240221 Quadratische Formen (V) (SoSe 2010)
Contents, comment
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Quadratische Formen sind Polynome in mehreren Variablen, wobei in jedem Term die Summe der Exponenten dieser Variablen gleich 2 ist. Sie treten in vielen Teilgebieten der Mathematik und ihrer Anwendungen auf. Die Vorlesung wird sich mit folgenden Themen beschäftigen:
- Diagonalisierung quadratischer Formen
- Gram-Schmidt-Orthogonalisierung
- Kurven und Flächen zweiter Ordnung
- Hessesche Formen
- Signatur quadratischer Formen
- Witt-Index quadratischer Formen
- Reduktion ganzzahliger quadratischer Formen
- Minkowskiraum und spezielle Relativitätstheorie
Requirements for participation, required level
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Kenntnisse in linearer Algebra sind hilfreich, aber nicht erforderlich.
Bibliography
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- A. Beutelspacher: Lineare Algebra. Vieweg-Verlag 1995/2001.
- K. Harbarth: Differentialrechnung für Funktionen mit mehreren Variablen. Verlag H. Deutsch 1978
- D. Buell, Binary quadratic forms. Springer-Verlag 1989.
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Subject assignments
| Degree programme/academic programme | Validity | Variant | Subdivision | Status | Semester | LP | |
|---|---|---|---|---|---|---|---|
| Mathematik / Bachelor | (Enrollment until SoSe 2007) | Kernfach | M.D.09K | Wahlpflicht | 4. 5. 6. | 8 | benotet |
| Mathematik / Bachelor | (Enrollment until SoSe 2007) | Nebenfach | M.D.05N | Wahlpflicht | 4. 5. 6. | 8 | benotet |
| Mathematik / Bachelor | (Enrollment until SoSe 2011) | Nebenfach | MD07N | Wahlpflicht | 8 | benotet | |
| Mathematik / Bachelor | (Enrollment until SoSe 2011) | Kernfach | MD09 | Wahlpflicht | 8 | benotet | |
| Mathematik (GHR) / Master of Education | (Enrollment until SoSe 2014) | M.D.09b | Wahlpflicht | 1. 2. | 8 | benotet | |
| Mathematik (GHR/SP) / Master of Education | (Enrollment until SoSe 2014) | M.D.09b | Wahlpflicht | 2. 3. | 8 | benotet |
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- Friday, December 11, 2015
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- Tuesday, June 1, 2010
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- Tuesday, June 1, 2010
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- lecture (V) / 4
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- Faculty of Mathematics
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- ECTS points
- 8
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