Ebook: Mathematical Aspects of Scientific Software

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.

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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.

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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.
Content:
Front Matter....Pages i-xi
Mathematical Aspects of Scientific Software....Pages 1-39
The Mapping Problem in Parallel Computation....Pages 41-57
Applications of Gr?bner Bases in Non-Linear Computational Geometry....Pages 59-87
Geometry in Design: The Bezier Method....Pages 89-99
Algebraic Curves....Pages 101-122
Performance of Scientific Software....Pages 123-155
Scratchpad II: An Abstract Datatype System for Mathematical Computation....Pages 157-182
Data Parallel Programming and Basic Linear Algebra Subroutines....Pages 183-196
Integrating Symbolic, Numeric and Graphics Computing Techniques....Pages 197-208

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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.
Content:
Front Matter....Pages i-xi
Mathematical Aspects of Scientific Software....Pages 1-39
The Mapping Problem in Parallel Computation....Pages 41-57
Applications of Gr?bner Bases in Non-Linear Computational Geometry....Pages 59-87
Geometry in Design: The Bezier Method....Pages 89-99
Algebraic Curves....Pages 101-122
Performance of Scientific Software....Pages 123-155
Scratchpad II: An Abstract Datatype System for Mathematical Computation....Pages 157-182
Data Parallel Programming and Basic Linear Algebra Subroutines....Pages 183-196
Integrating Symbolic, Numeric and Graphics Computing Techniques....Pages 197-208
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