Paperback | 2016 | ISBN: 9780691169651
392 pp. | 5 1/2 x 8 1/2 | 25 color illus. 10 halftones. 95 line illus.
This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015 makes available to a wide audience many articles not easily found anywhere else?and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates.
Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it’s worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more.
In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us?and where it is headed.
Mircea Pitici holds a PhD in mathematics education from Cornell University, where he teaches math and writing. He has edited The Best Writing on Mathematics since 2010.
1ere ed. 2016, XVII, 498 p. 3 ill.
Softcover
ISBN 978-3-662-49360-1
* Nouveau volume des Elements de mathematique de N. Bourbaki, le
premier a etre publie depuis 1998
* Contient les quatre premiers chapitres d'un nouveau livre consacre a
la topologie algebrique
* Se concentre sur la theorie des revetements et du groupe de Poincare
* Propose un grand nombre d'exercices interessants et difficiles
Ce livre des Elements de mathematique est consacre a la Topologie algebrique. Les quatre
premiers chapitres presentent la theorie des revetements d'un espace topologique et du
groupe de Poincare. On construit le revetement universel d'un espace connexe pointe
delacable et on etablit l'equivalence de categories entre revetements de cet espace et
actions du groupe de Poincare.
On demontre une version generale du theoreme de van Kampen exprimant le groupoide
de Poincare d'un espace topologique comme un coegalisateur de diagrammes de
groupoides. Dans de nombreuses situations geometriques, on en deduit une presentation
explicite du groupe de Poincare.
2016, XIII, 392 p. 48 illus., 8 illus. incolor.
A product of Birkhauser Basel
Hardcover
ISBN 978-3-319-29786-6
* Presents a wide range of material, from classical to brand new results
* Uses a modular presentation in which core material is kept brief,
allowing for a broad exposure to the subject without overwhelming
readers with too much information all at once
* Introduces topics by examining how they related to research
problems, providing continuity among diverse topics and
encouraging readers to explore these problems with research of their
own
The second edition of this highly praised textbook provides an expanded introduction
to the theory of ordered sets and its connections to various subjects. Utilizing a modular
presentation, the core material is purposely kept brief, allowing for the benefits of a
broad exposure to the subject without the risk of overloading the reader with too much
information all at once. The remaining chapters can then be read in almost any order,
giving the text a greater depth and flexibility of use. Most topics are introduced by
examining how they relate to research problems, some of them still open, allowing for
continuity among diverse topics and encouraging readers to explore these problems
further with research of their own.
A wide range of material is presented, from classical results such as Dilworth's, Szpilrajn's,
and Hashimoto's Theorems to more recent results such as the Li-Milner Structure
Theorem. Major topics covered include chains and antichains, lowest upper and greatest
lower bounds, retractions, algorithmic approaches, lattices, the dimension of ordered
sets, interval orders, lexicographic sums, products, enumeration, and the role of algebraic
topology. This new edition shifts the primary focus to finite ordered sets, with results
on infinite ordered sets presented toward the end of each chapter whenever possible.
Also new are Chapter 6 on graphs and homomorphisms, which serves to separate the
fixed clique property from the more fundamental fixed simplex property as well as to
discuss the connections and differences between graph homomorphisms and orderpreserving
maps, and an appendix on discrete Morse functions and their use for the fixed
point property for ordered sets.
Rich in examples, diagrams, and exercises, the second edition of Ordered Sets will be
an excellent text for undergraduate and graduate students and a valuable resource for
interested researchers. It will be especially useful to those looking for an introduction
to the theory of ordered sets and its connections to such areas as algebraic topology,
analysis, and computer science.
1st ed. 2016, XIV, 267 p. 58 illus., 55 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-29660-9
Series: Applied Mathematical Sciences, Vol. 195
* Includes computational algorithms and practical details of
implementation
* Illustrates implementation of the parameterization method with 12
fully detailed examples throughout the book
* Content covers theoretical and computational aspects of the
paramerterization method
* Access to codes available via webpage
This monograph presents some theoretical and computational aspects of the
parameterization method for invariant manifolds, focusing on the following contexts:
invariant manifolds associated with fixed points, invariant tori in quasi-periodically
forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant
manifolds. This book provides algorithms of computation and some practical details of
their implementation. The methodology is illustrated with 12 detailed examples, many
of them well known in the literature of numerical computation in dynamical systems. A
public version of the software used for some of the examples is available online.
The book is aimed at mathematicians, scientists and engineers interested in the theory
and applications of computational dynamical systems.
1st ed. 2016, XII, 241 p. 5 illus., 1 illus. in color.
Hardcover
ISBN 978-3-319-31088-6
Series: Graduate Texts in Mathematics, Vol. 274
* Provides a concise and rigorous presentation of stochastic
integration and stochastic calculus for continuous
semimartingalesPresents major applications of stochastic calculus to
Brownian motion and related stochastic processesIncludes important
aspects of Markov processes with applications to stochastic
differential equations and to connections with partial differential
equations
This book offers a rigorous and self-contained presentation of stochastic integration and
stochastic calculus within the general framework of continuous semimartingales. The
main tools of stochastic calculus, including Ito’s formula, the optional stopping theorem
and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The
book also contains an introduction to Markov processes, with applications to solutions
of stochastic differential equations and to connections between Brownian motion and
partial differential equations. The theory of local times of semimartingales is discussed in
the last chapter.
Since its invention by Ito, stochastic calculus has proven to be one of the most important
techniques of modern probability theory, and has been used in the most recent
theoretical advances as well as in applications to other fields such as mathematical
finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong
theoretical background to the reader interested in such developments.
Beginning graduate or advanced undergraduate students will benefit from this detailed
approach to an essential area of probability theory. The emphasis is on concise and
efficient presentation, without any concession to mathematical rigor. The material has
been taught by the author for several years in graduate courses at two of the most
prestigious French universities. The fact that proofs are given with full details makes the
book particularly suitable for self-study. The numerous exercises help the reader to get
acquainted with the tools of stochastic calculus.