Graduate Studies in Mathematics, Volume: 115
2010; 324 pp; hardcover
ISBN-13: 978-0-8218-5151-7
Expected publication date is June 24, 2010.
Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as political science, biology, and, more recently, computer science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises.
The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. Cooperative games are explained in detail, with bargaining and TU-games being treated as part of a general framework. The authors stress the relation between game theory and operations research.
Graduate students interested in game theory.
Introduction to decision theory
Strategic games
Extensive games
Games with incomplete information
Cooperative games
Bibliography
Notations
Index of authors
Index of solution concepts
Subject index
Student Mathematical Library, Volume: 53
2010; approx. 171 pp; softcover
ISBN-13: 978-0-8218-4977-4
Expected publication date is June 18, 2010.
This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra.
The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products.
The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations.
Undergraduates, graduate students and research mathematicians interested in combinatorics, graph theory, theoretical computer science, and geometry.
Fibonacci numbers, quickly
Fibonacci numbers, the formula
The clubs of Oddtown
Same-size intersections
Error-correcting codes
Odd distances
Are these distances Euclidean?
Packing complete bipartite graphs
Equiangular lines
Where is the triangle?
Checking matrix multiplication
Tiling a rectangle by squares
Three Petersens are not enough
Petersen, Hoffman-Singleton, and maybe 57
Only two distances
Covering a cube minus one vertex
Medium-size intersection is hard to avoid
On the difficulty of reducing the diameter
The end of the small coins
Walking in the yard
Counting spanning trees
In how many ways can a man tile a board?
More bricks--more walls?
Perfect matchings and determinants
Turning a ladder over a finite field
Counting compositions
Is it associative?
The secret agent and umbrella
Shannon capacity of the union: a tale of two fields
Equilateral sets
Cutting cheaply using eigenvectors
Rotating the cube
Set pairs and exterior products
Index
American Mathematical Society Translations--Series 2, Volume: 229
2010; approx. 257 pp; hardcover
ISBN-13: 978-0-8218-4997-2
Expected publication date is June 9, 2010.
This book contains papers that engage a wide set of classical and modern topics in partial differential equations, including linear and nonlinear equations, variational problems, the Navier-Stokes system, and the Boltzmann equation. The results include existence and uniqueness theorems, qualitative properties of solutions, a priori estimates, and nonexistence theorems.
Graduate students and research mathematicians interested in differential equations.
J. Andersson, H. Shahgholian, and G. S. Weiss -- Regularity below the C^2 threshold for a torsion problem, based on regularity for Hamilton-Jacobi equations
A. Arkhipova -- Signorini-type problem in mathbb{R}^N for a class of quadratic functionals
M. Bildhauer and M. Fuchs -- A 2D-invariant of a theorem of Uraltseva and Urdaletova for higher order variational problems
M. Bostan, I. M. Gamba, and T. Goudon -- The linear Boltzmann equation with space periodic electric field
L. Caffarelli and L. Silvestre -- Smooth approximations of solutions to nonconvex fully nonlinear elliptic equations
P. Constantin and G. Seregin -- Holder continuity of solutions of 2D Navier-Stokes equations with singular forcing
M. Giaquinta, P. Mariano, G. Modica, and D. Mucci -- Currents and curvature varifolds in continuum mechanics
N. M. Ivochkina -- On classic solvability of the m-Hessian evolution equation
N. V. Krylov -- About an example of N. N. Ural'tseva and weak uniqueness for elliptic operators
V. Mazya and R. McOwen -- On the fundamental solution of an elliptic equation in nondivergence form
G. Mingione -- Boundary regularity for vectorial problems
A. Nazarov and A. Reznikov -- Attainability of infima in the critical Sobolev trace embedding theorem on manifolds
M. V. Safonov -- Non-divergence elliptic equations of second order with unbounded drift
V. V. Zhikov and S. E. Pastukhova -- Global solvability of Navier-Stokes equations for a nonhomogeneous non-Newtonian fluid
University Lecture Series, Volume: 53
2010; 150 pp; softcover
ISBN-13: 978-0-8218-4963-7
This book is based on lectures given at Stanford University in 2009. The purpose of the lectures and of the book is to give an introductory overview of how to use Ricci flow and Ricci flow with surgery to establish the Poincare Conjecture and the more general Geometrization Conjecture for 3-dimensional manifolds. Most of the material is geometric and analytic in nature; a crucial ingredient is understanding singularity development for 3-dimensional Ricci flows and for 3-dimensional Ricci flows with surgery. This understanding is crucial for extending Ricci flows with surgery so that they are defined for all positive time. Once this result is in place, one must study the nature of the time-slices as the time goes to infinity in order to deduce the topological consequences.
The goal of the authors is to present the major geometric and analytic results and themes of the subject without weighing down the presentation with too many details. This book can be read as an introduction to more complete treatments of the same material.
Graduate students and research mathematicians interested in differential equations and topology.