Laurea in Matematica Applicata
Geometry (2010/2011)
| Course code |
4S00247 |
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Teacher
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Mauro Spera
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Coordinator
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Mauro Spera
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training credits
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6
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| Disciplinary sector |
MAT/03 - GEOMETRY
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| Teaching language |
Italian |
| Period |
II semestre dal Mar 1, 2011 al Jun 15, 2011.
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| Links |
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Lecture timetable
Educational objectives
Learning objectives
The course introduces and elaborates the fundamental ideas of general topology and of the differential geometry of curve and surfaces, in a rigorous yet concrete and
example-based manner, so as to further develop the students' geometric intuition,
abstraction and analytical computing ability, also in view of applications to parallel and successive courses.
Syllabus
*Programme
Topological spaces, continuous functions, omeomorphisms.
Compactness. Connectedness.
Plane and spatial curves: curvature, torsion, Fre'net's formulae. Fundamental theorem.
Regular parametric surfaces. First and second fundamental form.
Gaussian and mean curvature.
Gauss' Theorema Egregium. Covariant derivative, parallel transport.
Geodesics. The Gauss-Bonnet theorem.
Examples: quadrics, surfaces of revolution, ruled and minimal surfaces.
Projective, affine and metric classification of quadrics.
Exam methods
Assessment
Written test, followed by an oral exam.
| Statistics |
| Outcomes Exams |
Outcomes Percentages |
Average |
Standard Deviation |
| Passed |
49.12%
|
25
|
4
|
| Failed |
10.52%
|
|
| Absent |
36.84%
|
| Withdrawn |
3.50%
|
| Canceled |
--
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| Distribuzione degli esiti positivi |
| 18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
30 e Lode |
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7.1%
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7.1%
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0.0%
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14.2%
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3.5%
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3.5%
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7.1%
|
10.7%
|
7.1%
|
3.5%
|
3.5%
|
0.0%
|
10.7%
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21.4%
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Data from AA 2010/2011 based on 57 students. I valori in percentuale sono arrotondati al numero intero più vicino.
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