Cox, D. / Little, J. / O'Shea, D. :
Using Algebraic Geometry
In recent years, the discovery of new algorithms for dealing with polynomial equations,
coupled with their implementation on inexpensive yet fast computers,
has sparked a minor revolution in the study and practice of algebraic geometry.
These algorithmic methods and techniques have also given rise to some exciting
new applications of algebraic geometry.
One of the goals of this book is to illustrate the many uses of algebraic geometry
and to highlight the more recent applications of Grobner bases and resultants.
In order to do this, the authors provide an introduction to some algebraic objects
and techniques more advanced than one typically encounters in a first course,
but which are nonetheless of great utility.
Because the text is intended for beginning graduate students,
it does not require graduate algebra, and in particular,
does not assume that the reader is familiar with modules.
1998 496 pp.
3-540-98487-9 13,390. 3-540-98492-5 (Paper ed.)
Springer
Reiten, I. / Smalo, S. / Solberg, O.
(eds.):
Selected Works of Maurice Auslander
In view of Maurice Auslander's important contributions to manyparts of algebra,
there is great interest in the present volume.
This book features a broad selection of the core of his work,
including commutative algebra, singularity theory,
the theory of orders, and the representation theory of artin algebras.
Although Auslander worked in many areas,
there are characteristics common to most of his research.
Of particular note is his use of homological methods, including functor categories.
While his early work was concerned mostly with commutative rings
and his later work mainly with artin algebras,
he was always interested in finding common features and common settings.
The broad range and impact of Auslander's contributions are reflected clearly in this volume.
The editors haveincluded background material, interrelationships between papers
and indications of further developments.
A paper of note and onethat is not available readily is included:
the Queen Mary College Notes on "Representation Dimension of Artin Algebras".
This book is of interest for the historical development of algebra
over a 40-year period and for the use of homological methods in algebra,
covering both commutative ring theory and artin algebra theory.
Aug. 1998 1638 pp.
0-8218-0679-3 (2vols. Set)
Part 1: 895 pp. 0-8218-0998-9 Part 2: 743 pp. 0-8218-1000-6
A. M. S.
Howard, P. / Rubin, J. :
Consequences of the Axiom of Choice
The book, Consequences of the Axiom of Choice, is a comprehensive listing
of statements that have been proved in the last 100 years using the axiom of choice.
Each consequence, also referred to as a form of the axiom of choice, is assigned a number.
Part I is a listing of the forms by number. This part each form is
given together with a listing of all statements known to be equivalent
to it (equivalent in set theory without the axiom of choice).
Part II the forms are arranged by topic.
Part III we describe the models of set theory which are used to
show non-implications between forms.
Part IV, the notes section, contains definitions, summaries of important sub-areas
and proofs that are not readily available elsewhere.
Part V gives references for the relationships between forms and
Part VI is the bibliography.
Part VII is contained on the floppy disk
which is enclosed in the book.
Aug. 1998 432 pp.
0-8218-0977-6
A. M. S.
Reiten, I. / Smalo, S. / Solberg, O.
(eds.):
Algebras and Modules, I
This volume contains recent results on geometric aspects of representations of algebras,
a thorough treatment of the theory of quasitilted algebras,
new developments on infinite dimensional representations of finite dimensional algebras,
a bridge between representation of algebraic groups and representation theory
of finite dimensional algebras, and recent discoveries on modular representation theory.
In addition, the volume contains two papers devoted to some of
Maurice Auslander's many contributions both in the representation theory
of finite dimensional algebras and in commutative ring theory.
The invited contributions to this volume are based on lectures given
by leading researchers in the field at the Workshop on Representati-ons
of Algebras and Related Topics, Trondheim, Norway, in 1996.
June 1998 198 pp.
0-8218-0850-8
A. M. S.
Reiten, I. / Smalo, S. / Solberg, O.
(eds.):
Algebras and Modules, II
This volume contains 43 research papers based on results presented at
the Eighth International Conference on Representations of Algebras (ICRA VIII)
held in Geiranger, Norway, in 1996.
The papers, written by experts in the field, cover the most recent developments
in the representation theory of artin algebras and related topics.
The papers cover:
representation of tame, biserial, cellular, factorial hereditary, Hopf, Koszul,
non-polynomial growth, prepro-jective, Temperley-Lieb, tilted and quasitilted algebras.
Other topics include: tilting/cotilting modules and generalizations
as *-modules, exceptional sequences of modules and vector bundles,
homological conjectures, Hochschild cohomology, cyclic homology,
homologically finite subcategories, representations of posets, regular modules,
vector space categories, triangulated categories, moduli
spaces of representations of quivers, postprojective (and preprojective) partitions,
stable and derived equivalences, and pure-injective, infinite dimensional,
and endofinite representations.
A general background in noncommutative algebra including rings,
modules and homological algebra is required.
July 1998 569 pp.
