Mathematical Aspects of Scientific Software.- The Mapping Problem in Parallel Computation.- Applications of Gröbner Bases in Non-linear Computational Geometry.- Geometry in Design: The Bézier Method.- Algebraic Curves.- Performance of Scientific Software.- Scratchpad II: An Abstract Datatype System for Mathematical Computation.- Data Parallel Programming and Basic Linear Algebra Subroutines.- Integrating Symbolic, Numeric and Graphics Computing Techniques.

Since scientific software is the fuel that drives today's computers to solve a vast range of problems, huge efforts are being put into the development of new software, systems and algorithms for scientific problem solving. This book explores how scientific software impacts the structure of mathematics, how it creates new subfields, and how new classes of mathematical problems arise. The focus is on five topics where the impact is currently being felt and where important new challenges exist, namely: the new subfield of parallel and geometric computations, the emergence of symbolic computation systems into "general" use, the potential emergence of new, high-level mathematical systems, and the crucial question of how to measure the performance of mathematical problem solving tools.