Algorithmic Algebra and Number Theory

URL study guide

https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2WF70&collegejaar=2025&taal=en

Omschrijving

Algorithmic Number Theory:

• multi-precision arithmetic
• algorithms in (Z/nZ)*
• quadratic reciprocity
• prime number distribution
• continued fractions
• lattices, lattice basis reduction
  
  Algorithmic Algebra: Ideals and varieties in polynomial rings, i.e.
• polynomial rings
• ideals and varieties
• polynomial maps
• Nullstellensatz
• Hilbert's Basis Theorem
• monomial orders 
• Groebner basis
• Buchberger's algorithm
• elimination
• dimension
• various applications

Doelstellingen

To be able to work with a number of number theoretic algorithms, and to indicate their efficiency. To understand ideals and algebraic varieties from an algorithmic point of view, to be able to reformulate a wide variety of (discrete) mathematical problems in terms of ideals and varieties, and attack these problems with standard computer algebra packages.

Beoordelingsmethode

Oral examination