Preface; List of contributors; 1. The state of the art in Smale's 7th problem C. Beltrán; 2. The shape of data Gunnar Carlsson; 3. Upwinding in finite element systems of differential forms S. H. Christiansen; 4. On the complexity of computing quadrature formulas for SDEs S. Dereich, T. Müller-Gronbach and K. Ritter; 5. The quantum walk of F. Riesz F. A. Grünbaum and L. Velázquez; 6. Modulated Fourier expansions for continuous and discrete oscillatory systems E. Hairer and Ch. Lubich; 7. The dual role of convection in 3D Navier-Stokes equations T. Y. Hou, Z. Shi and S. Wang; 8. Algebraic and differential invariants Evelyne Hubert; 9. Through the kaleidoscope: symmetries, groups and Chebyshev-approximations from a computational point of view H. Munthe-Kaas, M. Nome and B. N. Ryland; 10. Sage: creating a viable free open source alternative to Magma, Maple, Mathematica and MATLAB W. Stein.