Pure and Applied Undergraduate Texts, Volume: 11
2010; 256 pp; hardcover
ISBN-13: 978-0-8218-5294-1
Expected publication date is October 9, 2010.
Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems and come equipped with hints when needed. Appropriate for both self-study and the classroom, the material is efficiently arranged so that milestones such as the Sylow theorems and Galois theory can be reached in one semester.
Undergraduate students interested in abstract algebra/modern algebra.
* Arithmetic
* Groups
* Rings
* Field theory
* Index
Contemporary Mathematics,Volume: 524
2010; 179 pp; softcover
ISBN-13: 978-0-8218-4827-2
Expected publication date is October 17, 2010. S
This volume contains a collection of papers from the Conference on Character Theory of Finite Groups, held at the Universitat de Valencia, Spain, on June 3-5, 2009, in honor of I. Martin Isaacs.
The topics include permutation groups, character theory, p-groups, and group rings. The research articles feature new results on large normal abelian subgroups of p-groups, construction of certain wreath products, computing idempotents in group algebras of finite groups, and using dual pairs to study representations of cross characteristic in classical groups. The expository articles present results on vertex subgroups, measuring theorems in permutation groups, the development of super character theory, and open problems in character theory.
Graduate students and research mathematicians interested in finite groups.
* V. A. Belonogov -- On character tables and abstract structure of finite groups
* N. Boston -- Large transitive groups with many elements having fixed points
* J. P. Cossey -- Vertex subgroups and vertex pairs in solvable groups
* P. Diaconis -- Threads through group theory
* S. M. Gagola, Jr. -- Tate's theorem, and other oddities, via transfer
* G. Glauberman -- A p-group with no normal large abelian subgroup
* A. Goren and M. Herzog -- General measuring arguments for finite permutation groups
* R. M. Guralnick -- Commutators and wreath products
* T. M. Keller -- Gaps in character degrees for groups with many conjugacy classes
* A. Mann -- The number of subgroups of metacyclic groups
* G. Navarro -- Problems in character theory
* T. Okuyama and T. Wada -- Eigenvalues of Cartan matrices of blocks in finite groups
* D. S. Passman -- Character theory and group rings
* G. R. Robinson -- Lifting theorems and applications to group algebras
* M. C. Slattery -- Character degrees of normally monomial maximal class 5-groups
* P. H. Tiep -- Dual pairs of finite classical groups in cross characteristic
Contemporary Mathematics, Volume: 525
2010; 161 pp; softcover
ISBN-13: 978-0-8218-4809-8
Expected publication date is October 30, 2010.
This volume contains state-of-the-art survey papers in complex analysis based on lectures given at the Second Winter School on Complex Analysis and Operator Theory held in February 2008 at the University of Sevilla, Sevilla, Spain.
Complex analysis is one of the most classical branches of mathematical analysis and is closely related to many other areas of mathematics, including operator theory, harmonic analysis, probability theory, functional analysis and dynamical systems. Undoubtedly, the interplay among all these branches gives rise to very beautiful and deep results in complex analysis and its neighboring fields. This interdisciplinary aspect of complex analysis is the central topic of this volume.
This book collects the latest advances in five significant areas of rapid development in complex analysis. The papers are: Local holomorphic dynamics of diffeomorphisms in dimension one, by F. Bracci, Nonpositive curvature and complex analysis, by S. M. Buckley, Virasoro algebra and dynamics in the space of univalent functions, by I. Markina and A. Vasil'ev, Composition operators \heartsuit Toeplitz operators, by J. H. Shapiro, and Two applications of the Bergman spaces techniques, by S. Shimorin.
The papers are aimed, in particular, at graduate students with some experience in basic complex analysis. They might also serve as introductions for general researchers in mathematical analysis who may be interested in the specific areas addressed by the authors. Indeed, the contributions can be considered as up-to-the-minute reports on the current state of the fields, each of them including many recent results which may be difficult to find in the literature.
Graduate students and research mathematicians interested in complex analysis and operator theory.
Proceedings of Symposia in Applied Mathematics, Volume: 68
2010; approx. 345 pp; hardcover
ISBN-13: 978-0-8218-4828-9
Expected publication date is November 11, 2010.
This volume is based on lectures delivered at the 2009 AMS Short Course on Quantum Computation and Quantum Information, held January 3-4, 2009, in Washington, D.C.
Part I of this volume consists of two papers giving introductory surveys of many of the important topics in the newly emerging field of quantum computation and quantum information, i.e., quantum information science (QIS). The first paper discusses many of the fundamental concepts in QIS and ends with the curious and counter-intuitive phenomenon of entanglement concentration. The second gives an introductory survey of quantum error correction and fault tolerance, QIS's first line of defense against quantum decoherence.
Part II consists of four papers illustrating how QIS research is currently contributing to the development of new research directions in mathematics. The first paper illustrates how differential geometry can be a fundamental research tool for the development of compilers for quantum computers. The second paper gives a survey of many of the connections between quantum topology and quantum computation. The last two papers give an overview of the new and emerging field of quantum knot theory, an interdisciplinary research field connecting quantum computation and knot theory. These two papers illustrate surprising connections with a number of other fields of mathematics.
In the appendix, an introductory survey article is also provided for those readers unfamiliar with quantum mechanics.
Graduate students and research mathematicians interested in quantum information theory and its relations to new research areas in mathematics.
Quantum information science
*P. Hayden -- Concentration of measure effects in quantum information
*D. Gottesman -- An introduction to quantum error correction and fault-tolerant quantum computation
Contributions to mathematics
*H. E. Brandt -- Riemannian geometry of quantum computation
*L. H. Kauffman and S. J. Lomonaco, Jr. -- Topological quantum information theory
*S. J. Lomonaco, Jr. and L. H. Kauffman -- Quantum knots and mosaics
*S. J. Lomonaco, Jr. and L. H. Kauffman -- Quantum knots and lattices, or a blueprint for quantum systems that do rope tricks
Appendix
*S. J. Lomonaco, Jr. -- A Rosetta Stone for quantum mechanics with an introduction to quantum computation