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A Panorama of Discrepancy Theory

  • Book
  • © 2014

Overview

Editors:
  1. William Chen

    1. Department of Mathematics, Macquarie University, Sydney, Australia

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  2. Anand Srivastav

    1. Department of Computer Science, Kiel University, Kiel, Germany

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  3. Giancarlo Travaglini

    1. Dipartimento di Statistica e Metodi Quantitativi, Università di Milano-Bicocca, Milano, Italy

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  • Provides an integrated view of discrepancy theory and its applications
  • The various areas of discrepancy theory are bridged with a focus on the state of the art
  • Serves as invitation to researchers and students to explore the different methods and to motivate interdisciplinary research

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

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About this book

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.

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Keywords

Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Classical and Geometric Discrepancy

    1. Front Matter

      Pages 1-1
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    2. Upper Bounds in Classical Discrepancy Theory

      • William Chen, Maxim Skriganov
      Pages 3-69

    3. Roth’s Orthogonal Function Method in Discrepancy Theory and Some New Connections

      • Dmitriy Bilyk
      Pages 71-158

    4. Irregularities of Distribution and Average Decay of Fourier Transforms

      • Luca Brandolini, Giacomo Gigante, Giancarlo Travaglini
      Pages 159-220

    5. Superirregularity

      • József Beck
      Pages 221-316

  3. Combinatorial Discrepancy

    1. Front Matter

      Pages 317-317
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    2. Multicolor Discrepancy of Arithmetic Structures

      • Nils Hebbinghaus, Anand Srivastav
      Pages 319-424

    3. Algorithmic Aspects of Combinatorial Discrepancy

      • Nikhil Bansal
      Pages 425-457

    4. Practical Algorithms for Low-Discrepancy 2-Colorings

      • Lasse Kliemann
      Pages 459-484

  4. Applications and Constructions

    1. Front Matter

      Pages 485-485
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    2. On the Distribution of Solutions to Diophantine Equations

      • Ákos Magyar
      Pages 487-538

    3. Discrepancy Theory and Quasi-Monte Carlo Integration

      • Josef Dick, Friedrich Pillichshammer
      Pages 539-619

    4. Calculation of Discrepancy Measures and Applications

      • Carola Doerr, Michael Gnewuch, Magnus Wahlström
      Pages 621-678

  5. Back Matter

    Pages 679-698
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Editors and Affiliations

  • Department of Mathematics, Macquarie University, Sydney, Australia

    William Chen

  • Department of Computer Science, Kiel University, Kiel, Germany

    Anand Srivastav

  • Dipartimento di Statistica e Metodi Quantitativi, Università di Milano-Bicocca, Milano, Italy

    Giancarlo Travaglini

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