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Pubupdate-Winter13.Pdf W OF THE AMERICAN MATHEMATICAL PUBLICATIONS SOCIETY AMS Member Discount As an individual member, receive substantial discounts up to % on all AMS published and co-published books! 20 CONTENTS AMS Textbooks Find the right textbook for your 3 Algebra and Algebraic Geometry course! e AMS publishes many 4 Analysis high-quality books for use in the classroom. To view a comprehensive 6 Differential Equations list of our textbook titles, please visit: 7 Discrete Mathematics and Combinatorics ams.org/bookstore/textbooks 8 General Interest 8 Geometry and Topology Applied 10 Mathematical Physics Mathematics 10 Number Theory e AMS is proud to off er a broad 11 Probability and Statistics and fl ourishing selection of applied and interdisciplinary mathematics 12 Contemporary Mathematics Series titles. Books in this program 13 Memoirs of the AMS white --> strengthen the connections between mathematics and other disciplines, 14 AMS-Distributed Publications highlighting the areas in which 16 Index mathematics is most relevant. To view all of our applied mathematics 18 Ordering Information publications, please visit: ams.org/bookstore/appliedmath Order Online | ams.org/bookstore Order by Phone | 401-455-4000 (Worldwide) or 800-321-4267 (U.S. and Canada) facebook.com/amermathsoc twitter: @amermathsoc Algebra and Algebraic Introduction to Quantum Mathematical Surveys and Monographs Graphs Geometry Volume 186 Introduction to Gregory Berkolaiko and Peter Quantum Graphs Dualities and Kuchment, Texas A&M University, Dualities and Gregory Berkolaiko College Station, TX Representations of Representations of Lie Peter Kuchment Lie Superalgebras Superalgebras A “quantum graph” is a graph considered as Shun-Jen Cheng a one-dimensional complex and equipped Weiqiang Wang American Mathematical Society Shun-Jen Cheng, Academia Sinica, with a differential operator (“Hamiltonian”). Graduate Studies in Mathematics Taipei, Taiwan, and , Quantum graphs arise naturally as simpli- Volume 144 Weiqiang Wang fied models in mathematics, physics, chemistry, and American Mathematical Society University of Virginia, Charlottesville, VA engineering when one considers propagation of waves of various nature through a quasi-one-dimensional This book gives a systematic account of the structure and (e.g., “meso-” or “nano-scale”) system that looks like a representation theory of finite-dimensional complex Lie super- thin neighborhood of a graph. Works that currently algebras of classical type and serves as a good introduction to would be classified as discussing quantum graphs have representation theory of Lie superalgebras. Several folklore been appearing since at least the 1930s, and since then, results are rigorously proved (and occasionally corrected in quantum graphs techniques have been applied successfully detail), sometimes with new proofs. Three important dualities in various areas of mathematical physics, mathematics are presented in the book, with the unifying theme of deter- in general and its applications. One can mention, for mining irreducible characters of Lie superalgebras. instance, dynamical systems theory, control theory, READERSHIP: Graduate students and research mathemati- quantum chaos, Anderson localization, microelectronics, cians photonic crystals, physical chemistry, nano-sciences, Graduate Studies in Mathematics, Volume 144 superconductivity theory, etc. 2012; 302 pp.; hardcover; ISBN: 978-0-8218-9118-6; List US$64; AMS Quantum graphs present many non-trivial mathematical members US$51.20; Order code: GSM/144 challenges, which makes them dear to a mathematician’s heart. Work on quantum graphs has brought together Formal Groups and tools and intuition coming from graph theory, combina- torics, mathematical physics, PDEs, and spectral theory. Formal Groups and Applications Applications This book provides a comprehensive introduction to the Michiel Hazewinkel Michiel Hazewinkel topic, collecting the main notions and techniques. It also This book is a comprehensive treatment contains a survey of the current state of quantum graph of the theory of formal groups and its research and applications. AMS CHELSEA PUBLISHING American Mathematical Society • Providence, Rhode Island numerous applications in several areas of READERSHIP: Graduate students and research mathe- mathematics. The seven chapters of the maticians book present basics and main results of Mathematical Surveys and Monographs, Volume 186 the theory, as well as very important applications in alge- 2013; 270 pp.; hardcover; ISBN: 978-0-8218-9211-4; List US$86; braic topology, number theory, and algebraic geometry. Each AMS members US$68.80; Order code: SURV/186 chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introduc- tory graduate