ALGEBRA AND GEOMETRY
Learning outcomes of the course unit
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.
Course contents summary
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.
L.A.Lomonaco, Un'introduzione all'algebra lineare, Aracne editori
S.Lipschutz-M.Lipson, Algebra Lineare, McGraw-Hill.
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.