Peter Petersen

This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra. This book has several distinguishing features that set it apart from other linear algebra texts. For example: Gaussian elimination is used as the key tool in getting at eigenvalues; it takes an essentially determinant-free approach to linear algebra; and systems of linear differential equations are used as frequent motivation for the reader. Another motivating aspect of the book is the excellent and engaging exercises that abound in this text. This textbook is written for an upper-division undergraduate course on Linear Algebra. The prerequisites for this book are a familiarity with basic matrix algebra and elementary calculus, although any student who is willing to think abstractly should not have too much difficulty in understanding this text.

Linear Algebra

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with positive curvature; presentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds. From reviews of the first edition: "The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type." ―Bernd Wegner, ZbMATH

Riemannian Geometry

Randy Petersen

1993 Edition

The Official Frequent Flyer Guidebook

Die Oper »Friedenstag« wurde während des »Dritten Reichs« geschrieben und 1938 in München mit Billigung der Nazis uraufgeführt. Die NS-Zensur hatte nicht herausbekommen, dass der Jude Stefan Zweig das pazifistische Sujet vorgeschlagen und das Szenario entworfen hatte. »Friedenstag« wurde in der regimetreuen Presse so kommentiert, dass der Einakter mit Hitlers offiziellen Friedensbeteuerungen in Einklang zu stehen schien. In der vorliegenden Monographie wird die von Richard Strauss im Alter von 71 Jahren komponierte »Friedenstag«-Partitur erstmals umfassend analysiert. Anschließend geht es um die Biographien der drei beteiligten Autoren und ihr Verhältnis zum NS-Regime. Im letzten Teil zeigt der Verfasser, dass »Friedenstag« zwar als pazifistische Oper angelegt war, dass sie aber unter den gegebenen politischen Umständen nur als missdeutetes Werk Erfolg haben konnte. Peter Petersen ist emeritierter Professor für Musikwissenschaft an der Universität Hamburg. Zu seinen wichtigsten Veröffentlichungen zählen Arbeiten über Alban Bergs »Wozzeck« (1985) und über das Oeuvre Hans Werner Henzes (1988, 1995, 1996, 2003, 2012, 2014). Er ist Initiator und Mitherausgeber des »Lexikons verfolgter Musiker und Musikerinnen der NS-Zeit« (www.lexm.uni-hamburg.de). Aus jüngerer Zeit stammt sein Entwurf einer grundlegend neuen Rhythmustheorie (dt. 2010, engl. 2013).

Peter Petersen

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