Softcover ISBN:  9781470470333 
Product Code:  STML/107 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
eBook ISBN:  9781470476632 
Product Code:  STML/107.E 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
Softcover ISBN:  9781470470333 
eBook: ISBN:  9781470476632 
Product Code:  STML/107.B 
List Price:  $118.00 $88.50 
MAA Member Price:  $94.40 $70.80 
Softcover ISBN:  9781470470333 
Product Code:  STML/107 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
eBook ISBN:  9781470476632 
Product Code:  STML/107.E 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
Softcover ISBN:  9781470470333 
eBook ISBN:  9781470476632 
Product Code:  STML/107.B 
List Price:  $118.00 $88.50 
MAA Member Price:  $94.40 $70.80 

Book DetailsStudent Mathematical LibraryVolume: 107; 2024; 325 ppMSC: Primary 51; 11; 32; 52
This book offers a gentle introduction to the geometry of numbers from a modern Fourieranalytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class.
Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.
ReadershipUndergraduate and graduate students and researchers interested in analysis and periodical structures.

Table of Contents

Chapters

Motivational problem: Tiling a rectangle with rectangles

Examples nourish the theory

The basics of Fourier analysis

Geometry of numbers, Part I: Minkowski meets Siegel

An introduction to Euclidean lattices

Geometry of numbers, Part II: Blichfedt’s theorem

The Fourier transform of a polytope via its vertex description: Brion’s theorem

What is an angle in higher dimensions?

Appendix A. Solutions and hints to selected problems

Appendix B. The dominated convergence theorem and other goodies


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This book offers a gentle introduction to the geometry of numbers from a modern Fourieranalytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class.
Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.
Undergraduate and graduate students and researchers interested in analysis and periodical structures.

Chapters

Motivational problem: Tiling a rectangle with rectangles

Examples nourish the theory

The basics of Fourier analysis

Geometry of numbers, Part I: Minkowski meets Siegel

An introduction to Euclidean lattices

Geometry of numbers, Part II: Blichfedt’s theorem

The Fourier transform of a polytope via its vertex description: Brion’s theorem

What is an angle in higher dimensions?

Appendix A. Solutions and hints to selected problems

Appendix B. The dominated convergence theorem and other goodies