Friedman, Avner, Ohio State University, Columbus, OH, USA;
Ross, David, Rochester Institute of Technology, Rochester, NY, USA

Mathematical Models in Photographic Sciences

2003V, 178 p. Hardcover
3-540-44219-7

This book presents mathematical models that arise in current photographic science. The book contains seventeen chapters, each dealing with one area of photographic science, and a final chapter containing exercises. Each chapter, except the two introductory chapters and the last one, begins with general background information at a level understandable by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical tools such as ordinary differential equations, partial differential equations, and stochastic processes. Next, some mathematical results are mentioned, often providing a partial solution to problems raised by the model. Finally, most chapters include open problems. The last chapter of the book contains "Modeling and Applied Mathematics" exercises based on the material presented in the earlier chapters.These exercises are intended primarily for graduate students and advanced undergraduates.

Keywords: coating flows, crystal growth, gelation, image formation, reaction diffusion systems

Contents: Sample Chapter for WWW: Chapter 10.

Series: Mathematics in Industry. Volume. 3


Gross, Mark, University of Warwick, UK; Huybrechts, Daniel, University of Cologne, Germany;
Joyce, Dominic, Lincoln College, Oxford, UK

Calabi-Yau Manifolds and Related Geometries
Lectures at a Summer School in Nordfjordeid, Norway, June, 2001

2003VI, 242 p. Softcover
3-540-44059-3

This book is an expanded version of lectures given at a summer school on symplectic geometry in Nordfjordeid, Norway, in June 2001. The unifying feature of the book is an emphasis on Calabi-Yau manifolds. The first part discusses holonomy groups and calibrated submanifolds, focusing on special Lagrangian submanifolds and the SYZ conjecture. The second studies Calabi-Yau manifolds and mirror symmetry, using algebraic geometry. The final part describes compact hyperkahler manifolds, which have a geometric structure very closely related to Calabi-Yau manifolds.
The book is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory and intended as an introductory text, requiring only limited background knowledge. Proofs or sketches are given for many important results. Moreover, exercises are provided.

Keywords: calabi-yau manifolds, hyperkahler manifolds, mirror symmetry, special lagrangian submanifolds

Contents: I. Riemannian holonomy groups and calibrated geometry by Dominic Joyce.- II. Calabi-Yau manifolds and mirror symmetry by Mark Gross.- III. Compact hyperkahler manifolds by Daniel Huybrechts.- References.- Index.

Series: Universitext.


Knottnerus, Paul, Statistics Netherlands, The Netherlands

Sample Survey Theory
Some Pythagorean Physics

2003Approx. 415 pp. Hardcover
0-387-95407-4

The volume deals with the classical question how from a sample survey with observations on a variable conclusions can be drawn doncering the mean value of that variable in the whole population. It provides a novel and systematic treatement of sampling theory considered from the angel of athe samle autocorrelation coefficient p (rho.)

Contents: Preface.- Notation and Introduction.- Elementary Statistic.- A "Normal" Approach to Unequal Probability Sampling.- A General rho Theory on Survey Sampling.- Variance Estimation for Some Standard Designs.- Multistage and Cluster (Sub)Sampling.- Some Speical (Sub)Cluster Sampling Designs.- Estimation of the Sample Autocorrelation Coeffcient pz.- Variance Approximations.- Systematic Sampling with Unequal Probabilities.- The Regression Estimator Revisited.- The General Restriction Estimator in Multisurvey Sampling.- Weighting Procedures.

Series: Springer Series in Statistics.


Polster, Burkard, Monash University, Clayton, VIC, Australia

The Mathematics of Juggling

2003Approx. 250 pp. 106 figs. Softcover
0-387-95513-5

Learn to juggle numbers! This book is the first comprehensive account of the mathematical techniques and results used in the modelling of juggling patterns. This includes all known and many new results about juggling sequences and matrices, the mathematical skeletons of juggling patterns.
Many useful and entertaining tips and tricks spice up the mathematical menu presented in this book. There are detailed descriptions of jugglable and attractive juggling sequences, easy zero-gravity juggling, robot juggling, as well as fun juggling of words, anti-balls, and irrational numbers.
The book also includes novel, or at least not very well known connections with topics such as bell ringing, knot theory, and the many body problem. In fact, the chapter on mathematical bell ringing has been expanded into the most comprehensive survey in the literature of the mathematics used by bell ringers.
Accessible at all levels of mathematical sophistication, this is a book for mathematically wired jugglers, mathematical bell ringers, combinatorists, mathematics educators, and just about anybody interested in beautiful and unusual applications of mathematics.

Keywords: Jonglieren, Juggling, Popular science

Contents: Juggling - an Introduction.- Simple Juggling.- Multiplex Juggling.- Multihand Juggling.- Practical Juggling.- Jingling, or, Ringing the Changes.- Juggling Loose Ends.- Appendix A: Stereograms of Hamiltonian Sycles.- References.- Index.


Serre, Jean-Pierre, College de France, Paris, France

Trees, 2nd printing 2003

1st ed. 1980. 2nd printing2003VI, 139 p. Hardcover
3-540-44237-5

The present book is an English translation of "Arbres, Amalgames, SL(2)", published in 1977 by J-P.Serre, and written with the collaboration of H.Bass. The first chapter describes the "arboreal dictionary" between graphs of groups and group actions on trees. The second chapter gives applications to the Bruhat-Tits tree of SL(2) over a local field.

Keywords: algebra, amalgams, graphs, groups

"In the case of an author like Serre, there is almost no need to underline the book's qualities of elegance and precision: over and above these, it provides abundant links to other topics, particularly by means of the remarks and the numerous exercises which, for the most part, are not easy to solve, but genuinely augment the content of the book. The greatest quality of this book however, is, in my opinion, that one finds in it many new and interesting ideas of very considerable substance, but presented in their very simplest form."
H. Behr, Frankfurt in: Jahresbericht der DMV, (84/3) 1982

Contents: Chapter I: Trees and Amalgams: Amalgams.- Trees.- Trees and free groups.- Trees and amalgams.- Structure of a group acting on a tree.- Amalgams and fixed points Chapter II: SL(2):The tree of SL(2) over a local field.- Arithmetic subgroups of the groups GL(2) and SL(2) over a function field of one variable.

Series: Springer Monographs in Mathematics.