Now in Paperback
Paper | October 2006 | ISBN: 0-691-12797-2
272 pp. | 6 x 9 | 89 line illus. 7 tables.
How does mathematics enable us to send pictures from space back
to Earth? Where does the bell-shaped curve come from? Why do you
need only 23 people in a room for a 50/50 chance of two of them
sharing the same birthday? In Strange Curves, Counting Rabbits,
and Other Mathematical Explorations, Keith Ball highlights how
ideas, mostly from pure math, can answer these questions and many
more. Drawing on areas of mathematics from probability theory,
number theory, and geometry, he explores a wide range of
concepts, some more light-hearted, others central to the
development of the field and used daily by mathematicians,
physicists, and engineers.
Each of the book's ten chapters begins by outlining key concepts
and goes on to discuss, with the minimum of technical detail, the
principles that underlie them. Each includes puzzles and problems
of varying difficulty. While the chapters are self-contained,
they also reveal the links between seemingly unrelated topics.
For example, the problem of how to design codes for satellite
communication gives rise to the same idea of uncertainty as the
problem of screening blood samples for disease.
Accessible to anyone familiar with basic calculus, this book is a
treasure trove of ideas that will entertain, amuse, and bemuse
students, teachers, and math lovers of all ages.
Keith Ball is Professor of Mathematics at University College
London and a Royal Society Leverhulme Research Fellow. Well known
for his entertaining public lectures on mathematics, he is also
the author of a graduate-level introduction to convex geometry in
a textbook on geometry.
Reviews:
"Keith Ball demonstrated that though math may not be laugh-out-loud
hilarious, it is deeply and gloriously satisfying. . . . Ball's
style is pacy and informal, and he does far more than just show
off polished results. This is math with the hood up and the
engine running."--Ben Longstaff, New Scientist
"A recreational math book with enough heft to give its
intended audience a series of mental workouts, ranging from the
rough equivalent of a stroll to the corner mailbox to a hard mile
run. The writing style is open and engaging."--Choice
"A gem. . . . Each topic is taken up in a setting that
immediately generates interest . . . Ball's achievement is to
have come up with a selection of topics which are fresh and
unusual. . . . It is a pleasure to report that the book is
written in limpid, graceful, elegant English prose--nowadays a
nearly vanished species."--Stacy G. Langton, MAA Online
"The author's writing style is informal, inviting, and clear.
. . . This book gives a lively and carefully written treatment of
a number of interesting topics. . . . The range of topics is
wide, so even the experienced mathematician may learn something
new."--Harold R. Parks, Notices of the American Mathematical
Society
Endorsements:
"This book belongs on the shelf next to the classic What is
Mathematics? as a resource for students who seek a broader view
of mathematics and for teachers and professors who want to enrich
their classes. A great addition to the books that spread the
beauty and substance of mathematics to a wide audience."--Sherman
Stein, author of How the Other Half Thinks
"This book represents a good mix of topics, covering a range
of classroom-tested material that is accessible to students. The
author's presentation is lucid and flows well."--Adam
McBride, University of Strathclyde
Cloth | November 2006 | ISBN: 0-691-11921-X
280 pp. | 6 x 9 | 8 line illus.
IIn Hadamard Matrices and Their Applications, K. J. Horadam
provides the first unified account of cocyclic Hadamard matrices
and their applications in signal and data processing. This
original work is based on the development of an algebraic link
between Hadamard matrices and the cohomology of finite groups
that was discovered fifteen years ago. The book translates
physical applications into terms a pure mathematician will
appreciate, and theoretical structures into ones an applied
mathematician, computer scientist, or communications engineer can
adapt and use.
The first half of the book explains the state of our knowledge of
Hadamard matrices, and of two important generalizations: matrices
with group entries and multidimensional Hadamard arrays. It
focuses on their applications in engineering and computer
science, as signal transforms, spreading sequences, error-correcting
codes, and cryptographic primitives.
The book's second half presents the new results in cocyclic
Hadamard matrices and their applications. Full expression of this
theory has been realized only recently, in the Five-fold
Constellation. This identifies cocyclic generalized Hadamard
matrices with particular "stars" in four other areas of
mathematics and engineering: group cohomology, incidence
structures, combinatorics, and signal correlation.
Pointing the way to possible new developments in a field ripe for
further research, this book formulates and discusses ninety open
questions.
