Math 677: Diophantine Approximation

Winter 2010, Section 1


Tuesday-Thursday 11:30 p.m- 1:00 pm.


Dennison 351


Jeffrey Lagarias, 3086 East Hall, 763-1186,

Office hours:

Tuesday-Thursday 5:00-6:30pm in Room B743.
(Or by appointment: call or email me)

Course homepage: Public/html/m677wi10.html


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.


Math 575, general mathematical maturity.
Some comfort with basic analysis, multivariable polynomials.
Basic knowledge about algebraic numbers is helpful.


[TBA] .