# Università degli Studi di Napoli "Parthenope"

## Teaching schedule

2017/2018
Belonging course:
Course of Bachelor's Degree Programme on MANAGEMENT ENGINEERING
Location:
Napoli
Disciplinary sector:
GEOMETRY (MAT/03)
Credits:
6
Year of study:
1
Teachers:
Cycle:
First Semester
Hours of front activity:
48

italian

### 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. (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

Linear algebra Vector spaces on R. Matrices Determinant of a square matrix and its property- Rank of a matrix- Invertible Matrices. Cramer's rule for solving linear systems, Liner maps. Matrices and linear applications. Endomorphisms and isomorphisms- Diagonalization of endomorphisms and matrices- Analytic geometry in the plane and space . Inner product standard- Vector product in the space of geometric vectors.

ons, applications, algebraic structures: group ring field. (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

### Teaching Methods

All the lectures contain both theory and exercises in order to solve
exercises with the correct theoretical background and not just
as a routine.
Big deal is given to the strong connection between theory and exercises.

### Textbooks

[ 1] P. Biondi , P.M. Lo Re -Appunti di Geometria- E.DI.SU [2] Seymour Lipschutz , Marc Lipson Algebra Lineare McGraw-Hill-Collana Shaums [3] A. Alvino, G. Trombetti Elementi di Matematica I- Liguori editore- pag. 192-208 [4] S. Pellegrini, A. Benini, F. Morini Alebra Lineare -esercizi [5] Nicola Melone Introduzione ai metodi di algebra lineare-Cedam[6]Derek J. S. Robinson,A Course in LINEAR ALGEBRA with Applications-World Scientific(2006).[7] K. W. Gruenberg
A.J. Weir, Linear Geometry -Springer- Verlgar New York

### Learning assessment

The exam in divided into two parts:
A written part, two hours, where the correct use of the theory
in order to solve exercises will be evaluated. Those students that
will be able to solve enough exercises with correct explanations
will procede to the oral part of the exam.
An oral part where the knowledge of the theory and the ability
to connect different arguments will be evaluated.
The final score will take into account both parts of the exams with
more enfasis to the oral part.