This book explains how a non-random method, based on congruences and Weyl’s theorems, can produce faster convergence than traditional random sampling in high-dimensional integrals. It outlines the ideas, the math, and practical implications for problems like chain reactions and other stochastic models.

Opening with the Monte Carlo method, the work then builds a framework for using orderly point sequences in the unit cube. It shows how carefully chosen, linearly independent irrational numbers determine a full sampling scheme and how this can lead to reduced fluctuations in estimates. The discussion spans theory, statistical treatment, and numerical results, with attention to when the improvement is most noticeable.

How systematic sampling differs from random sampling and when it helps most.
Connections between uniform distribution, Fourier series, and convergence rates.
Practical considerations for implementing the method, including error behavior and digits on a machine.
Numerical examples that illustrate the method’s impact on Monte Carlo calculations.

Ideal for readers of numerical analysis and Monte Carlo methods seeking a rigorous, implementable alternative to standard random sampling.

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