Proséminaire / Proseminar

  • Teaching

    Details

    Faculty Faculty of Science and Medicine
    Domain Mathematics
    Code UE-SMA.03801
    Languages English , French, German
    Type of lesson Seminar
    Level Bachelor
    Semester SA-2020

    Title

    French Proséminaire
    German Proseminar
    English Proseminar

    Schedules and rooms

    Summary schedule Thursday 15:15 - 17:00, Hebdomadaire, PER 08, Room 2.52
    Struct. of the schedule 2h par semaine durant 14 semaines
    Contact's hours 28

    Teaching

    Responsibles
    Teachers
    Description

    Thema: Differentialtopologie

    In dem Proseminar wollen wir gemeinsam das bekannte Büchlein “Topology from the Differentiable Viewpoint” von John Milnor lesen. Wir lernen dort zuerst über den Begriff der differenzierbaren Mannigfaltigkeit und die Eigenschaften differenzierbarer Abbildungen. Dann besprechen wir differentialtopologische Grundbegriffe wie Orientierbarkeit von Mannigfaltigkeiten, Homotopie und Isotopie von Abbildungen. Als erste differentialtopologische Invariante werden wir den Abbildungsgrad einer differenzierbaren Abbildung kennenlernen, den Index von Vektorfeldern definieren, und den Zusammenhang zur Euler-Charakteristik einer kompakten Mannigfaltigkeit studieren. Weitere Themen können sein: Isotopien von Einbettungen und Knotentheorie, Kobordismus von Mannigfaltigkeiten.

    Literatur:
    J. Milnor, “Topology from a differential viewpoint”, Virginia University Press, 1965.
    T. Bröcker, K. Jänich, “Einführung in die Differentialtopologie”, Springer Verlag, 1973.

    C. Livingston, “Knot Theory”, Mathematical Association of America, 1993.

    Erster Termin des Seminars (mit Einführung in das Thema): Donnerstag, 17. September 2020, um 15:15. Ort: Raum 2.52

    Hinweis: Alle Interessenten können sich für die ersten einführenden Vorträge (insbesondere Wiederholung aus der Vorlesung Algebra und Geometrie II) per email unter oliver.baues@unifr.ch oder Moodle schon jetzt registrieren. Sie erhalten dann auch die Liste der Vorträge und zugehörige Literatur.

    Training objectives The participants in a seminar learn to autonomously apprehend a mathematical text (with the help of the teacher) and to present it to an audience of fellow students.
    The proseminar is the first encounter with this type of instruction, with somewhat more pronounced guidance from the teacher.
    Softskills
    No
    Off field
    No
    BeNeFri
    Yes
    Mobility
    Yes
    UniPop
    No

    Documents

    Files and attachments
  • Dates and rooms
    Date Hour Type of lesson Place
    17.09.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    24.09.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    01.10.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    08.10.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    15.10.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    22.10.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    29.10.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    05.11.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    12.11.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    19.11.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    26.11.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    03.12.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    10.12.2020 15:15 - 17:00 Cours PER 08, Room 2.52
    17.12.2020 15:15 - 17:00 Cours PER 08, Room 2.52
  • Assessments methods

    Exposé

    Assessments methods By success/failure
    Descriptions of Exams Acceptation de l'exposé
  • Assignment
    Valid for the following curricula:
    Additional Courses in Sciences
    Version: ens_compl_sciences
    Paquet indépendant des branches > Advanced courses in Mathematics (Bachelor level)

    Additional Programme Requirements to the MSc in Computer Science [MA]
    Version: 2018_1/V_01
    Supplement to the MSc in Computer science > Advanced courses in Mathematics (Bachelor level)

    Additional Programme Requirements to the MSc in Computer Science [MA]
    Version: 2020_1/V_01
    Supplement to the MSc in Computer science > Advanced courses in Mathematics (Bachelor level)

    Additional Programme Requirements to the MSc in Mathematics [MA]
    Version: 2020_1/V_01
    Supplement to the MSc in Mathematics > Advanced courses in Mathematics (Bachelor level)

    Additional TDHSE programme in Mathematics
    Version: 2020_1/V_01
    Additional TDHSE Programme Requirements for Mathematics 60 or +30 > Programme 60 or +30 > Additional Programme Requirements to Mathematics +30 > Additional TDHSE programme for Mathematics +30 (from AS2018 on)
    Additional TDHSE Programme Requirements for Mathematics 60 or +30 > Programme 60 or +30 > Additional Programme Requirements to Mathematics 60 > Additional TDHSE programme for Mathematics 60 (from AS2018 on)

    Mathematics 120
    Version: 2020_1/V_01
    BSc in Mathematics, Major, 2nd-3rd year > Mathématiques, br. principale, Séminaires

    Mathematics +30 [MA] 30
    Version: 2020_1/V_01
    Minor in Mathematics +30 (MATH+30 for 90 ECTS) > Mathematics +30, Module C (from AS2020 on)

    Mathematics 60 (MATH 60)
    Version: 2020_1/V_01
    Mathematics (MATH 60), minor 60 (from AS2020 on) > Mathematics, minor MATH60, compulsory courses (from AS2020 on)

    Mathematics [3e cycle]
    Version: 2015_1/V_01
    Supplement to doctoral studies in Mathematics > Advanced courses in Mathematics (Bachelor level)

    Pre-Master-Programme to the MSc in Mathematics [PRE-MA]
    Version: 2020_1/V_01
    Prerequisite to the MSc in Mathematics > Advanced courses in Mathematics (Bachelor level)