Catalog of MAA Publications 2011 Annual : Page 8NEW Lie Groups A Problem-Oriented Introduction via Matrix Groups Harriet Pollatsek ■ MAA Textbooks Can be used as supplementary reading in a linear algebra course or as a primary text in a “bridge” course that helps students make the transition to courses that emphasize definition and proofs, as well as for an upper level elective. The work of the Norwegian mathematician So-phus Lie extends ideas of symmetry and leads to many applications in mathematics and physics. Ordinarily, the study of the “objects” in Lie’s theory (Lie groups and Lie algebras) requires exten-sive mathematical prerequisites beyond the reach of the typical undergrad-uate. By restricting to the special case of matrix Lie groups and relying on ideas from multivariable calculus and linear algebra, this lovely and im-portant material becomes accessible even to college sophomores. Working with Lie’s ideas fosters an appreciation of the unity of mathematics and the sometimes surprising ways in which mathematics provides a language to describe and understand the physical world. This is the only book in the undergraduate curriculum to bring this material to students so early in their mathematical careers. Geometric Transformations IV Circular Transformations I. M. Yaglom Translated by Abe Shenitzer ■ Anneli Lax NML The familiar plane geometry of high school— figures composed of lines and circles—takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. This book is the concluding Part IV of Geometric Transformations , but it can be studied independently of Parts I, II, and III, which appeared in this series as Volumes 8, 21, and 24. Part I treats the geometry of rigid motions of the plane (isometries); Part II treats the geometry of shape-preserving transformations of the plane (similarities); Part III treats the geometry of transformations of the plane that map lines to lines (affine and projective transformations) and introduces the Klein model of non-Euclidean geometry. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincaré model of hyper-bolic geometry. The straightforward, direct presentation assumes only some background in high school geometry and trigonometry. Numerous exercises lead the reader to a mastery of the methods and concepts. The second half of the book contains detailed solutions of all the problems. 164 pp., 2009 List: $63.95 ISBN: 978-0-88385-759-5 MAA Member: $51.95 Hardbound Catalog Code: LIG/YD11 Visual Group Theory Nathan Carter ■ Classroom Resource Materials Could serve as a text in abstract algebra/ group theory at the undergraduate level, or as supplementary reading at the graduate level. 296 pp., 2009 List: $46.95 ISBN: 978-0-88385-648-2 MAA Member: $36.95 Paperbound Catalog Code: NML-44/YD11 Over 300 illustrations printed in full color. In a New York Times article, Steven Strogatz of Cornell University calls Visual Group Theory a “terrific new book.” He describes the book as “one of the best introductions to group theory—or to any branch of higher math—I’ve ever read.” The more than 300 illustrations in Visual Group Theory bring groups, sub-groups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its mean-ing and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. Although the book stands on its own, the free software Group Explorer makes an excellent companion. It enables the reader to interact visually with groups, including asking questions, creating subgroups, defining homomorphisms, and saving visualizations for use in other media. It is open source software available for Windows, Macintosh, and Unix systems from http://groupexplorer.sourceforge.net. Flatland Edwin Abbott Notes and commentary by William F. Lindgren & Thomas F. Banchoff ■ Spectrum Flatland , Edwin Abbott’s story of a two-dimen-sional universe as told by one of its inhabitants who is introduced to the mysteries of three-dimensional space, has enjoyed an enduring popularity from the time of its publication in 1884. This fully annotated edition enables the modern-day reader to under-stand and appreciate the many “dimensions” of this classic satire. Mathe-matical notes and illustrations enhance the usefulness of Flatland as an elementary introduction to higher-dimensional geometry. Historical notes show connections to late-Victorian England and to classical Greece. Citations from Abbott’s other writings, as well as the works of Plato and Aristotle, serve to interpret the text. Commentary on language and literary style in-cludes numerous definitions of obscure words. An appendix gives a compre-hensive account of the life and work of Flatland ’s remarkable author. 334 pp., 2009 List: $71.95 ISBN: 978-0-88385-757-1 MAA Member: $57.50 Hardbound Catalog Code: VGT/YD11 296 pp., 2010 List: $14.99 ISBN: 978-0-52175-994-6 Paperbound Catalog Code: FTL/YD11 5 8 To Order : Call 1.800.331.1622 or Online at www.maa.org Publication List |
