Perspectives of Mathematics

To the homepage of Valentina Kiritchenko

Welcome to Perspectives of Mathematics homepage!

Jacobs University Bremen, Fall 2007

Announcement: the second midterm is scheduled on Monday, November 12 during usual class hours (8:15-9:30). The midterm will mostly cover continued fractions although there might be one or two problems on polytopes.

Homework 4 is posted.

Classes: Mo 8:15-9:30 am, We 2:15-3:30 pm East Hall 2
Instructor: Valentina Kiritchenko
office: Research I Room 125
phone:
e-mail: v.kiritchenko at jacobs-university dot de

Office Hours: We 10-11 am, Th 11:30 am-1:30 pm and by appointment

Course notes 1 (Compass and ruler constructions)	Course notes 3 (Continued fractions and good approximations)
Course notes 2 (Complex numbers and construction of regular polygons)	Homeworks 1,2,3,4

Topics:

Compass and ruler constructions and Galois theory: construction of regular polygons, field extensions, impossibility results.
Convex polytopes: Dehn-Sommerville relations on the number of faces, volume polynomial, Minkowski sum, mixed volumes.
Continued fractions and good approximations.

Suggested reading:

What is Mathematics? An elementary approach to ideas and methods, Richard Courant and Herbert Robbins
A Survey of Classical and Modern Geometries, Arthur Baragar (I have one copy of this book, which you can borrow)
Disquisitiones arithmeticae, Karl Fridriech Gauss

Grading: There will be 3 midterm tests, 75 minutes each, given in class. There will also be regular homeworks. In the end of the course, each of you is expected to do a presentation on a topic of your choice. Before this, by November 14 you are required to submit a paper describing what you are going to present. The final course grades will be determined as follows:

Welcome to Perspectives of Mathematics homepage!

Homework/Class Participation 30%, Tests 10% each, Paper/Presentation 40%