Mathematical Surveys and Monographs, Volume: 179
2011; 364 pp; hardcover
ISBN-13: 978-0-8218-0501-5
Expected publication date is December 25, 2011.
This book is intended as an overview of a research area that combines geometries for groups (such as Tits buildings and generalizations), topological aspects of simplicial complexes from p-subgroups of a group (in the spirit of Brown, Quillen, and Webb), and combinatorics of partially ordered sets. The material is intended to serve as an advanced graduate-level text and partly as a general reference on the research area. The treatment offers optional tracks for the reader interested in buildings, geometries for sporadic simple groups, and G-equivariant equivalences and homology for subgroup complexes.
Graduate students and research mathematicians interested in group theory and algebraic topology.
Introduction
Background material and examples
Background: Posets, simplicial complexes, and topology
Examples: Subgroup complexes as geometries for simple groups
Fundamental techniques
Contractibility
Homotopy equivalence
Basic applications
The reduced Euler characteristic {tilde{chi}} and variations on vanishing
The reduced Lefschetz module {tilde{L}} and projectivity
Group cohomology and decompositions
Some more advanced topics
Spheres in homology and Quillen's Conjecture
Connectivity, simple connectivity, and sphericality
Local-coefficient homology and representation theory
Orbit complexes and Alperin's Conjecture
Bibliography
Index
AMS Chelsea Publishing, Volume: 374
1978; 392 pp; hardcover
ISBN-13: 978-0-8218-5324-5
Expected publication date is December 1, 2011.
This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization.
In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.
Graduate students and research mathematicians interested in asymptotic and probabilistic methods in the analysis of partial differential equations.
Contemporary Mathematics, Volume: 558
2011; 519 pp; softcover
ISBN-13: 978-0-8218-4943-9
Expected publication date is December 18, 2011.
This volume contains the proceedings of the AMS-ASL Special Session on Model Theoretic Methods in Finite Combinatorics, held January 5-8, 2009, in Washington, DC.
Over the last 20 years, various new connections between model theory and finite combinatorics emerged. The best known of these are in the area of 0-1 laws, but in recent years other very promising interactions between model theory and combinatorics have been developed in areas such as extremal combinatorics and graph limits, graph polynomials, homomorphism functions and related counting functions, and discrete algorithms, touching the boundaries of computer science and statistical physics.
This volume highlights some of the main results, techniques, and research directions of the area. Topics covered in this volume include recent developments on 0-1 laws and their variations, counting functions defined by homomorphisms and graph polynomials and their relation to logic, recurrences and spectra, the logical complexity of graphs, algorithmic meta theorems based on logic, universal and homogeneous structures, and logical aspects of Ramsey theory.
Graduate students and research mathematicians interested in logic, combinatorics, and theoretical computer science.
MSRI Mathematical Circles Library, Volume: 8
2012; approx. 334 pp; softcover
ISBN-13: 978-0-8218-6874-4
Expected publication date is January 13, 2012.
Moscow has a rich tradition of successful math circles, to the extent that many other circles are modeled on them. This book presents materials used during the course of one year in a math circle organized by mathematics faculty at Moscow State University, and also used at the mathematics magnet school known as Moscow School Number 57.
Each problem set has a similar structure: it combines review material with a new topic, offering problems in a range of difficulty levels. This time-tested pattern has proved its effectiveness in engaging all students and helping them master new material while building on earlier knowledge.
The introduction describes in detail how the math circles at Moscow State University are run. Dorichenko describes how the early sessions differ from later sessions, how to choose problems, and what sorts of difficulties may arise when running a circle. The book also includes a selection of problems used in the competition known as the Mathematical Maze, a mathematical story based on actual lessons with students, and an addendum on the San Jose Mathematical Circle, which is run in the Russian style.
Undergraduate students interested in math circles, clever math problems, and high school education.
Contemporary Mathematics, Volume: 559
2011; 180 pp; softcover
ISBN-13: 978-0-8218-5301-6
Expected publication date is January 1, 2012.
This volume contains research and review articles written by participants of two related international workshops "Mathematical Methods in Emerging Modalities of Medical Imaging" (October 2009) and "Inverse Transport Theory and Tomography" (May 2010), which were held at the Banff International Research Station in Banff, Canada. These workshops brought together mathematicians, physicists, engineers, and medical researchers working at the cutting edge of medical imaging research and addressed the demanding mathematical problems arising in this area.
