Math 677: Diophantine Approximation
Winter 2010, Section 1
Time:
Tuesday-Thursday 11:30 p.m- 1:00 pm.
Place:
Dennison 351
Instructor:
Jeffrey Lagarias, 3086 East Hall, 763-1186,
lagarias@umich.edu
Office hours:
Tuesday-Thursday 5:00-6:30pm in Room B743.
(Or by appointment: call or email me)
Course homepage:
http://www.math.lsa.umich.edu/~lagarias/
Public/html/m677wi10.html
Textbook:
Course notes to be developed.
Reference Books :
(1) A. Baker,
Transcendental Number Theory,
Cambridge University Press 1990 (paperback)
(2) J. W. S. Cassels,
Introduction to Diophantine Approximation,
Cambridge University Press 1965. (paperback)
(3) D. Hensley,
Continued Fractions ,
World Scientific 2006.
Course description:
This is a topics course in Diophantine Approximation and
Transcendence. Topics may include:
(1) one-dimensional and
multidimensional Diophantine approximation,
continued fractions (one-dimensional and multidimensional).
(2) Lattices, geometry of numbers, and lattice basis
reduction.
(3) Topics in
irrationality and transcendence. These may include
Thue-Siegel-Roth theorem, Baker's method,
Gelfand-Schneider theorem, some topies in E-functions and
G-functions.
(4) Applications: Diophantine equations, units.
Prerequisites:
Math 575, general mathematical maturity.
Some comfort with basic analysis, multivariable polynomials.
Basic knowledge about algebraic numbers is helpful.
Grading:
[TBA]
.