Faculty of Mathematics and Computer Science

The geometry of the complex plane |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

Teaching Staff in Charge |

Prof. SALAGEAN Grigore Stefan, Ph.D., salagean@math.ubbcluj.ro |

Aims |

It points out some relations between Complex Analysis and Geometry; some methods of Complex Analysis are used to solve geometric problems. The cours is for the students which want to find interesting problems, some of them of low level (high school level) and which in the same time want to appropriate some special new chapters of mathematics, in order to skill for research. |

Content |

Some relations between Complex Analysis and Geometry are pointed out and some methods of Complex Analysis are used to solve geometric problems
The principal chapters are: - The use of complex numbers in geometry; - Analitical complex geometry; - Important complex mappings; - Lobatchevsky's geometry; - Riemann surfaces |

References |

1. P. Hamburg, P. Mocanu, N. Negoescu, Analiza matematica (Functii complexe), E.D.P. Bucuresti, 1982.
2. O. Mayer, Teoria functiilor de o variabila complexa, vol.I, Ed. Acad. Romane, 1981. 3. O. Mayer, Probleme speciale de teoria functiilor de o variabila complexa, Ed. Acad. Romane, Bucuresti, 1990. 4. D.V. Ionescu, Complemente de matematici pentru licee, E.D.P., Bucuresti, 1978. 5. N. Mihaileanu, Utilizarea numerelor complexe in geometrie. Ed. Tehnica, Bucuresti, 1968. 6. N. Mihaileanu, Geometrie neeuclidiana, Ed. Acad., 1954. 7. G. Salagean, Geometria planului complex, Ed. ProMedia Plus, Cluj-Napoca, 1997. 8. S. Stoilow, Teoria functiilor de o variabila complexa, Ed. Acad. Romane, Bucuresti, 1954. |

Assessment |

Exam. |