K. J. Horadam is Professor of Mathematics and leads the
Information Theory and Security Research Group at RMIT
University, Melbourne, Australia.
Endorsements:
"The material on applications of Hadamard matrices is, in a
word, excellent. Researchers and students in communications,
cryptography, and experimental design will find this to be an
excellent source, while research mathematicians will find the
second part just as interesting. The book is insightful and
rewarding. It is definitely a book that I will have on my most
accessible shelf."--Charles Colbourn, Arizona State
University
"This book will surely be a welcome contribution to the
existing literature. The book can be used by researchers in the
early stages of their work and as a source for a course in the
subject."--Christos Koukouvinos, National Technical
University of Athens
Annals of Mathematics Studies, vol.162.
Paper | December 2006 | ISBN: 0-691-12862-6
Cloth | December 2006 | ISBN: 0-691-12741-7
168 pp. | 6 x 9 | 14 line illus.
Among the many differences between classical and p-adic objects,
those related to differential equations occupy a special place.
For example, a closed p-adic analytic one-form defined on a
simply-connected domain does not necessarily have a primitive in
the class of analytic functions. In the early 1980s, Robert
Coleman discovered a way to construct primitives of analytic one-forms
on certain smooth p-adic analytic curves in a bigger class of
functions. Since then, there have been several attempts to
generalize his ideas to smooth p-adic analytic spaces of higher
dimension, but the spaces considered were invariably associated
with algebraic varieties.
This book aims to show that every smooth p-adic analytic space is
provided with a sheaf of functions that includes all analytic
ones and satisfies a uniqueness property. It also contains local
primitives of all closed one-forms with coefficients in the sheaf
that, in the case considered by Coleman, coincide with those he
constructed. In consequence, one constructs a parallel transport
of local solutions of a unipotent differential equation and an
integral of a closed one-form along a path so that both depend
nontrivially on the homotopy class of the path.
Both the author's previous results on geometric properties of
smooth p-adic analytic spaces and the theory of isocrystals are
further developed in this book, which is aimed at graduate
students and mathematicians working in the areas of non-Archimedean
analytic geometry, number theory, and algebraic geometry.
Vladimir G. Berkovich is Matthew B. Rosenhaus Professor of
Mathematics at the Weizmann Institute of Science in Rehovot,
Israel. He is the author of Spectral Theory and Analytic Geometry
over Non-Archimedean Fields.
Cloth | December 2006 | ISBN: 0-691-11768-3
664 pp. | 6 x 9 | 45 line illus.
There are many mathematics textbooks on real analysis, but they
tend to focus on topics not readily helpful for studying economic
theory or they are inaccessible to most graduate students of
economics. Real Analysis with Economic Applications aims to fill
this gap by providing an ideal textbook and reference on real
analysis tailored specifically to the concerns of such students.
The emphasis throughout is on topics directly relevant to
economic theory. In addition to addressing the usual topics of
real analysis, this book discusses the elements of order theory,
convex analysis, optimization, correspondences, linear and
nonlinear functional analysis, fixed-point theory, dynamic
programming, and calculus of variations. Efe Ok complements the
mathematical development with applications that provide concise
introductions to various topics from economic theory, including
individual decision theory and games, welfare economics,
information theory, general equilibrium and finance, and
intertemporal economics. Moreover, apart from direct applications
to economic theory, his book includes numerous fixed point
theorems and applications to functional equations and
optimization theory.
The book is rigorous, but accessible to those who are relatively
new to the ways of real analysis. The formal exposition is
accompanied by discussions that describe the basic ideas in
relatively heuristic terms, and by over 1,000 exercises of
varying difficulty.
This book will be an indispensable resource in courses on
mathematics for economists and as a reference for graduate
students working on economic theory.
Efe A. Ok is Associate Professor of Economics at New York
University.
Endorsements:
"Because of its comprehensive coverage of the basic topics
of real analysis that are of primary interest to economists, this
is a much needed contribution to the current selection of
mathematics textbooks for students of economics, and it will be a
good addition to any economist's library. It includes a large
number of economics applications that will motivate students to
learn the math, and its number and variety of exercises--forty to
fifty in each chapter--is a further asset."--Susan Elmes,
Columbia University
"This book is poised to be a standard reference. Its author
gets high marks for care of execution and obvious devotion to,
and command of, the topics."--Wei Xiong, Princeton
University
"This very well written book displays its author's engaging
style, and offers interesting questions between topics that make
them entertaining to read through."--Darrel Duffie, James I.
