## S.V.Duzhin

### Algorithms of Continuous Mathematics

#### Lectures at the University of Pereslavl, Autumn 2000

**Time and place:** Fridays 8:00--11:20, Main building
of UP.

Materials available so far:

- Course program

- September 8. Lecture 1: Polynomials and algebraic varieties.
PostScript (gzipped),

page 1,
page 2,
page 3.

- September 15. Lecture 2: Ideals in polynomial rings.
PostScript (gzipped),

page 1,
page 2.
page 3.

- September 22. Lecture 3: Buchberger's algorithm.
PostScript (gzipped).

page 1,
page 2,
page 3.

- September 29. Lecture 4: Groebner bases.
PostScript (gzipped).

page 1,
page 2,
page 3.

- October 6. Lecture 5: Investigation of systems of algebraic
equations.

- October 13. Test on Groebner bases.
Variant 1,
Variant 2.

- October 20. Lecture 6: Localization of roots. Sturm's algorithm.

- October 27. Lecture 7: Visualization of 3D objects.

Page 1,
Page 2,
Page 3,
Page 4,
PostScript file.

- November 3. Programming exercises (moving polyhedra).

- November 10. Lecture 8: Parallel and central projection.

- November 17. Lecture 9: Bezier curves.

PostScript file.

- November 24. Lecture 10: Basic algorithms of convex geometry.

S.V.Duzhin