The articles, written by leading experts, address important analytic, numerical, and physical issues of the newly developing imaging modalities (e.g., photoacoustics, current impedance imaging, hybrid imaging techniques, elasticity imaging), as well as the recent progress in resolving outstanding problems of more traditional modalities, such as SPECT, ultrasound imaging, and inverse transport theory. Related topics of invisibility cloaking are also addressed.
Graduate students and research mathematicians interested in inverse problems, imaging, tomography, and radiation transport.
B. Cox, T. Tarvainen, and S. Arridge -- Multiple illumination quantitative photoacoustic tomography using transport and diffusion models
G. Bal and A. Jollivet -- Combined source and attenuation reconstructions in SPECT
G. Bal and K. Ren -- Non-uniqueness result for a hybrid inverse problem
J. Boman -- Local non-injectivity for weighted radom transforms
A. L. Bukhgeim -- Inverse gravimetry approach to attenuated tomography
N. Hoell -- Complexification in reconstructive integral geometry
H. Liu and T. Zhou -- Transformation optics and approximate cloaking
S. McDowall, P. Stefanov, and A. Tamasan -- Stability of the Gauge equivalent classes in inverse stationary transport in refractive media
J. McLaughlin, A. Thomas, and J.-R. Yoon -- Basic theory for generalized linear solid viscoelastic models
A. Nachman, A. Tamasan, and A. Timonov -- Current density impedance imaging
F. Natterer -- Possibilities and limitations of time domain wave equation imaging
L. V. Nguyen -- On singularities and instability of reconstruction in thermoacoustic tomography
D. R. Eaker, S. M. Jorgensen, C. Cui, and E. L. Ritman -- Micro-tomography of coherent x-ray scatter using an x-ray collinator and spectral imaging array
Contemporary Mathematics, Volume: 560
2011; approx. 201 pp; softcover
ISBN-13: 978-0-8218-5295-8
Expected publication date is January 15, 2012.
This volume contains the proceedings of a conference held from June 4-6, 2010, at Oklahoma State University, in honor of William (Bus) Jaco's 70th birthday. His contributions to research in low dimensional geometry and topology and to the American mathematical community, especially through his work for the American Mathematical Society, were recognized during the conference.
The focus of the conference was on triangulations and geometric structures for three-dimensional manifolds. The papers in this volume present significant new results on these topics, as well as in geometric group theory.
Graduate students and research mathematicians interested in geometry and topology of 3-manifolds and geometric group theory.
I. Agol -- Ideal triangulations of pseudo-Anosov mapping tori
F. Luo -- A note on complete hyperbolic structures on ideal triangulated 3-manifolds
T. Kobayashi and Y. Rieck -- A linear bound on the tetrahedral number of manifolds of bounded volume (after Jorgensen and Thurston)
J. Johnson -- Layered models for closed 3-manifolds
Z. Liu -- Triangulations and nonorientable incompressible surfaces
B. Foozwell and H. Rubinstein -- Introduction to the theory of Haken n-manifolds
H. Segerman and S. Tillmann -- Pseudo-developing maps for ideal triangulations I: Essential edges and generalised hyperbolic gluing equations
P. B. Shalen -- A generic Margulis number for hyperbolic 3-manifolds
J. E. Grigsby and S. M. Wehrli -- On gradings in Khovanov homology and sutured Floer homology
R. Myers -- Hyperbolic knots in irreducible Heegaard surfaces
D. Calegari and D. Zhuang -- Stable W-length
N. Brady, M. Clay, and M. Forester -- Turn graphs and extremal surfaces in free groups
F. Bonahon and H. Wong -- Kauffman brackets, character varieties and triangulations of surfaces
J. H. Rubinstein -- Problems at the Jacofest
Translations of Mathematical Monographs, Volume: 241
2012; approx. 335 pp; hardcover
ISBN-13: 978-0-8218-4680-3
Expected publication date is March 10, 2012.
This book offers a systematic presentation of cryptographic and code-theoretic aspects of the theory of Boolean functions. Both classical and recent results are thoroughly presented. Prerequisites for the book include basic knowledge of linear algebra, group theory, theory of finite fields, combinatorics, and probability. The book can be used by research mathematicians and graduate students interested in discrete mathematics, coding theory, and cryptography.
Research mathematicians interested in discrete mathematics, coding theory, and cryptography.
Arithmetics of finite fields and polynomials
Boolean functions
Classifications of Boolean functions
Linear codes over the field mathbb{F}
Reed-Muller codes
Nonlinearity
Correlation immunity and resiliency
Codes, Boolean mappings and their cryptographic properties
Basics of cryptanalysis
Bibliography
Index