Approximation Techniques in Algebra and Analysis

This class will investigate various constructions in algebra and analysis which rely on the approximation of complicated objects through simple ones. No special prerequisites are assumed.

Examples of approximations are:

• irrational numbers and continued fractions
• completions of Q
• differentiable functions, derivatives and Taylor expansion
• calculus of inverses of mappings and operators
• approximation of polynomials and power series through monomials (Gröbner bases)
• rectification of vector fields
• normal forms of automorphisms
• congruences and reduction modulo p
• Lie-algebras of Lie-groups

Time:

This two-hour class will be held in the spring term 2010 in blocks of five units, each consisting of 3+3 hours on two consecutive days (the third hour each day will be devoted to exercises and problems).

Preliminary schedule:

Mo/Tu March 8/9,
Mo/Tu April 12/13,
Mo/Tu April 19/20,
Mo/Tu May 10/11

Mo: 11:30-13:00, Tu: 9:00-11:00

RICAM seminar room AS50