Algorithmic Number Theory WS 2014/15

# Algorithmic Number Theory WS 2014/15

#### Schedule

 Lecture: Mon., 1:45–3:15 p.m., room 48-208 Thurs., 1:45–3:15 p.m., room 48-208 Tutorial: Wed., 1:45–3:15 p.m., room 48-438

#### Problem sets

Problem set 1, PDF, due to 31.10.2014, 14:00

Problem set 2, PDF, due to 10.11.2014, 14:00

Problem set 3, PDF, due to 17.11.2014, 14:00

Problem set 4, PDF, due to 24.11.2014, 14:00

Problem set 5, PDF, due to 01.12.2014, 14:00

Problem set 6, PDF, due to 08.12.2014, 14:00

Problem set 7, PDF, due to 15.12.2014, 14:00

Problem set 8, PDF, due to 05.01.2015, 14:00

Problem set 9, PDF, due to 12.01.2015, 14:00

Problem set 10, PDF, due to 19.01.2015, 14:00

Problem set 11, PDF, due to 26.01.2015, 14:00

Problem set 12, PDF, due to 02.02.2015, 14:00

Problem set 13, PDF, due to 09.02.2015, 14:00

#### Literature

Constructive number theory (or algorithmic number theory) is a rather new subject, hence the literature is sparse. To mention some:

• Henri Cohen, A Course in Computational Algebraic Number Theory, Springer, 1993
(This contains almost all algorithms we are going to cover, but almost no proofs)
• Michael Pohst und Hans Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge University Press, 1997
(Full of interesting theory, but the algorithms are sometimes hard to recognize)
• Michael Pohst, Computational Algebraic Number Theory, Birkhäuser Verlag, 1993
(A readable summary of the book of Pohst and Zassenhaus)
• Klaus Wildanger, Konstruktive Zahlentheorie, Lecture notes, 1993 (link
(German lecture notes of a lecture of Pohst)

The theoretical part is covered in any book with title "Algebraic Number Theory", e.g.,

• Daniel Marcus, Number fields, Springer1977
(Only theoretical, but nicely presented and almost constructive proofs)
• Jürgen Neukirch, Algebraic Number Theory, Springer, 1977
(Highbrow introduction to algebraic number theory. Covers more theory then necessary)

#### Lecture notes

There are lecture notes from the lecture "Algorithmic Number Theory" from winter term 2013/14. They are still growing. The current version can be found here:

alg_nt_c.pdf (30. January, 2014)

Please report any errors you find (e.g. via e-mail).