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This textbook introduces readers to the basic concepts of
quasi-Monte Carlo methods for numerical integration and to the
theory behind them. The comprehensive treatment of the subject with
detailed explanations comprises, for example, lattice rules,
digital nets and sequences and discrepancy theory. It also presents
methods currently used in research and discusses practical
applications with an emphasis on finance-related problems. Each
chapter closes with suggestions for further reading and with
exercises which help students to arrive at a deeper understanding
of the material presented. The book is based on a one-semester,
two-hour undergraduate course and is well-suited for readers with a
basic grasp of algebra, calculus, linear algebra and basic
probability theory. It provides an accessible introduction for
undergraduate students in mathematics or computer science.
This book is summarizing the results of the workshop "Uniform
Distribution and Quasi-Monte Carlo Methods" of the RICAM Special
Semester on "Applications of Algebra and Number Theory" in October
2013. The survey articles in this book focus on number theoretic
point constructions, uniform distribution theory, and quasi-Monte
Carlo methods. As deterministic versions of the Monte Carlo method,
quasi-Monte Carlo rules enjoy increasing popularity, with many
fruitful applications in mathematical practice, as for example in
finance, computer graphics, and biology. The goal of this book is
to give an overview of recent developments in uniform distribution
theory, quasi-Monte Carlo methods, and their applications,
presented by leading experts in these vivid fields of research.
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