Judith R. Goodstein, California Institute of Technology, Pasadena, CA

The Volterra Chronicles:
The Life and Times of an Extraordinary Mathematician 1860-1940

History of Mathematics, Volume: 31
2007; approx. 315 pp; hardcover
ISBN-10: 0-8218-3969-1
ISBN-13: 978-0-8218-3969-0

The life of Vito Volterra, one of the finest scientists and mathematicians Italy ever produced, spans the period from the unification of the Italian peninsula in 1860 to the onset of the Second World War--an era of unparalleled progress and unprecedented turmoil in the history of Europe. Born into an Italian Jewish family in the year of the liberation of Italy's Jewish ghettos, Volterra was barely in his twenties when he made his name as a mathematician and took his place as a leading light in Italy's modern scientific renaissance. By his early forties, he was a world-renowned mathematician, a sought-after figure in European intellectual and social circles, the undisputed head of Italy's mathematics and physics school--and still living with his mother, who decided the time was ripe to arrange his marriage. When Italy entered World War I in 1915, the fifty-five-year-old Volterra served with distinction and verve as a lieutenant and did not put on civilian clothes again until the Armistice of 1918. By 1925, he was president of the world's oldest scientific society, the Accademia dei Lincei, the founder and president of Italy's National Research Council, a mentor to the brilliant and restless Enrico Fermi, and "Mr. Italian Science" to the rest of the world. But none of this was enough to keep the government of Benito Mussolini from stripping him of all his honors and affiliations in 1931, when he was one of only twelve professors in the entire country to refuse to sign an oath of loyalty to the Fascist regime.

This book, based in part on unpublished personal letters and interviews, traces the extraordinary life and times of one of Europe's foremost scientists and mathematicians, from his teenage struggles to avoid the stifling life of a "respectable" bank clerk in Florence, to his seminal mathematical work--which today influences fields as diverse as economics, physics, and ecology--and from his spirited support of Italy's scientific and democratic institutions during his years as an Italian Senator, to his steadfast defiance of the Fascists and Mussolini. In recounting the life of this outstanding scientist, European Jewish intellectual, committed Italian patriot, and devoted if frequently distracted family man, The Volterra Chronicles depicts a remarkable individual in a prodigious age and takes the reader on a vivid and splendidly detailed historical journey.

Copublished with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.

Readership

Undergraduates interested in history and the history of mathematics.

Table of Contents

"The Jewish mathematician"
"A new era is dawning," 1860
"This, above all, I promise," 1863-1870
"That damned passion," 1874-1877
"Long live the republic," 1878-1882
"Professor by deed," 1880-1883
"Our professor of small intervals," 1883-1893
"The life I live," 1887-1895
"Demonstrations of their resentment," 1893-1900
"God liberate us from his symbols"
"It is the greatest desire of my life," 1900
"Most important for our fatherland"
"Will they create a new world?"
"A political man"
"A professor in America"
"Empires die"
Epilogue
Illustrations
Sir Edmund Whittaker, "Vito Volterra, 1860-1940"
On the attempts to apply mathematics to the biological and social sciences
Science at the present moment and the new Italian society for the progress of science
Acknowledgments
Selected bibliography
Notes
Index


Edited by: JongHae Keum, Korea Institute for Advanced Study, Seoul, Korea,
and Shigeyuki Kondo, Nagoya University, Japan

Algebraic Geometry

Contemporary Mathematics, Volume: 422
2007; approx. 234 pp; softcover
ISBN-10: 0-8218-4201-3
ISBN-13: 978-0-8218-4201-0

This volume contains the proceedings of the Korea-Japan Conference on Algebraic Geometry in honor of Igor Dolgachev on his sixtieth birthday. The articles in this volume explore a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered by this volume are algebraic curve theory, algebraic surface theory, moduli space, automorphic forms, Mordell-Weil lattices, and automorphisms of hyperkahler manifolds. This book is an excellent and rich reference source for researchers.

Readership

Graduate students and research mathematicians interested in algebraic geometry.

