Contemporary Mathematics, Volume: 624
2014; 229 pp; softcover
ISBN-13: 978-0-8218-9866-6
Expected publication date is October 6, 2014.
This volume contains the proceedings of two AMS Special Sessions on The Mathematics of Decisions, Elections, and Games, held January 4, 2012, in Boston, MA, and January 11-12, 2013, in San Diego, CA.
Decision theory, voting theory, and game theory are three intertwined areas of mathematics that involve making optimal decisions under different contexts. Although these areas include their own mathematical results, much of the recent research in these areas involves developing and applying new perspectives from their intersection with other branches of mathematics, such as algebra, representation theory, combinatorics, convex geometry, dynamical systems, etc.
The papers in this volume highlight and exploit the mathematical structure of decisions, elections, and games to model and to analyze problems from the social sciences.
Graduate students and research mathematicians interested in decision making, voting, and games.
2014; 173 pp; softcover
ISBN-13: 978-1-4704-1699-7
Expected publication date is November 3, 2014.
Vladimir Arnold, an eminent mathematician of our time, is known both for his mathematical results, which are many and prominent, and for his strong opinions, often expressed in an uncompromising and provoking manner. His dictum that "Mathematics is a part of physics where experiments are cheap" is well known.
This book consists of two parts: selected articles by and an interview with Vladimir Arnold, and a collection of articles about him written by his friends, colleagues, and students. The book is generously illustrated by a large collection of photographs, some never before published. The book presents many a facet of this extraordinary mathematician and man, from his mathematical discoveries to his daredevil outdoor adventures.
Mathematicians of all levels: teachers, researchers, graduate and undergraduate students, and other scientists interested in the recent history and ideology of mathematics.
B. A. Khesin and S. L. Tabachnikov -- Epigraph
By Arnold
V. I. Arnold -- Arnold in his own words
V. I. Arnold -- From Hilbert's superposition problem to dynamical systems
J. Moser -- Recollections
V. I. Arnold -- Polymathematics: Is mathematics a single science or a set of arts?
V. I. Arnold -- A mathematical trivium
B. A. Khesin and S. L. Tabachnikov -- Comments on "A Mathematical Trivium
V. I. Arnold -- About Vladimir Abramovich Rokhlin
About Arnold
A. Givental -- To whom it may concern
Y. Sinai -- Remembering Vladimir Arnold: Early years
S. Smale -- Vladimir I. Arnold
M. Berry -- Memories of Vladimir Arnold
D. Fuchs -- Dima Arnold in my life
Y. Ilyashenko -- V. I. Arnold, as I have seen him
Y. Eliashberg -- My encounters with Vladimir Igorevich Arnold
B. A. Khesin -- On V. I. Arnold and hydrodynamics
A. Khovanskii and A. Varchenko -- Arnold's seminar, first years
V. Vassiliev -- Topology in Arnold's work
H. Hofer -- Arnold and symplectic geometry
M. Sevryuk -- Some recollections of Vladimir Igorevich
L. Polterovich -- Remembering V. I. Arnold
A. Vershik -- Several thoughts about Arnold
S. Yakovenko -- Vladimir Igorevich Arnold: A view from the rear bench
American Mathematical Society Translations--Series 2, Volume: 234
2014; approx. 389 pp; hardcover
ISBN-13: 978-1-4704-1871-7
Expected publication date is December 1, 2014.
Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
Graduate students and research mathematicians interested in applications of geometry and topology to mathematical physics.
A. V. Alexeevski and S. M. Natanzon -- Algebras of conjugacy classes of partial elements
I. Beloshapka and A. Sergeev -- Harmonic spheres in the Hilbert-Schmidt Grassmannian
F. Bogomolov and C. Bohning -- On uniformly rational varieties
M. Boiti, F. Pempinelli, and A. K. Pogrebkov -- IST of KPII equation for perturbed multisoliton solutions
V. Buchstaber and J. Grbi? -- Hopf algebras and homology of loop suspension spaces
L. O. Chekhov and M. Mazzocco -- Quantum ordering for quantum geodesic functions of orbifold Riemann surfaces
V. Dragovi? -- Pencils of conics and biquadratics, and integrability
B. Dubrovin -- Gromov-Witten invariants and integrable hierarchies of topological type
I. Dynnikov and A. Skripchenko -- On typical leaves of a measured foliated 2-complex of thin type
A. A. Gaifullin -- Volume of a simplex as a multivalued algebraic function of the areas of its two-faces
G. M. Kemp and A. P. Veselov -- Discrete analogues of Dirac's magnetic monopole and binary polyhedral groups
H. M. Khudaverdian and Th. Th. Voronov -- Geometric constructions on the algebra of densities
I. Krichever -- Amoebas, Ronkin function and Monge-Ampere measures of algebraic curves with marked points
A. Ya. Maltsev -- The averaging of multi-dimensional Poisson brackets for systems having pseudo-phases
A. E. Mironov -- Periodic and rapid decay rank two self-adjoint commuting differential operators
O. I. Mokhov -- Commuting ordinary differential operators of arbitrary genus and arbitrary rank with polynomial coefficients
M. V. Pavlov and S. P. Tsarev -- Classical mechanical systems with one-and-a-half degrees of freedom and Vlasov kinetic equation
O. K. Sheinman -- Lax operator algebras of type G2
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Publication planned for: October 2014
availability: Not yet published - available from October 2014
format: Hardback
isbn: 9780980232790
Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
Preface
1. First order equations
2. Second order equations
3. Graphical and numerical methods
4. Linear equations and inverse matrices
5. Vector spaces and subspaces
6. Eigenvalues and eigenvectors
7. Applied mathematics and ATA
8. Fourier and Laplace transforms
Matrix factorizations
Properties of determinants
Index
Linear algebra in a nutshell.
EMS Series of Lectures in Mathematics, Volume: 19
2014; 111 pp; softcover
ISBN-13: 978-3-03719-141-5
Expected publication date is October 21, 2014.
This book is based on a lecture course given by the author at the Educational Center of Steklov Mathematical Institute in 2011. It is designed for a one-semester course for undergraduate students familiar with basic differential geometry and complex and functional analysis.
The universal Teichmuller space T is the quotient of the space of quasisymmetric homeomorphisms of the unit circle modulo Mobius transformations. The first part of the book is devoted to the study of geometric and analytic properties of T. It is an infinite-dimensional Kahler manifold which contains all classical Teichmuller spaces of compact Riemann surfaces as complex submanifolds, which explains the name "universal Teichmuller space". Apart from classical Teichmuller spaces, T contains the space S of diffeomorphisms of the circle modulo Mobius transformations. The latter space plays an important role in the quantization of the theory of smooth strings.
The quantization of T is presented in the second part of the book. In contrast with the case of diffeomorphism space S, which can be quantized in frames of the conventional Dirac scheme, the quantization of T requires an absolutely different approach based on the noncommutative geometry methods.
The book concludes with a list of 24 problems and exercises which can used to prepare for examinations.
Undergraduate students familiar with basic differential geometry and complex and functional analysis.
Quasiconformal maps
Universal Teichmuller space
Subspaces of universal Teichmuller space
Grassmann realization of the universal Teichmuller space
Quantization of space of diffeomorphisms
Quantization of Teichmuller space
Instead of an afterword. Universal Teichmuller space and string theory
Problems
Bibliographical comments
Bibliography
Index