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Now available in Third Edition: AMSTEXT/37
This book is about using game theory in mathematical
modelling. It is an introductory text, covering the basic ideas and
methods of game theory as well as the necessary ideas from the vast
spectrum of scientific study where the methods are applied.
It has by now become generally apparent that game theory is a
fascinating branch of mathematics with both serious and recreational
applications. Strategic behavior arises whenever the outcome of an
individual's action depends on actions to be taken by other
individuals—whether human, as in the Prisoners' Dilemma, or
otherwise, as in the “duels of damselflies”. As a result,
game-theoretic mathematical models are applicable in both the social
and natural sciences. In reading this book, you can learn not just
about game theory, but also about how to model real situations so that
they can be analyzed mathematically.
Mesterton-Gibbons includes the familiar game theory examples where they are
needed for explaining the mathematics or when they provide a valuable
application. There are also plenty of new examples, in particular from
biology, such as competitions for territory or mates, games among
kin versus games between kin, and cooperative wildlife management.
Prerequisites are modest. Students should have some mathematical
maturity and a familiarity with basic calculus, matrix algebra,
probability, and some differential equations. As Mesterton-Gibbons
writes, “The recurring theme is that game theory is fun to
learn, doesn't require a large amount of mathematical rigor, and has
great potential for application.”
This new edition contains a significant amount of updates and new material,
particularly on biological games. An important chapter on population games now
has virtually all new material. The book is absolutely up-to-date with
numerous references to the literature. Each chapter ends with a commentary
which surveys current developments.
This book helps not only to make game theory accessible, but also to convey both its power and scope in a variety of applications. The books deals in a unified manner with the central ideas of both classical and evolutionary game theory. The key ideas are illustrated by a variety of well-chosen examples.
-- Zentralblatt MATH
Mesterton-Gibbons' book deals with mathematical modelling, not by an abstract discussion of how modelling should be done, but rather by presenting many concrete examples … The mathematics described [in the book] is fascinating and well worth studying … The examples are great, and the author has clearly put enormous effort into building this collection … a perfect source of problems for a Moore method course … a valuable contribution to the literature … Everyone interested in game theory or mathematical modelling should take a look at it.
-- MAA Online
Readers will be hard-pressed to find a general introduction to game theory that blends biological and mathematical approaches more expertly. It is both a well-rounded survey and a reference work of lasting value.
-- Behavioral Ecology
This book is an introduction to game theory with two specific features: it is written by a mathematician … and it is written from the perspective of a mathematical modeller. This last characteristic implies that all chapters start with examples and the general concepts are only presented once the specific examples have been carefully developed … I find this book excellent and … worth considering when teaching an undergraduate course in game theory to students having some mathematical maturity (some calculus, some knowledge of matrix analysis and probability).
-- Zentralblatt MATH
Many people have heard two things about Archimedes: he was the greatest mathematician of antiquity, and he ran naked from his bath crying “Eureka!”. However, few people are familiar with the actual accomplishments upon which his enduring reputation rests, and it is the aim of this book to shed light upon this matter. Archimedes' ability to achieve so much with the few mathematical tools at his disposal was astonishing. He made fundamental advances in the fields of geometry, mechanics, and hydrostatics. No great mathematical expertise is required of the reader, and the book is well illustrated with over 100 diagrams. It will prove fascinating to students and professional mathematicians alike.
The author's writing style is elegant yet logical... In short, the book is eminently readable... Highly recommended for all teachers of mathematics.
-- The Australian Mathematics Teacher
Highly recommended to anyone interested in mathematics and its history, as it is an eye-opening and a great read.
-- Choice Magazine, March 2000
The topics in this volume are treated carefully clearly, and with many illustrations.
-- AAAS, Science Books and Films/May-June 2000
Now available in Second Edition:
TEXT/43
This book presents a modern treatment of material
traditionally covered in the sophomore-level course in ordinary
differential equations. While this course is usually required for
engineering students the material is attractive to students in any
field of applied science, including those in the biological
sciences.
