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AMS Notices: October 2017
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Feature Column: Untangling Your Square Dance by David Austin
Explore Origami works by Robert J. Lang on Mathematical Imagery
AMS Bulletin: July 2017 issue
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Markov Chains and Mixing TimesMarkov Chains and Mixing Times
David A. Levin
Yuval Peres
Featuring three new chapters (on monotone chains, the exclusion process, and stationary times), the second edition of this introduction to the modern theory of Markov chains includes smaller additions and corrections throughout, with updated notes at the end of each chapter informing the reader of recent research developments.

A First Course in Sobolev Spaces: Second EditionA First Course in Sobolev Spaces: Second Edition
Giovanni Leoni
The second edition of this book about differentiation of functions focuses more on higher order derivatives and has the potential to be used as two separate textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions.

Nonlinear PDEs: A Dynamical Systems ApproachNonlinear PDEs: A Dynamical Systems Approach
Guido Schneider
Hannes Uecker
This introductory textbook on nonlinear dynamics of PDEs uses an example-oriented presentation and develops new mathematical tools, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs.

Bulletin of the AMS

Bulletin of the AMS Hamiltonian and symplectic symmetries: An introduction
( view abstract )
Hamiltonian and symplectic symmetries: An introduction
Classical mechanical systems are modeled by a symplectic manifold $ (M,\omega )$, and their symmetries are encoded in the action of a Lie group $ G$ on $ M$ by diffeomorphisms which preserve $ \omega $. These actions, which are called symplectic, have been studied in the past forty years, following the works of Atiyah, Delzant, Duistermaat, Guillemin, Heckman, Kostant, Souriau, and Sternberg in the 1970s and 1980s on symplectic actions of compact Abelian Lie groups that are, in addition, of Hamiltonian type, i.e., they also satisfy Hamilton's equations. Since then a number of connections with combinatorics, finite-dimensional integrable Hamiltonian systems, more general symplectic actions, and topology have flourished. In this paper we review classical and recent results on Hamiltonian and non-Hamiltonian symplectic group actions roughly starting from the results of these authors. This paper also serves as a quick introduction to the basics of symplectic geometry.

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