MTH702U (MAS400) / MTHM032: Advanced Algorithmic Mathematics
Prerequisites
With the changes in course code the prerequisites have also been changed from
“MAS201 Algebraic Structures I, MAS212 Linear Algebra I, MAS202 Algorithmic Mathematics,
or consult the module organiser” to “Consult the module organiser”.
If I am consulted I shall recommend the following (people who do not have the required prerequisites
[first two courses] should come to see me):
- MAS201 / MTH5100 Algebraic Structures I. Required prerequisite.
In particular, one must be comfortable with ideals of rings (commutative with 1), which
are used throughout the Gröbner Basis part of the course (approximately 2/3 of the course).
- MAS212 / MTH5112 Linear Algebra I. Required prerequisite.
Used in the LLL part of the course.
- MAS212 Algorithmic Mathematics. This course last ran in 2005–06, and thus
canNot be a prerequisite anymore.
Despite the similarity in name, this course was the one that was least needed, and in fact
the content of the two courses is largely orthogonal.
Algorithms done in that course such as polynomial g.c.d. which we need are (re-)done in my course.
Anyway, a web-book of this course is here.
This book was prepared by Prof. L. H. Soicher and Prof. F. Vivaldi.
(There are some minor differences in pseudo-code between my course and their book,
for example I use end if;, end for; and end while; instead of
fi;, od; and od;.
There is a major difference in our polynomial g.c.d. algorithms in that I do not
recurse, and do not need back substitution to find a and b such that
gcd(f, g) = af + bg.)
- MAS236 / MTH6105 Algorithmic Graph Theory. Not a prerequisite.
Does contain several algorithms (not in pseudo-code), and it may be useful for
people to have seen algoritms and their proofs of correctness before.
However, no individual algorithm in this course has any relevance to my course whatsoever.
Also the courses MAS305 / MTH6104 Algebraic Structures II and
MAS317 / MTH6140 Linear Algebra II are an advantage
for getting people used to Mathematics in this area, such as ideals.
However, I will not assume anything from these courses
that is not in MAS201 / MTH5100 or MAS212 / MTH5112.
Exercises
Exercises 1:
TeX-format;
DVI-format;
PDF-format.
Exercises 2:
TeX-format;
DVI-format;
PDF-format.
Exercises 3:
TeX-format;
DVI-format;
PDF-format.
Exercises 4:
TeX-format;
DVI-format;
PDF-format.
Exercises 5:
TeX-format;
DVI-format;
PDF-format.
Exercises 6:
TeX-format;
DVI-format;
PDF-format.
Exercises 7:
TeX-format;
DVI-format;
PDF-format.
Exercises 8:
TeX-format;
DVI-format;
PDF-format.
Solutions
Solutions 1:
TeX-format;
DVI-format;
PDF-format.
Solutions 2:
TeX-format;
DVI-format;
PDF-format.
Solutions 3:
TeX-format;
DVI-format;
PDF-format.
Solutions 4:
TeX-format;
DVI-format;
PDF-format.
Solutions 5:
TeX-format;
DVI-format;
PDF-format.
Solutions 6:
TeX-format;
DVI-format;
PDF-format.
Solutions 7:
TeX-format;
DVI-format;
PDF-format.
Solutions 8:
TeX-format;
DVI-format;
PDF-format.
Algorithms
Has algorithms for the whole course.
Algorithms:
TeX-format;
DVI-format;
PDF-format.
Past papers
2007 (PDF-format).
2006 (PDF-format).
2005 (PDF-format).
2004 (PDF-format).
2003 (PDF-format).
2001 (PDF-format).
Syllabus
TeX-format;
DVI-format;
PDF-format.
People wishing to LaTeX or pdfLaTeX this for themselves will also need QM.ps
or QM.pdf respectively.
(The DVI-file also needs QM.ps in the same directory in order to be read
and printed as intended.)
This page is maintained by Dr John N. Bray. The views and opinions expressed in these pages
are mine.
The contents of these pages have not been reviewed or approved by Queen Mary, University of London.
Last updated: 19th September 2008.