Luca VITAGLIANO | GEOMETRY I / II GEOMETRY
Luca VITAGLIANO GEOMETRY I / II GEOMETRY
cod. 0512300004
GEOMETRY I / II GEOMETRY
| 0512300004 | |
| DIPARTIMENTO DI MATEMATICA | |
| EQF6 | |
| MATHEMATICS | |
| 2017/2018 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2016 | |
| ANNUALE |
| SSD | CFU | HOURS | ACTIVITY | ||
|---|---|---|---|---|---|
| GEOMETRIA II | |||||
| MAT/03 | 8 | 64 | LESSONS | ||
| GEOMETRIA I | |||||
| MAT/03 | 8 | 64 | LESSONS | ||
| 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 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 AND THE THEORY OF AFFINE SPACES. 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. TWO PARTIAL TESTS WILL BE HELD DURING THE COURSE RESPECTIVELY AFTER HALF OF THE LESSONS AND AT THE END OF THE PERIOD. PASSING THESE TESTS WILL EXONERATE FROM THE RELATIVE WRITTEN AND ORAL EXAMS. THE EXEMTION WILL LAST UNTIL SEPTEMBER. THE FINAL VOTE WILL BE THE AVERAGE OF THE TWO PARTIAL VOTES |
| 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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