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Lecture Notes on Lattices, Bases, and the Reduction Problem: Expository Notes (Classic Reprint) - Softcover
Synopsis
A practical tour of lattices, bases, and reduction methods for numbers and spaces.
This book introduces the geometry of numbers, lattice bases, and the famous LLL basis reduction algorithm with clear definitions, theorems, and proofs.
Geared toward readers with a solid math background, it explains how a lattice can have many bases that relate through unimodular transformations. The text covers determinants as a lattice invariant, dual lattices, and Gram–Schmidt orthogonalization, with Hadamard’s inequality tying geometry to linear algebra. It then moves to algorithmic questions: how to find nice bases and short lattice vectors, and what problems are computationally hard.
- What a lattice is, how bases and determinants work, and why unimodular transformations matter.
- How Gram–Schmidt orthogonalization connects basis vectors to orthogonal components.
- Theoretical bounds and practical algorithms for reducing bases and finding short vectors.
- Key results like Minkowski’s theorem, Hermite’s bound, and the LLL reduction procedure.
Ideal for readers of advanced mathematics or theoretical computer science who want solid, applicable insight into lattice reduction and its limits.
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Lecture Notes on Lattices, Bases, and the Reduction Problem: Expository Notes
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Paperback. Condition: New. Print on Demand. This book delves into the enigmatic world of lattices, bases, and the captivating reduction problem. Once exclusively explored within esoteric mathematical circles, the author unveils these concepts with an accessible approach, demonstrating their applications in contemporary computer science. The book ingeniously reformulates complex problems as geometric puzzles involving lattices, providing a novel perspective that has revolutionized algorithms in diverse fields. The author masterfully weaves together classical theory and cutting-edge insights, offering a comprehensive guide to this fascinating mathematical landscape. Through captivating historical accounts and illuminating examples, this book empowers readers to delve into the depths of lattice theory, unravel the reduction problem, and appreciate its profound implications for both theoretical and practical domains. With its lucid explanations and illuminating approach, this book offers a captivating journey into a world of mathematical elegance and computational ingenuity. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332150113_0
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Lecture Notes on Lattices, Bases, and the Reduction Problem Expository Notes Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332150113
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Lecture Notes on Lattices, Bases, and the Reduction Problem Expository Notes Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332150113
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