The standard analytic methods for solving first and
second-order differential equations are covered in the first three
chapters. Numerical and graphical methods are considered, side-by-side
with the analytic methods, and are then used throughout the text. An
early emphasis on the graphical treatment of autonomous first-order
equations leads easily into a discussion of bifurcation of solutions
with respect to parameters. The fourth chapter begins the study of
linear systems of first-order equations and includes a section
containing all of the material on matrix algebra needed in the
remainder of the text. Building on the linear analysis, the fifth
chapter brings the student to a level where two-dimensional nonlinear
systems can be analyzed graphically via the phase plane. The study of
bifurcations is extended to systems of equations, using several
compelling examples, many of which are drawn from population
biology. In this chapter the student is gently introduced to some of
the more important results in the theory of dynamical systems. A
student project, involving a problem recently appearing in the
mathematical literature on dynamical systems, is included at the end
of Chapter 5. A full treatment of the Laplace transform is given in
Chapter 6, with several of the examples taken from the biological
sciences. An appendix contains completely worked-out solutions to all
of the odd-numbered exercises.
The book is aimed at students
with a good calculus background that want to learn more about how
calculus is used to solve real problems in today's world. It can be
used as a text for the introductory differential equations course, and
is readable enough to be used even if the class is being "flipped."
The book is also accessible as a self-study text for anyone who has
completed two terms of calculus, including highly motivated high
school students. Graduate students preparing to take courses in
dynamical systems theory will also find this text useful.
An instructor's manual for this title is available electronically
to those instructors who have adopted the textbook for classroom
use. Please send email to textbooks@ams.org for more information.
Most questions from this textbook are available in
WebAssign. WebAssign is a leading provider of
online instructional tools for both faculty and students.
This is a textbook that could be used for a standard undergraduate course in ordinary differential equations. It is substantially cheaper than most of the alternatives from commercial publishers, it is well-written, and it appears to have been carefully proofread. The target audience seems to be students whose background in mathematics is not particularly strong. … The approach is modern in the sense that computer algebra systems are presented as important tools for the student, and also in the sense that geometric treatment of nonlinear equations gets substantial attention.
-- Christopher P. Grant, Mathematical Review Clippings
Although Noonburg's book is slim, it covers (and covers well) all of the familiar topics one expects to find in a first semester sophomore-level ODE course, and then some. It also has some interesting features that distinguish it from most of the existing textbook literature … The author's writing style is very clear and should be quite accessible to most students reading the book. There are lots of worked examples and interesting applications, including some fairly unusual ones. … This book offers a clean, concise, modern, reader-friendly approach to the subject, at a price that won t make an instructor feel guilty about assigning it. It is certainly worth a very serious look.
-- Mark Hunacek MAA Reviews
… The writing is clear, the problems are good, and the material is well motivated and largely self-contained. Some previous acquaintance with linear algebra would, however, be helpful. In summary, this new book is highly recommended for students anxious to discover new techniques.
-- SIAM Review
Ramsey theory is the study of the structure of mathematical objects
that is preserved under partitions. In its full generality, Ramsey
theory is quite powerful, but can quickly become complicated. By
limiting the focus of this book to Ramsey theory applied to the set of
integers, the authors have produced a gentle, but meaningful,
introduction to an important and enticing branch of modern
mathematics. Ramsey Theory on the Integers offers students a glimpse
into the world of mathematical research and the opportunity for them
to begin pondering unsolved problems.
For this new edition, several sections have been added and others
have been significantly updated. Among the newly introduced topics
are: rainbow Ramsey theory, an “inequality” version of Schur's
theorem, monochromatic solutions of recurrence relations, Ramsey
results involving both sums and products, monochromatic sets avoiding
certain differences, Ramsey properties for polynomial progressions,
generalizations of the Erdős-Ginzberg-Ziv theorem, and the number
of arithmetic progressions under arbitrary colorings. Many new results
and proofs have been added, most of which were not known when the
first edition was published. Furthermore, the book's tables,
exercises, lists of open research problems, and bibliography have all
been significantly updated.
This innovative book also provides the first cohesive study of
Ramsey theory on the integers. It contains perhaps the most
substantial account of solved and unsolved problems in this blossoming
subject. This breakthrough book will engage students, teachers, and
researchers alike.
Reviews of the Previous Edition:
Students will enjoy it due to the highly accessible exposition of the material provided by the authors.
—MAA Horizons
What a wonderful book! … contains a very “student friendly” approach to one of the richest areas of mathematical research … a very good way of introducing the students to mathematical research … an extensive bibliography … no other book on the subject … which is structured as a textbook for undergraduates … The book can be used in a variety of ways, either as a textbook for a course, or as a source of research problems … strongly recommend this book for all researchers in Ramsey theory … very good book: interesting, accessible and beautifully written. The authors really did a great job!
