Mathematics and Computation, a Contemporary View

The 2006 Abel symposium is focusing on contemporary research involving interaction between computer science, computational science and mathematics. In recent years, computation has been affecting pure mathematics in fundamental ways. Conversely, ideas and methods of pure mathematics are becoming increasingly important within computational and applied mathematics. At the core of computer science is the study of computability and complexity for discrete mathematical structures. Studying the foundations of computational mathematics raises similar questions concerning continuous mathematical structures. There are several reasons for these developments. The exponential growth of computing power is bringing computational methods into ever new application areas.

Equally important is the advance of software and programming languages, which to an increasing degree allows the representation of abstract mathematical structures in program code. Symbolic computing is bringing algorithms from mathematical analysis into the hands of pure and applied mathematicians, and the combination of symbolic and numerical techniques is becoming increasingly important both in computational science and in areas of pure mathematics.

Top-level computational mathematicians wrote on current research topics inspired by an Abel Foundation sponsored workshop Includes supplementary material: sn.pub/extras

Contenu
Geometric Methods in Engineering Applications.- Boundary Integral Equations for the Laplace-Beltrami Operator.- Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations.- Energy-Preserving and Stable Approximations for the Two-Dimensional Shallow Water Equations.- A Conjecture about Molecular Dynamics.- The Dynamics of Transition to Turbulence in Plane Couette Flow.