This set includes two humorous and quirky collections of mathematical morsels by Burkard Polster (YouTube's Mathologer) and Marty Ross-Putting Two and Two Together: Selections from the Mathologer Files and A Dingo Ate My Math Book: Mathematics from Down Under. The stories in both volumes were written for a general audience and cover current ......
The Markov chain ergodic theorem is well-understood if either the time-line or the state space is discrete. However, there does not exist a very clear result for general state space continuous-time Markov processes. Using methods from mathematical logic and nonstandard analysis, we introduce a class of hyperfinite Markov processes-namely, general ......
A Dynamical Systems Approach to Theory and Practice
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincare's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our ......
This book is a lightly edited version of the unpublished manuscript Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen-Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal ......
This volume is based on lectures delivered at the 2020 AMS Short Course ""Mean Field Games: Agent Based Models to Nash Equilibria,"" held January 13-14, 2020, in Denver, Colorado. Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued ......
This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series. Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many ......
The Number Line through Guided Inquiry is designed to give future secondary teachers a deep understanding of the real numbers and functions on the reals. By presenting just that part of the subject that underlies the high school curriculum, this book offers an alternative to a standard real analysis sequence for advanced undergraduate or beginning ......
This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market ......
