## Cabrera, J., Rutgers University, Piscataway, NJ, USA McDougall, A., Montclair State University, Upper Montclair, NJ, USA

## Statistical Consulting

2002. Approx. 410 pp. Hardcover

0-387-98863-7

This book sets out to develop the communication skills of statistics students so they can easily integrate into the work place. In addition, the book/course provides the resource skills that will be needed to function in the statistical consulting environment. The authors expect merely a minimum background of elementary statistics, with some basic knowledge of SAS and/or other statistical softwre.

Keywords: Statistical consulting, consulting process, effective communication, communicatoin skills

Contents: Introduction to Statistical Consulting.- Statistical Consulting Environments.- Development of Communication Skills.- Methodological Aspects.- Introduction to Case Studies.- Case Studies from Group I.- Case Studies from Group II.- Case Studies from Group III.

## Schneider, P., University of Munster, Germany

## Nonarchimedean Functional Analysis

2002. VII, 156 pp. Hardcover

3-540-42533-0

Recommended Retail Price: DM 79,90 *

The present book is a self-contained text which leads the reader through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. One can observe an increasing interest in methods from nonarchimedean functional analysis, particularly in number theory and in the representation theory of p-adic reductive groups. The book gives a concise and clear account of this theory, it carefully lays the foundations and also develops the more advanced topics. Although the book will be a valuable reference work for experts in the field, it is mainly intended as a streamlined but detailed introduction for researchers and graduate students who wish to apply these methods in different areas.

Keywords: Functional analysis, nonarchimedean, p-adic, locally convex vector space .

Series: Springer Monographs in Mathematics.

## Rosen, M., Brown University, Providence, RI, USA

## Number Theory in Function Fields

2002. Approx. 310 pp. Hardcover

0-387-95335-3

Elementary number theory is concerned with arithmetic properties of the ring of integers. Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting, for example, analogues of the theorems of Fermat and Euler, Wilson theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet theorem on primes in an arithmetic progression. After presenting the required foundational material on function fields, the later chapters explore the analogy between global function fields and algebraic number fields. A variety of topics are presented, including: the ABC-conjecture, Artin conjecture on primitive roots, the Brumer-Stark conjecture, Drinfeld modules, class number formulae, and average value theorems.

The first few chapters of this book are accessible to advanced undergraduates. The later chapters are designed for graduate students and professionals in mathematics and related fields who want to learn more about the very fruitful relationship between number theory in algebraic number fields and algebraic function fields. In this book many paths are set forth for future learning and exploration.

Michael Rosen is Professor of Mathematics at Brown University, where he been since 1962. He has published over 40 research papers and he is the co-author of A Classical Introduction to Modern Number Theory, with Kenneth Ireland. He received the Chauvenet Prize of the Mathematical Association of America in 1999 and the Philip J. Bray Teaching Award in 2001.

Keywords: Number Theory, Function Fields, Algebraic Geometry, Algebraic Function Fields

Contents: Polynomials over Finite Fields.- Primes, Arithmetic Functions, and the Zeta Function.- The Reciprocity Law.- Dirichlet L-series and Primes in an Arithmetic Progression.- Algebraic Function Fields and Global Function Fields.- Weil Differentials and the Canonical Class.- Extensions of Function Fields, Riemann-Hurwitz, and the ABC Theorem.- Constant Field Extensions.- Galois Extensions - Artin and Hecke L- functions.- Artin's Primitive Root Conjecture.- The Behavior of the Class Group in Constant Field Extensions.- Cyclotomic Function Fields.- Drinfeld Modules, An Introduction.- S-Units, S-Class Group, and the Corresponding L-functions.- The Brumer-Stark Conjecture.- Class Number Formulas in Quadratic and Cyclotomic Function Fields.- Average Value Theorems in Function Fields.

Series: Graduate Texts in Mathematics. VOL. 210

## Hoyrup, J., University of Roskilde, Denmark

## Lengths, Widths, Surfaces

A Portrait of Old Babylonian Algebra and its Kin

2002. Approx. 400 pp. 89 figs. Hardcover

0-387-95303-5

In the 1920s it was recognized that Babylonian cuneiform texts included many mathematical texts. These were chiefly concerned with metrology and computation, but some also appeared to deal with algebra. In this new examination of the texts, Jens Hoyrup proposes an interesting interpretation of them based on the fact that the tablets are almost entirely students'workbooks. The knowledge of mathematics expressed in these tablets is entirely 'practical', for use in surveying, accounting, and building. Hoyrup argues that the notion of algebraic manipulation, like other parts of a theoretical mathematics is indeed a later invention. Craftsmen, he argues, prefer to know how to solve a problem, rather than why the answer will be true, and it is only the latter attitude that characterizes mathematics; the former is, perhaps, more akin to modern engineering. The book provides a detailed reading of many tablets and a careful examination of the context in which they were produced.''

