A Panorama of Discrepancy Theory

• Corporate Author: SpringerLink (Online service)
• Other Authors: Chen, William (Editor), Srivastav, Anand (Editor), Travaglini, Giancarlo (Editor)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Lecture Notes in Mathematics, 2107
• Subjects: Mathematics.; Fourier analysis.; Algorithms.; Numerical analysis.; Number theory.; Probabilities.; Combinatorics.; Number Theory.; Fourier Analysis.; Mathematics of Algorithmic Complexity.; Probability Theory and Stochastic Processes.; Numerical Analysis.

Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling. Discrepancy theory is currently at a crossroads between number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. There are several excellent...

Table of Contents:

• Preface
• Classical and Geometric Discrepancy
• Upper Bounds in Classical Discrepancy Theory
• Roth’s Orthogonal Function Method in Discrepancy Theory and Some New Connections.- Irregularities of distribution and average decay of Fourier transforms.- Superirregularity
• Combinatorial Discrepancy
• Multicolor Discrepancy of Arithmetic Structures
• Algorithmic Aspects of Combinatorial Discrepancy
• Practical Algorithms for Low-Discrepancy 2-Colorings
• Applications and Constructions
• On the distribution of solutions to diophantine equations
• Discrepancy theory and quasi-Monte Carlo integration
• Calculation of Discrepancy Measures and Applications
• Author index
• Subject index.