# Università degli Studi di Napoli "Parthenope"

## Teaching schedule

2018/2019
Partition:
Cognomi M-Z
Teaching:
Belonging course:
Course of Bachelor's Degree Programme on MANAGEMENT ENGINEERING
Disciplinary sector:
GEOMETRY (MAT/03)
Credits:
6
Year of study:
1
Teachers:
Cycle:
First Semester

Italian

### Course description

The aim of this course is to learn analitic algebra and analitic geometry topics. A further aim is to apply these techniques in other scientific disciplines. Learning outcomes (declined compared with the Dublin descriptors)
-Knowledge and understanding: Knowledge of analitic algebra and analitic geometry topics. The student will be able to state and prove basic theorems. -Ability to apply knowledge and understanding: The ability to understand the problems proposed during the course, the ability to correctly apply the theoretical knowledge. The student will be able to study of the graphs of elementary functions, to solve integration problems of elementary character, to discuss the nature of numerical sequences and series.
-Making judgments: Develop the ability to critically evaluate the problems and propose the most appropriate approach.
-Communication skills: Ability to report and present the results with a logical-deductive and synthetic exposition
-Ability to learn:Ability to develop outline, summarize the contents.

### 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

-sets, operations applications, algebraic structures: group ring field. (1 ECTS- 8 hours)
- 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-8 hours)

-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-8 hours)

-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-8 hours)

-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-8 hours)
-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
Distance between sets in space - (1CFU-8hours)
- Exercises related to each topic

-sets, operations applications, algebraic structures: group ring field. (1 ECTS- 8 hours)
- 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-8 hours)

-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-8 hours)

-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-8 hours)

-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-8 hours)
-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
Distance between sets in space - (1CFU-8hours)
- Exercises related to each topic

### 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]Derek J. S. Robinson,A Course in LINEAR ALGEBRA with Applications-World Scientific(2006).
[2] K. W. Gruenberg
A.J. Weir, Linear Geometry -Springer- Verlgar New York
spazio

### 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

You can find me on monday from 11 to 12 :30 .For any question or for student reception you can send an email to the address :roberta.digennaro@uniparthenope.it
Lectures are in Italian. The professor is fluent in English and is available to interact with students in English, also during the examination.

## Mutuazioni

• Study course INGEGNERIA INFORMATICA, BIOMEDICA E DELLE TELECOMUNICAZIONI - Training course in PERCORSO GENERICO
• Study course INGEGNERIA CIVILE E AMBIENTALE PER LA MITIGAZIONE DEI RISCHI - Training course in PERCORSO GENERICO