Stillwell, J., Monash University, Clayton, VIC, Australia
1st ed. 1989. Corr. 5th printing 1999. X, 371 pp. 163 figs.
3-540-96981-0
A concise, unified view of mathematics together with its
historical development. Aiming at
mathematicians who have mastered the basic topics but wish to
gain a better grasp of
mathematics as a whole, the author gives the reasons for the
emergence of the main fields of
modern mathematics, and explains the connections between them by
tracing the course of a few
mathematical themes from ancient times down to the 20th century.
The emphasis here is on
history as a method for unifying and motivating mathematics,
rather than as an end in itself, and
there is more mathematical detail than in other general
histories. However, no historical expertise is
assumed, and classical mathematics is rephrased in modern terms
where needed. Nevertheless,
there are copious references to original sources for readers
wishing to explore the classics for
themselves. In summary, readers will be able to add to their
mathematical knowledge as well as
gaining a new perspective on what they already know.
Contents: The Theorem of Pythagoras.- Greek Geometry.- Greek
Number Theory.- Infinity in Greek
Mathematics.- Polynomial Equations.- Analytic Geometry.-
Projective Geometry.- Calculus.- Infinite
Series.- The Revival of Number Theory.- Elliptic Functions.-
Mechanics.- Complex Numbers in
Algebra.- Complex Numbers and Curves.- Complex Numbers and
Functions.- Differential
Geometry.- Noneuclidean Geometry.- Group Theory.- Topology.-
Sets, Logic, and Computation.-
References.- Index.
Series: Undergraduate Texts in Mathematics.
Brown, K.S., Cornell University, Ithaca, NY, USA
1st ed. 1989. 2nd printing 1999. Approx. 225 pp. 22 figs.
0-387-98624-3
This book gives an introduction to Jacques Tit's theory of
buildings, a subject in which there is a
rich interplay between group theory and geometry. The book starts
from scratch, with a discussion
of finite reflection groups, and takes the reader to the
literature on buildings. The prerequisites are
kept to a minimum, and careful attention is paid to motivating
new concepts that are introduced.
The book should be accessible to any mathematics graduate student
who knows very little group
theory and topology.
Contents: Finite Reflection Groups.- Abstract Reflection Groups.-
Coxeter Complexes.- Buildings.-
Buildings and Groups.- Euclidean Buildings.- Applications to
Group Cohomology.
Series: Springer Monographs in Mathematics.
Drensky, V., Bulgarian Academy of Sciences, Sofia, Bulgaria
A Graduate Course in Algebra
1999. Approx. 240 pp.
981-4021-48-2
The book is devoted to the combinatorial theory of polynomial
algebras, free associative and free
Lie algebras, and algebras with polynomial identities. It also
examines the structure of
automorphism groups of free and relatively free algebras. It is
based on graduate courses and short
cycles of lectures presented by the author at several
universities and its goal is to involve the reader
as soon as possible in the research area, to make him or her able
to read books and papers on the
considered topics. It contains both classical and contemporary
results and methods. A specific
feature of the book is that it includes as its inseparable part
more than 250 exercises and
examples with detailed hints (50 % of the numbered statements),
some of them treating serious
mathematical results. The exposition is accessible for graduate
and advanced undergraduate
students with standard background on linear algebra and some
elements of ring theory and group
theory. The professional mathematician working in the field of
algebra and other related topics also
will find the book useful for his or her research and teaching.
Contents: Introduction 1. Commutative, Associative and Lie
Algebras: Basic properties of algebras;
Free algebras; The PoincarEBirkhoff-Witt theorem. 2. Algebras
with Polynomial Identities:
Definitions and examples of PI-Algebras; Varieties and relatively
free algebras; The theorem of
Birkhoff. 3. The Specht Problem: The finite basis property; Lie
algebras in characteristic 2. 4.
Numerical Invariants of T-Ideals: Graded vector spaces;
Homogeneous and multilinear polynomial
identities; Proper polynomial identities. 5. Polynomial
Identities of Concrete Algebras: Polynomial
identities of the Grassmann algebra; Polynomial identities of the
upper triangular matrices. 6.
