CISC881, Continuous Coordinate Transformations: Winter 2017

Course Description:

Coordinate transformations are essential in the application of computational techniques to real-world geometrical and dynamical problems. The first part of this course will examine the essential elements of the displacement of points and coordinate frames, mathematically and computationally.

The second part of this course will examine the theory, representation and calculation of elementary concepts in differential topology and differential geometry. By translating these ideas into current computing terminology, in particular by carefully drawing the distinction between syntax and semantics of vectors, the goal is to provide insight into the Einsteinian style of transforming coordinates and measuring distances in manifolds. The successful student should, by the end of the course, be able to read modern literature in computational shape descriptions as well as differential geometry.

Current problems, such as descriptions of anatomical shapes derived from medical images, will be occasionally referenced as the course proceeds but the emphasis of the course is on the representation and semantics of vectors.

Recent Course News (as of February 2)

  • The first four weeks of notes are now available
  • Assignment #2 is available

  • Last updated February 2, 2017