Greaves, G., University of Wales, Cardiff, UK

Sieves in Number Theory

2001. XII, 304 pp. Hardcover
3-540-41647-1

This book surveys the current state of the "small" sieve methods developed by Brun, Selberg and
later workers.. A self-contained treatment is given to topics that are of central importance in the
subject. These include the upper bound method of Selberg, Brun's method, Rosser's sieve as
developed by Iwaniec, with a bilinear form of the remainder term, the sieve with weights, and the
use of Selberg's ideas in deriving lower-bound sieves. Further developments are introduced with the
support of references t. The book is suitable for university graduates making their first acquaintance
with the subject, leading them towards the frontiers of modern research and unsolved problems in
the subject area.

Keywords: Number theory, sieves, sieves with weights, bilinear remainder term, sieves of "
dimension " exceeding 1 .

Contents: The Structure of Sifting Arguments.- Selberg's Upper Bound Method.- Combinatorial
Methods.- Rosser's Sieve.- The Sieve with Weights.- The Remainder Term in the Linear Sieve.-
Lower Bound Sieves when k > 1.- References.- Index.

Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge /VOL. 43

Chen, H., University of British Columbia, Vancouver, BC, Canada
Yao, D.D., Columbia University, New York, NY, USA

Fundamentals of Queuing Networks
Performance, Asymptotics, and Optimization

2001. Approx. 400 pp. 30 figs. Hardcover
0-387-95166-0

This accessible and timely book collects in a single volume the essentials of stochastic networks,
from the classical product-form theory to the more recent developments such as diffusion and fluid
limits, stochastic comparisons, stability, control (dynamic scheduling) and optimization.
The book was developed from the authors' teaching stochastic networks over many years. It will be
useful to students from engineering, business, mathematics, and probability and statistics.
As stochastic networks have become widely used as a basic model of many physical systems in a
diverse range of fields, the book can also be used as a reference or supplementary readings for
courses in operations research, computer systems, communication networks, production planning
and logistics, and by practitioners in the field.

Contents: Preface.- 1. Birth-Death Queues.- 2. Jackson Networks.- 3. Stochastic Comparisons.- 4.
Kelly Networks.- 5. Technical Desiderata.- 6. Single-Station Queues.- 7. Generalized Jackson
Networks.- 8. A Two-Station Multi-Class Network.- 9. Feedforward Networks.- 10. Brownian
Approximations.- 11. Conservation Laws.- 12. Scheduling of Fluid Networks.- Index.

Series: Applications of Mathematics.VOL. 46

Newton, P.K., University of Southern Carolina, Los Angeles, CA, USA

The N-Vortex Problem
Analytical Techniques

2001. Approx. 430 pp. 79 figs. Hardcover
0-387-95226-8

This book is an introduction to current research on the N- vortex problem of fluid mechanics. Its
goal is to describe the Hamiltonian aspects of vortex dynamics so that graduate students and
researchers can use the book as an entry point into the rather large literature on integrable and
non-integrable vortex problems within the broader context of dynamical systems. It is as
self-contained as possible: the only training required of the reader is a good background in
advanced calculus and ordinary and partial differential equations at the level of a typical
undergraduate engineering, physics, or applied mathematics major. Exercises of varying difficulty
are found at the end of each chapter which often require the reader to fill in details of proofs or
complete examples.

Keywords: Vortex Dynamics, N-Vortex Problem of Fluid Mechanics,

Contents: N-Vortices in the Plane.- Domains with Boundaries.- Vortex Motion on a Sphere.-
Geometric Phases.- Statistical Point Vortex Theories.- Vortex Patch Models.- Vortex Filament
Models.- References.

Series: Applied Mathematical Sciences.VOL. 145

Souza, P.N.de, University of California at Berkeley, Berkeley, CA, USA
Silva, J.-N., University of Lisbon, Portugal

Berkeley Problems in Mathematics

2nd ed. 2001. Approx. 545 pp. 42 figs. Hardcover
0-387-95184-9

2nd ed. 2001. Approx. 545 pp. 42 figs. Softcover
0-387-95207-1

In 1977 the Mathematics Department at the University of California, Berkeley, instituted a written
examination as one of the first major requirements toward the Ph.D. degree in Mathematics. Its
purpose was to determine whether first-year students in the Ph.D. program had successfully
mastered basic mathematics in order to continue in the program with the likelihood of success.
Since its inception, the exam has become a major hurdle to overcome in the pursuit of the degree.
The purpose of this book is to publicize the material and aid in the preparation for the examination
during the undergraduate years since a) students are already deeply involved with the material and
b) they will be prepared to take the exam within the first month of the graduate program rather than
in the middle or end of the first year. The book is a compilation of approximately nine hundred
problems which have appeared on the preliminary exams in Berkeley over the last twenty years. It
is an invaluable source of problems and solutions for every mathematics student who plans to enter
a Ph.D. program. Students who work through this book will develop problem solving skills in areas
such as real analysis, multivariable calculus, differential equations, metric spaces, complex
analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an
increasing level of difficulty. Tags with the exact exam year provide the opportunity to rehearse
complete examinations. The appendix includes instructions on accessing electronic versions of the
exams as well as a syllabus, statistics of passing scores, and a Bibliography used throughout the
solutions. This new edition contains approximately 120 new problems and 200 new solutions. It is
an ideal means for students to strengthen their foundation in basic mathematics and to prepare for
graduate studies.

Contents: I: PROBLEMS. Real Analysis; Multivariable Calculus; Differential Equations; Metric
Spaces; Complex Analysis; Algebra; Linear Algebra. II: SOLUTIONS. Real Analysis; Multivariable
Calculus; Differential Equations; Metric Spaces; Complex Analysis; Algebra; Linear Algebra. III:
Appendix. A: How to get the exams. B: Passing scores. C: The Syllabus.

Series: Problem Books in Mathematics.

Jensen, A., Aalborg University, Denmark
la Cour-Harbo, A., Aalborg University, Denmark

Ripples in Mathematics - The Discrete Wavelet Transform

2001. XII, 248 pp. Softcover
3-540-41662-5

This book gives an introduction to the discrete wavelet transform and some of its applications. It is
based on a novel approach to discrete wavelets called lifting. The first part is a completely
elementary introduction to the subject, and the prerequisites for this part are knowledge of basic
calculus and linear algebra. The second part requires some knowledge of Fourier series and digital
signal analysis. The connections of filter theory are presented and the wavelet packet transforms
are defined. The time-frequency plane is used for interpretation of signals. The problems with finite
length signals are treated in detail. MATLAB is used as the computational environment for
examples and implementation of transforms. The book is well suited for undergraduate
mathematics and electric engineering students and engineers in industry.

Keywords: Wavelets, wavelet packets, signal processing, time-frequency analysis, lifting

Contents: 1. Introduction.- 2. A First Example.- 3. The Discrete Wavelet Transform via Lifting.- 4.
Analysis of Synthetic Signals.- 5. Interpretation.- 6. Two Dimensional Transforms.- 7. Lifting and
Filters I.- 8. Wavelets Packets.- 9. The Time-Frequency Plane.- 10. Finite Signals.- 11.
Implementation.- 12. Lifting and Filters II.- 13. Wavelets in Matlab.- 14. Applications and Outlook.-
A. Wavelet resources.- References.- Index.