# Matematica | GEOMETRY II

## Matematica GEOMETRY II

 0512300040 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2022/2023

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2018 SPRING SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/03 8 64 LESSONS BASIC COMPULSORY SUBJECTS

 GIOVANNI SPARANO T
ExamDate
GEOMETRIA II17/04/2023 - 14:00
Objectives
THE AIM OF THIS COURSE IS TO INTRODUCE THE STUDENTS TO THE THEORY OF EUCLIDEAN VECTOR SPACES AND TO THE THEORY OF AFFINE AND EUCLIDEAN GEOMETRY.

EXPECTED LEARNING RESULTS

KNOWLEDGE AND UNDERSTANDING:

THE COURSE AIMS TO PROVIDE THE STUDENTS WITH A SOLID BASIC KNOWLEDGE OF EUCLIDEAN VECTOR SPACES, AFFINE SPACES AND AFFINE AND ISOMETRIC MAPS.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE COURSE FURTHER AIMS TO ENABLE STUDENTS TO SOLVE PROBLEMS CONCERNING EUCLIDEAN VECTOR SPACES AND AFFINE SPACES, PARTICULARLY IN DIMENSION 2 AND 3.

Prerequisites
IT IS REQUIRED A KNOWLEDGE OF THE TOPICS COVERED IN THE COURSE GEOMETRY I
Contents
1. BILINEAR FORMS

2. EUCLIDEAN VECTOR SPACES

3. DIAGONALIZATION OF ENDOMORPHISMS ON EUCLIDEAN VECTOR SPACES

4. HERMITIAN FORMS

5. AFFINE AND EUCLIDEAN AFFINE SPACES
Teaching Methods
64 HOURS OF LECTURES DIVIDED BETWEEN THEORETICAL LESSONS AND EXERCISES.
Verification of learning
THE EXAM IS AIMED TO ASSES KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED IN CLASS AND THE ABILITY TO APPLY SUCH KNOWLEDGE TO THE SOLUTION OF SIMPLE PROBLEMS.
THE TEST IS DIVIDED INTO A SELECTIVE WRITTEN EXAM AND AN ORAL EXAM. THE WRITTEN EXAM CONSISTS OF TWO EXERCISES FINALIZED TO VERIFY THE STUDENT ABILITY TO APPLY THE METHODOLOGIES RELATIVE TO EUCLIDEAN VECTOR SPACES, DIAGONALIZZATION OF ENDOMORPHISMS AND AFFINE GEOMETRY. THE ORAL EXAM EVALUATES THE ACQUIRED KNOWLEDGE OF THE THEORY OF EUCLIDEAN VECTOR SPACES, THE DIAGONALIZZATION OF ENDOMORPHISMS AND THE THEORY OF AFFINE SPACES.
THE FINAL EVALUATION IS EXPRESSED WITH A VOTE FROM 0 TO 30. THE WRITTEN EXAM IF PASSED GIVES ACCESS TO THE ORAL EXAM WHICH FULLY DETERMINES THE FINAL MARK. THE MINIMUM MARK FOR THE ORAL EXAM REQUIRES KNOWLEDGE OF THE FUNDAMENTAL CONCEPTS OF THE TOPICS MENTIONED ABOVE. THE MAXIMUM MARK IS OBTAINED WHEN THE STUDENT SHOWS MASTERY IN THE DISCUSSION OF SUCH TOPICS.
Texts
R. ESPOSITO, A. RUSSO, LEZIONI DI GEOMETRIA, PARTE PRIMA, LIGUORI.
E. SERNESI, GEOMETRIA 1, BOLLATI BORINGHIERI.
S. LIPSCHUTZ, ALGEBRA LINEARE MCGRAW-HILL.