# Matematica | GEOMETRY I / II GEOMETRY

## Matematica GEOMETRY I / II GEOMETRY

 0512300004 DIPARTIMENTO DI MATEMATICA MATHEMATICS 2013/2014

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2010 ANNUALE
 SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY 1 GEOMETRIA I MAT/03 6 48 LESSONS BASIC COMPULSORY SUBJECTS MAT/03 2 24 EXERCISES BASIC COMPULSORY SUBJECTS 2 GEOMETRIA II MAT/03 6 48 LESSONS BASIC COMPULSORY SUBJECTS MAT/03 2 24 EXERCISES BASIC COMPULSORY SUBJECTS
 GIOVANNI SPARANO21 T LUCA VITAGLIANO21
Objectives
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 ALSO AIMS TO ENABLE STUDENTS TO USE THE RELATED CALCULATION TOOLS. IN PARTICULAR, THE STUDENT WILL LEARN HOW TO OPERATE WITH MATRICES, SOLVING SYSTEMS OF LINEAR EQUATIONS AND DEALING WITH ISSUES RELATED TO VECTOR SPACES, LINEAR APPLICATIONS, AFFINE AND EUCLIDEAN SPACES PARTICULARLY IN DIMENSION TWO AND THREE.

COMMUNICATION SKILLS:
THE COURSE WILL IMPROVE THE STUDENT'S ABILITY TO PRESENT IN A CLEAR AND RIGOROUS WAY THE ACQUIRED KNOWLEDGE.

MAKING JUDGEMENTS:
THE STUDENTS ARE GUIDED TO LEARN IN A CRITICAL AND RESPONSIBLE WAY EVERYTHING THAT IS EXPLAINED TO THEM AND ENRICH THEIR JUDGMENT THROUGH THE STUDY OF THE SUGGESTED TEACHING MATERIAL.

LEARNING SKILLS:
THE COURSE WILL TEND TO INTRODUCE THE STUDENT, BESIDES THE SPECIFIC TOPICS TREATED, TO THE MATHEMATICAL THINKING AND, AS A CONSEQUENCE, TO DEVELOP THOSE LEARNING SKILLS NECESSARY TO DEAL WITH THE SUBSEQUENT STUDIES.

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
144 HOURS OF LECTURES DIVIDED BETWEEN THEORY 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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