00470 - Geometry

Course contents

Algebraic structures: groups, rings, fields. Matrices: matrices; operations; determinant; inverse matrix. Vector spaces: vector spaces; subspaces; linear dependence; bases and dimension. Linear maps: linearity; isomorphisms; kernel and range; matrix rank; matrix representation of linear maps; change of basis. Systems of linear equations: systems of linear equations and their solvability; methods of solution; representation of subspaces. Polynomial equations: polynomial equations. Eigenvalues: eigenvalues and eigenspaces; matrix similarity; characteristic polynomial; diagonalizability. Euclidean vector spaces: inner products; orthogonality; orthonormal sets; orthogonal operators; orthogonal complement. Euclidean spaces: affine euclidean spaces; subspaces; representation of subspaces; parallelism; orthogonality. Bilinear and quadratic forms: bilinear forms; matrix representation; symmetric matrices; quadratic forms; canonical forms. Hyperquadrics: hyperquadrics; real conics and quadrics, classification.

Readings/Bibliography

M. R. Casali, C. Gagliardi, L. Grasselli, "Geometria", Progetto Leonardo, ed. Esculapio, Bologna, 2010

Teaching methods

classroom lecture

Assessment methods

A mandatory written test and an oral test. Both tests deal with all the topics covered by the lectures .
The written test consists of two parts: a part about theory consisting of mutiple choice questions, and a part about exercises. For the part about theory it is not allowed to use notes, books, calculators, etc.  Each written test allows to perform just one oral test in the same exam session. 

Teaching tools

informations will be available at the website
http://www.dm.unibo.it/~regonati/rimini.html

Links to further information

http://www.dm.unibo.it/~regonati/rimini.html

Office hours

See the website of Francesco Regonati