Jurgen Moser and Eduard J. Zehnder
Notes on Dynamical Systems
Description
This book is an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. The authors aimed at keeping the requirements of mathematical techniques minimal but giving detailed proofs and many examples and illustrations from physics and celestial mechanics. After all, the celestial N-body problem is the origin of dynamical systems and gave rise in the past to many mathematical developments.
Jurgen Moser (1928-1999) was a professor at the Courant
Institute, New York, and then at ETH Zurich. He served as
president of the International Mathematical Union and received
many honors and prizes, among them the Wolf Prize in mathematics.
Jurgen Moser is the author of several books, among them Stable
and Random Motions in Dynamical Systems. Eduard Zehnder is a
professor at ETH Zurich. He is coauthor with Helmut Hofer of the
book Symplectic Invariants and Hamiltonian Dynamics.
Readership
Graduate students and research mathematicians interested in
dynamical systems.
Contents
Transformation theory
Periodic orbits
Integrable Hamiltonian systems
Bibliography
Details:
Series: Courant Lecture Notes, Volume: 12
Publication Year: 2005
ISBN: 0-8218-3577-7
Paging: 256 pp.
Binding: Softcover
Emil Artin
Algebraic Numbers and Algebraic Functions
Description
Famous Norwegian mathematician Niels Henrik Abel advised that one
should "learn from the masters, not from the pupils".
When the subject is algebraic numbers and algebraic functions,
there is no greater master than Emil Artin. In this classic text,
originated from the notes of the course given at Princeton
University in 1950-1951 and first published in 1967, one has a
beautiful introduction to the subject accompanied by Artin's
unique insights and perspectives. The exposition starts with the
general theory of valuation fields in Part I, proceeds to the
local class field theory in Part II, and then to the theory of
function fields in one variable (including the Riemann-Roch
theorem and its applications) in Part III.
Prerequisites for reading the book are a standard first-year
graduate course in algebra (including some Galois theory) and
elementary notions of point set topology. With many examples,
this book can be used by graduate students and all mathematicians
learning number theory and related areas of algebraic geometry of
curves.
Readership
Graduate students and research mathematicians interested in
number theory and algebraic geometry.
Contents
General valuation theory
Valuations of a field
Complete fields
e, f and n
Ramification theory
The different
Local class field theory
Preparations for local class field theory
The first and second inequalities
The norm residue symbol
The existence theorem
Applications and illustrations
Product formula and function fields in one variable
Preparations for the global theory
Characterization of fields by the product formula
Differentials in PF-fields
The Riemann-Roch theorem
Constant field extensions
Applications of the Riemann-Roch theorem
Differentials in function fields
Theorems on p-groups and Sylow groups
Index of symbols
Subject index
Details:
Series: AMS Chelsea Publishing Publication
Year: 2006
ISBN: 0-8218-4075-4
Paging: 349 pp.
Binding: Hardcover
Christoph Thiele
Wave Packet Analysis
Description
The concept of "wave packet analysis" originates in Carleson's famous proof of almost everywhere convergence of Fourier series of L^2 functions. It was later used by Lacey and Thiele to prove bounds on the bilinear Hilbert transform. For quite some time, Carleson's wave packet analysis was thought to be an important idea, but that it had limited applications. But in recent years, it has become clear that this is an important tool for a number of other applications. This book is an introduction to these tools. It emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development. However, the book closes with a dedicated chapter on more recent results.
Carleson's original theorem is sometimes cited as one of the most
important developments of 20th century harmonic analysis. The set
of ideas stemming from his proof is now seen as an essential
element in modern harmonic analysis. Indeed, Thiele won the Salem
prize jointly with Michael Lacey for work in this area.
The book gives a nice survey of important material, such as an
overview of the theory of singular integrals and wave packet
analysis itself. There is a separate chapter on "further
developments", which gives a broader view on the subject,
though it does not exhaust all ongoing developments.
Readership
Graduate students and research mathematicians interested in
classical analysis and harmonic analysis.
Contents
Introduction
Wavelets and square functions
Interpolation of multilinear operators
Paraproducts
Wave packets
Multilinear forms with modulation symmetries
Carleson's theorem
The Walsh model
Further applications of wave packet analysis
Bibliography
Details:
Series: CBMS Regional Conference Series in Mathematics, Number:
105
Publication Year: 2006
ISBN: 0-8218-3661-7
Paging: 86 pp.
Binding: Softcover
Edited by: Chandler Davis and Erich W. Ellers
The Coxeter Legacy: Reflections and Projections
Description
Donald Coxeter infused enthusiasm, even passion, for mathematics
in people of any age, any background, any profession, any walk of
life. Enchanted by Euclidean geometry, he was interested in the
beauty, the description, and the exploration of the world around
us. His involvement in art and with artists earned him admiration
and friends in the intellectual community all over the globe.
Coxeter's devotion to polytopes and his interest in the theory of
configurations live on in his students and followers. Coxeter
groups arise in various subjects in applied mathematics, and they
have a permanent place in some of the most demanding and
fascinating branches of abstract mathematics, such as Lie
algebras, algebraic groups, Chevalley groups, and Kac-Moody
groups. This collection of articles by outstanding researchers
and expositors is intended to capture the essence of the Coxeter
legacy. It is a mixture of surveys, up-to-date information,
history, storytelling, and personal memories; and it includes a
rich variety of beautiful illustrations.
Readership
Mathematicians, artists, model makers with a university degree,
preferably in mathematics.
Contents
B. Muhlherr -- The isomorphism problem for Coxeter groups
A. V. Borovik -- Coxeter theory: The cognitive aspects
M. Ronan -- From Galois and Lie to Tits buildings
B. Kostant -- The Coxeter element and the branching law for the finite subgroups of SU(2)
R. Kellerhals -- Hyperbolic Coxeter groups and space forms
P. McMullen and E. Schulte -- Regular and chiral polytopes in low
dimensions
B. Monson and A. I. Weiss -- Polytopes, honeycombs, groups and
graphs
J. M. Wills -- Equivelar polyhedra
A. Khovanskii -- Combinatorics of sections of polytopes and
Coxeter groups in Lobachevsky spaces
M. Senechal -- Donald and the golden rhombohedra
B. Grunbaum -- Configurations of points and lines
J. Richter-Gebert -- Meditations on Ceva's theorem
D. Schattschneider -- Coxeter and the artists: Two-way
inspiration
M. Emmer -- The visual mind: Art, mathematics and cinema
Publications of H. S. M. Coxeter
Index
Details:
Publication Year: 2006
ISBN: 0-8218-3722-2
Paging: 320 pp.
Binding: Hardcover