algebra course, including certain familiarity with Conference Board of the Mathematical Sciences CBMS Deformation Theory category theory. Regional Conference Series in Mathematics Number 116 of Algebras and Their READERSHIP: Graduate students and research mathemati- Deformation Theory Diagrams of Algebras cians and Their Diagrams AMS Chelsea Publishing, Volume 375 Martin Markl Martin Markl, Academy of Sciences 2012; 573 pp.; hardcover; ISBN: 978-0-8218-5349-8; List US$72; AMS of the Czech Republic, Praha, Czech members US$64.80; Order code: CHEL/375.H American Mathematical Society with support from the Republic National Science Foundation A self-contained presentation of both the classical and current aspects of deforma- tion theory. Get the content you want, READERSHIP: Graduate students and research mathemati- electronically. cians The AMS o ers over 2,500 pure A co-publication of the AMS and CBMS. and applied mathematics titles CBMS Regional Conference Series in Mathematics, Number 116 in eBook form via Google Play. 2012; 129 pp.; softcover; ISBN: 978-0-8218-8979-4; List US$35; AMS Start reading today at: members US$28; All Individuals US$28; Order code: CBMS/116 play.google.com/store 3 Order by Phone | 401-455-4000 (Worldwide) or 800-321-4267 (U.S. and Canada) Topics in The book is self-contained and only relies on a back- ground in functions of a single variable and the elements Noncommutative of metric spaces. Following the author’s belief that the Geometry best way to learn is to start with the particular and proceed to the more general, it contains numerous exam- Guillermo Cortiñas, Universidad de ples and exercises. Buenos Aires, Argentina, Editor READERSHIP: Undergraduate and graduate students Topics in this volume concern noncom- Graduate Studies in Mathematics, Volume 141 mutative geometry in a broad sense, encompassing various mathematical and physical theories that 2012; 367 pp.; hardcover; ISBN: 978-0-8218-9083-7; List US$75; AMS members US$60; Order code: GSM/141 incorporate geometric ideas into the study of noncommutative phenomena. READERSHIP: Graduate students and research mathema- ticians Higher Order Fourier Titles in this series are co-published with the Clay Mathematics Higher Order Analysis Institute (Cambridge, MA). Fourier Analysis Clay Mathematics Proceedings, Volume 16 Terence Tao Terence Tao, University of California, 2012; 276 pp.; softcover; ISBN: 978-0-8218-6864-5; List US$79; AMS Los Angeles, CA Graduate Studies members US$63.20; Order code: CMIP/16 in Mathematics Volume 142 Traditional Fourier analysis, which American Mathematical Society has been remarkably effective in many contexts, uses linear phase functions to Proceedings of Symposia in Recent Developments in study functions. Some questions, such as P URE M ATHEMATICS problems involving arithmetic progressions, naturally Volume 86 Lie Algebras, Groups and lead to the use of quadratic or higher order phases. Higher Recent Developments in Lie Algebras, Groups Representation Theory order Fourier analysis is a subject that has become very and Representation Theory active only recently. Gowers, in groundbreaking work, Kailash C. Misra Daniel K. Nakano Kailash C. Misra, North Carolina State developed many of the basic concepts of this theory in Brian J. Parshall Editors University, Raleigh, NC, Daniel K. order to give a new, quantitative proof of Szemerédi’s , University of Georgia, Athens, theorem on arithmetic progressions. However, there are American Mathematical Society Nakano GA, and Brian J. Parshall, University also precursors to this theory in Weyl’s classical theory ofVirginia, Charlottesville, VA, Editors of equidistribution, as well as in Furstenberg’s structural theory of dynamical systems. Some of the articles in this volume, written by experts in the This book, which is the first monograph in this area, aims field, survey recent developments, while others include new to cover all of these topics in a unified manner, as well as results in Lie algebras, quantum groups, finite groups, and to survey some of the most recent developments, such as algebraic groups. the application of the theory to count linear patterns in READERSHIP: Graduate students and research mathema- primes. The book serves as an introduction to the field, ticians giving the beginning graduate student in the subject a Proceedings of Symposia in Pure Mathematics, Volume 86 high-level overview of the field. The text focuses on 2012; 310 pp.; hardcover; ISBN: 978-0-8218-6917-8; List US$80; AMS the simplest illustrative examples of key results, serving members US$64; Order code: PSPUM/86 as a companion to the existing literature on the subject. There are numerous exercises with which to test one’s Analysis knowledge. READERSHIP: Graduate
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