A Panorama of Discrepancy Theory

✍ Scribed by William Chen, Anand Srivastav, Giancarlo Travaglini (eds.)

Publisher: Springer International Publishing
Year: 2014
Tongue: English
Leaves: 708
Series: Lecture Notes in Mathematics 2107
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory.

Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling and is currently located at the crossroads of number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. This book presents an invitation to researchers and students to explore the different methods and is meant to motivate interdisciplinary research.

✦ Table of Contents

Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Upper Bounds in Classical Discrepancy Theory....Pages 3-69
Roth’s Orthogonal Function Method in Discrepancy Theory and Some New Connections....Pages 71-158
Irregularities of Distribution and Average Decay of Fourier Transforms....Pages 159-220
Superirregularity....Pages 221-316
Front Matter....Pages 317-317
Multicolor Discrepancy of Arithmetic Structures....Pages 319-424
Algorithmic Aspects of Combinatorial Discrepancy....Pages 425-457
Practical Algorithms for Low-Discrepancy 2-Colorings....Pages 459-484
Front Matter....Pages 485-485
On the Distribution of Solutions to Diophantine Equations....Pages 487-538
Discrepancy Theory and Quasi-Monte Carlo Integration....Pages 539-619
Calculation of Discrepancy Measures and Applications....Pages 621-678
Back Matter....Pages 679-698

✦ Subjects

Number Theory; Combinatorics; Fourier Analysis; Mathematics of Algorithmic Complexity; Probability Theory and Stochastic Processes; Numerical Analysis

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