Miller Professor of Finance, Stanford University, author of
Dynamic Asset Pricing Theory
"The idea of doing such a math book directed toward graduate
students of economics and finance is an excellent one. There are
many students who are interested in this topic, and--until now--the
existing math books have not directed their examples and
exercises toward an economics approach."--Salih Neftci, City
University of New York
ARGUMENTAIRE
SUJET
Ce recueil de 1404 exercices est principalement destine aux
etudiants du premier cycle universitaire qui suivent un cours sur
le calcul differentiel et integral concernant les fonctions
reelles d’une variable reelle, mais s’adresse aussi a tous
ceux qui souhaitent parfaire leurs connaissances dans l’un ou l’autre
des sujets traites.
L’ouvrage contient 9 chapitres divises chacun en 2 parties. La
premiere est un rappel de toutes les principales definitions et
resultats qu’il faut connaitre sur la matiere traitee. Les
propositions sont enoncees avec precisions mais sans
demonstration. La deuxieme partie est constituee d’un recueil d’exercices
en rapport avec chacun des chapitres, accompagnes de leurs
solutions.
ORIGINALITE
Tres grand nombre d'exercices resolus, solutions developpees en
detail.
PUBLIC
Etudiants de premier cycle universitaire, eleves-ingenieurs et
classes preparatoires, enseignants.
AUTEUR
Jacques Douchet est mathematicien, diplome de l'Ecole
polytechnique federale de Lausanne et docteur es sciences de
cette meme institution. Depuis plusieurs annees, il enseigne au
Departement de mathematiques de l'EPFL. Son domaine de recherche
est l'analyse non lineaire.
SOMMAIRE
Introduction - Table des matieres - Nombres reels - Suites
numeriques - Nombres complexes - Fonctions d'une variable -
Calcul differentiel - Calcul integral - Integrales generalisees -
Series - Equations differentielles - Solutions des exercices -
Formulaires - Bibliographie - Index
ISBN: 2-88074-669-8
2006, 540 pages, 16x24cm, broche.,
≪Quoi de plus naturel, lorsqu’un systeme peut etre decrit
formellement, que de tenter de l’ameliorer? L’auteur de cet
ouvrage conduit le lecteur avec patience (et humour) a la
decouverte de methodes algorithmiques qui permettent d’aborder
cette question. Son propos se distingue par une approche
progressive et detaillee, amplement supportee par des projets et
exercices, par l’etendue du domaine couvert, par la qualite de
sa documentation, ainsi que par un souci pedagogique constant et
un souci permanent de l’illustration pertinente. Il propose
ainsi une excellente introduction a un sujet en plein essor, tant
du point de vue des applications, aujourd’hui innombrables, que
de la comprehension plus profonde des concepts≫. Prof. Philippe
Toint, Facultes Universitaires Notre-Dame de la Paix, Namur,
Belgique.
Seul ouvrage en francais sur le sujet destine a un puiblic
d'ingenieurs et d'utilisateurs d'outils d'optimisation. Presente
de maniere synthetique et didactique les principales methodes
d'optimisation, illustrees de nombreux exemples.
Professeurs, etudiants, ingenieurs et chercheurs en sciences de
l'ingenieur, mathematiques, physique, experts en optimisation.
Formulation et analyse du probleme: Formulation - Fonction
objectif - Contraintes - Introduction a la dualite. Conditions
d'optimalite: Optimisation sans contrainte - Optimisation avec
contraintes. Resolution d'equations: Methode de Newton - Methode
quasi-Newton. Optimisation sans contrainte: Problemes
quadratiques - Methode de Newton pure - Methodes de descente -
Region de confiance - Methodes quasi-Newton - Le probleme de
Rosenbrock - Methode des moindres carres - Methode de recherche
directe. Optimisation avec contraintes: Methode du simplexe -
Methode de Newton contrainte - Methodes de points inferieurs -
Lagrangien augmente - programmation quadratique sequentielle -
Annexes.
