Computational Algebra and Number Theory

Computers have stretched the limits of what is possible in mathematics, by giving rise to various fields of mathematical study. Topics discussed in this book include: the analysis of new and traditional algorithms; the creation of new paradigms for implementing computational methods; the viewing of old techniques from a concrete algorithmic vantage point; and others. This text highlights many examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed.