Expected publication date is June 19, 2004
Description
This volume consists of a selection of papers based on
presentations made at the international conference on number
theory held in honor of Hugh Williams' sixtieth birthday. The
papers address topics in the areas of computational and explicit
number theory and its applications. The material is suitable for
graduate students and researchers interested in number theory.
Contents
A. Agashe, K. Lauter, and R. Venkatesan -- Constructing elliptic
curves with a known number of points over a prime field
S. Akiyama, T. Borbely, H. Brunotte, A. Petho, and J. M.
Thuswaldner -- On a generalization of the radix representation-A
survey
W. D. Banks, J. B. Friedlander, C. Pomerance, and I. E.
Shparlinski -- Multiplicative structure of values of the Euler
function
W. D. Banks and I. E. Shparlinski -- Congruences and exponential
sums with the Euler function
L. D. Baumert and D. M. Gordon -- On the existence of cyclic
difference sets with small parameters
D. J. Bernstein -- Doubly focused enumeration of locally square
polynomial values
W. Bosma -- Cubic reciprocity and explicit primality tests for
hcdot 3^kpm1
R. P. Brent and P. Zimmermann -- Algorithms for finding almost
irreducible and almost primitive trinomials
J. Brillhart -- Commentary on Lucas' test
J. Buchmann, T. Takagi, and U. Vollmer -- Number field
cryptography
D. A. Buell, S. Devarkal, and H. A. Wake -- Reconfigurable
computing machines and their applications in computational number
theory
J. Buhler, C. Pomerance, and L. Robertson -- Heuristics for class
numbers of prime-power real cyclotomic fields
H. Cohen -- Counting A_4 and S_4 number fields with given
resolvent cubic
K. Dilcher and J. Knauer -- On a conjecture of Feit and Thompson
M. Garcia, J. M. Pedersen, and H. te Riele -- Amicable pairs, a
survey
A. Granville -- On the research contributions of Hugh C. Williams
H. G. Grundman and L. E. Lippincott -- Hilbert modular fourfolds
of arithmetic genus one
E. Herrmann and P. G. Walsh -- Values of ternary recurrence
sequences and torsion on certain curves arising from the work of
Hugh Williams
S. Hernandez and F. Luca -- Divisibility of exponents of class
groups of pure cubic number fields
J. Holden and P. Moree -- New conjectures and results for small
cycles of the discrete logarithm
M. Jacobson, Jr., A. Menezes, and A. Stein -- Hyperelliptic
curves and cryptography
S. Louboutin -- Remarks on S. Chowla's hypothesis implying that L(s,chi
)>0 for s>0 and for real characters chi
S. Muller -- On the computation of cube roots modulo p
R. D. Patterson and A. J. van der Poorten -- Jeepers, creepers,
ldots
K. Rubin and A. Silverberg -- Algebraic tori in cryptography
J. P. Sorenson -- An analysis of the generalized binary GCD
algorithm
E. Teske -- An elliptic curve trapdoor system (extended abstract)
A. J. van der Poorten -- Periodic continued fractions and
elliptic curves
S. S. Wagstaff, Jr. -- The Cunningham project
A. Weng -- Extensions and improvements for the CM method for
genus two
A. J. van der Poorten and A. Stein -- Advice to referees of
submissions to High Primes and Misdemeanours
Details:
Series: Fields Institute Communications, Volume: 41
Publication Year: 2004
ISBN: 0-8218-3353-7
Paging: 392 pp.
Binding: Hardcover
Expected publication date is June 25, 2004
Description
The notion of singularity is basic to mathematics. In algebraic
geometry, the resolution of singularities by simple algebraic
mappings is truly a fundamental problem. It has a complete
solution in characteristic zero and partial solutions in
arbitrary characteristic.
The resolution of singularities in characteristic zero is a key
result used in many subjects besides algebraic geometry, such as
differential equations, dynamical systems, number theory, the
theory of mathcal{D}-modules, topology, and mathematical physics.
This book is a rigorous, but instructional, look at resolutions.
A simplified proof, based on canonical resolutions, is given for
characteristic zero. There are several proofs given for
resolution of curves and surfaces in characteristic zero and
arbitrary characteristic.
