Complexity and Information

• 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.

'Clearly written, filled with interesting examples, important theorems and tantalising conjectures, this is destined to be a classic.' New Scientist