0-8218-1076-6
A. M. S.
Recent Titles in CMS Conference Proceedings,
* Vol. 22: Dlab, V. / Marki, L. (eds.):
Trends in Ring Theory: Proceedings of a Conference at Miskolc, 1996
Nov. 1997 239 pp. 0-8218-0849-4
Vol. 21: Drury, S. W. / Murty, M. (eds.):
Harmonic Analysis and Number Theory: Papers in Honour of Carl S. Herz
Aug. 1997 227 pp. 0-8218-0794-3
Igari Satoru :
Real Analysis
---with an Introduction to
Wavelet Theory
This introduction to real analysis is based on a series of lectures
by the author at Tohoku University. The text covers real numbers,
the notion of general topology, and a brief treatment of the Riemann integral,
followed by chapters on the classical theory of the Lebesgue integral
on Euclidean spaces;
the differentiation theorem and
functions of bounded variation;
Lebesgue spaces; distribution theory;
the classical theory of the Fourier transform and Fourier series;
and wavelet theory.
June 1998 198 pp.
0-8218-0850-8 .
A. M. S.
Xingde Dai / Larson, D. :
Wandering Vectors for Unitary
Systems and Orthogonal Wavelets
This book concerns some general methods for the analysis of those orthonormal bases
for a separable complex infinite dimensional
Hilbert space which are generated by the action of a system of
unitary transformations on a single vector, which is called
a complete wandering vector for the system.
The main examples are the orthonormal wavelet bases.
Topological and structural properties
of the set of all orthonormal dyadic wavelets are investigated
in this way by viewing them as complete wandering vectors for an affiliated
unitary system and then applying techniques of operator algebra
and operator theory.
July 1998 68 pp.
0-8218-0800-1
A. M. S.
Petera, J. (ed.):
Quasicrystals and Discrete
Geometry
The common topic of the eleven articles in this volume is ordered
aperiodic systems realized either as point sets with
the Delone property or as tilings of a Euclidean space.
This emerging field of study is found at the crossroads of algebra, geometry,
Fourier analysis, number theory, crystallography, and theoretical physics.
The volume brings together contributions by leading specialists.
Important advances in understanding the foundations of this
new field are presented.
Aug. 1998 289 pp.
0-8218-0682-3
A. M. S.
Newstead, P. E. :
Algebraic Geometry
Presents a compendium of original, refereed, never-before-published papers selected
from the Europroj conferences held in Catania and Barcelona.
Contains state-of-the-art research in algebraic geometry with emphasis on
claccification problems, and in particular studies on the structure of moduli problems,
and in particular studies on the classification of curves and surfaces.
Mar. 1998 328 pp.
0-8247-0234-4
Recent Titles
Vol. 199: Jones, W. B. / Sri Ranga, A. (eds.) :
Orthogonal Functions, Moment Theory, and Continues Fractions
July 1998 440 pp. 0-8247-0207-7 33,000.
Vol. 198: Drensky, V. / Giambruno, A. / Sehgal, S. (eds.):
Methods in Ring Theory
Mar. 1998 328 pp. 0-8247-0183-6 29,250.
Vol. 197: Caenepeel, S. / Verschoren, A. (eds.):
Rings, Hopf Algebras, and Brauer Groups
Feb. 1998 332 pp. 0-8247-0153-4 34,120.
Marcell Dekker
Halter-Koch, F. :
Ideal Systems:
An Introduction to Multiplicative Ideal
Theory
Provides for the first time a concise introduction to general
and multiplicative ideal theory, valid for commutative rings and
monoids and presented in the language of ideal systems on (commutative) monoids.
Apr. 1998 440 pp.
0-8247-0186-0
Recent Titles
Vol. 213: Cross, R. :
Multivalued Linear Operators
June 1998 352 pp. 0-8247-0219-0 .
Vol. 212: Govil, N. / Mohapatra, R. / Nashed, O. / Sharma, A. / Szabados, J. (eds.):
Approximation Theory: In Memory of A. K. Varma
May 1998 552 pp. 0-8247-0185-2
Vol. 209: Haynes, T. / Hedetniemi, S. / Slater, P. (eds.):
Domination in Graphs: Advanced Topics
Dec. 1997 520 pp. 0-8247-0034-1
Marcel Dekker
Differential Equations and
Applications:
U. S. Chinese Conference
Over 120 mathematicians met at Zhejiang University in Hangzhou,
People's Republic of China, in June, 1996.
Speakers came primarity from the Pacific Rim nations
with sponsorship shared by the United State and China.
The Meeting established the state of the art in
the field of differential equations for those nations represented.
The 34 papers listed below illustrate the presentations which were given at the conference.
1997 363 pp.
1-57146-048-9
International Press
Operator Algebras and Quantum Field
Theory:
Honoring D. Kastler
A collection of papers presented at the conference in Rome
honoring Daniel Kastler's 70th birthday.
The conference explores the field started by the work of von Neumann,
Gelfand, and Naimark and contained by Araki, Haag, and Kastler.