Besides explaining the tools needed for understanding
resolutions, Cutkosky explains the history and ideas, providing
valuable insight and intuition for the novice (or expert). There
are many examples and exercises throughout the text.
The book is suitable for a second course on an exciting topic in
algebraic geometry. A core course on resolutions is contained in
Chapters 2 through 6. Additional topics are covered in the final
chapters. The prerequisite is a course covering the basic notions
of schemes and sheaves.
Contents
Introduction
Non-singularity and resolution of singularities
Curve singularities
Resolution type theorems
Surface singularities
Resolution of singularities in characteristic zero
Resolution of surfaces in positive characteristic
Local uniformization and resolution of surfaces
Ramification of valuations and simultaneous resolution
Smoothness and non-singularity
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics,Volume: 63
Publication Year: 2004
ISBN: 0-8218-3555-6
Paging: approximately 192 pp.
Binding: Hardcover
Expected publication date is June 12, 2004
Description
This volume contains a selection of papers based on presentations
given at the S. P. Novikov seminar held at the Steklov
Mathematical Institute in Moscow. Topics and speakers were chosen
by the well-known expert, S. P. Novikov, one of the leading
mathematicians of the twentieth century. His diverse interests
are the tradition of the seminar and are reflected in the topics
presented in the book.
The book begins with Novikov's paper analyzing the position of
mathematics and theoretical physics at the beginning of the new
millennium. Following is an interview with Novikov published in
the Newsletter of the European Mathematical Society presenting
the genesis of many of his ideas and his scientific school. The
remaining articles address topics in geometry, topology, and
mathematical physics. The volume is suitable for graduate
students and researchers interested in the corresponding areas of
mathematics and physics.
Contents
S. P. Novikov -- The second half of the 20th century and its
conclusion: Crisis in the physics and mathematics community in
Russia and in the West
V. M. Buchstaber -- Interview with Sergey P. Novikov
V. M. Buchstaber and S. Yu. Shorina -- The w-function of the KdV
hierarchy
A. Campillo, F. Delgado, and S. M. Gusein-Zade -- On the zeta
functions of a meromorphic germ in two variables
B. Dubrovin -- On almost duality for Frobenius manifolds
I. A. Dynnikov -- Finitely presented semigroups in knot theory.
Oriented case
M. Farber and S. Yuzvinsky -- Topological robotics: Subspace
arrangements and collision free motion planning
P. G. Grinevich and P. M. Santini -- The initial-boundary value
problem on the interval for the nonlinear Schrodinger equation.
The algebro-geometric approach. I
H. M. Khudaverdian and T. Voronov -- On odd Laplace operators. II
Yu. Klimov, A. Korzh, and S. Natanzon -- From 2D Toda hierarchy
to conformal maps for domains of the Riemann sphere
I. Krichever -- Integrable chains on algebraic curves
S. B. Kuksin -- Fifteen years of KAM for PDE
D. V. Millionschikov -- Graded filiform Lie algebras and
symplectic nilmanifolds
A. G. Sergeev -- Adiabatic limit in the Seiberg-Witten equations
O. K. Sheinman -- Affine Krichever-Novikov algebras, their
representations and applications
I. A. Taimanov -- Tame integrals of motion and o-minimal
structures
Details:
Series: American Mathematical Society Translations--Series 2,
Volume: 212
Publication Year: 2004
ISBN: 0-8218-3613-7
Paging: 324 pp.
Binding: Hardcover
Expected publication date is July 9, 2004
Description
This book is a collection of papers from the proceedings of the
first symposium of the Japan Association for Mathematical
Sciences. Topics covered center around problems of geometric
analysis in relation to heat kernels, random walks, and Poisson
boundaries on discrete groups, graphs, and other combinatorial
objects.
The material is suitable for graduate students and research
mathematicians interested in heat kernels and random works on
groups and graphs.
