# Matematica | GEOMETRY I

## Matematica GEOMETRY I

 0512300039 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2020/2021

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

 GIOVANNI SPARANO T LUCA VITAGLIANO
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

Teaching Methods
THE COURSE CONSISTS IN 64 FRONT TEACHING HOURS, DIVIDED INTO 50 HOURS OF THEORETICAL LECTURES AND 14 HOURS OF EXERCISES. DURING THE LECTURES WE WILL DISCUSS THEORETIC TOPICS, TOGETHER WITH CONCRETE PROBLEMS TO BE SOLVED BY THE STUDENTS UNDER THE INSTRUCTOR GUIDANCE, DURING THE EXERCISE SESSIONS
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 LINEAR ALGEBRA, VECTOR SPACES, LINEAR APPLICATIONS, DUAL SPACES AND BILINEAR FORMS.THE ORAL EXAM EVALUATES THE ACQUIRED KNOWLEDGE OF THE THEORY OF LINEAR ALGEBRA, VECTOR SPACES, LINEAR APPLICATIONS, DUAL SPACES AND BILINEAR FORMS.
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.
M. MANETTI, ALGEBRA LINEARE PER MATEMATICI.
S. LIPSCHUTZ, ALGEBRA LINEARE MCGRAW-HILL.
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