28570 - Geometry and Algebra T-A (A-K)

Course contents

Set Theory:

Operations with sets, partitions, applications. Algebraic structures.

Analytic Geometry:

Cartesian coordinates on the line, the plane and 3-space. Geometric loci, equations (cartesian or parametric) of lines and planes in 3-space. Vectors. Plane conics. Planes and lines in 3-space, equations, parallelism, ortogonality.

Linear Algebra:

Vector spaces, linear dependence, generators and bases. Dimension and subspaces.
Linear systems . Matrices - Row reduction - rank of a matrix - Theorem of Rouché-Capelli . Determinant -linear transforms - Base change.
Eigenvalues and eigenvectors - Diagonalizing matrices.
Metric spaces, scalar product- Norm - Orthonormal Bases

Readings/Bibliography

1) P. MAROSCIA: INTRODUZIONE ALLA GEOMETRIA E ALL'ALGEBRA LINEARE ( ZANICHELLI BOLOGNA 2000).

2) Notes of the course.

3) M.Abate, C.de Fabritiis: Esercizi di Geometria ,  McGrow-Hill. (Book of exercises).

(all in Italian)

Assessment methods

The final exam is made of a written test and (if the test is passed) an oral.
The exam is unique for this module and the "Analisi Matematica" one.

Teaching tools

On the web site:

http://elearning.ing.unibo.it/index_s.php

one can find notes of the course (in Italian). Moreover on the web site:

http://www.dm.unibo.it/matematica/

There are pages dedicated to Linear Algebra and Geometry in 3-spaces.

Links to further information

http://www.dm.unibo.it/~gimiglia

Office hours

See the website of Alessandro Gimigliano