Table of Contents

L. A. Borisov -- Holomorphic Eisenstein series with Jacobian twists
E. Dardanelli and B. van Geemen -- Hessians and the moduli space of cubic surfaces
M. Gizatullin -- On covariants of plane quartic associated to its even theta characteristic
J. Keum -- A rationality criterion for projective surfaces-Partial solution to Kollar's conjecture
S. Kondo -- The moduli space of 8 points on mathbb{P}^1 and automorphic forms
E. Looijenga -- Invariants of quartic plane curves as automorphic forms
V. V. Nikulin -- On correspondences of a K3 surface with itself. II
K. Oguiso -- Automorphisms of hyperkahler manifolds in the view of topological entropy
I. Shimada and D.-Q. Zhang -- K3 surfaces with ten cusps
T. Shioda -- Classical Kummer surfaces and Mordell-Weil lattices
D.-Q. Zhang -- Niemeier lattices and K3 groups

Leo Dorst / Informatics Institute, Faculty of Sciences, University of Amsterdam, The Netherlands
Daniel Fontijne / Intelligent Autonomous Systems, University of Amsterdam, The Netherlands
Stephen Mann / University of Waterloo, Ontario, Canada

Geometric Algebra for Computer Science
An Object-Oriented Approach to Geometry

The first book on Geometric Algebra for programmers in computer graphics and entertainment computing
Written by leaders in the field providing essential information on this new technique for 3D graphics
This full colour book includes a website with GAViewer, a program to experiment with GA

Contents

Preface; 1 Introduction; 2 The Spanning Product of Geometric Algebra; 3 The Metric Products of Geometric Algebra; 4 Linear Transformations of Subspaces; 5 The Fundamental Product of Geometric Algebra; 6 Rotations and Reflections as Versors; 7 Homogeneous Models of Geometry; 8 The Conformal Model of Euclidean Geometry; 9 Structure; 10 Using the Geometry; 11 Using the Geometry in a Ray Tracing Application; 12 Implementation; Appendices; A. Glossary; B. Matrices; C. Inferior Inner Products; D. GaViewer

Readership: Professionals working in fields requiring complex geometric computation such as robotics, computer graphics, and computer games. Students in graduate or advanced undergraduate programs in computer science.

Series: The Morgan Kaufmann Series in Computer Graphics

ISBN: 0-12-369465-5 Hardback
Measurements: 7 1/2 X 9 1/4 in
Pages: 500

Karl Friston (Editor)
Functional Imaging Laboratory, Wellcome Department of Imaging Neuroscience, University College London, London,

Statistical Parametric Mapping: The Analysis of Functional Brain Images

Description

In an age where the amount of data collected from brain imaging is increasing constantly, it is of critical importance to analyse those data within an accepted framework to ensure proper integration and comparison of the information collected. This book describes the ideas and procedures that underlie the analysis of signals produced by the brain. The aim is to understand how the brain works, in terms of its functional architecture and dynamics. This book provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically, Statistical Parametric Mapping provides a widely accepted conceptual framework which allows treatment of all these different modalities. This rests on an understanding of the brain's functional anatomy and the way that measured signals are caused experimentally. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. Critically, the material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. The book also serves as a companion to the software packages that have been developed for brain imaging data analysis.

Contents

INTRODUCTION
A short history of SPM.
Statistical parametric mapping.
Modelling brain responses.

SECTION 1: COMPUTATIONAL ANATOMY
Rigid-body Registration.
Nonlinear Registration.
Segmentation.
Voxel-based Morphometry.

SECTION 2: GENERAL LINEAR MODELS
The General Linear Model.
Contrasts & Classical Inference.
Covariance Components.
Hierarchical models.
Random Effects Analysis.
Analysis of variance.
Convolution models for fMRI.
Efficient Experimental Design for fMRI.
Hierarchical models for EEG/MEG.

SECTION 3: CLASSICAL INFERENCE
Parametric procedures for imaging.
Random Field Theory & inference.
Topological Inference.
False discovery rate procedures.
Non-parametric procedures.

SECTION 4: BAYESIAN INFERENCE
Empirical Bayes & hierarchical models.
Posterior probability maps.
Variational Bayes.
Spatiotemporal models for fMRI.
Spatiotemporal models for EEG.

SECTION 5: BIOPHYSICAL MODELS
Forward models for fMRI.
Forward models for EEG and MEG.
Bayesian inversion of EEG models.
Bayesian inversion for induced responses.
Neuronal models of ensemble dynamics.
Neuronal models of energetics.
Neuronal models of EEG and MEG.
Bayesian inversion of dynamic models
Bayesian model selection & averaging.

SECTION 6: CONNECTIVITY
Functional integration.
Functional Connectivity.
Effective Connectivity.
Nonlinear coupling and Kernels.
Multivariate autoregressive models.
Dynamic Causal Models for fMRI.
Dynamic Causal Models for EEG.
Dynamic Causal Models & Bayesian selection.

APPENDICES
Linear models and inference.
Dynamical systems.
Expectation maximisation.
Variational Bayes under the Laplace approximation.
Kalman Filtering.
Random Field Theory.

Readership: Scientists actively involved in neuroimaging research and the analysis of data, as well as students at a masters and doctoral level studying cognitive neuroscience and brain imaging.

ISBN: 0-12-372560-7 Book/Hardback
Measurements: 8 1/2 X 11 in
Pages: 656