Methods of Commutative Algebra: Rational Hilbert series;
Nonmatrix polynomial identities;
Commutative and noncommutative invariant theory. 7. Polynomial
Identities of the Matrix Algebras:
The Amitsur-Levitzki theorem; Generic matrices; Central
polynomials; Various identities of
matrices. 8. Multilinear Polynomial Identities: The codimension
theorem of Regev; Algebras with
polynomial growth of codimensions; The Nagata-Higman theorem; The
theory of Kemer. 9. Finitely
Generated PI-Algebras: The problems of Burnside and Kurosch; The
Shirshov theorem; Growth of
algebras and Gelfand-Kirillov dimension; Gelfand-Kirillov
dimension of PI-Algebras. 10.
Automorphisms of Free Algebras: Automorphisms of groups and
algebras; The polynomial algebra
in two variables; The free associative algebra of rank two;
Exponential automorphisms;
Automorphisms of relatively free algebras. 11. Free Lie Algebras
and Their Automorphisms: Bases
and subalgebras of free Lie algebras; Automorphisms of free Lie
algebras; Automorphisms of
relatively free Lie algebras. 12. The Method of Representation
Theory: Representations of finite
groups; The symmetric group; Multilinear polynomial identities;
The action of the general linear
group; Proper polynomial identities; Polynomial identities of
matrices.
Kollar, J., University of Princeton, NJ, USA
1st ed. 1996. Corr. 2nd printing 1999. VIII, 321 pp.
3-540-60168-6
The aim of this book is to provide an introduction to the
structure theory of higher dimensional
algebraic varieties by studying the geometry of curves,
especially rational curves, on varieties. The
main applications are in the study of Fano varieties and of
related varieties with lots of rational
curves on them. This Ergebnisse volume provides the first
systematic introduction to this field of
study. The book contains a large number of examples and exercises
which serve to illustrate the
range of the methods and also lead to many open questions of
current research.
Keywords: Chow varieties, cone of curves, Fano varieties,
rational connected
varieties, uniruled varieties, Hilbert schemes
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3.
Folge / A Series of Modern Surveys
in Mathematics.VOL. 32
Mumford, D.B., Brown University, Providence, RI, USA
Includes the Michigan Lectures (1974) on Curves and their
Jacobians
2nd corr. ed. 1999. X, 304 pp. 5 figs.
3-540-63293-X
Mumford's famous Red Book gives a simple readable account of the
basic objects of algebraic
geometry, preserving as much as possible their geometric flavor
and integrating this with the tools
of commutative algebra. It is aimed at graduate students or
mathematicians in other fields wishing
to learn quickly what algebraic geometry is all about.
This new edition also includes an overview of the theory of
curves, their moduli spaces and their
Jacobians, one of the most exciting fields within algebraic
geometry. The book is aimed at graduate
students and professors seeking to learn
i) the concept of "scheme" as part of their study of
algebraic geometry and
ii) an overview of moduli problems for curves and of the use of
theta functions to study these.
Keywords: Algebraic varieties Schemes Curves Theta functions
Schottky
problem
Contents: Varieties.- Preschemes.- Local properties of schemes.-
References.- Appendix: Curves
and their Jacobians.- Survey of work on the Schottky problem up
to 1996 (by Enrico Arbarello).-
References.- Guide to the Literature and References (Curves and
Their Jacobians).- Supplementary
Bibliography on the Schottky Problem.
Series: Lecture Notes in Mathematics.VOL. 1358
Shum, K.P., Chinese University of Hong Kong, China
Taft, E.J., Rutgers University, New Brunswick, NJ, USA
Wan, Z.X., Academia Sinica, Beijing, China
(Eds.)
International Congress, 1997, Hong Kong
1999. Approx. 450 pp.
981-4021-31-8
This volume contains the refereed and edited versions of papers
presented at the First International
Congress in Algebra & Combinatorics, held in July 1997 in
Hong Kong. Research work in algebra
and combinatorics, which has never been published before, is
introduced, along with expository
papers in semigroups, groups, rings, general algebras, ordered
algebras, graphs and
combinatorics. The work is a useful reference book for
researchers and graduate students working
in these fields of mathematics.
