Lehrende/r: Jun. Prof. Dr. Ariyan Javan Peykar
Veranstaltungsart: Hauptseminar
Anzeige im Stundenplan: ZTH-001
Semesterwochenstunden: 2
Credits: 4,0
Unterrichtssprache: Deutsch
Min. | Max. Teilnehmerzahl: - | -
Voraussetzungen / Organisatorisches: Die Anmeldung erfolgt nicht über Jostustine, sondern wird Anfang des Sommersemesters durch das Studienbüro vorgenommen.
Inhalt: A complex number x is an algebraic number if there is a non-constant polynomial f with rational coefficients such that f(x) =0. A non-algebraic complex number is called a transcendental number. One of the first things we will prove in this seminar is the classical theorem of Lindemann-Weierstrass. This beautiful theorem implies the transcendence of pi, exp(1), and many more real numbers appearing in "nature". We also investigate the finiteness (or non-finiteness) or certain Diophantine equations. This naturally leads to studying the unit equation, but also approximation theorems due to Roth and Schmidt.
