Coursebooks 2017-2018

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Differential geometry of framed curves

MATH-423

Lecturer(s) :

Maddocks John

Language:

English

Remarque

Summary

The Differential Geometry of curves, tubes & ribbons

Content

This course will describe the classic differential geometry of curves, tubes and ribbons, and associated coordinate systems. We will prove various classic mathematical theorems such as the Weyl-Hotelling formula for tube volumes, and the relation between Link, Twist and Writhe, which couples differential geometry and topological invariance for closed and knotted framed curves. While we will not consider applications explicitly in this course, much of the mathematical material that will be described is central in various problems of mechanics, including nanostructures and topological fluid mechanics.

Learning Prerequisites

Required courses

1st & 2nd year courses in math or physics, (or with teacher's permission)

Recommended courses

Ordinary Differential Equations, BA Math (MATH-301)

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Ex cathedra lecture and exercises in the classroom

Assessment methods

Written exam

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Resources

Bibliography

Will be given at the beginning of the course

In the programs

  • Mathematics - master program, 2017-2018, Master semester 2
    • Semester
      Spring
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Differential geometry of framed curves
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 2
    • Semester
      Spring
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Differential geometry of framed curves
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 4
    • Semester
      Spring
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Differential geometry of framed curves
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German