The book covers a wide range of developments in the field including
C* -Algebras and their Invariants, Von Neumann Algebras, inclusions,
and Automorphisms, Noncommutative Geometry, Quantization, and Deformation,
Free Entropy and Noncommutative Dynamical Systems,
and Quantum Field Theory.
1998 677 pp.
1-57146-047-0
International Press
Chern, A Great Geometer
New Expanded Edition for 1998!
In the summer of 1990, S. Y. Cheng and S.-T. Yau organized a
conference in Los Angels in honor of their Professor S. S. Chern
on the occasion of his seventy-ninth birthday.
Published here are personal reminiscences from Chern's large group of friends and
students. These lectures reflect the wisdom of this great mathematician
and his warmth in interacting with young geometers.
The editors hope that through this book, the readers might get
a glimse of the life of a great geometer.
Contributors:
S. S. Chern, R. Palasi and C. Terng, A. Weil, W. Chow, I. Singer,
I. Kaplansky, L. Nirenberg, R. Bott, H. Suzuki, L. Auslander, P. Griffiths,
W. Klingenberg, M. do Carmo, C. Hsiung, et al.
1998 368 pp.
962-7670-02-2
International Press
Wilson, J. :
Profinite Groups
This is the first book to be dedicated entirely to profinite groups,
an area of algebra with important links to number theory and other areas of mathematics.
It provides a comprehensive overview of the subject;
prerequisite knowledge is kept to a minimum, and
several major theorems are presented in an accessible form.
The book would provide a valuable introduction for postgraduate students,
or form a useful reference for researchers in other areas.
Sep. 1998 304 pp.
0-19-8500082-3
Oxford Univ.
Chemin, J. -Y. :
Perfect Incompressible Fluids
Published in 1995 by S. M. F. as
Asterisque, No.230
This work forms a unique and authoritative account on
various important mathematical developments in fluid machines.
It offers to the reader a self-contained presentation of the theory of
Euler equations describing a perfect incompressible fluid.
It nicely complements the fluid mechanics books
by P. L. Lions published in the same series.
Aug. 1998 208 pp.
0-19-850397-0
Recent Titles
Vol. 11: Tutte, W. : Graph Theory As I Have Known It
May 1998 176 pp. 0-19-850251-6
Vol. 9: Lions, P. -L. : Mathematical Topics in Fluid Mechanics, Vol. 2
Mar. 1998 432 pp. 0-19-851488-3 .
Oxford Univ.
Schwab, C. :
p- and hp- Finite Element Methods:
Theory and Applicaions to Solid and
Fluid Mechanics
The finite element method (FEM) is a numerical procedure for solving differential equations.
Ever-increasing computing power means that engineers and applied mathematicians are seeking
more complicated and sophisticated numerical methods to obtain progressively
more accurate answers to problems in solid and fluid mechanics.
Aug. 1998 384 pp.
0-19-850390-3
Oxford Univ.
Voevodsky, V. / Suslin, A. :
Cycles, Transfers, and Motivic Homology
Theories
The original goal that ultimately led to this volume was
the construction of "motivic cohomology theory" whose existence
was conjectures by A. Beilinson and S. Lichtenbaum.
This is achieved in the book's fourth paper, using results of the other papers,
whose additional role is to contribute to our understanding
of various properties of algebraic cycles.
The material presented provides the foundations for the recent proof
of the celebrated "Milnor Conjecture" by Vladimir Voevodsky.
The theory of sheaves of relative cycles is developed in the first paper of this volume.
The theory of presheaves with transfers and more specifically homotopy invariant presheaves
with transfers is the main them of the second paper.
The Friedlander-Lawson moving lemma for families of algebraic cycles appears in
the third paper in which a bivariant theory called bivariant cycle cohomology is constructed.
The fifth and last paper in the volume gives a proof of the fact
that bivariant cycle cohomology groups are canonically isomorphic
(in Appropriate cases) to Bloch's higher Chow groups, thereby providing a kink
between our theory and Bloch's original approach to motivic (co-)homology.
Aug. 1998 208 pp.
0-691-04815-0 ,0-691-04814-2 (Paper ed.)
Princeton Univ.
Graczyk, J. / Swiatek, G. :
The Real Fatou Conjecture
In 1920, Pierre Fatou expressed the conjecture that
---except for special cases---
all critical points of a rational map of the Riemann sphere tend to periodic orbits
under iteration. This conjecture remains the main open problem in
the dynamics of iterated maps.
For the logistic family x-> ax(l -x),
it can be interpreted to mean that for a dense set of parameters "a",
an attracting periodic orbit exists.
The same question appears naturally in science.
In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof
of the Real Fatou Conjecture.
In spite of the apparently elementary nature of the problem,
its solution requires advanced tools of complex analysis.
The authors have written a self-contained and complete version of the argument,
accessible to someone with no knowledge of complex dynamics
and only basic familiarity with interval maps.
Oct. 1998 ....
0-691-00257-6 /0-691-00258-4 paperback
Princeton Univ.