Preface -- Contents -- Metric number theory, lacunary series and systems of dilated functions -- 1 Uniform distribution modulo 1 -- 2 Metric number theory -- 3 Discrepancy -- 4 Lacunary series -- 5 Almost everywhere convergence -- 6 Sums involving greatest common divisors -- Strong uniformity -- 1 Introduction -- 2 Superuniformity and super-duper uniformity -- 2.1 Superuniformity of the typical billiard paths -- 2.2 Super-duper uniformity of the 2-dimensional ray -- 3 Superuniformmotions -- 3.1 Billiards in other shapes -- 3.2 Superuniformity of the geodesics on an equifacial tetrahedron surface -- Discrepancy theory and harmonic analysis -- 1 Introduction -- 2 Exponential sums -- 3 Fourier analysis methods -- 3.1 Rotated rectangles -- 3.2 The lower bound for circles -- 3.3 Further remarks -- 4 Dyadic harmonic analysis: discrepancy function estimates -- 4.1 Lp -discrepancy, 1 < p < ∞ -- 4.2 The L∞ discrepancy estimates -- 4.3 The other endpoint, L1 -- Explicit constructions of point sets and sequences with low discrepancy -- 1 Introduction -- 2 Lower bounds -- 3 Upper bounds -- 4 Digital nets and sequences -- 5 Walsh series expansion of the discrepancy function -- 6 The construction of finite point sets according to Chen and Skriganov -- 7 The construction of infinite sequences according to Dick and Pillichshammer -- 8 Extensions to the Lq discrepancy -- 9 Extensions to Orlicz norms of the discrepancy function -- Subsequences of automatic sequences and uniform distribution -- 1 Introduction -- 2 Automatic sequences -- 3 Subsequences along the sequence nc -- 4 Polynomial subsequences -- 5 Subsequences along the primes -- On Atanassov's methods for discrepancy bounds of low-discrepancy sequences -- 1 Introduction -- 2 Atanassov's methods for Halton sequences -- 2.1 Review of Halton sequences.

2.2 Review of previous bounds for the discrepancy of Halton sequences -- 2.3 Atanassov's methods applied to Halton sequences -- 2.4 Scrambling Halton sequences with matrices -- 3 Atanassov's method for (t,s)-sequences -- 3.1 Review of (t,s)-sequences -- 3.2 Review of bounds for the discrepancy of (t,s)-sequences -- 3.3 Atanassov'smethod applied to (t,s)- sequences -- 3.4 The special case of even bases for (t,s)-sequences -- 4 Atanassov's methods for generalized Niederreiter sequences and (??, e, ??)- sequences -- The hybrid spectral test: a unifying concept -- 1 Introduction -- 2 Adding digit vectors -- 3 Notation -- 4 The hybrid spectral test -- 5 Examples -- 5.1 Example I: Integration lattices -- 5.2 Example II: Extreme and star discrepancy -- Tractability of multivariate analytic problems -- 1 Introduction -- 2 Tractability -- 3 A weighted Korobov space of analytic functions -- 4 Integration in H(Ks,a,b) -- 5 L2-approximation in H(Ks,a,b) -- 6 Conclusion and outlook -- Discrepancy estimates for sequences: new results and open problems -- 1 Introduction -- 2 Metrical and average type discrepancy estimates for digital point sets and sequences and for good lattice point sets -- 3 Discrepancy estimates for and applications of hybrid sequences -- 4 Miscellaneous problems -- A short introduction to quasi-Monte Carlo option pricing -- 1 Overview -- 2 Foundations of financial mathematics -- 2.1 Bonds, stocks and derivatives -- 2.2 Arbitrage and the no-arbitrage principle -- 2.3 The Black-Scholesmodel -- 2.4 SDE models -- 2.5 Lévy models -- 2.6 Examples -- 3 MC and QMC simulation -- 3.1 Nonuniform random number generation -- 3.2 Generation of Brownian paths -- 3.3 Generation of Lévy paths -- 3.4 Multilevel (quasi-)Monte Carlo -- 3.5 Examples.

The construction of good lattice rules and polynomial lattice rules -- 1 Lattice rules and polynomial lattice rules -- 1.1 Lattice rules -- 1.2 Polynomial lattice rules -- 2 The worst-case error -- 2.1 Koksma-Hlawka error bound -- 2.2 Lattice rules -- 2.3 Polynomial lattice rules -- 3 Weighted worst-case errors -- 4 Some standard spaces -- 4.1 Lattice rules and Fourier spaces -- 4.2 Randomly-shifted lattice rules and the unanchored Sobolev space -- 4.3 Tent-transformed lattice rules and the cosine space -- 4.4 Polynomial lattice rules and Walsh spaces -- 5 Component-by-component constructions -- 5.1 Component-by-component construction -- 5.2 Fast component-by-component construction -- 6 Conclusion -- Index.