—MAA Online
Undergraduate and graduate students interested in combinatorics, number theory, and Ramsey theory.
This is an excellent undergraduate text which provides students with an introduction to research; it is also a source for all those who are interested in combinatorial or number theoretic problems. ... The textbook is carefully written. I recommend it to students interested in combinatorics and to their teachers as well.
-- Monatshafte für Mathematik
Now available in Second Edition:
STML/79
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.
this is an excellent, well-written textbook which is strongly recommended to a wide audience of readers interested in mathematics and its applications. The book is suitable for a one-semester undergraduate lecture course in matrix groups, and would also be useful supplementary reading for more general group theory courses.
-- Mathematical Reviews
Now available in Second Edition:
MBK/112
This book is about writing in the professional mathematical
environment. While the book is nominally about
writing, it's also about how to function in the mathematical
profession. In many ways, this text complements Krantz's previous
bestseller, How to Teach Mathematics. Those who are familiar
with Krantz's writing will recognize his lively, inimitable style.
In this volume, he addresses these nuts-and-bolts issues:
This book is about writing in the professional mathematical environment. While the book is nominally about writing, it's also about how to function in the mathematical profession. Krantz's frank and straightforward approach makes this particularly suitable as a textbook. He does not avoid difficult topics.
-- Zentralblatt für Didaktik der Mathematik
Krantz provides brief but helpful advice on writing a survey article, an opinion piece, a letter of recommendation, a book review, a referee's report, a talk, a grant application, a curriculum vitae, a job application, and email. He concludes his book with a chapter called 'The modern writing environment' which discusses the use of computers, TeX, spell checkers, etc. Krantz's book is lively, entertaining and provides many amusing anecdotes … [an] excellent and worthy candidate for a statistician's library … more useful on your personal bookshelf than in a shared library, so it can be consulted regularly.
-- Australian and New Zealand Journal of Statistics
Krantz, a prolific and distinguished mathematical author, discourses engagingly (yet seriously) on the art and etiquette of virtually all types of writing an academic mathematician is likely to encounter … Grammatical points, stylistic and typesetting issues, and the correct and effective use of mathematical notation are handled deftly and with good humor … [Hopefully] senior faculty will consider it mandatory reading for graduate students and even upper-division undergraduates. An enjoyable way to learn some fundamentals of good mathematical writing. Highly recommended.
-- CHOICE
Well written in a lively style and will be found useful by anybody who is aware of the power and significance of writing in the mathematical profession.
-- European Mathematical Society Newsletter
[Krantz has] expanded and elaborated the material in Halmos's article [1970] and added discussions of the uses of computer technology in mathematical writing … enjoyable to read … worth having on your bookshelf … written in a very personal style that is meant to engage the reader in a lively conversation … In addition, he has a chapter on how to write a book and sections on other sorts of professional prose such as referee's reports and letters of recommendation. In keeping with his general approach, he also has more to say about the psychological and sociological aspect of mathematical communication …
-- American Mathematical Monthly
[The book] provides a compact set of questions to consider before undertaking the writing process, questions particularly well suited for mathematical exposition. In addition to being of value to faculty interested in thinking about what they write, A Primer of Mathematical Writing would make an excellent gift for a graduate student or junior colleague.
-- Journal of the American Statistical Association
In this paper the authors first develop various enhancements
of the theory of spectral invariants of Hamiltonian Floer homology and
of Entov-Polterovich theory of spectral symplectic quasi-states and
quasi-morphisms by incorporating bulk deformations, i.e.,
deformations by ambient cycles of symplectic manifolds, of the Floer
homology and quantum cohomology. Essentially the same kind of
construction is independently carried out by Usher in a slightly less
general context. Then the authors explore various applications of
these enhancements to the symplectic topology, especially new
construction of symplectic quasi-states, quasi-morphisms and new
Lagrangian intersection results on toric and non-toric manifolds.
The most novel part of this paper is its use of open-closed
Gromov-Witten-Floer theory and its variant involving closed orbits of
periodic Hamiltonian system to connect spectral invariants (with bulk
deformation), symplectic quasi-states, quasi-morphism to the
Lagrangian Floer theory (with bulk deformation).
