Expected publication date is July 17, 2005
Description
This book brings the beauty and fun of mathematics to the
classroom. It offers serious mathematics in a lively, reader-friendly
style. Included are exercises and many figures illustrating the
main concepts.
The first chapter talks about the theory of manifolds. It
includes discussion of smoothness, differentiability, and
analyticity, the idea of local coordinates and coordinate
transformation, and a detailed explanation of the Whitney
imbedding theorem (both in weak and in strong form). The second
chapter discusses the notion of the area of a figure on the plane
and the volume of a solid body in space. It includes the proof of
the Bolyai-Gerwien theorem about scissors-congruent polynomials
and Dehn's solution of the Third Hilbert Problem.
This is the third volume originating from a series of lectures
given at Kyoto University (Japan). It is suitable for classroom
use for high school mathematics teachers and for undergraduate
mathematics courses in the sciences and liberal arts. The first
and second volumes are available as Volume 19 and Volume 20 in
the AMS series, Mathematical World.
Contents
The story of the birth of manifolds
The prelude to the birth of manifolds
The birth of manifolds
The story of area and volume from everyday notions to
mathematical concepts
Transition from the notion of "size" to the concept of
"area"
Scissors-congruent polygons
Scissors-congruent polyhedra
Details:
Series: Mathematical World, Volume: 23
Publication Year: 2005
ISBN: 0-8218-3284-0
Paging: approximately 128 pp.
Binding: Softcover
Expected publication date is July 1, 2005
Description
Matrix groups are a beautiful subject and are central to many
fields in mathematics and physics. They touch upon an enormous
spectrum within the mathematical arena. This textbook brings them
into the undergraduate curriculum. It is excellent for a one-semester
course for students familiar with linear and abstract algebra and
prepares them for a graduate course on Lie groups.
Matrix Groups for Undergraduates is concrete and example-driven,
with geometric motivation and rigorous proofs. The story begins
and ends with the rotations of a globe. In between, the author
combines rigor and intuition to describe basic objects of Lie
theory: Lie algebras, matrix exponentiation, Lie brackets, and
maximal tori. The volume is suitable for graduate students and
researchers interested in group theory.
Contents
Why study matrix groups?
Matrices
All matrix groups are real matrix groups
The orthogonal groups
The topology of matrix groups
Lie algebras
Matrix exponentiation
Matrix groups are manifolds
The Lie bracket
Maximal tori
Bibliography
Index
Details:
Series: Student Mathematical Library, Volume: 29
Publication Year: 2005
ISBN: 0-8218-3785-0
Paging: 166 pp.
Binding: Softcover
Expected publication date is July 1, 2005
Description
Written by Luis Caffarelli and Sandro Salsa, this book offers an
excellent exposition on free boundary problems.
Free or moving boundary problems appear in many areas of analyis,
geometry, and applied mathematics. A typical example is the
evolving interphase between a solid and liquid phase: if we know
the initial configuration well enough, we should be able to
reconstruct its evolution, in particular, the evolution of the
interphase.
In this book the authors present a series of ideas, methods, and
techniques for treating the most basic issues of such a problem.
In particular, they describe the very fundamental tools of
geometry and real analysis that make this possible: properties of
harmonic and caloric measure in Lipschitz domains, a relation
between parallel surfaces and elliptic equations, monotonicity
formulas and rigidity, etc. The tools and ideas presented here
will serve as a basis for the study of more complex phenomena and
problems.
This book is useful for supplementary reading or will be a fine
independent study text. It is suitable for graduate students and
researchers interested in partial differential equations.
Contents
Elliptic problems
An introductory problem
Viscosity solutions and their asymptotic developments
The regularity of the free boundary
Lipschitz free boundaries are C^{1,gamma}
Flat free boundaries are Lipschitz
Existence theory
Evolution problems
Parabolic free boundary problems
Lipschitz free boundaries: Weak results
Lipschitz free boundaries: Strong results
Flat free boundaries are smooth
Complementary chapters: Main tools
Boundary behavior of harmonic functions
Monotonicity formulas and applications
Boundary behavior of caloric functions
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics, Volume: 68
Publication Year: 2005
ISBN: 0-8218-3784-2
Paging: approximately 280 pp.
Binding: Hardcover
Expected publication date is July 1, 2005
Description
The Latin-American conference on algebra, the XV Coloquio
Latinoamericano de Algebra (Cocoyoc, Mexico), consisted of
plenary sessions of general interest and special sessions on
algebraic combinatorics, associative rings, cohomology of rings
and algebras, commutative algebra, group representations, Hopf
algebras, number theory, quantum groups, and representation
theory of algebras.
This proceedings volume contains original research papers related
to talks at the colloquium. In addition, there are several
surveys presenting important topics to a broad mathematical
audience. There are also two invited papers by Raymundo Bautista
and Roberto Martinez, founders of the Mexican school of
representation theory of algebras.
The book is suitable for graduate students and researchers
interested in algebra.
Contents
R. Alfaro and A. Kelarev -- Recent results on ring constructions
for error-correcting codes
I. Assem, F. U. Coelho, M. Lanzilotta, D. Smith, and S. Trepode
-- Algebras determined by their left and right parts
E. L. Green -- The work of Roberto Martinez-Villa
E. Guardo -- A survey on fat points on a smooth quadric
C. M. Ringel -- Bautista and the development of the
representation theory of Artin algebras
M. Takeuchi -- A survey on Nichols algebras
Y. Yoshino -- Approximations by modules of G-dimension zero
M. Aguiar and N. Andruskiewitsch -- Representations of matched
pairs of groupoids and applications to weak Hopf algebras
V. A. Artamonov -- On symmetries of quasicrystals
M. J. Asiain -- Frattini-type and Fitting-type subgroups
N. M. Atakishiyev and A. U. Klimyk -- Representations of the
quantum algebra su_q(1,1) and duality of q-orthogonal polynomials
G. Bohm -- Internal bialgebroids, entwining structures and
corings
R. Coquereaux -- The A_2 Ocneanu quantum groupoid
W. Cortes -- Skew Armendariz rings and annihilator ideals of skew
polynomial rings
D. Flores de Chela -- Quantum symmetric algebras as braided Hopf
algebras
I. Gitler, E. Reyes, and R. H. Villarreal -- Blowup algebras of
ideals of vertex covers of bipartite graphs
D. Happel and L. Unger -- Minimal elements in the poset of
tilting modules
E. Karolinsky, A. Stolin, and V. Tarasov -- Dynamical twists and
quantization
V. K. Kharchenko and A. Andrade -- On the combinatorial rank of
Hopf algebras
I. Lizasoain -- A tensor product of projective G-groups
L. Marino -- The minimum degree of a surface that passes through
all the points of a 0-dimensional scheme but a point P
S. Montgomery -- Primitive ideals and Jacobson radicals in Hopf
Galois extensions
R. C. Orellana -- On the algebraic decomposition of a centralizer
algebra of the hyperoctahedral group
S. Rodriguez-Romo -- Quantum group global symmetries of quantum
chains. States for linear chains with left end open and right end
closed
S. Rodriguez-Romo and E. J. Taft -- One-sided Hopf algebras
F. L. Williams -- BTZ black hole and Jacobi inversion for
fundamental domains of infinite volume
T. Yanai -- Galois correspondence theorem for Hopf algebra
actions
A. G. Zavadskij -- On two-point differentiation and its
generalization
Details:
Series: Contemporary Mathematics, Volume: 376
Publication Year: 2005
ISBN: 0-8218-3630-7
Paging: 436 pp.
Binding: Softcover