Contents
N. Lohoue and G. Alexopoulos -- On the asymptotic behavior of
convolution powers and heat kernels on Lie groups
Y. Higuchi and T. Shirai -- Some spectral and geometric
properties for infinite graphs
S. Ishiwata -- Asymptotic behavior of a transition probability
for a random walk on a nilpotent covering graph
M. Izumi -- Non-commutative Poisson boundaries
V. A. Kaimanovich -- Boundary amenability of hyperbolic spaces
T. Kato -- Spectral analysis on tree like spaces from gauge
theoretic view points
S. Kojima and S. Mizushima -- The Dehn filling space of a certain
hyperbolic 3-orbifold
M. Kotani -- An asymptotic of the large deviation for random
walks on a crystal lattice
B. M. Hambly and T. Kumagai -- Heat kernel estimates and law of
the iterated logarithm for symmetric random walks on fractal
graphs
A. Lubotzky and Y. Shalom -- Finite representations in the
unitary dual and Ramanujan groups
N. Monod -- Stabilization for SL_n in bounded cohomology
H. Nagoshi -- Spectral theory of certain arithmetic graphs
A. Nevo -- Radial geometric analysis on groups
H. Urakawa -- The heat kernel and the Green kernel of an infinite
graph
Details:
Series: Contemporary Mathematics, Volume: 347
Publication Year: 2004
ISBN: 0-8218-3351-0
Paging: approximately 273 pp.
Binding: Softcover
Expected publication date is September 4, 2004
"The book's originality lies in its structure, which brings
to the surface significant links between the mathematics of
centuries ago and up to date abstract mathematical theories. The
author has written an elegant and charming book not lacking in
substance and depth. We welcome this work as an aid in the wider
realms of mathematical education."
-- Zentralblatt MATH
Description
This book offers a very interesting panorama of the development
of mathematics from the ancient Babylonians and Greeks to the
present. It is written in a lucid style with very readable
mathematical content. Understanding the material requires some
broad mathematical education, but not a lot of specialized
knowledge.
One of the strongest sections deals with the accomplishments of
the Greeks. The author clearly explains the problems tackled in
ancient Greece, places them in context, outlines the
accomplishments (some with concise proofs), and compares these
with our present understanding of the subject. He also places the
mathematical achievements of ancient Greece in the context of
early Ionian Philosophy, Platonism, Aristotelism, or in the
mindset of the Alexandrians.
The chapters on the seventeenth and eighteenth centuries are
presented clearly with emphasis on the great figures of these two
centuries. Mathematics of the nineteenth and twentieth centuries
are presented more thematically than chronologically. Analysis,
in particular functional analysis, receives a very good overview.
An appendix contains a transcript of the talk by Laurent Schwartz
on the historical roots and basic notions of the theory of
distributions.
Other chapters discuss topics such as modern algebra, set theory,
logic, group representations, calculus of variations, celestial
mechanics, fractals, the fast Fourier transform, and wavelets.
The book is supplemented with a chronological table and two
detailed indices. It is suitable for graduate students, research
mathematicians, and those interested in the history of
mathematics and related areas.
Contents
Part I
Remarks on the history and the philosophy of mathematics
Mathematics of the Egyptians
Mathematics of the Babylonians
Prime numbers
Mathematics of the Greeks-The beginnings
Pythagoras-The Pythagorean school
Heraclitus, Parmenides, Zeno, Empedocles, and Democritus
The mathematical school of Athens
Plato and Aristotle
Groups
The impossibility of solving the three classical problems of
antiquity
Euclid
Hilbert's foundation of Euclidean geometry
Basic properties of axiomatic systems
Spaces and geometries
Non-Euclidean geometries
The geometry of experience
Aristarchus, Archimedes, Apollonius, and Eratosthenes
The period from 200 B.C. to 500 A.D. in Alexandria
A brief review of the history of Greek mathematics
Mathematics of China and India
Mathematics of the Arabs
Europe during the middle ages
Renaissance (1400-1600)
The seventeenth century
The eighteenth century
Part II
Short biographies of mathematicians of the 19th and the 20th
centuries
Revival of synthetic geometry
The system of real numbers
The system of complex numbers and the quaternions
The fundamental theorem of algebra
Set theory
Logic
Functional analysis
Topology
Functions of real variables
Abstract algebra
Categories and functors
Recent discoveries and achievements
Language
The fast Fourier transform
The theory of wavelets
A short curriculum vitae of the author
Bibliography
Chronological table
Subject index
Name index
Details:
Publication Year: 2004
ISBN: 0-8218-3403-7
Paging: approximately 472 pp.
Binding: Hardcover