Topics:

1. Algebraic Number Fields

• How many fields share a common discriminant? (Multiplicity problem)
• Relatively cyclic fields of prime degree

2. Quadratic Fields

• Try yourself to calculate the Fundamental Unit, Regulator, and Period Length of a real quadratic field !

3. Cubic Fields

• Test a cubic polynomial for Reducibility !
• Polynomials of the 3rd degree as generators of cubic fields

• An exceptional totally real cubic field: Arnie's monster
• My extension of ANGELL's table of totally real cubic fields
• Principal factorization types of totally real cubic fields

• Mysterious pure cubic fields: Daniel's exotic secret
• Principal factors in pure cubic fields
• Algorithm of VORONOI in pure cubic fields
• Principal factorization types of pure cubic fields

• Complex cubic fields of IIMURA's polynomials
• Principal factorization types of complex cubic fields

4. Quartic Fields

• Connections between cubic and dual quadratic fields
• Class rank configurations in SCHOLZ's mirror theorem

5. Quintic Fields

• Galois groups of the normal hull of quintic fields

Current topics:

6. Table Errata

• Fung's table of complex cubic fields
• Authors' Funny Menu

7. Annual Banners

• Memorial 2009
• Year of Mathematics 2008
• Research Targets 2007
• Super Computing Centre 2006
• World Year of Physics 2005
• Centennial 2004
• Mysterion 2003
• Joint Research 2002
• Vienna Congress 2001

Topics in preparation (interactive JAVA Applets):

• Try yourself to calculate the Ludolph circle number !
• Number of Ideal Classes of Complex Quadratic Fields
• Fundamental Unit, Regulator, and Period Length of Pure Cubic Fields