Lecturer: Fulvio Bisi  

Course name: Geometry And Algebra
Course code: 500473
Degree course: Ingegneria Industriale
Disciplinary field of science: MAT/03
L'insegnamento costituisce attività di base per: Ingegneria Industriale
University credits: ECTS 6
Course website: n.d.

Specific course objectives

This is a basic course on Linear Algebra and Analytic Geometry. Particular emphasis will be given to topics useful in other disciplines, with a great deal of motivation and many computational examples. A tutoring staff, composed by experienced graduate or undergraduate students, provides an expert help and support for students attending the course.

Course programme

Preliminaries
Polynomials and algebraic equations. Complex numbers and the Fundamental Theorem of Algebra.

Analytic Geometry I
Coordinate systems in 2- and 3-dimensional spaces; straight lines and planes.

Vector spaces
Vector spaces, vectors of R^n, linear subspaces; linear span of a set of vectors; spanning sets and linear independence, basis, coordinates, and dimension.

Matrices
Operations with matrices, determinant and rank of a matrix, inverse of a matrix.

Linear systems
Linear systems, Rouché-Capelli and Cramer theorems, Gauss elimination method, representation of the set of the solutions of a linear system.

Linear mappings
Linear mappings between vector spaces, kernel and image, matrix associated with a linear mapping.

Linear operators
Eigenvalues and eigenvectors of a linear operator, diagonalisation of a linear operator.

Inner product in R^n
Inner product in R^n, orthonormal basis, Gram-Schmidt process. Orthogonal matrices. Real quadratic forms. Spectral theorem: real symmetric matrices and orthogonal diagonalisation.

Analytic Geometry II
Canonical forms of plane conics. Quadric surfaces.

Course entry requirements

The same mathematics prerequisites for enrollment into the Engineering Faculty. In particular: polynomial algebra; equations and inequalities; elementary trigonometry (basic trigonometric functions; basic trigonometric formulae; basic theorems for triangles); plane cartesian coordinates; plane and three-dimensional Euclidean geometry.

Course structure and teaching

Lectures (hours/year in lecture theatre): 30
Practical class (hours/year in lecture theatre): 30
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

F. Bisi, F. Bonsante, S. Brivio. Lezioni di Geometria e Algebra. Edizioni LaDotta - Casalecchio di Reno (BO).

Testing and exams

The final exam consists of a written and an oral test. Both have to be passed within the same session. A minimum grade in the written test will be required to be admitted to the oral test.