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.
Prerequisites
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.
Full programme
Algebraic structures;linear congruences, Euler Theorem;
Vector Spaces and Subspaces, Linear Independence, Basis and Dimension, Change of Basis . Linear Transformations; the Kernel and Range of a Linear Transformation ; Matrices, Determinants, and the matrix of a Linear Trasformation; Systems of Linear Equations, Eigenvalues and Eigenvectors ; Orthogonality, The Gram-Schmidt Process, Orthogonal Diagonalization of Symmetric Matrices. Geometry of plane and space, Conics.
Bibliography
L.A.Lomonaco, Un'introduzione all'algebra lineare, Aracne editori
S.Lipschutz-M.Lipson, Algebra Lineare, McGraw-Hill.
Teaching methods
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Assessment methods and criteria
written test, and oral test.
Other information
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