General
Contact
For questions, remarks or corrections about the lecture or exercise sheet, contact tobias.boege@aalto.fi.
Schedule
Lectures are Mondays and Tuesdays from 12:15 to 14:00 in Y405. Exercise sessions are on Thursdays also from 12:15 to 14:00 but in Y228b.
Contents
The course is taking place in the 6 weeks from 24 April to 1 June. The lecture on May 1 and the exercise session on May 18 fall on public holidays. There will be no replacement for them. The preliminary table of contents is, by week:
- Ordered fields and real closure
- Semialgebraic sets
- Quantifier elimination
- Applications of quantifier elimination
- Stellensätze
Organization and credits
Lectures and exercises are in person. Lecture notes and exercise sheets will be posted on this MyCourses page after the lectures of each week. You are nevertheless encouraged to take your own notes during class.
The course is worth 5 credit points which are earned by regular participation in the lectures and exercise sessions and by getting at least 60% of points on homework problems. You should be ready to present any of your solutions during the exercise sessions. Homework due on Thursday in week n+1 is based on the lectures of Monday and Tuesday in week n. Submit your solutions to the corresponding MyCourses assignment by Thursday noon.
Literature
- Bochnak, Coste, Roy: Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, vol. 36, Springer (1998).
- Marker: Model theory: An introduction, Graduate texts in Mathematics, vol. 217, Springer (2002).
- Marshall: Positive polynomials and sums of squares, Mathematical Surveys and Monographs, vol. 146, AMS (2008).
- FileChapter 1: Ordered and real-closed fields FilePDF document
- FileChapter 2: Semialgebraic sets FilePDF document
- FileChapter 5: Stellensätze and non-negativity FilePDF document
- FileAppendix A: Review of commutative algebra FilePDF document
- FileAppendix B: Concepts from model theory FilePDF document
- FileBibliography FilePDF document