Paul Bamberg (Department of Mathematics)
First-Year Seminar 53C | 4 Credits (Spring 2025) | CANVAS SITE
Thursday, 03:00 PM–05:00 PM
Projective planes were discovered by Renaissance artists who needed to depict tiled floors on canvas. Quaternions, discovered in the nineteenth century, were used by physicists to represent rotations in three dimensions, which to not commute with one another, In the early 20th century, American mathematicians discovered that quaternions could also be used as coordinates in projective planes where certain theorems of Euclidean geometry fail and the rules of ordinary algebra do not apply to coordinates.This seminar focuses on a single article published at the dawn of the computer era by the great American geometer Marshall Hall, which describes an exhaustive search, with the aid of a primitive computer, for all finite planes of order 9. We will replicate, and perhaps extend, Halls results using the R scripting language, in the process delving into finite geometry, abstract algebra, graph theory, and theory of computation.
Prerequisites: Linear algebra: Mathematics 21b (perhaps concurrently), 22a, 25a, or 55a. No experience with R is required, though some computing background would be helpful.