# ALGEBRA AND GEOMETRY cod. 18728

1° year of course - Second semester
Professor
Geometria (MAT/03)
Field
Formazione matematico-fisica
Type of training activity
Basic
72 hours
of face-to-face activities
9 credits
hub: PARMA
course unit
in - - -

## Learning objectives

Linear Algebra is an entry point into mathematics; it has links with many branches of mathematics: abstract algebra, discrete mathematics, diggerential equations, geometry, numerical methods.
I hope that students can apreciate the beauty, power and utility of linera algebra.

no

## Course unit content

Elementary concepts of
logic, set theory.
Relations, functions. Semigroups, groups, rings, fields, linear congruences; Euler's function,Piccolo Teorema di Fermat; Ring of polynomials over field:
Vector Spaces and Subspaces, Linear Indipendence, Basis and Dimension; Change of basis; Matrix Algebra,Linear Transformations: The Kernel and Range of a Linear Transformation, The Matrix of a Linear Transformation.Linear Systems and metods for solving these; Eigenvalues and Eigenvectors.
Euclidean Spaces; Orthogonality,Orthogonal Complement and Ortogonal Projection; the Gram-Schmidt Process.
Affine euclidean Spaces; conics.

- - -

## Bibliography

L.A.Lomonaco, Un'introduzione all'algebra lineare, Aracne editori

S.Lipschutz-M.Lipson, Algebra Lineare, McGraw-Hill.

## Teaching methods

Privileged education mode is the frontal lesson that offered arguments from a formal point of view, accompanied by significant examples, applications and exercises.

## Assessment methods and criteria

Verification of learning takes place through a written test and an oral. In the written examination through the exercises proposed by the student must demonstrate that they possess the basica knowledge of linear algebra and analytical geometry. In the oral examination the student must be able to conduct its own demonstraions relating to the themes of the course using an appropriate language and mathematical formalism.

- - -