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 ...

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, includin...

The grand narratives of European music history are informed by the dichotomy of placements and displacements. Yet musicology has thus far largely ignored the phenomenon of displacement and underestimated its significance for musical landscapes and music history. Music and Displacement: Diasporas, Mobilities, and Dislocations in Europe and Beyond constitutes a pioneering volume that aims to fill this gap as it explores the interactions between music and displacement in theoretical and pract...

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds.Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes di...

Every culture on Earth has music. Every culture that's ever existed has had it, but we don't exactly know why. Music is not like food, shelter, or having opposable thumbs. We don't need it to live, and yet we can't seem to live without it. Glenn Dixon travels the globe exploring how and why people make music. From a tour of Bob Marley's house to sitar lessons in India, he experiences music around the world and infuses the stories with the latest in brain research, genetics, and evolutionar...

Linear Algebra is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorems for linear maps, including eigenvectors and eigenvalues, quadric and hermitian forms, diagonalization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. The book also includes a useful chapter on convex sets and the finite-dimensional ...

This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part ...

With extensive photographs and an audio CD, this guide to Balinese music showcases the history, culture and art of the gamelan ceremony.Bali has developed and nourished an astonishing variety of musical ensembles—called gamelan—comprising dozens of instruments mainly made of bronze or bamboo, and organized into groups with as many as 30 to 40 players. In Balinese Gamelan Music, Michael Tenzer, a noted Professor of Music at the University of Britis...

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view.This book, unlike other introductory t...

Rooted in a pedagogically successful problem-solving approach to linear algebra, this work fills a gap in the literature that is sharply divided between, on the one end, elementary texts with only limited exercises and examples, and, at the other end, books too advanced in prerequisites and too specialized in focus to appeal to a wide audience. Instead, it clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while...

"Russian folk songs are a living history of the Russian people, rich, vivid and truthful, revealing their entire life," wrote the great Russian writer Nikolai Gogol.Russian folk songs have always played an essential part in Russian life, culture, and music. They have played an important part in the work of many great Russian composers including Glinka, Rimsky-Korsakov, Borodin, Tchaikovsky, Prokoviev, and Stravinsky. In this new study, Vadim Prokhorov provides a historical survey a...

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesi...