Complexity and Information
Complexity and Information
A. G. Werschulz , Fordham University and Columbia University, New York
Looking for an examination copy?
This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.
$64.00
USDThe twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.
- First book for a general audience on the computational complexity of continuous models of science
- Coverage of new, improved methods for mathematical finance
- Comprehensive bibliography covering the last decade's progress in this exciting area
Reviews & endorsements
"This short volume packs so much information into so small a space that it stretches the imagination as to know how the authors did it. Clearly written, filled with interesting examples, important theorems and tantalizing conjectures, this book should be taken as holiday reading by everyone concerned with using a computer to solve real problems. It's destined to be a classic." New Scientist
"The exposition is straightforward and clear, with well-chosen diagrams to smooth the way...The broad expanse between technical and general themes may be one of the more challenging and appealing aspects of the book...This book provides worthwhile evidence that IBC (information based complexity) is an important, albeit highly specialized, approach to understanding and applying information in modeling the complexity of a variety of mathematically formulated problems." Complexity
"...gives a good grounding in the essential issues of complexity and information. For an overview of the larger issues, this small book is excellent." Bulletin of the AMS
"Really a jewel...written with loving care and in an elegant style." Institute of Discrete Mathematics
"Highly recommended." Choice
"Anyone interested in numerical analysis and scientific computing can profit from the book and its many insights." Siam Review
Product details
January 1999Paperback
9780521485067
154 pages
216 × 140 × 9 mm
0.2kg
10 b/w illus. 5 tables
Available
Table of Contents
- Part I. Fundamentals:
- 1. Introduction
- 2. Information-based complexity
- 3. Breaking the curse of dimensionality
- Part II. Some Interesting Topics:
- 4. Very high-dimensional integration and mathematical finance
- 5. Complexity of path integration
- 6. Are ill-posed problems solvable?
- 7. Complexity of nonlinear problems
- 8. What model of computation should be used by scientists?
- 9. Do impossibility theorems from formal models limit scientific knowledge? 10. Complexity of linear programming
- 11. Complexity of verification
- 12. Complexity of implementation testing
- 13. Noisy information
- 14. Value of information in computation
- 15. Assigning values to mathematical hypotheses
- 16. Open problems
- 17. A brief history of information-based complexity
- Part III. References:
- 18. A guide to the literature
- Bibliography
- Subject index
- Author index.
