Mathematics and Computation, a Contemporary View

The Abel Symposium 2006 Proceedings of the Third Abel Symposium, Alesund, Norway, May 25–27, 2006

  • Hans Munthe-Kaas
  • Brynjulf Owren
Part of the Abel Symposia book series (ABEL, volume 3)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Xianfeng Gu, Yalin Wang, Hsiao-Bing Cheng, Li-Tien Cheng, Shing-Tung Yau
    Pages 1-19
  3. S. Gemmrich, N. Nigam, O. Steinbach
    Pages 21-37
  4. P. F. Tupper
    Pages 95-108

About these proceedings

Introduction

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.

We are witnessing a development where a focus on computability, computing and algorithms is contributing towards a unification of areas of computer science, applied and pure mathematics. The 2006 Abel symposium brought together some of the leading international researchers working in these areas, presented a snapshot of current state of the art, and raised questions about future research directions.

Keywords

Abel symposia algorithms applied mathematics complexity computability computational mathematics computer science programming

Editors and affiliations

  • Hans Munthe-Kaas
    • 1
  • Brynjulf Owren
    • 2
  1. 1.Department of MathematicsUniversity of BergenBergenNorway
  2. 2.Department of Mathematical SciencesNTNUTrondheimNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-68850-1
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-68848-8
  • Online ISBN 978-3-540-68850-1