Felipe Cucker is Chair Professor of the Department of Mathematics at the City University of Hong Kong. Teresa Krick is Professor of Mathematics at the University of Buenos Aires. Allan Pinkus is Professor of Mathematics at the Technion – Israel Institute of Technology. Agnes Szanto is Associate Professor of Mathematics at North Carolina State University.

• 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.