See also the
description at the mastermath site.
|Start: ||6 Februari 2007|
|Location: ||Amsterdam, VU: WG S205|
|Day and Time:|| Tuesday, 14:00 - 17:45|
The course material will consist of the pdf files for the slides,
handouts (copies of Chapters of books) and exercises sets that will
be handed out and posted here as well.
In the twelfth (and thirteenth) lecture we discussed some ideas behind
the factorization of integer polynomials (Berlekamp-Hensel) and the relation
with Newton iteration for the location of real zeroes of a polynomial,
as well as Newton poytopes.
lecture (May 1, 2007) will be concerned with Gröbner bases of
noncommutative polynomials; handout available.
We will also discuss the more
general Knuth-Bendix methods;
recommmended reading: A.J.J. Dick, An introduction to Knuth-Bendix completion.
lecture (April 24, 2007) is concerned with group theoretic algorithms.
Recommended reading: Chapter 8 of the TAPAS book.
In the ninth lecture we covered the basic theory for (commutative)
lecture was concerned with some applications of LLL, including
those mentioned in the
Also, a few exercises.
lecture the LLL algorithm was treated, along the lines of sections
of Henri Cohen's book on Computational Algebraic Number Theory.
and sixth lectures dealt with the Gaussian elimination algorithm,
in particular PRS-like variants to compute fraction free determinants
(Bareiss), and Hermite and Smith normal forms.
We followed essentially Chapter 10 of Yap, which was handed out.
lecture dealt with the Chinese Remainder Algorithm, and with
Polynomial Remainder Sequences. I handed out part of a Chapter on this
topic by Geddes, Czapor, Labahn. Also handed out were some elementary
exercises to get going with Magma.
third and fourth sets of exercises were also handed out.
first part of the third lecture I discussed Euclidean domains and the Euclidean
algorithm; the second part was mainly about the integer case, in the guise
of continued fractions.
I handed out (in week 4) a copy of my notes on continued fractions (in Dutch).
For the hands-on sessions I handed out the Appendix by Geoff Bailey on the
Magma language (from Bosma/Cannon: Discovering Mathematics with Magma)
lecture was concerned with the Fast Fourier transform. Some sections
of Modern Computer Algebra were handed out.
There are three exercises; two on FFT and one on Huffman coding. Here is the
from Johnsonbaugh's description of Huffman coding.
lecture concerned a general introduction, as well as some examples.
I handed out copies of Chapter 0 of Yap.
Here is the first exercise set.
Last update: 11 april 2007