Geometric Discrepancy

The book "Geometric Discrepancy" by Jiri Matousek provides a comprehensive introduction to discrepancy theory, which deals with the irregular distribution of points in geometric spaces. It addresses fundamental questions regarding the optimal distribution of points in the unit square and quantifies the irregularities that occur in any such distribution. The theory has its roots in number theory and has developed into a broad and diverse field of research since the 1930s. The book is aimed at students of mathematics and theoretical computer science, offering both basic and advanced content that has previously only been accessible in research papers. It highlights the connections to Ramsey theory, hypergraphs, and provides practical methods for numerical integration and related applications in areas such as financial calculations, computer graphics, and computational physics.