Diophantine approximation
MATH-540 / 5 crédits
Enseignant:
Langue: Anglais
Remark: pas donné en 2024-25
Summary
The main theme in Diopahntine approximation is to approximate a real number by a rational number with a certain denominator bound. The course covers the case of one real number, that is classical and well understood, and proceeds to simultaneous Diophantine approximations.
Content
- Continued Fractions and convergents
- Convergents as best approximations
- Approximation theorems and Liouville's theorem
- Quadratic irrational numbers and periodic continued fractions
- Simultaneous Diophantine approximation
- Dirichtets Theorems and algorithms
- Applications of Simultaneous Diophantine approximation in Discrete Optitization
- Lower bounds based on covering
- Schmidt's subspace theorem and open research questions
Learning Prerequisites
Required courses
Analysis 1+2
Linear Algebra 1+2
Rings and Fields
Assessment methods
Written exam at the end of the semester
Resources
Bibliography
A. Ya. Khinchin: Continued Fractions
Wolfgang Schmidt: Diophantine Approximation
Some research papers.
Ressources en bibliothèque
Moodle Link
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Diophantine approximation
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Diophantine approximation
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Diophantine approximation
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Diophantine approximation
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
Semaine de référence
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8-9 | |||||
9-10 | |||||
10-11 | |||||
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21-22 |