# Matematica | GEOMETRY I / II GEOMETRY

## Matematica GEOMETRY I / II GEOMETRY

 0512300004 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2016/2017

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2016 ANNUALE
 SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY 1 GEOMETRIA II MAT/03 8 64 LESSONS BASIC COMPULSORY SUBJECTS 2 GEOMETRIA I MAT/03 8 64 LESSONS BASIC COMPULSORY SUBJECTS
 GIOVANNI SPARANO12 T LUCA VITAGLIANO12
Objectives
THE AIM OF THIS COURSE IS TO INTRODUCE THE STUDENTS TO THE THEORY OF VECTOR SPACES AND TO THE THEORY OF AFFINE AND EUCLIDEAN GEOMETRY

EXPECTED LEARNING RESULTS

KNOWLEDGE AND UNDERSTANDING:

THE COURSE AIMS TO PROVIDE THE FUNDAMENTAL TOOLS OF LINEAR ALGEBRA WHICH, BESIDES THEIR GENERAL USEFULNESS, ARE ESSENTIAL FOR THE STUDY OF AFFINE GEOMETRY. WITH THE USE OF THESE TOOLS THE STUDENTS WILL BE INTRODUCED TO THE STUDY OF AFFINE AND EUCLIDEAN SPACES, AFFINE AND ISOMETRIC MAPS.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE COURSE FURTHER AIMS TO ENABLE STUDENTS TO USE THE RELATED CALCULATION TOOLS. IN PARTICULAR, THE STUDENT WILL KNOW HOW TO OPERATE WITH MATRICES, SOLVING SYSTEMS OF LINEAR EQUATIONS AND DEALING WITH ISSUES RELATED TO VECTOR SPACES, LINEAR APPLICATIONS AND THEIR PHYSICAL APPLICATIONS.

Prerequisites
IT IS REQUIRED A KNOWLEDGE OF THE BASIC TOPICS IN MATHEMATICS, COVERED IN HIGH SCHOOL.
Contents
1. VECTOR SPACES

2. MATRICES, DETERMINANTS AND SYSTEMS OF LINEAR EQUATIONS

3. LINEAR MAPS

4. LINEAR AND BILINEAR FORMS

5. EUCLIDEAN VECTOR SPACES

6. THE PROBLEM OF DIAGONALIZATION

7. HERMITIAN FORMS

8. AFFINE AND EUCLIDEAN AFFINE SPACES
Teaching Methods
128 HOURS OF LECTURES DIVIDED BETWEEN THEORETICAL LESSONS AND EXERCISES
Verification of learning
THE MONITORING AND EVALUATION OF THE LEVEL OF LEARNING BY THE STUDENT WILL OCCUR THROUGH A FINAL EXAM CONSISTING OF A WRITTEN EXAM FOLLOWED BY AN ORAL EXAMINATION. TO BE ADMITTED TO THE ORAL EXAMINATION, THE STUDENT MUST HAVE OBTAINED A SUFFICIENT EVALUATION FOR THE WRITTEN EXAM. THE EXAM MAY BE REPLACED BY TWO SEPARATE EXAMS DURING THE YEAR.
Texts
R. ESPOSITO, A. RUSSO, LEZIONI DI GEOMETRIA, PARTE PRIMA, LIGUORI.
E. SERNESI, GEOMETRIA 1, BOLLATI BORINGHIERI.
S. LIPSCHUTZ, ALGEBRA LINEARE MCGRAW-HILL.
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