un único examen escrito acerca de los contenidos de la materia.

 

Material no permitido durante el desarrollo de las pruebas de evaluación:

Durante el desarrollo de las pruebas de evaluación queda terminantemente prohibida la tenencia y el uso de dispositivos móviles y/o electrónicos. La simple tenencia de dichos dispositivos así como de apuntes, libros, carpetas o materiales diversos no autorizados durante las pruebas de evaluación, supondrá la retirada inmediata del examen, su expulsión del mismo y su calificación como suspenso, comunicándose la incidencia a la Autoridad Académica del Centro para que realice las actuaciones previstas en las Pautas de Actuación en los Supuestos de Plagio, Copia o Fraude en Exámenes o Pruebas de Evaluación, aprobadas por la Comisión Permanente del Consejo de Gobierno de 29 de enero de 2015.

Sources of information
Access to Recommended Bibliography in the Catalog ULE

Basic

Anton. (1994). Elementary linear algebra (7th ed.). John Wiley & Sons Inc.

Anton. (2008). Introducción al álgebra lineal (4a ed.). Limusa.

Arvesú Carballo. (2005). Problemas resueltos de álgebra lineal (Marcellán & J. Sánchez Ruiz, Eds.). Thomson-Paraninfo.

Biggs. (1994). Matemática discreta (Noy, Ed.; 1a ed.). Vicens Vives.

Bujalance (Ed.). (1993). Problemas de matemática discreta. Sanz y Torres.

Bujalance (Ed.). (2005). Elementos de matemática discreta (3a ed.). Sanz y Torres.

Castellet, Llerena, I., Casacuberta, C., & Castellet, M. (2000). Álgebra lineal y geometría. Editorial Reverté.

García Merayo. (2003). Problemas resueltos de matemática discreta (Hernández Peñalver & A. Nevot Luna, Eds.). Thomson.

García Merayo. (2005). Matemática discreta (2a ed.). Thomson-Paraninfo.

Grimaldi. (1998). Matemáticas discreta y combinatoria: una introducción con aplicaciones (1a reimp.). Addison Wesley Longman.

Lipschutz, & Lipson, M. L. (2009). Matemáticas discretas (3a. ed.). McGraw-Hill Interamericana.

Merino González. (2007). Álgebra lineal con métodos elementales (Santos Aláez, Ed.; 1a ed., 2a impresión , p. 400). Thomson.
Complementary

Students will be provided:

  • Summaries of the theoretical contents of each topic.
  • Problem sheets proposed for each topic.

Recommendations


Subjects that it is recommended to have taken before
DIFFERENTIAL AND INGTEGRAL CALCULUS / 00709001
DISCRETE MATHEMATICS / 00709002
 
Other comments
It is recommended to be fluent with the contents related to Linear Algebra taught in High School.