The Method of Evaluation

Grading in this part is based on submitted reports on homeworks which will be assigned during the course. (No submission therefore means Nonattendance.)

References

Course notes will be provided at the first lecture time or you can directly refer to the source papers below.
[1] C.-A. Faure, An elementary proof of the fundamental theorem of projective geometry, Geom. Dedicata, 90(2002), 145–151.
[2] P.G. Vroegindewey, An algebraic generalization of a theorem of E.C. Zeeman, Indagationes Mathematica, 77(1974), 77–81.

The Plan of the Course

Part 1 is scheduled to be 4/14, 4/21, 4/28, 5/12.
1. Review on affine spaces. 2. Touch of projective spaces. 3. The fundamental theorem of projective geometry. 4. Wigner’s theorem on describing symmetry in quantum mechanics. 5. Alexandrov-Zeeman’s theorem on describing symmetry in special relativity.

Keywords

Projective geometry, affine geometry, symmetry in physics.

Required Knowledge

Basic knowledge and skills in linear algebra and set theory.

Attendance

This course is open for all students in Nagoya University as a part of open subject program. Certain amount of experience in the set-theoretic framework of mathematics is required, however, to get benefits from this part of the course.

Additional Advice

Use office hours (Wed, 13:00–14:00) as a substantial portion of courseworks.