Hardcover ISBN:  9781470476236 
Product Code:  GSM/247 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Softcover ISBN:  9781470478957 
Product Code:  GSM/247.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470478964 
Product Code:  GSM/247.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470478957 
eBook: ISBN:  9781470478964 
Product Code:  GSM/247.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 
Hardcover ISBN:  9781470476236 
Product Code:  GSM/247 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Softcover ISBN:  9781470478957 
Product Code:  GSM/247.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470478964 
Product Code:  GSM/247.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470478957 
eBook ISBN:  9781470478964 
Product Code:  GSM/247.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsGraduate Studies in MathematicsVolume: 247; 2024; Estimated: 611 ppMSC: Primary 11; 28; 30; 35; 42; 44; 58
This book offers a comprehensive exploration of fractal dimensions, selfsimilarity, and fractal curves. Targeting undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book.
Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to selfsimilar sets and their construction via the iteration of contraction mappings.
The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including wellknown fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a standalone resource and a gateway to deeper explorations in fractal geometry.
ReadershipUndergraduate and graduate students interested in fractals.

Table of Contents

Preliminary material

Introduction to concepts in fractal geometry

Metric spaces and fixed point theorem

Measure theory and integrals

Dimension theory

Iterated function systems and selfsimilarity

Introduction to Hausdorff measure and dimension

$\delta$Approximate Hausdorff measures, via Carathéodory’s theory

Construction and properties of Hausdorff measure

Minkowski content and Minkowski dimension

Fractal curves and their complex dimensions

Epilogue: A primer of fractal curves and their complex dimensions

Appendices

Upper and lower limits

Carathéodory’s approach to measure theory

Acknowledgments

Bibliography

Index of symbols

Author index

Subject index


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
This book offers a comprehensive exploration of fractal dimensions, selfsimilarity, and fractal curves. Targeting undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book.
Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to selfsimilar sets and their construction via the iteration of contraction mappings.
The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including wellknown fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a standalone resource and a gateway to deeper explorations in fractal geometry.
Undergraduate and graduate students interested in fractals.

Preliminary material

Introduction to concepts in fractal geometry

Metric spaces and fixed point theorem

Measure theory and integrals

Dimension theory

Iterated function systems and selfsimilarity

Introduction to Hausdorff measure and dimension

$\delta$Approximate Hausdorff measures, via Carathéodory’s theory

Construction and properties of Hausdorff measure

Minkowski content and Minkowski dimension

Fractal curves and their complex dimensions

Epilogue: A primer of fractal curves and their complex dimensions

Appendices

Upper and lower limits

Carathéodory’s approach to measure theory

Acknowledgments

Bibliography

Index of symbols

Author index

Subject index