2004, Approx. 100 p., Softcover
ISBN: 1-931914-22-2
A Key College Publishing book
Due: January 2004
About this textbook
Colin Adams, well-known for his advanced
research in topology and
knot theory, is the author of this exciting
new book that brings
his findings and his passion for the subject
to a more general
audience. This beautifully illustrated comic
book is appropriate
for many mathematics courses at the undergraduate
level such as
liberal arts math, and topology. Additionally,
the book could
easily challenge high school students in
math clubs or honors
math courses and is perfect for the lay math
enthusiast. Each
copy of Why Knot? is packaged with a plastic
manipulative called
the Tangle R. Adams uses the Tangle because
"you can open it
up, tie it in a knot and then close it up
again." The Tangle
is the ultimate tool for knot theory because
knots are defined in
mathematics as being closed on a loop. Readers
use the Tangle to
complete the experiments throughout the brief
volume. Adams also
presents a illustrative and engaging history
of knot theory from
its early role in chemistry to modern applications
such as DNA
research, dynamical systems, and fluid mechanics.
Real math,
unreal fun!
Written for:
Mathematics courses at the undergraduate
level such as liberal
arts math, and topology; high school students
in math clubs or
honors math courses; lay math enthusiast
Series: Applied Mathematical Sciences, Vol.
158
2004, Approx. 600 p., Hardcover
ISBN: 0-387-40437-6
About this textbook
This book is an update and extension of the
classic textbook by
Ludwig Prandtl, Essentials of Fluid Mechanics.
It is based on the
10th German edition with additional material
included. Chapters
on wing aerodynamics, heat transfer, and
layered flows have been
revised and extended, and there are new chapters
on fluid
mechanical instabilities and biomedical fluid
mechanics.
References to the literature have been kept
to a minimum, and the
extensive historical citations may be found
by referring to
previous editions. This book is aimed at
science and engineering
students who wish to attain an overview of
the various branches
of fluid mechanics. It will also be useful
as a reference for
researchers working in the field of fluid
mechanics.
Written for:
Senior undergraduates, graduate students,
researchers
Keywords:
fluid mechanics
Table of contents
Introduction.- Properties of Liquids and
Gases.- Kinematics of
Liquids and Gases.- Dynamics of Liquids and
Gases.- Fundamental
Equations of Fluid Mechanics.- Aerodynamics.-
Turbulent Flows.-
Fluid Mechanical Instabilities.- Convective
Heat and Mass
Transport.- Multi-Phase Flows.- Flows with
Chemical Reactions.-
Flows in the Atmosphere and in the Ocean.-
Biofluid Mechanics.-
Thermal Flow Machinery.
Series: Lecture Notes in Mathematics, Vol.
1835
2004, XIV,190p., Softcover
ISBN: 3-540-20728-7
About this book
The geometric approach to the algebraic theory
of quadratic forms
is the study of projective quadrics over
arbitrary fields.
Function fields of quadrics have been central
to the proofs of
fundamental results since the 1960's. Recently,
more refined
geometric tools have been brought to bear
on this topic, such as
Chow groups and motives, and have produced
remarkable advances on
a number of outstanding problems. Several
aspects of these new
methods are addressed in this volume, which
includes an
introduction to motives of quadrics by A.
Vishik, with various
applications, notably to the splitting patterns
of quadratic
forms, papers by O. Izhboldin and N. Karpenko
on Chow groups of
quadrics and their stable birational equivalence,
with
application to the construction of fields
with u-invariant 9, and
a contribution in French by B. Kahn which
lays out a general
framework for the computation of the unramified
cohomology groups
of quadrics and other cellular varieties.
Table of contents
Cohomologie non ramifiee des quadriques (B.
Kahn).- Motives of
Quadrics with Applications to the Theory
of Quadratic Forms (A.
Vishik).- Motives and Chow Groups of Quadrics
with Applications
to the u-invariant (N.A. Karpenko after O.T.
Izhboldin).- Virtual
Pfister Neigbors and First Witt Index (O.T.