ISBN: 2-88074-668-X
2006, 256 pages, 16x24cm, broche.,
Cet ouvrage propose une presentation didactique et homogene de la
theorie des processus stochastiques, vue comme une extension de
la theorie des probabilites. Il s’adresse donc tout autant aux
etudiants ingenieurs qu’aux ingenieurs souhaitant s’initier a
ce puissant outil de modelisation et d’analyse. Les concepts
essentiels des processus stochastiques sont tout d’abord
decrits, commentes et illustres d’exemples dans le traitement
du signal aleatoire. Plusieurs cas concrets de processus
stochastiques (processus gaussiens ou de Poisson, chaines de
Markov) sont ensuite presentes dans differents contextes d’applications
reelles (files d’attente, analyse de donnees medicales…). De
tres nombreux exercices corriges illustrent l’ouvrage, et
permettent au lecteur de se familiariser avec certains points
particuliers de l’expose.
Cet ouvrage propose une presentation didactique et homogene de la
theorie des processus stochastiques, vue comme une extension de
la theorie des probabilites.
Eleves-ingenieurs et etudiants des 2e et 3e cycles
universitaires, praticiens dans les domaines de la modelisation
et du traitement statistique des phenomenes physiques.
Theorie du calcul des probabilites - Processus stochastiques -
Processus gaussiens - Processus de Poisson - Chaines de Markov -
Exemples d'application - Exercices - References bibliographiques.Contenu:
Theorie du calcul des probabilites ? Processus stochastiques ?
Processus Gaussiens ? Processus de Poisson ? Chaines de Markov.
Mathematical Modeling and Computation 12
“There really is not a book that is directly comparable.
Students will be able to study any area of biology with a
mathematical perspective. The projects and the introduction to
computation are a real bonus.” ? Fred Brauer, Department of
Mathematics, University of British Columbia
The field of mathematical biology is growing rapidly. Questions
about infectious diseases, heart attacks, cell signaling, cell
movement, ecology, environmental changes, and genomics are now
being analyzed using mathematical and computational methods. A
Course in Mathematical Biology: Quantitative Modeling with
Mathematical and Computational Methods is the only book that
teaches all aspects of modern mathematical modeling and that is
specifically designed to introduce undergraduate students to
problem solving in the context of biology.
With a focus on integrating analytical and computational tools in
the modeling of biological processes, the authors provide an
integrated package of theoretical modeling and analysis tools,
computational modeling techniques, and parameter estimation and
model validation methods. Divided into three parts, the book
covers basic analytical modeling techniques; introduces
computational tools used in the modeling of biological problems;
and provides a source of open-ended problems from epidemiology,
ecology, and physiology. All chapters include realistic
biological examples, and there are many exercises related to
biological questions. In addition, the book includes 25 open-ended
research projects that can be used by students. The book is
accompanied by a Web site that contains solutions to most of the
exercises and a tutorial for the implementation of the
computational modeling techniques. Calculations can be done in
modern computing languages such as Maple, Mathematica, and
MATLABR.
Audience
Intended for upper level undergraduate students in mathematics or
similar quantitative sciences, Course in Mathematical Biology:
Quantitative Modeling with Mathematical and Computational Methods
is also appropriate for beginning graduate students in biology,
medicine, ecology, and other sciences. It will also be of
interest to researchers interested in entering the field of
mathematical biology.
About the Authors
Gerda de Vries is Associate Professor in the Department of
Mathematical and Statistical Sciences at the University of
Alberta, Canada.
Thomas Hillen is a Professor in the Department of Mathematical
and Statistical Sciences at the University of Alberta, Canada.
Mark Lewis is Professor and Senior Canada Research Chair in
Mathematical Biology in the Department of Mathematical and
Statistical Sciences and the Department of Biological Sciences at
the University of Alberta, Canada.
Johannes Muller is Professor of Mathematical Methods in Molecular
Biology and Biochemistry in the Center for Mathematical Sciences
at the Technical University, Munich.
Birgitt Schonfisch is a Scientific Employee in the Department of
Medical Biometry at the University of Tubingen, Germany.
A portion of the royalties from the sale of this book are
contributed to the SIAM Student Travel Fund.
This book has not yet published and is not available for
immediate shipment.
Available July 2006 / Approx. xii + 311 pages / Softcover
ISBN 10: 0-89871-612-8 / ISBN 13: 978-0-898716-12-2