AMS Chelsea Publishing
2007; 148 pp; hardcover
ISBN-10: 0-8218-4179-3
ISBN-13: 978-0-8218-4179-2
This book provides a clear and logical path to understanding what
quantum mechanics is about. It will be accessible to
undergraduates with minimal mathematical preparation: all that is
required is an open mind, a little algebra, and a first course in
undergraduate physics.
Quantum mechanics is arguably the most successful physical theory.
It makes predictions of incredible accuracy. It provides the
structure underlying all of our electronic technology, and much
of our mastery over materials. But compared with Newtonian
mechanics, or even relativity, its teachings seem obscure--they
have no counterpart in everyday experience, and they sometimes
contradict our simplest notions of how the world works. A full
understanding of the theory requires prior mastery of very
advanced mathematics. This book aims at a different goal: to
teach the reader, step by step, how the theory came to be and
what, fundamentally, it is about.
Most students learn physics by learning techniques and formulas.
This is especially true in a field like quantum mechanics, whose
content often contradicts our common sense, and where it's
tempting to retreat into mathematical formalism. This book goes
behind the formalism to explain in direct language the conceptual
content and foundations of quantum mechanics: the experiments
that forced physicists to construct such a strange theory, and
the essential elements of its strangeness.
Readership
Undergraduates, graduate students, and research mathematicians
interested in quantum mechanics.
Table of Contents
The failure of classical theory
Consequences of a mistrust of theory
Properties of electrons, photons; The De Broglie relations
An analysis of electron diffraction
Heisenberg's principle of indeterminancy
Interpretations of the Heisenberg principle
Dynamical properties of microsystems
Determinism and state; Statistical determinism
Probability amplitudes; The superposition principle
Summary and comment
Index
IAS/Park City Mathematics Series, Volume: 12
2007; 427 pp; hardcover
ISBN-10: 0-8218-2873-8
ISBN-13: 978-0-8218-2873-1
The theory of automorphic forms has seen dramatic developments in
recent years. In particular, important instances of Langlands
functoriality have been established. This volume presents three
weeks of lectures from the IAS/Park City Mathematics Institute
Summer School on automorphic forms and their applications. It
addresses some of the general aspects of automorphic forms, as
well as certain recent advances in the field.
The book starts with the lectures of Borel on the basic theory of
automorphic forms, which lay the foundation for the lectures by
Cogdell and Shahidi on converse theorems and the Langlands-Shahidi
method, as well as those by Clozel and Li on the Ramanujan
conjectures and graphs. The analytic theory of GL(2)-forms and L-functions
are the subject of Michel's lectures, while Terras covers
arithmetic quantum chaos. The volume also includes a chapter by
Vogan on isolated unitary representations, which is related to
the lectures by Clozel.
This volume is recommended for independent study or an advanced
topics course. It is suitable for graduate students and
researchers interested in automorphic forms and number theory.
Titles in this series are co-published with the Institute for
Advanced Study/Park City Mathematics Institute. Members of the
Mathematical Association of America (MAA) and the National
Council of Teachers of Mathematics (NCTM) receive a 20% discount
from list price.
Readership
Graduate students and research mathematicians interested in
automorphic forms and number theory.
Table of Contents
Introduction
Armand Borel, Automorphic Forms on Reductive Groups
Automorphic forms on reductive groups
Bibliography
L. Clozel, Spectral Theory of Automorphic Forms
Spectral theory of automorphic forms
Mostly SL(2)
The spectral decomposition of L^2(G(\mathbb{Q})\backslash G(\mathbb{A})):
Arthur's conjectures
Known bounds for the cuspidal spectrum and the Burger-Sarnak
method
Applications: Control of the spectrum
All reductive adelic groups are tame
Bibliography
James W. Cogdell, L-functions and Converse Theorems for GL_n
L-functions and converse theorems for GL_n
Fourier expansions and multiplicity one
Eulerian integrals for GL_n
Local L-functions
Global L-functions
Converse theorems
Converse theorems and functoriality
Bibliography
Philippe Michel, Analytic Number Theory and Families of
Automorphic L-functions
Analytic number theory and families of automorphic L-functions
Analytic properties of individual L-functions
A review of classical automorphic forms
Large sieve inequalities
The subconvexity problem
Some applications of subconvexity
Bibliography
Freydoon Shahidi, Langlands-Shahidi Method
Langlands-Shahidi Method
Basic concepts
Eisenstein series and L-functions
Functional equations and multiplicativity
Holomorphy and boundedness; Applications
Bibliography
Audrey Terras, Arithmetical Quantum Chaos
Arithmetical quantum chaos
Finite models
Three symmetric spaces
Bibliography
David A. Vogan, Jr., Isolated Unitary Representations
Isolated unitary representations
Bibliography
Wen-Ching Winnie Li, Ramanujan Graphs and Ramanujan Hypergraphs
Ramanujan graphs and Ramanujan hypergraphs
Ramanujan graphs and connections with number theory
Ramanujan hypergraphs
Bibliography
Student Mathematical Library, Volume: 37
2007; 152 pp; softcover
ISBN-10: 0-8218-4220-X
ISBN-13: 978-0-8218-4220-1
The book gives an introduction to p-adic numbers from the point
of view of number theory, topology, and analysis. Compared to
other books on the subject, its novelty is both a particularly
balanced approach to these three points of view and an emphasis
on topics accessible to undergraduates. In addition, several
topics from real analysis and elementary topology which are not
usually covered in undergraduate courses (totally disconnected
spaces and Cantor sets, points of discontinuity of maps and the
Baire Category Theorem, surjectivity of isometries of compact
metric spaces) are also included in the book. They will enhance
the reader's understanding of real analysis and intertwine the
real and p-adic contexts of the book.
The book is based on an advanced undergraduate course given by
the author. The choice of the topic was motivated by the internal
beauty of the subject of p-adic analysis, an unusual one in the
undergraduate curriculum, and abundant opportunities to compare
it with its much more familiar real counterpart. The book
includes a large number of exercises. Answers, hints, and
solutions for most of them appear at the end of the book. Well
written, with obvious care for the reader, the book can be
successfully used in a topic course or for self-study.
Readership
Undergraduate and graduate students interested in p-adic numbers
Contents
Graduate Studies in Mathematics,Volume: 82
2007; 168 pp; hardcover
ISBN-10: 0-8218-3454-1
ISBN-13: 978-0-8218-3454-1
This book presents two essential and apparently unrelated
subjects. The first, microlocal analysis and the theory of pseudo-differential
operators, is a basic tool in the study of partial differential
equations and in analysis on manifolds. The second, the Nash-Moser
theorem, continues to be fundamentally important in geometry,
dynamical systems, and nonlinear PDE.
Each of the subjects, which are of interest in their own right as
well as for applications, can be learned separately. But the book
shows the deep connections between the two themes, particularly
in the middle part, which is devoted to Littlewood-Paley theory,
dyadic analysis, and the paradifferential calculus and its
application to interpolation inequalities.
An important feature is the elementary and self-contained
character of the text, to which many exercises and an
introductory Chapter 0 with basic material have been added. This
makes the book readable by graduate students or researchers from
one subject who are interested in becoming familiar with the
other. It can also be used as a textbook for a graduate course on
nonlinear PDE or geometry.
Readership
Graduate students and research mathematicians interested in
microlocal analysis, PDE, and geometry.
Table of Contents
General introduction
Notation and review of distribution theory
Pseudo-differential operators
Nonlinear dyadic analysis, microlocal analysis, energy estimates
Implicit function theorems
Bibliography
Main notation introduced
Index
American Mathematical Society Translations--Series 2, Volume:
220
2007; 244 pp; hardcover
ISBN-10: 0-8218-4209-9
ISBN-13: 978-0-8218-4209-6
This volume is devoted to the memory of the famous Saint
Petersburg mathematician Olga Aleksandrovna Ladyzhenskaya. For
many years she ran the Saint Petersburg Seminar on mathematical
physics, which became a basis for the scientific school she
created. The ten articles in the volume, written by students and
colleagues of O. A. Ladyzhenskaya, are mainly devoted to boundary
value problems for partial differential equations and to spectral
problems for differential operators.
Readership
Graduate students and research mathematicians interested in
partial differential equations.
Table of Contents
A. Arkhipova -- Quasireverse Holder inequalities in parabolic
metric and their applications
M. Sh. Birman and N. D. Filonov -- Weyl asymptotics of the
spectrum of the Maxwell operator with non-smooth coefficients in
Lipschitz domains
A. M. Budylin and V. S. Buslaev -- Semiclassical
pseudodifferential operators with discontinuous symbols and their
applications to the problems of statistical physics
L. D. Faddeev -- What is complete integrability in quantum
mechanics
N. Ivochkina -- Geometric evolution equations preserving
convexity
B. A. Plamenevskii -- On spectral properties of elliptic problems
in domains with cylindrical ends
N. Kikuchi and G. Seregin -- Weak solutions to the Cauchy problem
for the Navier-Stokes equations satisfying the local energy
inequality
V. A. Solonnikov -- Schauder estimates for the evolutionary
generalized Stokes problem
T. A. Suslina -- Homogenization of a periodic parabolic Cauchy
problem
N. N. Uraltseva -- Boundary estimates for solutions of elliptic
and parabolic equations with discontinuous nonlinearities