Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch. Most of this can be read by a student with a basic knowledge of complex analysis. The next part treats complex multiplication, including a discussion of Deuring's theory of l-adic and p-adic representations, and elliptic curves with singular invariants. Part three covers curves...

This is the first half of a text for a two semester course in mathematical statistics at the senior/graduate level for those who need a strong background in statistics as an essential tool in their career. To study this text, the reader needs a thorough familiarity with calculus including such things as Jacobians and series but somewhat less intense familiarity with matrices including quadratic forms and eigenvalues. For convenience, these lecture notes were divided into two parts: Volume I, Probability for Statistics, for the first semester, and Volume II, Statistical Inference, for the...

The Statistical Analysis of Discrete Data provides an introduction to cur- rent statistical methods for analyzing discrete response data. The book can be used as a course text for graduate students and as a reference for researchers who analyze discrete data. The book's mathematical prereq- uisites are linear algebra and elementary advanced calculus. It assumes a basic statistics course which includes some decision theory, and knowledge of classical linear model theory for continuous response data. Problems are provided at the end of each chapter to give the reader an opportunity to ap- ply...

various places of the world. Thus, it is hoped that this up-to-date subseries would increase the "awareness" of the world's citizens and encourage governments to devote more attention and resources to address this issue. The series editors thank the international panel of contributors for bringing this timely series into completion. We also wish to acknowledge the very insightful input of the following colleagues: Prof. A. L. Page ofthe University of California, Prof. T. C. Hutchinson of the University of Toronto, and Dr. Steve Lindberg of the Oak Ridge National Laboratory. We also wish to...

Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have...

Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.

A Second Course in Statistics The past decade has seen a tremendous increase in the use of statistical data analysis and in the availability of both computers and statistical software. Business and government professionals, as well as academic researchers, are now regularly employing techniques that go far beyond the standard two-semester, introductory course in statistics. Even though for this group of users shorl courses in various specialized topics are often available, there is a need to improve the statistics training of future users of statistics while they are still at colleges and...

My goal in writing this book has been to provide teachers and students of multi variate statistics with a unified treatment ofboth theoretical and practical aspects of this fascinating area. The text is designed for a broad readership, including advanced undergraduate students and graduate students in statistics, graduate students in bi ology, anthropology, life sciences, and other areas, and postgraduate students. The style of this book reflects my beliefthat the common distinction between multivariate statistical theory and multivariate methods is artificial and should be abandoned. I hope...

Applying Generalized Linear Models describes how generalized linear modelling procedures can be used for statistical modelling in many different fields, without becoming lost in problems of statistical inference. Many students, even in relatively advanced statistics courses, do not have an overview whereby they can see that the three areas - linear normal, categorical, and survival models - have much in common. The author shows the unity of many of the commonly used models and provides the reader with a taste of many different areas, such as survival models, time series, and spatial...

Now available in paperback. This is a text comprising the major theorems of probability theory and the measure theoretical foundations of the subject. The main topics treated are independence, interchangeability, and martingales; particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familar with measure theory as indicated by the guidelines in...