A Panorama of Discrepancy Theory

  • William Chen
  • Anand Srivastav
  • Giancarlo Travaglini

Part of the Lecture Notes in Mathematics book series (LNM, volume 2107)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Classical and Geometric Discrepancy

    1. Front Matter
      Pages 1-1
    2. William Chen, Maxim Skriganov
      Pages 3-69
    3. Luca Brandolini, Giacomo Gigante, Giancarlo Travaglini
      Pages 159-220
    4. József Beck
      Pages 221-316
  3. Combinatorial Discrepancy

    1. Front Matter
      Pages 317-317
    2. Nils Hebbinghaus, Anand Srivastav
      Pages 319-424
  4. Applications and Constructions

    1. Front Matter
      Pages 485-485
    2. Josef Dick, Friedrich Pillichshammer
      Pages 539-619
    3. Carola Doerr, Michael Gnewuch, Magnus Wahlström
      Pages 621-678
  5. Back Matter
    Pages 679-698

About this book

Introduction

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 books on discrepancy theory but perhaps no one of them actually shows the present variety of points of view and applications covering the areas "Classical and Geometric Discrepancy Theory", "Combinatorial Discrepancy Theory" and "Applications and Constructions".

Our book consists of several chapters, written by experts in the specific areas, and focused on the different aspects of the theory. The book should also be an invitation to researchers and students to find a quick way into the different methods and to motivate interdisciplinary research.

Keywords

11K38;11K06;11J71;11B25;11D75;11K60;65D30;65C05;11K45 Combinatorial Discrepancy Counting Problems Geometric Discrepancy Quasi-Monte Carlo Integration

Editors and affiliations

  • William Chen
    • 1
  • Anand Srivastav
    • 2
  • Giancarlo Travaglini
    • 3
  1. 1.Department of MathematicsMacquarie UniversitySydneyAustralia
  2. 2.Department of Computer ScienceKiel UniversityKielGermany
  3. 3.Dipartimento di Statistica e Metodi QuantitativiUniversità di Milano-BicoccaMilanoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-04696-9
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-04695-2
  • Online ISBN 978-3-319-04696-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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