Preface; 1. Singularities and computation of minimizers for variational problems J. M. Ball; 2. Adaptive finite element methods for flow problems R. Becker, M. Braack and R. Rannacher; 3. Newton's method and some complexity aspects of the zero-finding problem J.-P. Dedieu; 4. Kronecker's smart little black boxes M. Giusti and J. Heintz; 5. Numerical analysis in Lie groups A. Iserles; 6. Feasibility control in nonlinear optimization M. Marazzi and J. Nocedal; 7. Six lectures on the geometric integration of ODEs R. I. MaLachlan and G. R. Quispel; 8. When are integration and discrepancy tractable? E. Novak and H. Wozniakowski; 9. Moving frames - in geometry, algebra, computer vision, and numerical analysis P. J. Olver; 10. Harmonic map flows and image processing G. Sapiro; 11. Statistics from computations H. Sigurgeirsson and A. M. Stuart; 12. Simulation of stochastic processes and applications D. Talay; 13. Real-time numerical solution to Duncan-Mortensen-Zakai equation S.-T. Yau and S. S.-T. Yau.