Competencies and objectives

 

Course context for academic year 2024-25

Esta asignatura es de carácter optativo y se ubica en el módulo Avanzado y dentro de él en la materia “Matemáticas Generales”. Dicha materia incluye además las asignaturas: “Teoría de la Medida”, “Teoría de Grupos” y “Topología Algebraica”.

Aunque el estudio sistemático de los conjuntos convexos se inició a finales del siglo XIX, es a mediados del siglo XX cuando la convexidad es reconocida como una rama bien establecida de las matemáticas. De hecho, el estudio de los conjuntos convexos y de los problemas geométricos relacionados ocupa el lugar 52 en la relación de 97 grandes temas de que se compone la clasificación conjunta de las bases de datos del Mathematical Reviews y del Zentralblatt für Mathematik (MSC Subject Classification 2010). La convexidad utiliza herramientas conceptuales de la geometría, del análisis, del álgebra lineal y de la topología, y juega un papel relevante en optimización, en la teoría de juegos, en la teoría de números, en la teoría de desigualdades y en la geometría combinatoria. El alumno tomó contacto con los poliedros convexos en Programación Lineal (4º semestre) y con las funciones convexas en Optimización I (5º semestre).

La asignatura de Análisis Convexo está centrada en el estudio de los conjuntos convexos generales y de las funciones convexas extendidas y de sus aplicaciones en optimización convexa.

 

 

 

Course content (verified by ANECA in official undergraduate and Master’s degrees) for academic year 2024-25

Specific Competences (CE)

  • CE1 : Understand and use mathematical language. Acquire the capacity to enunciate propositions in different fields of Mathematics, to construct demonstrations and transmit the mathematical knowledge acquired.
  • CE10 : Communicate, both orally and in writing, mathematical knowledge, procedures, results and ideas.
  • CE14 : Solve qualitative and quantitative problems using previously developed models.
  • CE2 : Understand rigorous demonstrations of certain classical theorems in different fields of Mathematics.
  • CE3 : Assimilate the definition of a new mathematical object in terms of others already known and be able to use said object in different contexts.
  • CE5 : Propose, analyse, validate and interpret models of simple real-life situations, using the most appropriate mathematical tools for the purpose.
  • CE6 : Solve mathematical problems using basic calculus skills and other techniques, planning their resolution according to the tools available and any time and resource restriction.
  • CE8 : Develop programmes that solve mathematical problems using the appropriate computational environment for each particular case.
  • CE9 : Use bibliographic search tools for Mathematics.

 

Specific Generic UA Competences

  • CGUA1 : Understand scientific English.
  • CGUA2 : Possess computer skills relevant to the field of study.
  • CGUA3 : Acquire or possess basic Information and Communications Technology skills and correctly manage the information gathered.

 

Generic Degree Course Competences

  • CG1 : Develop the capacity for analysis, synthesis and critical reasoning.
  • CG2 : Show the capacity for effective and efficient management/direction: entrepreneurial spirit, initiative, creativity, organisation, planning, control, decision making and negotiation.
  • CG3 : Solve problems effectively.
  • CG4 : Show capacity for teamwork.
  • CG5 : Commitment to ethics, the values of equality and social responsibility as a citizen and professional.
  • CG6 : Self-learning.
  • CG7 : Show the capacity to adapt to new situations.
  • CG9 : Show the ability to transmit information, ideas, problems and solutions to both specialist and non-specialist audiences.

 

 

 

Learning outcomes (Training objectives)

No data

 

 

Specific objectives stated by the academic staff for academic year 2024-25

No data

 

 

General

Code: 25051
Lecturer responsible:
ARAGON ARTACHO, FRANCISCO JAVIER
Credits ECTS: 6,00
Theoretical credits: 1,80
Practical credits: 0,60
Distance-base hours: 3,60

Departments involved

  • Dept: MATHEMATICS
    Area: STATISTICS AND OPERATIONS RESEARCH
    Theoretical credits: 1,8
    Practical credits: 0,6
    This Dept. is responsible for the course.
    This Dept. is responsible for the final mark record.

Study programmes where this course is taught