Contents: From the contents: Semiretracts and the Intersection of
Retracts (JA Anderson).- Some
Inequalities for Linear Extensions of Posets and Ideals (T
Bier).- Gröbner-Shirshov Bases for
Relations of a Lie Algebra and Its Enveloping Algebra (L Bokut
& P Malcolmson).- Constructing
Tree Lattices (LJ Carbone).- Regular-solid Varieties of
Commutative and Idempotent Groupoids (K
Denecke & P Jampachon).- L1-Embeddable Bifaced Polyhedra (M
Deza & V Grishukhin).-
Nonstandard Representation of the Malcev Clone of a Strong
Variety (HJ Hoehnke).- On Rings with
Inverse Adjoint Semigroups (AV Kelarev).- On Hamilton Cycles in
Caylay Graphs of Order pqr (Li
Dengxin).- Implicative Identities in Groups (BH Neumann).-
Isomorphism Theorem, Embedding
Theorem and Replacement Techniques for Primitive Rings (KP Shum,
Xu Yonghua).- On
Morphisms between Partial Algebras (HJ Vogel).- Geometry of
Matrices Revisited (Zhe-Xian Wan).-
Semiperfect Coalgebras over Rings (R Wisbauer).- And other
papers.
Pytlak, R., Military University of Technology, Warsaw, Poland
1999. XV, 215 pp.
3-540-66214-6
While optimality conditions for optimal control problems with
state constraints have been
extensively investigated in the literature the results pertaining
to numerical methods are relatively
scarce. This book fills the gap by providing a family of new
methods. Among others, a novel
convergence analysis of optimal control algorithms is introduced.
The analysis refers to the
topology of relaxed controls only to a limited degree and makes
little use of Lagrange multipliers
corresponding to state constraints. This approach enables the
author to provide global convergence
analysis of first order and superlinearly convergent second order
methods. Further, the
implementation aspects of the methods developed in the book are
presented and discussed. The
results concerning ordinary differential equations are then
extended to control problems described
by differential-algebraic equations in a comprehensive way for
the first time in the literature.
Keywords: Optimal Control State Constrained Problems Necessary
Optimality Conditions Numerical Algorithms Nonlinear Programming
Contents: Preface.- Introduction.- Estimates on Solutions to
Differential Equations and Their
Approximations.- A First Order Method.- Implementation.- A Second
Order Method.- Runge-Kutta
Based Procedure for Optimal Control f Differential - Algebraic
Equations.- A Primal Range-Space
Method for Piecewise-Linear Quadratic Programming.- References.-
List of Symbols.- Subject
Index.
Series: Lecture Notes in Mathematics.VOL. 1707
@
Karatzas, I., Columbia University, New York, NY,
USA
Shreve, S.E., Carnegie-Mellon University, Pittsburgh, PA, USA
1st ed. 1998. Corr. 2nd printing 1999. XV, 407 pp.
0-387-94839-2
This sequel to Brownian Motion and Stochastic Calculus by the
same authors develops contingent
claim pricing and optimal consumption/investment in both complete
and incomplete markets, within
the context of Brownian-motion-driven asset prices. The latter
topic is extended to a study of
equilibrium, providing conditions for existence and uniqueness of
market prices which support
trading by several heterogeneous agents. Although much of the
incomplete-market material is
available in research papers, these topics are treated for the
first time in a unified manner. The book
contains an extensive set of references and notes describing the
field, including topics not treated
in the book. This book will be of interest to researchers wishing
to see advanced mathematics
applied to finance. The material on optimal consumption and
investment, leading to equilibrium, is
addressed to the theoretical finance community. The chapters on
contingent claim valuation
present techniques of practical importance, especially for
pricing exotic options.
Contents: A Brownian Motion of Financial Markets.- Contingent
Claim Valuation in a Complete
Market.- Single-Agent Consumption and Investment.- Equilibrium in
a Complete Market.-
Contingent Claims in Incomplete Markets.- Constrained Consumption
and Investment.