Izhboldin).- Some New
Results Concerning Isotropy of Low-dimensional
Forms (O.T.
Izhboldin).- Izhboldin's Results on Stably
Birational Equivalence
of Quadrics (N.A. Karpenko).- My recollections
about Oleg
Izhboldin (A.S. Merkurjev).
Series: Lecture Notes in Mathematics, Vol.
1836
2004, XII, 304 p., Softcover
ISBN: 3-540-20746-5
About this book
The topic of this book, graded algebra, has
developed in the past
decade to a vast subject with new applications
in noncommutative
geometry and physics. Classical aspects relating
to group actions
and gradings have been complemented by new
insights stemming from
Hopf algebra theory. Old and new methods
are presented in full
detail and in a self-contained way. Graduate
students as well as
researchers in algebra, geometry, will find
in this book a useful
toolbox. Exercises, with hints for solution,
provide a direct
link to recent research publications. The
book is suitable for
courses on Master level or textbook for seminars.
Table of contents
The Category of Graded Rings.- The Category
of Graded Modules.-
Modules over Stronly Graded Rings.- Graded
Clifford Theory.-
Internal Homogenization.- External Homogenization.-
Smash
Products.- Localization of Graded Rings.-
Application to
Gradability.- Appendix A: Some Category Theory.-
Appendix B:
Dimensions in an Abelian Category.- Bibliography.-
Index.
2004, Approx. 620 p., Hardcover
ISBN: 3-540-20614-0
Due: May 2004
About this book
Arnold's Problems contains mathematical problems
which have been
brought up by Vladimir Arnold in his famous
seminar at Moscow
State University over several decades. In
addition, there are
problems published in his numerous papers
and books. The
invariable peculiarity of these problems
was that mathematics was
considered not as a game with deductive reasonings
and symbols,
but as a part of natural science (especially
of physics), i.e. as
an experimental science. Many of these problems
are at the
frontier of research still today and are
still open, and even
those that are mainly solved keep stimulating
new research
appearing every year in journals all over
the world. The second
part of the book is a collection of comments
of mostly Arnold's
former students about the current progress
in the problems'
solution (featuring bibliography inspired
by them). This book
will be of great interest to researchers
and graduate students in
mathematics and mathematical physics.
Written for:
Researchers and graduate students in mathematics
and mathematical
physics
2004, XIII, 864 p. 606 illus., 40 in color.,
Hardcover
ISBN: 0-387-20229-3
Due: February 2004
About this textbook
The fourteen chapters of this book cover
the central ideas and
concepts of chaos and fractals as well as
many related topics
including: the Mandelbrot set, Julia sets,
cellular automata, L-systems,
percolation and strange attractors. This
new edition has been
thoroughly revised throughout. The appendices
of the original
edition were taken out since more recent
publications cover this
material in more depth. Instead of the focussed
computer programs
in BASIC, the authors provide 10 interactive
JAVA-applets for
this second edition.
Written for:
Teachers and students of main fields, teachers
and students of
secondary fields, interested lay people
Table of contents
Introduction: Causality Principle, Deterministic
Laws and Chaos.-
The Backbone of Fractals: Feedback and the
Iterator.- Classical
Fractals and Self-Similarity.- Limits and
Self-Similarity.-
Length, Area, and Dimension: Measuring Complexity
and Scaling
Properties.- Encoding Images by Simple Transformations.-
The
Chaos Game: How Randomness Creates Deterministic
Shapes.-
Recursive Structures: Growing Fractals and
Plants.- Pascal's
Triangle: Cellular Automata and Attractors.-
Irregular Shapes:
Randomness in Fractal Constructions.- Deterministic
Chaos:
Sensitivity, Mixing, and Periodic Points.-
Order and Chaos:
Period-Doubling and Its Chaotic Mirror.-
Strange Attractors: The
Locus of Chaos.- Julia Sets: Fractal Basin
Boundaries.- The
Mandelbrot Set: Ordering the Julia Set.