## 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]
.