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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 Five stages of accepting constructive mathematics
( view abstract )
Five stages of accepting constructive mathematics
On the odd day, a mathematician might wonder what constructive mathematics is all about. They may have heard arguments in favor of constructivism but are not at all convinced by them, and in any case they may care little about philosophy. A typical introductory text about constructivism spends a great deal of time explaining the principles and contains only trivial mathematics, while advanced constructive texts are impenetrable, like all unfamiliar mathematics. How then can a mathematician find out what constructive mathematics feels like? What new and relevant ideas does constructive mathematics have to offer, if any? I shall attempt to answer these questions.

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