Math 677: Diophantine Approximation
Winter 2010, Section 1
Time: Tuesday-Thursday 11:30 p.m- 1:00 pm.
Place: Dennison 351
Jeffrey Lagarias, 3086 East Hall, 763-1186,
Tuesday-Thursday 5:00-6:30pm in Room B743.
(Or by appointment: call or email me)
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.
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
(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
(4) Applications: Diophantine equations, units.
Math 575, general mathematical maturity.
Some comfort with basic analysis, multivariable polynomials.
Basic knowledge about algebraic numbers is helpful.