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Affine and Projective Geometry 2012

Actualización curso 2012. Geometría afín, proyectiva y métrica. El espacio y sus transformaciones. Aplicaciones a sistemas de representación. Estudio afín, métrico y proyectivo de cónicas y cuádricas. Determinación y construcción.

Imagen de la asignatura

Mª Eugenia Rosado
Sonia Luisa Rueda

 

Departamento: Matemática Aplicada a la Edificación, al Urbanismo y al Medio Ambiente
Escuela Técnica Superior de Arquitectura

Asignatura: Elementary, 1st Semester.
Grado en Arquitectura

Fecha de la última revisión (octubre 2012).

Jimena Campillo González

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Créditos: ECTS totales 6 (presenciales 3.6).

 

REQUIREMENTS AND PRIOR KNOWLEDGE 

To follow this course properly only an elementary mathematical level of education is needed (highschool level in Spain, or equivalent in other countries). Some material to be highlighted: Elementary theory of discussion and resolution of systems of linear equations.  Basic matrix algebra.

 

GENERAL DESCRIPTION OF THE SUBJECT

This course starts with an introduction to Linear Algebra. These concepts will be used to study the affine euclidean space and its transformations. In particular, we will focus on the study of isometries in the affine plane and space. The third part of the course is an affine and projective study of conics and quadrics.

 

OBJECTIVES: KNOWLEDGE AND SKILLS

General goals:

1. Development of a geometrical way of thinking, both in the qualitative and quantitative sense.

2. To provide a rigurous introduction to Linear Algebra, Affine Geometry and the study of conics and quadrics.

Specific goals:

1. To achieve a Basic knowledge of the euclidean affine space.

2. Classify and determine vector and affine isometries.

3. Work with homogeneous coordinates in the projective space.

4. Classify affine conics and quadrics. Learn how to obtain their more important elements.

 

TEACHING MATERIAL

Class material

Working plan

Vocabulary English/Spanish

 

EVALUATION ACTIVITIES OR PRACTICAL TASKS

Lab assignments and partial exams.

 

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Copyright 2009, Autores y colaboradores. Reconocer autoría/Citar obra. Rosado, M., Rueda, S. L. (2010, March 08). Affine and Projective Geometry 2012. Retrieved July 24, 2017, from OCW UPM - OpenCourseWare de la Universidad Politécnica de Madrid Web site: http://ocw.upm.es/algebra/affine-and-projective-geometry-1. Esta obra se publica bajo una licencia Licencia Creative Commons Licencia Creative Commons