The authors use this open-closed Gromov-Witten-Floer theory to
produce new examples. Using the calculation of Lagrangian
Floer cohomology with bulk, they produce examples of compact
symplectic manifolds \((M,\omega)\) which admits uncountably
many independent quasi-morphisms \(\widetilde{{\rm Ham}}(M,\omega)
\to {\mathbb{R}}\). They also obtain a new intersection result
for the Lagrangian submanifold in \(S^2 \times S^2\).
This book is a collection of 34 curiosities,
each a quirky and delightful gem of mathematics and each a shining
example of the joy and surprise that mathematics can bring. Intended
for the general math enthusiast, each essay begins with an intriguing
puzzle, which either springboards into or unravels to become a
wondrous piece of thinking. The essays are self-contained and rely
only on tools from high-school mathematics (with only a few pieces
that ever-so-briefly brush up against high-school calculus).
The gist of each essay is easy to pick up with a cursory
glance—the reader should feel free to simply skim through some
essays and dive deep into others. This book is an invitation to play
with mathematics and to explore its wonders. Much joy awaits!
In the interest of fostering a greater awareness and appreciation of
mathematics and its connections to other disciplines and everyday life, MSRI
and the AMS are publishing books in the Mathematical Circles Library series as
a service to young people, their parents and teachers, and the mathematics
profession.
Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
Math circles students and organizers, participants and organizers of math summer camps for high-school students, and anyone interested in learning or teaching mathematics at the high-school level.
Now available in Second Edition:
MBK/107
This book is an introduction to the modern approach to the
theory of Markov chains. The main goal of this approach is to
determine the rate of convergence of a Markov chain to the stationary
distribution as a function of the size and geometry of the state
space. The authors develop the key tools for estimating convergence
times, including coupling, strong stationary times, and spectral
methods. Whenever possible, probabilistic methods are emphasized. The
book includes many examples and provides brief introductions to some
central models of statistical mechanics. Also provided are accounts
of random walks on networks, including hitting and cover times, and
analyses of several methods of shuffling cards. As a prerequisite,
the authors assume a modest understanding of probability theory and
linear algebra at an undergraduate level. Markov Chains and Mixing
Times is meant to bring the excitement of this active area of
research to a wide audience.
Markov Chains and Mixing Times is a magical book, managing to be both friendly and deep. It gently introduces probabilistic techniques so that an outsider can follow. At the same time, it is the first book covering the geometric theory of Markov chains and has much that will be new to experts. It is certainly THE book that I will use to teach from. I recommend it to all comers, an amazing achievement.
-- Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University
A superb introduction to Markov chains which treats riffle shuffling and stationary times...
-- Sami Assaf, University of Southern California, Persi Diaconis, Stanford University, and Kannan Soundararajan, Stanford University, in their paper "Riffle Shuffles with Biased Cuts"
In this book, [the authors] rapidly take a well-prepared undergraduate to the frontiers of research. Short, focused chapters with clear logical dependencies allow readers to use the book in multiple ways.
-- CHOICE Magazine
This book is a beautiful introduction to Markov chains and the analysis of their convergence towards a stationary distribution. Personally, I enjoyed very much the lucid and clear writing style of the exposition in combination with full mathematical rigor and the fascinating relations of the theory of Markov chains to several other mathematical areas.
-- Zentralblatt MATH
Throughout the book, the authors generously provide concrete examples that motivate theory and illustrate ideas. I expect this superb book to be widely used in graduate courses around the world, and to become a standard reference.
-- Mathematical Reviews
Now available in Second Edition: MAWRLD/30
Have you ever wondered ... why elections often
produce results that seem to be displeasing to many of the voters
involved? Would you be surprised to learn that a perfectly fair
election can produce an outcome that literally nobody likes? When
voting, we often think about the candidates or proposals in the
election, but we rarely consider the procedures that we use to express
our preferences and arrive at a collective decision.
The Mathematics of Voting and Elections: A Hands-On
Approach will help you discover answers to these and many other
questions. Easily accessible to anyone interested in the subject, the
book requires virtually no prior mathematical experience beyond basic
arithmetic, and includes numerous examples and discussions regarding
actual elections from politics and popular culture. It is recommended
for researchers and advanced undergraduates interested in all areas of
mathematics and is ideal for independent study.
The book by Hodge and Klima is an excellent entry into this field ... has plenty of material for a one-semester course ... friendly and clear style that students will appreciate ... well-written and well-edited ... Every instructor teaching this subject should consider this as the textbook, and should have this book regardless of what textbook chosen.
-- MAA Reviews