Discrepancy Theory 1st edition by Dmitriy Bilyk, Josef Dick, Friedrich Pillichshammer – Ebook PDF Instant Download/Delivery: 3110651157, 978-3110651157
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Product details:
ISBN 10: 3110651157
ISBN 13: 978-3110651157
Author: Dmitriy Bilyk, Josef Dick, Friedrich Pillichshammer
The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory.
Discrepancy Theory 1st Table of contents:
-
Introduction to Discrepancy Theory
- What is Discrepancy Theory?
- Historical Background and Motivation
- Basic Definitions and Concepts
- Discrepancy in Geometry, Number Theory, and Combinatorics
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Mathematical Foundations of Discrepancy
- Basic Set Theory and Functions
- Randomized Algorithms in Discrepancy Theory
- Linear Algebra in Discrepancy Problems
- Probability Theory and Expected Discrepancy
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Types of Discrepancy
- Classical Discrepancy Measures (Star Discrepancy, Cartesian Product Discrepancy)
- Geometrical Discrepancy and Point Distributions
- Discrepancy of Set Systems
- Bounds on Discrepancy
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Low Discrepancy Sequences
- Definition and Properties of Low Discrepancy Sequences
- Applications to Numerical Integration and Sampling
- The Role of Quasi-Monte Carlo Methods
- Construction of Low Discrepancy Sequences (e.g., Halton, Sobol Sequences)
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Discrepancy in High-Dimensional Settings
- High-dimensional Discrepancy Problems
- Generalized Discrepancy Bounds
- Techniques for Studying Discrepancy in Higher Dimensions
- Applications in Approximation Theory and Optimization
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Algorithmic Approaches in Discrepancy Theory
- Greedy Algorithms for Discrepancy Minimization
- Randomized Algorithms for Discrepancy Bounds
- Approximation Algorithms and Techniques
- Computational Complexity in Discrepancy Theory
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Applications of Discrepancy Theory
- Applications to Numerical Integration and Quasi-Monte Carlo Methods
- Data Approximation and Clustering
- Discrepancy in Coding Theory and Cryptography
- Applications in Random Sampling and Data Analysis
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Recent Advances in Discrepancy Theory
- New Bounds and Techniques in Discrepancy
- Contributions from Modern Combinatorics and Geometry
- Connections to Other Fields (e.g., Learning Theory, Computational Geometry)
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Open Problems and Future Directions
- Key Open Problems in Discrepancy Theory
- Research Directions and Areas for Further Exploration
- Interdisciplinary Connections and Applications
Appendices
- A: Mathematical Preliminaries (Linear Algebra, Probability, and Set Theory)
- B: Selected Proofs and Theorems
- C: List of Key Results and Conjectures
- D: Bibliography and Further Reading
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Dmitriy Bilyk,Josef Dick,Friedrich Pillichshammer,Discrepancy Theory