Math
180
Continued fractions and geometric coding
Course Flier
Description
An upper-level undergraduate topics course on an interface between number theory and geometry,
taught by
Moon Duchin
, with TAs
Gabe Amos
and
Dustin Pluta
.
Materials
Problem sets:
One
,
Two
,
Three
,
Four
,
Five
,
Six
,
Seven
(on handout),
Eight
,
Nine
Selected solutions
Minitests:
One
,
Two
,
Three
,
Four
Sources
Artin's
Algebra
, Chapter 5, "Symmetry"
David Angell's text
Irrationality and Transcendence
: Chapter 4, "Continued Fractions"
Allen Hatcher's course notes for an elementary-level seminar on numbers and geometry:
Part One
,
Part Two
,
Part Three
.
My handouts introducing the hyperbolic plane:
Handout One
,
Handout Two
For reference, a rigorous
short book
on hyperbolic geometry (Cannon-Floyd-Kenyon-Parry)
Links
Continued fraction calculator
Wikipedia:
transcendental number
Lester Ford's
original 1938 article
on Ford Circles
A short paper by Doris Schattschneider on a funky
multiplicative metric
An expository article on
Lorenz and modular flow
where you should see lots of familiar notions (and some cool movies)
Watch Stephen Colbert discuss Perelman's work on geometrization:
Part One
,
Part Two