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Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Fundamentals of Stochastic Filtering Encyclopedia of Optimization A. Bain, BNP Paribas, London, UK C. A. Floudas , Princeton University, NJ, 2ND EDITION D. Crisan , Imperial College, London, UK USA; P. M. Pardalos , University of Florida, of the American Mathematical Society The objective of stochastic fi ltering is to determine the best Gainesville, USA (Eds.) March 2008 Volume 55, Number 3 estimate for the state of a stochastic dynamical system from The Encyclopedia of Optimization introduces the reader to a partial observations. The solution of this problem in the complete set of topic that show the wide spectra of research, linear case is the well known Kalman-Bucy fi lter which has richness of ideas, and breadth of applications. This revised and found widespread practical application. The purpose of this greatly expanded edition of a successful reference work, now book is to provide a rigorous mathematical treatment of the in seven volumes, consists of more than 150 completely new non-linear stochastic fi ltering problem using modern entries, with signifi cant attention to new areas of optimization methods. Particular emphasis is placed on the theoretical theories and techniques: e.g., in health science and transpor- analysis of numerical methods for the solution of the fi ltering tation, with such articles as “Algorithms for Genomics,” problem via particle methods. “Optimization and Radiotherapy Treatment Design,” and “Crew The book should provide suffi cient background to enable Scheduling.” study of the recent literature. While no prior knowledge of The fi rst edition (2001) was acclaimed by J. B. Rosen as Undecidability in stochastic fi ltering is required, readers are assumed to be “an indispensable resource,” and by Ding-Zhu Du who familiar with measure theory, probability theory and the announced it as “the standard most important reference in Number Theory basics of stochastic processes. this very dynamic research fi eld.” page 344 2008. Approx. 380 pp. (Stochastic Modelling and Applied 2nd ed. 2008. Springer Reference Probability, Volume 60) Print (Hardcover), Approx. 4000 p. ISBN 978-0-387-76895-3 7 approx. $59.95 ISBN 978-0-387-74758-3 7 $2500.00 Prepublication price 7 $2000.00 The Father of Atlas of Functions eReference ISBN 978-0-387-74759-0 7 $2500.00 the Father of with Equator, the Atlas Function 2ND EDITION Prepublication price 7 $2000.00 Calculator Print + eReference Package American K. B. Oldham , J. Myland , Trent University, ISBN 978-0-387-74760-6 7 $3125.00 Mathematics Peterborough, ON, Canada; J. Spanier , University of Prepublication price 7 $2500.00 California, Irvine, CA All prepublication prices valid until November 30, 2008 page 352 Appropriate for researchers and students in the science, technology and mathematics disciplines, from mathematics to Braid Groups chemistry, biology, physics and computer science, this book C. Kassel , V. Turaev , Université Louis Pasteur - CNRS, provides comprehensive information on several hundred Strasbourg, France Claremont functions or function families. Beginning with simple integer- Motivated by numberous examples and problems, the authors valued functions, the book progresses to polynomials, introduce the basic theory of braid groups, highlighting Meeting exponential, trigonometric, Bessel, and hypergeometric several defi nitions that show their equivalence; this is functions, and more. In addition to providing defi nitions and Volume 55, Number 3, Pages 337–440, March 2008 page 420 followed by a treatment of the relationship between braids, simple properties for every function, each chapter catalogs knots and links. Important results then treat the linearity and interrelationships as well as other characteristics of the orderability of the subject. Relevant additional material is function. Many chapters close with a concise exposition on a included in fi ve large appendices. topic in applied mathematics associated with the particular function or function family. The book is packed with Equator, a 2008. Approx. 