Contents: I. Introduction.- II. A New Reading.- III. Select Textual Examples.- IV. Methods.- V. Further "Algebraic" Texts.- VI. Quasi-Algebraic Geometry.- VII. Old Babylonian "Algebra": A Global Characterization.- VIII. The Historical Framework.- IX. The "Finer Structure" of the Old Babylonian Corpus.- X. The Origin and Transformations of Old Babylonian Algebra.- XI. Repercussions and Influences.- XII. Index of Tablets.- XIII. Index of Akkadian and Sumerian Terms and Key Phrases.- XIV. Name Index.- XV. Subject Index.- XVI. Abbreviations and Bibliography

Series: Sources and Studies in the History of Mathematics and Physical Sciences.

## Pflaum, M.J., Humboldt-University, Berlin, Germany

## Analytic and Geometric Study of Stratified Spaces

Contributions to Analytic and Geometric Aspects

2001. VIII, 230 pp. Softcover

3-540-42626-4

The book provides an introduction to stratification theory leading the reader up to modern research topics in the field. The first part presents the basics of stratification theory, in particular the Whitney conditions and Mather's control theory, and introduces the notion of a smooth structure. Moreover, it explains how one can use smooth structures to transfer differential geometric and analytic methods from the arena of manifolds to stratified spaces. In the second part the methods established in the first part are applied to particular classes of stratified spaces like for example orbit spaces. Then a new de Rham theory for stratified spaces is established and finally the Hochschild (co)homology theory of smooth functions on certain classes of stratified spaces is studied. The book should be accessible to readers acquainted with the basics of topology, analysis and differential geometry.

Keywords: Stratified spaces, smooth structures, singularities MSC ( 2000 ): 58Axx, 32S60, 35S35, 16E40, 14B05, 13D03

Contents: Introduction Notation 1 Stratified Spaces and Functional Structures 1.1 Decomposed spaces 1.2 Stratifications 1.3 Smooth Structures 1.4 Local Triviality and the Whitney conditions 1.5 The sheaf of Whitney functions 1.6 Rectifiable curves and regularity 1.7 Extension theory for Whitney functions on regular spaces 2 Differential Geometric Objects on Singular Spaces 2.1 Stratified tangent bundles and Whitney's condition (A) 2.2 Derivations and vector fields 2.3 Differential forms and stratified cotangent bundle 2.4 Metrics and length space structures 2.5 Differential operators 2.6 Poisson structures 3 Control Theory 3.1 Tubular neighborhoods 3.2 Cut point distance and maximal tubular neighborhoods 3.3 Curvature moderate submanifolds 3.4 Geometric implications of the Whitney conditions 3.5 Existence and uniqueness theorems 3.6 Tubes and control data 3.7 Controlled vector fields and integrability 3.8 Extension theorems on controlled spaces 3.9 Thom's first isotopy lemma 3.10 Cone spaces 4 Orbit Spaces 4.1 Differentiable G-Manifolds 4.2 Proper Group Actions 4.3 Stratification of the Orbit Space 4.4 Functional Structure 5 DeRham-Cohomology 5.1 The deRham complex on singular spaces 5.2 DeRham cohomology on C^/infty-cone spaces 5.3 DeRham theorems on orbit spaces 5.4 DeRham cohomology of Whitney functions 6 Homology of Algebras of Smooth Functions 6.1 Topological algebras and their modules 6.2 Homological algebra for topological modules 6.3 Continuous Hochschild homology 6.4 Hochschild homology of algebras of smooth functions A Supplements from linear algebra and functional analysis A.1 The vector space distance A.2 Polar decomposition A.3 Topological tensor products B Kahler differentials B.1 The space of Kahler differentials B.2 Topological version B.3 Application to locally ringed spaces C Jets, Whitney functions and a few C^/infty -mappings C.1 Frechet topologies for C^/infty -functions C.2 Jets C.3 Whitney functions C.4 Smoothing of the angle

Series: Lecture Notes in Mathematics. VOL. 1768