Series: Applications of Mathematics.VOL. 39
@
Habault, D., CNRS, Marseille, France
(Ed.)
1999. VII, 304 pp. 135 figs.
3-211-83147-9
The subject of the book is directly related to environmental
noise and vibration phenomena (sound
emission by vibrating structures, prediction and reduction, ...).
Transportation noise is one of the
main applications. The book presents an overview of the most
recent knowledge on interaction
phenomena between a structure and a fluid, including nonlinear
aspects. It covers all aspects of the
phenomena, from the mathematical modeling up to the applications
to automotive industrial
problems. The aim is to provide readers with a good understanding
of the physical phenomena as
well as the most recent knowledge of predictive methods.
Contents: Modelling of Fluid/Structure Interactions (P. J. T.
Filippi).- Vibroacoustics of
Fluid-Excited Structures (D. Juv, C. Bailly, C. Durant, F.
Robert).- Some Analytical Methods for
Fluid-Structure Interaction Problems (N. Peake).- Some
Computational Methods for Sound
Radiation Problems (D. Habault).- Finite Difference and Finite
Element Methods (U. R. Kristiansen,
M. Dhainaut, T. F. Johansen).- Nonlinear Dynamics of Structures
Excited by Flows: Quasi-Steady
Modelling and Asymptotic Analysis (A. H. P. van der Burgh).-
Acoustic Applications in Vehicle
Engineering (R. Freymann).
Series: CISM International Centre for Mechanical Sciences.NR. 396
Portugali, J., Tel Aviv University, Israel
1999. XII, 319 pp. 120 figs.
3-540-65483-6
This book integrates the theories of complex self-organizing
systems with the rich body of
discourse and literature developed in what might be called
"social theory of cities and urbanism".
This is done in several ways: First, by an explicit comparative
discussion of the two theoretical
bodies in conjunction with some classical issues such as the
nature of cities, the urban process,
urban and regional planning, decision making, and the urban
revolution (or rather revolutions).
Second, by developing a new family of heuristic models and using
them to study the issue of
socio-cultural spatial segregation in cities. We term these
models FACS models (Free Agents in a
Cellular Space). Third, by developing a synergetic/pattern
recognition theory of cities and of
decision-making in the context of city planning.
Keywords: Geography Urban Architecture Computer Science Sociology
Cellular modeling
Contents: From the contents: Cities as Concepts.- Prototype
Urbanisms.- Self-Organzing Cities.-
Free Agents in a Cellular Space.- City: The Greens and the
Blues.- International Migration and the
Internal Structure of Cities.- Spatial Cognitive Dissonance and
Socio-Spatial Emergence in a
Self-Organizing City.- Individuals' Cultural Code and Residential
Self-Organization in the City.- From
CA- to GIS-City.- Groups Internal Complexity and Socio-Spatial
Segregation in a Self-Organizing
City.- Self-Organization and City Planning.- Artificial Planning
Experience.- Synergetic Cities I: The
Pattern Recognition Approach.- Synergetic Cities II: Pattern
Recognition, Cognitive Mapping and
Decision-Making.- Self-Organization and Urban Revolutions.
Series: Springer Series in Synergetics.
Young, K.D., Hong Kong University of Science and
Technology, Hong Kong, People's
Republic of China
1999. VIII, 386 pp.
1-85233-197-6
This book comprises a selection of papers that were first
presented at VSS98 (5th
International Workshop on Variable Structure Systems) held in
Sarasota, Florida. This
workshop was the fifth in a series of VSS international
workshops, and the first to be held
in the United States. Work presented herein on theoretical
developments and
applications on VSS and Sliding Mode, reflects how trends have
advanced beyond the
original ideas that are now well documented in a number of books
and research
monographs. In particular, the concepts of Sliding Sector and
Second Order Sliding Mode
introduced in this volume, will stimulate discussions and invite
further extensions. Also,
the focus on Sampled Data systems represents a positive trend
towards practical
industrial implementations of sliding mode controllers.
Contents: Sliding Sector for Variable Structure System.- On
Discrete Variable Structure
Control with Switching Sector.- Variable Structure Control of
Nonlinear Sampled Data
Systems by Second Order Sliding Modes.- On Sampled Data Variable
Structure Control
Systems.- Sliding Mode Control of Systems with Delayed States and
Controls.- On
Global Stabilization of Nonlinear Dynamical Systems.- A General
Canonical Form for
Sliding Mode Control of Nonlinear Systems.- Handling Stiction
with Variable Structure
Control.- Equivalent Value Filters in Disturbance Estimation and
State Observation.-
Sliding Mode Control of a Car-Like Mobile Robot Using
Single-Track Dynamic Model.-
Park Vector Based Sliding Mode Control of UPS With Unbalanced and
Nonlinear Load.-
Dynamical Adaptive Sliding Mode Control of Observable
Minimum-Phase Uncertain
Nonlinear Systems.- Symbolic Computing Tools for Nonsmooth
Dynamics and Control.-
Sliding Mode Control with Gain Scheduled Hyperplane for LPV
Plant.- A Study on
Parameterized Output Feedback Sliding Mode Controller.- Sliding
Mode Tracking Control
of Systems with Unstable Zero Dynamics.- On Second Order Sliding
Mode Controllers.-
A Tale of Two Discontinuities.- The Problem of Chattering: an
Averaging Approach.
Series: Lecture Notes in Control and Information Sciences.VOL.
247
Gurtin, M.E., Carnegie Mellon University, Pittsburgh, PA, USA
1999. Approx. 270 pp. 7 figs.
0-387-98667-7
For the last decade, the author has been working to extend
continuum mechanics to treat moving
boundaries in materials focusing, in particular, on problems of
metallurgy. This monograph presents
a rational treatment of the notion of configurational forces; it
is an effort to promote a new viewpoint.
Included is a presentation of configurational forces within a
classical context and a discussion of
their use in areas as diverse as phase transitions and fracture.
The work should be of interest to
materials scientists, mechanicians, and mathematicians.
Contents: Introduction.- Configurational forces within a
classical context.- The use of
configurational forces to characterize coherent phase
interfaces.- An equivalent formulation of the
theory. Infinitesimal deformations.- Evolving interfaces
neglecting bulk behavior.- Coherent phase
interfaces with interfacial energy and deformation.-
Solidification.- Fracture.- Appendices on the
principle of virtual work for coherent phase interfaces.-
References.
Series: Applied Mathematical Sciences.VOL. 137
Hutter, K., Technische Universität Darmstadt,
Germany
Wang, Y., Technische Universität Darmstadt, Germany
Beer, H., Technische Universität Darmstadt, Germany
(Eds.)
Technological, Environmental, and Climatological Impact
Proceedings of
the 6th International Symposium Held in Damstadt, Germany, 22-25
August
1999
1999. XX, 608 pp.
3-540-66333-9
This book consists of peer-reviewed articles and reviews
presented as lectures at the Sixth
International Symposium on Thermal Engineering and Sciences for
Cold Regions in Darmstadt,
Germany. It addresses all relevant aspects of thermal physics and
engineering in cold regions,
such as the Arctic regions. These environments present many
unique freezing and melting
phenomena and the relevant heat and mass transfer processes are
of basic importance with
respect to both the technological applications and the natural
context in which they occur. Intended
for physicists, engineers, geoscientists, climatologists and
cryologists alike, these proceedings
cover topics such as: ice formation and decay, heat conduction
with phase change, convection with
freezing and melting, thermal properties at low temperature,
frost heave and permafrost, climate
impact in cold regions, thermal design of structures,
bio-engineering in cold regions, and many
more.
Keywords: thermal engineering, glaciology, porous media, ice,
snow,
avalanches, bio - engineering, thermo - mechanics, permafrost
Contents: Part I: Phase Change Phenomena.- Part II: Ice Physics.-
Part III: Large Ice Masses: Ice
Sheets, Sea Ice.- Part IV: Snow Thermo-Mechanics, Avalanches.-
Part V: Glaciers, Permafrost,
Porous Media.- Part VI: Heat Storage, Heat Recovery.
Series: Lecture Notes in Physics.