Competencies and objectives

 

Course context for academic year 2024-25

El objetivo de la Topología es desarrollar herramientas matemáticas para estudiar la forma de los objetos y también para analizar las nociones de continuidad y proximidad. La Topología permite considerar la forma y la estructura de un objeto con independencia de su tamaño o de las distancias entre sus partes.

La topología es un ejemplo de teoría axiomática que se construye a partir de la definición de espacio topológico: las
definiciones van surgiendo al añadir nuevas propiedades a los espacios con los que se trabaja y los ejemplos
desempeñan un papel fundamental en la comprensión de los conceptos que se van introduciendo. Esta asignatura
debe servir al estudiante para afianzar su capacidad de abstracción.
  
Para una correcta comprensión de la misma el estudiante necesita muchas nociones de otras asignaturas del primer año: Fundamentos matemáticos, Análisis de una variable real I y Análisis de una variable real II. A su vez los contenidos de esta asignatura serán muy útiles para otras asignaturas del Grado: Análisis real de varias variables I , Curvas y superficies, Análisis real de varias variables II, Análisis de variable compleja, Topología avanzada, Teoría global de superficies y Análisis funcional.

 

 

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.
  • 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.
  • CE4 : Know how to abstract the structural properties (of mathematical objects, of observed reality and other contexts) distinguishing them from those that are purely occasional and be able to prove them with demonstrations or refute them with counter-examples, as well as identify errors of incorrect reasoning.
  • 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.

 

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: 25022
Lecturer responsible:
Teruel Carretero, Jose Luis
Credits ECTS: 6,00
Theoretical credits: 1,32
Practical credits: 1,08
Distance-base hours: 3,60

Departments involved

  • Dept: MATHEMATICS
    Area: GEOMETRY AND TOPOLOGY
    Theoretical credits: 1,32
    Practical credits: 1,08
    This Dept. is responsible for the course.
    This Dept. is responsible for the final mark record.

Study programmes where this course is taught