
Course unit
GEOMETRY 1
SC01122868, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/03 
Geometry 
14.0 
Course unit organization
Period 
Annual 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
6.0 
60 
90.0 
No turn 
Lecture 
8.0 
64 
136.0 
No turn 
Prerequisites:

None 
Target skills and knowledge:

Fundamental notions of linear algebra and their applications to geometry, with particular attention to the study of vector spaces and linear functions.
Solving linear systems, application of determinants and determination of the Jordan form for the matrix of an endomorphism.
Linear subvarieties and their properties in affine and euclidean spaces.
Volume of simplices in euclidean space.
Spectral theorem (for symmetric and normal operators) and its applications.
Euler' classification of isometries in the plane and in tridimensional space. 
Examination methods:

Written test consisting in resolution of exercises and easy problems, followed by an oral assessment. 
Course unit contents:

Introduction to linear algebra and its applications to the geometry of finite dimensional affine and euclidean spaces. 
Textbooks (and optional supplementary readings) 

Bertapelle A, Candilera M, Algebra lineare e primi elementi di Geometria. Milano: McGrawHill, 2011.

Kostrikin A I, Manin Yu I, Linear Algebra and Geometry. Moscow, London, New York: Gordon and Breach, 1989.

Hoffmann K, Kunze R, Linear Algebra (2nd Edition). : Prentice Hall, 1971. (la parte di Geometria รจ carente)