340 p. 60 illus. (Graduate Texts in Mathe matics, CD which eliminates the need for tables or programming to Volume) Hardcover fi nd numerical values. ISBN 978-0-387-33841-5 7 approx. $59.95 2nd ed. 2008. XX, 700 p. 330 illus., 70 in color. With CD-ROM. Hardcover ISBN 978-0-387-48806-6 7 approx. $129.95 Easy Ways to Order for the Americas 7 Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA 7 Call: (toll free) 1-800-SPRINGER 7 Fax: 1-201-348-4505 7 Email: [email protected] or for outside the Americas 7 Write: Springer Distribution Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany 7 Call: +49 (0) 6221-345-4301 7 Fax: +49 (0) 6221-345-4229 7 Email: [email protected] 7 Prices are subject to change without notice. All prices are net prices. 013519x Julia Robinson and Hilbert's Tenth Problem (see page 380) Trim: 8.25" x 10.75" 104 pages on 40 lb Cougar Opaque • Spine: 3/16" • Print Cover on 9pt Carolina ,!4%8 ,!4%8 ,!4%8 Pro AMERICAN MATHEMATICAL SOCIETY ematics th M a e M e t t i n n i g o s J J 8 an 0 JMM 2008 BESTSELLERS ua 20 ry 6–9, p -adic Analysis 1001 Problems in Popular Course Compared with Classical Number Adoption Titles Real Theory COURSE ADOPTION Svetlana Katok, Jean-Marie De Koninck, Pennsylvania State Université Laval, Quebec, Approximately University, University QC, Canada, and Armel Calculus Park, PA Mercier, Université du Québec à Chicoutimi, QC, Canada Shahriar Shahriari, This book is co-published with Mathematics Pomona College, Advanced Study Semesters. 2007; 336 pages; Hardcover; ISBN: 978-0-8218-4224-9; Claremont, CA List US$49; AMS members US$39; Order code PINT Student Mathematical Library, Volume 37; 2007; Presents a deep under- 152 pages; Softcover; ISBN: 978-0-8218-4220-1; List standing of calculus and US$29; AMS members US$23; Order code STML/37 Geometry of Conics its infinite power to approximate A. 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COURSE and algebra CBMS Issues in Mathematics Education, Volume ADOPTION 14; 2007; 223 pages; Softcover; ISBN: 978-0-8218- Shigeyuki Morita, Tokyo Institute 4194-5; List US$49; AMS members US$39; Order code A View from the Top of Technology, Japan, Koji Shiga, CBMATH/14 Analysis, Combinatorics Yokohama, Japan, Toshikazu SunadaMathematical World, Mathematical World Volume 17 Tohoku University, Sendai, Japan, and Volume 17 and Number Theory A Mathematical Chaotic Elections! A Kenji Ueno, Kyoto University, Japan A Mathematical Alex Iosevich, University Gift, I Gift, II Mathematician Looks Individual volumes are available for purchase. of Missouri, Columbia, The interplay between The interplay between topology, functions, topology, functions, at Voting MO Set: Mathematical World; 2005;geometry, 392 pages; and algebra geometry, and algebra Softcover; ISBN: 978-0-8218-3859-4; List US$75; AMS Donald G. 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  • Math 126 Lecture 4. Basic Facts in Representation Theory

    Math 126 Lecture 4. Basic Facts in Representation Theory

    Math 126 Lecture 4. Basic facts in representation theory. Notice. Definition of a representation of a group. The theory of group representations is the creation of Frobenius: Georg Frobenius lived from 1849 to 1917 Frobenius combined results from the theory of algebraic equations, geometry, and number theory, which led him to the study of abstract groups, the representation theory of groups and the character theory of groups. Find out more at: http://www-history.mcs.st-andrews.ac.uk/history/ Mathematicians/Frobenius.html Matrix form of a representation. Equivalence of two representations. Invariant subspaces. Irreducible representations. One dimensional representations. Representations of cyclic groups. Direct sums. Tensor product. Unitary representations. Averaging over the group. Maschke’s theorem. Heinrich Maschke 1853 - 1908 Schur’s lemma. Issai Schur Biography of Schur. Issai Schur Born: 10 Jan 1875 in Mogilyov, Mogilyov province, Russian Empire (now Belarus) Died: 10 Jan 1941 in Tel Aviv, Palestine (now Israel) Although Issai Schur was born in Mogilyov on the Dnieper, he spoke German without a trace of an accent, and nobody even guessed that it was not his first language. He went to Latvia at the age of 13 and there he attended the Gymnasium in Libau, now called Liepaja. In 1894 Schur entered the University of Berlin to read mathematics and physics. Frobenius was one of his teachers and he was to greatly influence Schur and later to direct his doctoral studies. Frobenius and Burnside had been the two main founders of the theory of representations of groups as groups of matrices. This theory proved a very powerful tool in the study of groups and Schur was to learn the foundations of this subject from Frobenius.