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Mathematics and Algorithms for Computer Algebra

The intention of this course is to recapitulate basic mathematical structures from a constructive and algorithmic viewpoint, and then present some of the fundamental algorithms on these structures that underlie computer algebra. It will be primarily a theoretical course that is not tied to any particular computer algebra system, although we may occasionally refer to Maple, REDUCE and Derive for examples of actual implementations. It is proposed to consist of about 28 2-hour lectures, together with typeset lecture notes. The following syllabus shows in broad outline the material that we intend to cover, but we reserve the right to vary the details. The course language will be English, which we will attempt to speak slowly, and there will be people who can translate.