Advanced Algorithmic Mathematics

MSci: Course code MAS400
MSc: Course code MTHMG65; Level (b)

Course Organiser Dr Francis J. Wright

Welcome to the course website.

The course provides an introduction to a couple of important modern mathematical algorithms, which are typical of those implemented in mathematical computation systems such as Maple, Mathematica, REDUCE, etc.  The flavour of the course is pure mathematical and it will include proofs of some of the theorems and algorithms.  No actual machine computation or programming language will be used.

Course texts

These should be available in the College Library and possibly the College bookshop, amazon.co.uk, etc.

Main

Modern Computer Algebra by Joachim von zur Gathen & Jürgen Gerhard [Cambridge University Press, 1999] £32.50

An amazing book and very good value; it covers all of this course and very much more.  [Unfortunately, the College bookshop tells me that it is temporarily out of print until a new edition is published in March 2003.  The previous edition may still be available elsewhere and the College Library has one copy on one-week loan.]

Background

Ideals, Varieties, and Algorithms by D. Cox, J. Little & D. O'Shea [Springer-Verlag, 1998] £29.50

The Gröbner Basis section of the course was originally based on this book.

Computing with Maple by Francis Wright [Chapman & Hall / CRC Press, 2001] £25

The second half of Chapters 12 is based on the Gröbner Basis section of the course.

Prerequisite knowledge

• Essential: Abstract Algebra (polynomial rings) and Linear Algebra
• Desirable: An introduction to Mathematical Algorithms and/or Mathematical Computing (e.g. Maple)

Teaching

Lectures: 10 am   12 noon on Mondays from 13th January to 31st March 2003 in Room G2, Mathematics Building, Queen Mary, Mile End Road.

Exercises will be set occasionally and some solutions provided later.

The key objectives and past exam papers for 2001, 2002 and 2003 are available online in PDF.