1st Semester 2008/09: Groups, Rings and Fields for Non-Mathematicians
- Groups, Rings and Fields are standard items in the toolkit of todays Mathematician regardless whether she works in pure or applied fields. The theory of algebraic structures is independent of the application field (in that sense the title "X for the non-mathematicians" is misleading); the perspective on this theory however can change.
Rings and Fields involve abstract structures modeling a domain within which computations are performed. Groups arise also in the study of structure preserving transformations of a mathematical structure onto itself.
A focal topic could be "the perspective on the use of Algebraic structures in ILLC related applications".
Since this project is initiated on demand of the students, they are expected to contribute the type of applications they have in mind. Preferably before the start of the project. (Alternatively you can expect that the prime target will become understanding finite fields.)
- This project preferably should be organised as a reading and discussion group rather than a class.
- Around 1980-83, when the computer science program was initiated in our University your teacher was the person responsible for the course on elementary algebra in this program. The old material in part still survives but with a problem: similar to the contemporary syllabi published by the Korteweg de Vries Institute it is written in Dutch. Presumably a good opportunity to exercise your Dutch together with the Mathematics. My favourtite textbook from the era (around 1964) I learned Algebra myself: van der Waerden, Moderne Algebra, will not be helpful either; it is a German text (but there should also exist an English version).