Game Theory: A Playful Introduction Matt DeVos Deborah A. Kent
Designed as a textbook for an undergraduate mathematics class, this book offers a dynamic and rich tour of the mathematics of both sides of game theory, combinatorial and classical, and includes generous sets of exercises at various levels.
Innovation, Growth and the Art of Balance
AMS Associate Executive Director Robert Harington reflects on the importance of balance amongst growth and innovation in the publishing industry. Read more at the Scholarly Kitchen.
MSC Revision Now Underway
The editors of Mathematical Reviews and zbMATH have launched a collaborative effort to revamp the Mathematics Subject Classification. Visit msc2020.org to read more about the MSC2020 project and to leave your comments.
An introduction to large deviations for random graphs
This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed by a description of some large deviation questions about random graphs and an outline of the recent progress on this topic. A more elaborate discussion follows, with a brief account of graph limit theory and its application in constructing a large deviation theory for dense random graphs. The role of Szemerédi's regularity lemma is explained, together with a sketch of the proof of the main large deviation result and some examples. Applications to exponential random graph models are briefly touched upon. The remainder of the paper is devoted to large deviations for sparse graphs. Since the regularity lemma is not applicable in the sparse regime, new tools are needed. Fortunately, there have been several new breakthroughs that managed to achieve the goal by an indirect method. These are discussed, together with an exposition of the underlying theory. The last section contains a list of open problems.