Algorithmic Algebra

While pure algebra is mainly concerned with analyzing the structure of abstract objects, algorithmic algebra deals with questions of constructiveness and effectivity. Problems that appear simple from the structural point of view, suddenly become extremely challenging! A famous example for this phenomenon is the problem of primality testing and factoring integers.

The goal of the lecture is to introduce students to some methods and results in this area. This course complements my lectures on (structural) Algebra I and Algebra II at TU Berlin. Basic knowledge of algebra should be sufficient to follow the course. 

• The page was made bilingual and contains information about the oral exams.
• Note that the start date for the course is tuesday, 22nd of April.
• The prospective contents of the course have been published.

The oral exams will take place in the period from Monday 8/11/2014 to Saturday 8/16/2014. For more information, please refer to the German version of the page or contact Jesko.

The lectures start on tuesday, the 22nd of April.

• Discrete and fast Fourier transform, rapid multiplication and division of polynomials
• Euclidean algorithm and some of its applications
• Factoring polynomials of finite fields
• Efficient primality testing

• Joachim von zur Gathen, Gerhard: Modern Computer Algebra, Cambridge University Press, second edition, 2003
• Mignotte: Mathematics for computer algebra, Springer, 1992
• C.K. Yap: Fundamental Problems of Algorithmic Algebra, Oxford University Press, 2000