Abstract
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.
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