Logistics

  • Seminar begins: October 18th, 2016.
  • Seminar time: Tuesdays 12:00-14:00
  • Seminar location: M102
  • Organizational meeting: July 11th, 14:00 in M201.
  • Tutorial on Mondays 12:00-14:00 in M206.
  • Niko Naumann and I are available by appointment for additional assistance with talk preparation.
  • Detailed list of topics.

Plan

Dieses Seminar richtet sich ausdrücklich, aber nicht nur, an Studenten des gymnasialen Lehramtes, die meine Algebra Vorlesung parallel hören. Ziel ist es, Themen der Vorlesung, die besonders schulrelevant sind, ausführlicher als im Rahmen der Vorlesung möglich, zu behandeln. Der Stoff umfasst:

  • Klassische Konstruktionen mit Zirkel und Lineal (Dreiteilung des Winkels, Quadratur des Kreises, Würfelproblem, Konstruktion des regelmsigen n-Ecks)
  • Auflösung von Gleichungen durch Radikale mit Galoistheorie
  • elementare Fälle von Fermate letztem Satz
  • quadratische Formen

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    This seminar is expressly, but not exclusively, aimed at, students aiming to teach in a Gymnasium while attending Naumann's algebra course. The goal of this seminar is take topics from the course which are particularly relevant for teachers and treat them in detail. These topics include:

  • Classical constructions with compass and straightedge (trisection of an angle, squaring the circle, and doubling the cube)
  • Solving polynomial equations through radicals via Galois theory
  • Elementary cases of Fermat's last theorem
  • Quadratic forms

    •

    Schedule

    • 25.10.2016 (Julia-Sofie Berghammer) Polynomial equations over finite fields.
    • 8.11.2016 (Sebastian Wolf) Supporting lemmas for the quadratic reciprocity theorem.
    • 15.11.2016 (Marion Liedke) Quadratic reciprocity.
    • 22.11.2016 (Norbert Ludwig) Quadratic forms.
    • 29.11.2016 (Johannes Gawron) Isotropic spaces and bases.
    • 6.12.2016 (Niklas Kipp) Witt's theorem and translations.
    • 13.12.2016 (Tobias Prey) Quadratic forms over finite fields.
    • 20.12.2016 (Michael Seyler) The four square theorem.
    • 10.1.2016 (Michael Schaeffler) Pythagorean triples.
    • 17.1.2017 (Benjamin Albersdoerfer) First cases of Fermat's last theorem.
    • 24.1.2017 (Jonas Neumayer) Geometric constructions.
    • 31.1.2017 (Anna-Sabine Stibbe) Solvable groups and the insolvability of the alternating and symmetric groups.
    • 7.2.2017 (Gurkan Dogan) Solvable field extensions and iterated extensions.