2004, Approx. 400 p., Hardcover
ISBN: 1-85233-834-2
About this book
Geometry is the cornerstone of computer graphics and computer
animation, and provides the framework and tools for solving
problems in two and three dimensions. This may be in the form of
describing simple shapes such as a circle, ellipse or parabola,
or complex problems such as rotating 3D objects about an
arbitrary axis. Geometry for Computer Graphics draws together a
wide variety of geometric information that will provide a
sourcebook of facts, examples and proofs for students, academics,
researchers and professional practitioners. The book is divided
into 4 sections: the first summarizes hundreds of formulae used
to solve 2D and 3D geometric problems. The second section places
these formulae in context in the form of worked examples. The
third provides the origin and proofs of these formulae and
communicates mathematical strategies for solving geometric
problems. The last section is a glossary of terms used in
geometry.
Table of contents
Series : Graduate Texts in Mathematics , Vol. 227
2004, Approx. 410 p., Hardcover
ISBN: 0-387-22356-8
2005, Approx. 420 p., Softcover
ISBN: 0-387-23707-0
About this textbook
Combinatorial commutative algebra is an active area of research
with thriving connections to other fields of pure and applied
mathematics. This book provides a self-contained introduction to
the subject, with an emphasis on combinatorial techniques for
multigraded polynomial rings, semigroup algebras, and
determinantal rings. The eighteen chapters cover a broad spectrum
of topics, ranging from homological invariants of monomial ideals
and their polyhedral resolutions, to hands-on tools for studying
algebraic varieties with group actions, such as toric varieties,
flag varieties, quiver loci, and Hilbert schemes. Over 100
figures, 250 exercises, and pointers to the literature make this
book appealing to both graduate students and researchers.
Table of contents
Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional
staircases.- Cellular resolutions.- Alexander duality.- Generic
monomial ideals.- Semigroup algebras.- Multigraded polynomial
rings.- Syzygies of lattice ideals.- Toric varieties.-
Irreducible and injective resolutions.- Ehrhart polynomials.-
Local cohomology.- Plucker coordinates.- Matrix Schubert
varieties.- Antidiagonal initial ideals.- Minors in matrix
products.- Hilbert schemes of points.- Bibliography.- Glossary of
notation.
Series : Springer Series in Operations Research and Financial
Engineering
2nd ed., 2005, XX, 355 p. 38 illus., Hardcover
ISBN: 0-387-22199-9
About this textbook
Fierce competition in today's global market provides a powerful
motivation for developing ever more sophisticated logistics
systems. This book, written for the logistics manager and
researcher, presents a survey of the modern theory and
application of logistics. The goal of the book is to present the
state-of-the-art in the science of logistics management. As a
result, the authors have written a timely and authoritative
survey of this field that many practitioners and researchers will
find makes an invaluable companion to their work.
Table of contents
Series : Probability and its Applications
2005, Approx. 510 p. 33 illus., Hardcover
ISBN: 1-85233-892-X
About this book
Stochastic geometry is a relatively new branch of mathematics.
Although its predecessors such as geometric probability date back
to the 18th century, the formal concept of a random set was
developed in the beginning of the 1970s. Theory of Random Sets
presents a state of the art treatment of the modern theory, but
it does not neglect to recall and build on the foundations laid
by Matheron and others, including the vast advances in stochastic
geometry, probability theory, set-valued analysis, and
statistical inference of the 1990s. The book is entirely self-contained,
systematic and exhaustive, with the full proofs that are
necessary to gain insight. It shows the various interdisciplinary
relationships of random set theory within other parts of
mathematics, and at the same time, fixes terminology and notation
that are often varying in the current literature to establish it
as a natural part of modern probability theory, and to provide a
platform for future development.
Table of contents
Random Closed Sets and Capacity Functionals.- Expectations of
Random Sets.- Minkowski Addition.- Unions of Random Sets.- Random
Sets and Random Functions. Appendices: Topological Spaces.-
Linear Spaces.- Space of Closed Sets.- Compact Sets and the
Hausdorff Metric.- Multifunctions and Continuity.- Measures and
Probabilities.- Capacities.- Convex Sets.- Semigroups and
Harmonic Analysis.- Regular Variation. References.- List of
Notation.- Name Index.- Subject Index.
Series : Sources and Studies in the History of Mathematics and
Physical Sciences
2005, Approx. 770 p. 22 illus., Hardcover
ISBN: 0-387-22836-5
About this book
This book deals with the development of the terms of analysis in
the 18th and 19th centuries, the two main concepts being negative
numbers and infinitisimals. Schubring studies often overlooked
texts, in particular German and French textbooks, and reveals a
much richer history than previously thought while throwing new
light on major figures, such as Cauchy.
Table of contents
* Question and Method * Paths Towards Algebraization ?
Development until the 18th Century. The Number Field * The
development of negative numbers * Paths towards
algebraization?The field of limits: The development of infinitely
small quantities * Culmination of Algebraization and retour du
refoule * Le Retour du Refoule: From the Perspective of
Mathematical Concepts * Cauchy’s Compromise Concept *
Development of Pure Mathematics in Prussia/Germany * Conflicts
Between Confinement to Geometry and Algebraization in France *
Summary and Outlook * References * Appendix
Series : Springer Texts in Statistics
2005, Approx. 620 p., Hardcover
ISBN: 0-387-22833-0
About this book
"I know it's trivial, but I have forgotten why". This
is a slightly exaggerated characterization of the unfortunate
attitude of many mathematicians toward the surrounding world. The
point of departure of this book is the opposite. This textbook on
the theory of probability is aimed at graduate students, with the
ideology that rather than being a purely mathematical discipline,
probability theory is an intimate companion of statistics. The
book starts with the basic tools, and goes on to chapters on
inequalities, characteristic functions, convergence, followed by
the three main subjects, the law of large numbers, the central
limit theorem, and the law of the iterated logarithm. After a
discussion of generalizations and extensions, the book concludes
with an extensive chapter on martingales. The main feature of
this book is the combination of rigor and detail. Instead of
being sketchy and leaving lots of technicalities to be filled in
by the reader or as easy exercises, a more solid foundation is
obtained by providing more of those not so trivial matters and by
integrating some of those not so simple exercises and problems
into the body of text. Some results have been given more than one
proof in order to illustrate the pros and cons of different
approaches. On occasion we invite the reader to minor extensions,
for which the proofs reduce to minor modifications of existing
ones, with the aim of creating an atmosphere of a dialogue with
the reader (instead of the more typical monologue), in order to
put the reader in the position to approach any other text for
which a solid probabilistic foundation is necessary. Allan Gut is
a professor of Mathematical Statistics at Uppsala University,
Uppsala, Sweden. He is the author of the Springer monograph
"Stopped Random Walks" (1988), the Springer textbook
"An Intermediate Course in Probability" (1995), and has
published around 60 articles in probability theory. His interest
in attracting a more general audience to the beautiful world of
probability has been manifested in his Swedish popular science
book Sant eller Sannolikt ("True or Probable"),
Norstedts forlag (2002).
Table of contents
Introductory Measure Theory.- Random Variables.- Inequalities.-
Characteristic Functions.- Convergence.- The Law of Large Numbers.-
The Central Limit Theorem.- The Law of Iterated Logarithm.- Limit
Theorems; Extensions and Generalizations.- Martingales