Portale di Ateneo - En.Unibs.it

Borrowed courses

ALGEBRA AND GEOMETRY

INGEGNERIA ELETTRONICA E DELLE TELECOMUNICAZIONI

comune

Other Courses of the Study Programme

Course year: 1

ALGEBRA AND GEOMETRY - 9 credits - Basic
BASIC CHEMISTRY - 6 credits - Basic
COMPUTER SCIENCE
Attendance grouping
12 credits - Raggruppamento di frequenza
EXPERIMENTAL PHYSICS 1 (MECH., TERM.) - 9 credits - Basic
INTRODUCTION TO BASIC MATTERS - MATHEMATICS - Student's own choice
MATHEMATICAL ANALYSIS I (SECTION 1) - 9 credits - Basic
PROBABILITY AND STATISTICS - 6 credits - Basic
TEST OF ENGLISH - 3 credits - Language/Final Examination
TEST OF FRENCH - 3 credits - Language/Final Examination
TEST OF GERMAN - 3 credits - Language/Final Examination
TEST OF SPANISH - 3 credits - Language/Final Examination

Course year: 2

ADVANCED PROGRAMMING JAVA, C - 9 credits - Characterising
APPLIED ECONOMICS IN ENGINEERING - 6 credits - Related/Supplementary
COMMUNICATION NETWORKS
Attendance grouping
9 credits - Raggruppamento di frequenza
COMPUTER ORGANIZATION AND DESIGN - 6 credits - Characterising
ELECTRICAL CIRCUITS FOR ELECTRONICS - 6 credits - Related/Supplementary
EXPERIMENTAL PHYSICS 1 (ELECTROMAG, OPTICS) - 6 credits - Basic
FUNDAMENTALS OF SYSTEMS AND CONTROL - 9 credits - Characterising
MATHEMATICAL ANALYSIS AND OPERATIONS RESEARCH
Attendance grouping
12 credits - Raggruppamento di frequenza

Course year: 3

ALGEBRA FOR CODING THEORY AND CRYPTOGRAPHY - 6 credits - Student's own choice
CELLULAR NETWORKS AND 5G
Attendance grouping
6 credits - Raggruppamento di frequenza
DEVICES FOR TELECOMMUNICATIONS - 6 credits - Student's own choice
DIGITAL CONTROL SYSTEMS - 6 credits - Student's own choice
FINAL THESIS - 3 credits - Language/Final Examination
FUNDAMENTALS OF SIGNALS AND SYSTEMS - 6 credits - Characterising
GENERAL ELECTRONICS
Attendance grouping
9 credits - Raggruppamento di frequenza
LEGISLATION AND REGULATION FOR TELECOMMUNICATIONS - 6 credits - Characterising
OPERATING SYSTEMS AND COMPUTING INFRASTRUCTURES
Attendance grouping
12 credits - Raggruppamento di frequenza
PRINCIPLES OF BIOLOGY AND BIOMEDICINE
Attendance grouping
6 credits - Raggruppamento di frequenza - Student's own choice
PROGRAMMING LANGUAGES & INTRODUCTION TO DATABASES
Attendance grouping
12 credits - Raggruppamento di frequenza
SIGNALS AND SYSTEMS - 9 credits - Student's own choice
SOFTWARE ENGINEERING - 9 credits - Characterising
STAGE - 12 credits - Student's own choice
SYSTEMS FOR INDUSTRY AND PLC - 6 credits - Student's own choice
TECHNOLOGIES OF ARTIFICIAL LANGUAGES - 6 credits - Student's own choice
UNCERTAIN DYNAMICAL SYSTEMS - 6 credits - Student's own choice

ALGEBRA AND GEOMETRY

Alphabetic division AL-MZ

Course Sheet

Course code:

A000017

Academic Year of enrolment:

2019/2020

Academic Year of provision:

2019/2020

Divisions:

M-Z

Type of Course:

Basic

Degree:

Bachelor's Degree Programme in COMPUTER SCIENCE AND ENGINEERING

Disciplinary Sector:

GEOMETRY

Is part of:

ALGEBRA AND GEOMETRY

Grouping type:

Credits:

Programme Year:

Professor and Collaborators:

PELLEGRINI Silvia Professor

PAPARINI SILVIA Collaborator

PICCINELLI ANTONIO Collaborator

Cycle:

First semester

Hours of classroom activity:

108

Hours of individual study:

117

This course is in the first semester of the first year; as such there are no other university courses which can be considered as its prerequisites. However it is taken for granted that the students should be familiar from their previous education at least the following topics: polynomials in one indeterminate and their factoring, naive set theory, equations and inequalities of degrees 1 or 2 in one indeterminate, trigonometric functions; basic arithmetic. Notions of definition, theorem, proof and also proof by induction and proof by contradiction.

Educational Goals

The aim of this course is to introduce the students to linear algebra and its applications and basic geometry in dimension 2 and 3. Linear algebra is a foundational topic for many engineering applications (ranging from signal analysis, error correction, cryptography, modelling and algorithm theory, etc) and the students, upon completing the course, are supposed to have an insight on its language, its theory and its methods.
More in detail, the first part of the course shall be about vector spaces over commutative fields and their applications, with special regard to the resolution of linear systems and the diagonalization of matrices. Also, quadratic forms and scalar products shall be introduced. In the second part of the course, the theory previously developed shall be applied to the construction and study of affine and projective geometries in dimension 2 and 3. Conics and quadrics shall also be presented.

Content

Linear Algebra; Vector Spaces; Linear Systems; Morphisms of Vector spaces; diagonalization; euclidean vector spaces.
Affine and projective geometry in dimension 2 and 3; algebraic curves and conics; quadrics.

Extended Syllabus

1. Naive set theory; functions and relations; groups, rings and fields
2. Vector spaces: linear dependency; generating systems; Steinitz's lemma; bases and dimension; subspaces; sum and intersection; Grassmann's formula.
3. Matrix algebra; row/column product; rank and determinant; eigenvalues and eigenvectors; diagonalization.
4. Bilinear and quadratic forms: norms and scalar products; Gram-Schmidt orthonormalization algorithm; orthogonal matrices and real symmetric matrices; the spectral theorem.
5. Affine and euclidean geometry in dimension 2 and 3; lines, planes, circles and spheres.
6. Projective geometry and complexified geometries.
7. Conics and polarities in dimension 2.
8. Quadrics in dimension 3.

Recommended Bibliography

1) S. Pellegrini, Algebra Lineare e Geometria Analitica, Ed. Apollonio - Brescia (2018)
2) S. Pellegrini, Esercizi di Algebra Lineare e Geometria Analitica, Ed. Apollonio - Brescia. (2018)

Teaching Methods

Traditional lectures in the classroom with exercise classes; tutoring for small groups of students will be also organized.

The content of the lectures SHALL NOT be published online.

Assessment Methods

Written exam with exercises followed (when successful) by an oral exam on the theory. During the written part of the exam it is possible for the students to bring and use the textbook.

The written part of the exam is considered successful if its score is at least 18/30. It is up to the lecturer to lower this minimum score, at his discretion.

The oral part is about the theory developed during the classes, but it requires also to be able to carry on some computations. It begins with a topic chosen by the student. In any case sufficient knowledge of both Algebra and Geometry is required in order to pass the exam.

The final score will be determined by the oral part of the exam.

Assessment:

Final Mark

Programme of Educational Activities

Start date of teaching period:

Monday, September 16, 2019

End date of teaching period:

Friday, December 20, 2019