# Università degli Studi di Napoli "Parthenope"  ## Teaching schedule

2017/2018
Belonging course:
Course of Bachelor's Degree Programme on COMPUTER, BIOMEDICAL AND TELECOMMUNICATION ENGINEERING
Location:
Napoli
Disciplinary sector:
GEOMETRY (MAT/03)
Credits:
6
Year of study:
1
Teachers:
DE MARI Fausto
Cycle:
First Semester
Hours of front activity:
60

### Course description

Knowledge and comprehension of the main analitic algebra and analitic geometry topics.
Capability to solve linear algebra and linear geometry exercises studied during the course.
Ability to find a solution: solve in a critical way exercises using a quick method giving logical and theorical reasons for the results.
Communicative abilities: ability summurise and to talk clearly about the topics studied.
Ability to learn: Be able to integrate the topics presented with extra resources books in order to further widen their knowledge.

### Prerequisites

Elementary Algebra. Elements of Euclidean geometry. Elements of analytic geometry in the plane. First elements of mathematical logic : concepts , theorem , demonstration , role of examples and counterexamples.

### Syllabus

ons, applications, algebraic structures: group ring field. Field of complex numbers definition- Algebraic shape of a complex number. The complex plane. trigonometric form of a complex number. Operations with complex numbers. Notes on the theory of polynomials on complex field. Fundamental theorem of algebra (1 ECTS) Linear Algebra Vectors Matrices- Linear Systems. Vector spaces on R. Internal and external operations. Subspaces. Subspaces generated by a sequences of vectors. Linear dependence and independence-independent systems - Basis and dimension of a vector space. Changes reference- (1 ECTS) Matrices Determinant of a square matrix and its property- Rank of a matrix- Invertible Matrices. Cramer's rule for solving linear systems, linear representation of subspaces of R^n by using linear systems. (1 ECTS) Liner maps, definition and first properties. Kernel and Immage of a liner map.
Isomorphisms between vector spaces. Matrices and linear applications. Endomorphisms and isomorphisms- Diagonalization of endomorphisms and matrices- definitions and properties - characterizations of endomorphisms and diagonalization matrices - Isomorphism and coordinated representation of subspaces of a vector space by any linear systems in a given frame. (1 ECTS) Analytic geometry in the plane and space Linear dependence in the plane and in the space of geometric vector. Inner product standard- Orthogonal frames. Cartesian orthogonal monometric frame in spaces- Changes of frames. Representation of the line in the space- Direction cosines of a directed line. intersection of two lines and parallelism conditions. Orthogonality between lines. Midpoint and axis of a segment. (1 ECTS) Monometric frame in Cartesian space-Changes of frames- Vector product in the space of geometric vectors. Representation of line-parallelism and orthogonality between planes- Representation of the line in space-Directions a line - Pencil of planes- parallelism and othogonality between lines. Orthogonality and parallelism between lines and planes. Midpoint

### Textbooks

[ 1] P. Biondi , P.M. Lo Re ?Appunti di Geometria- E.DI.SU  Seymour Lipschutz , Marc Lipson Algebra Lineare McGraw-Hill-Collana Shaums  A. Alvino, G. Trombetti Elementi di Matematica I- Liguori editore- pag. 192-208  S. Pellegrini, A. Benini, F. Morini Alebra Lineare -esercizi  Nicola Melone Introduzione ai metodi di algebra lineare-CedamDerek J. S. Robinson,A Course in LINEAR ALGEBRA with Applications-World Scientific(2006). K. W. Gruenberg
A.J. Weir, Linear Geometry -Springer- Verlgar New York

### Learning assessment

Written verification and oral examination.