Approximation by algebraic numbers

Includes index

Includes bibliography references (p. 240-272)

1. Approximation by rational numbers 2. Approximation to algebraic numbers 3. Classifications of Mahler and Koksma 4. Mahler's conjecture on S-numbers 5. Hausdorff dimension of exceptional sets 6. Deeper results on the measure of exceptional sets 7. On T-numbers and U-numbers 8. Other classifications of real and complex numbers 9. Approximation in other fields 10. Conjectures and open questions

An accessible and broad account of the approximation and classification of real numbers suited for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the comprehensive list of more than 600 references.