# Matematica | GEOMETRY I

## Matematica GEOMETRY I

 0512300039 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2022/2023

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

 CHIARA ESPOSITO T
ExamDate
GEOMETRIA I16/06/2023 - 12:00
GEOMETRIA I05/07/2023 - 12:00
Objectives
THE AIM OF THIS COURSE IS TO INTRODUCE THE STUDENTS TO THE THEORY OF VECTOR SPACES AND LINEAR APPLICATIONS

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.

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 AND LINEAR 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. DIAGONALIZATION
Teaching Methods
64 HOURS OF LECTURES DIVIDED BETWEEN THEORETICAL LESSONS AND EXERCISES
Verification of learning
THE EXAM IS AIMED TO EVALUATE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED IN CLASS AND THE ABILITY TO APPLY SUCH KNOWLEDGE TO THE SOLUTION OF SIMPLE PROBLEMS.
THE EXAMINATION IS DIVIDED INTO A SELECTIVE WRITTEN EXAM AND AN ORAL EXAM. THE WRITTEN EXAM CONSISTS OF SOME EXERCISES. THE ORAL EXAM EVALUATES THE ACQUIRED KNOWLEDGE OF LINEAR ALGEBRA, VECTOR SPACES AND LINEAR APPLICATIONS.
THE FINAL EVALUATION IS EXPRESSED BY A VOTE FROM 0 TO 30. THE WRITTEN EXAM IF PASSED GIVES ACCESS TO THE ORAL EXAM WHICH DETERMINES THE FINAL VOTE IN FULL.
Texts
LECTURE NOTES
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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