Fall Semester 2004

Perspectives of Mathematics

Course No. 100 291




Basic Information:
Time: Wednesday and Friday 11:15 to 12:30
Room: Lecture Hall in Research II
Instructor Office Tel. Email (at iu-bremen.de)
Ivan Penkov Res. I, Room 1113180i.penkov
Michael Stoll Res. I, Room 1323214 m.stoll
Marcel Oliver Res. I, Room 1073212m.oliver
Peter Oswald Res. I, Room 1063179p.oswald
Dierk Schleicher  Res. I, Room 115 3213dierk

Official Course Description

While the mathematical core courses have to help build the foundation for a solid mathematical knowledge, this course tries to illustrate some beautiful or interesting mathematical areas which need not be part of a systematic education, but which show mathematics as a lively, active and varied subject. This course tries to convey the spirit why mathematicians enjoy their subject by discussing selected topics. Over the years, the topics vary (so that the course may be taken more than once); they have included combinatorial game theory, hyperbolic and spherical geometries, manifolds, Fourier analysis and wavelets, the Banach-Tarski-paradox, and others. Instead of a final exam, the students write a term paper on a mathematical subject of their choice and present is to the class; this helps to develop writing and presentation skills. For students in mathematics and computational science, this course is designed to be taken at the same time as Analysis I and/or Linear Algebra I. It is open to anyone with interest and some experience in mathematics (for others, Foundations of Mathematics is recommended).

Grading Policy

The final grade will be computed from three components:

Homeworks

Each module of the course (see the schedule below for the various modules) will involve at least one homework assignment. The homeworks grade component is computed from all the homeworks.

Term Paper

Every student has to pick a topic on which to write a short term paper. Please talk to the instructors regarding possible topics, or suggest one yourself (which could also be supervised by some faculty member who is not teaching one of the modules)! In order to avoid having to work on the term paper while also preparing for final exams in your other courses, it is recommended to pick a topic fairly early in the semester and work on it before the semester approaches its end. (That way you will also have more time to prepare your presentation.)

First submission deadline: Friday, Dec 3.
Please submit a first version of your paper to your term paper advisor. You will then get a quick feedback, and you will have the opportunity to revise your paper. You should also take into account any feedback you get while presenting your paper. The presentations will be scheduled soon; you should be prepared to give your presentation as early as Nov 24. You are strongly encouraged to submit the first version of your paper a few days before your presentation, so that you can profit from comments of your advisor when preparing the presentation.

Second and final submission deadline: Friday, Dec 17.

Presentation

In the last two weeks of the semester, every student will give a presentation of 15-20 min on their term paper. The idea is that you should try to explain what you did in such a way that your fellow students (and the professors) can understand it and will appreciate your work.

Schedule

DateInstructorTopic
Sep 01Ivan Penkov Infinite dimensional vector spaces and dual systems
Sep 03Ivan Penkov 
Sep 08Ivan Penkov 
Sep 10Ivan Penkov 
Sep 15Ivan Penkov 
Sep 17Michael Stoll Diophantine equations and geometry
Introduction and Pythagorean Triples
Notes
Sep 22Michael Stoll Ternary Quadratic Forms: Necessary Conditions
Notes see above
Sep 24Michael Stoll Ternary Quadratic Forms: Legendre's Theorem
Notes see above
Homework
Sep 29Michael Stoll Sums of Four Squares
Notes see above
Oct 01Michael Stoll Pell's Equation
Notes see above
Suggestions for term papers at end of notes!
Oct 06Marcel Oliver Sequential data assimilation by nudging
Notes
Oct 08Marcel Oliver 
Oct 13Marcel Oliver 
Oct 15Marcel Oliver 
Oct 20Marcel Oliver  
Oct 22Peter OswaldProblems in Linear and Nonlinear Approximation
Reading Material
Oct 27Peter Oswald 
Oct 29Peter Oswald 
Nov 03Peter Oswald 
Nov 05Peter Oswald  
Nov 10Dierk Schleicher Geometry beyond Euclidean Three-Space
Nov 12Dierk Schleicher 
Nov 17Dierk Schleicher 
Nov 19Dierk Schleicher 
Nov 24In West 4!Presentations
Nov 26In West 4!Presentations
Dec 01In West 4!Presentations
Dec 03In West 4!Presentations

Last modified: 2004-11-15
Michael Stoll