Terry Gannon
University of Alberta

Moonshine beyond the Monster
The Bridge Connecting Algebra, Modular Forms and Physics

Series: Cambridge Monographs on Mathematical Physics
Hardback (ISBN-13: 9780521835312 | ISBN-10: 0521835313)

Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster, the first book of its kind, describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between modern mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry, and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

* This is the first authored book on Moonshine and it will have wide appeal
* A burgeoning research area, showing the connectedness of a variety of topics
* Written in a clear and pedagogical style, emphasising the fundamental ideas and interesting examples

Contents

Introduction: glimpses of the theory beneath Monstrous moonshine; 1. Classical algebra; 2. Modular stuff; 3. Gold and brass: Affine algebras and generalisations; 4. Conformal field theory: The physics of Moonshine; 5. Vertex operator algebras; 6. Modular group representations throughout the realm; 7. Monstrous Moonshine; Epilogue; References.

S. G. Hoggar
University of Glasgow

Mathematics of Digital Images
Creation, Compression, Restoration, Recognition

Hardback (ISBN-13: 9780521780292 | ISBN-10: 0521780292)

Compression, restoration and recognition are three of the key components of digital imaging. The mathematics needed to understand and carry out all these components are explained here in a style that is at once rigorous and practical with many worked examples, exercises with solutions, pseudocode, and sample calculations on images. The introduction lists fast tracks to special topics such as Principal Component Analysis, and ways into and through the book, which abounds with illustrations. The first part describes plane geometry and pattern-generating symmetries, along with some on 3D rotation and reflection matrices. Subsequent chapters cover vectors, matrices and probability. These are applied to simulation, Bayesian methods, Shannon's information theory, compression, filtering and tomography. The book will be suited for advanced courses or for self-study. It will appeal to all those working in biomedical imaging and diagnosis, computer graphics, machine vision, remote sensing, image processing and information theory and its applications.

* Written to be understood not only by engineers but by all concerned with digital image issues
* Builds up the required probability and information theory from scratch
* Draws on material from author's successful earlier book

Contents

Introduction; 1. Isometries; 2. How isometries combine; 3. The braid patterns; 4. Plane patterns and symmetries; 5. The 17 plane patterns; 6. More plane truth; 7. Vectors and matrices; 8. Matrix algebra; 9. Probability; 10. Random vectors; 11. Sampling and inference; 12. Entropy and coding; 13. Information and error-correction; 14. The Fourier transform; 15. Transforming images; 16. Scaling; 17. B-spline wavelets; 18. Further methods; References; Symbols; Selected answers; Index.