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Algorithmic Number Theory WS 2014/15

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Algorithmic Number Theory WS 2014/15

Lecturer

Prof. Dr. Claus Fieker

Assistant

Tommy Hofmann


Content

To add.


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).