An introduction to contemporary quasi Monte Carlo methods, digital nets and sequences, and discrepancy theory. Includes many exercises, examples and illustrations.

Josef Dick is a lecturer in the School of Mathematics and Statistics at the University of New South Wales, Australia.

Preface; Notation; 1. Introduction; 2. Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces; 3. Geometric discrepancy; 4. Nets and sequences; 5. Discrepancy estimates and average type results; 6. Connections to other discrete objects; 7. Duality Theory; 8. Special constructions of digital nets and sequences; 9. Propagation rules for digital nets; 10. Polynomial lattice point sets; 11. Cyclic digital nets and hyperplane nets; 12. Multivariate integration in weighted Sobolev spaces; 13. Randomisation of digital nets; 14. The decay of the Walsh coefficients of smooth functions; 15. Arbitrarily high order of convergence of the worst-case error; 16. Explicit constructions of point sets with best possible order of L2-discrepancy; Appendix A. Walsh functions; Appendix B. Algebraic function fields; References; Index.