Difference equations are models of the world around us. From clocks to computers to chromosomes, processing discrete objects in discrete steps is a common theme. Difference equations arise naturally from such discrete descriptions and allow us to pose and answer such questions as: How much? How many? How long? Difference equations are a necessary part of the mathematical repertoire of all modern scientists and engineers. In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron—Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply polynomials quickly. The book contains many worked examples and over 250 exercises. While these exercises are accessible to students and have been class-tested, they also suggest further problems and possible research topics. Paul Cull is a professor of Computer Science at Oregon State University. Mary Flahive is a professor of Mathematics at Oregon State University. Robby Robson is president of Eduworks, an e-learning consulting firm. None has a rabbit.
Spectral geometry runs through much of contemporary mathematics, drawing on and stimulating developments in such diverse areas as Lie algebras, graph theory, group representation theory, and Riemannian geometry. The aim is to relate the spectrum of the Laplace operator or its graph-theoretic analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Spectral Geometry, held in July 1993 at the University of Washington in Seattle. With contributions from some of the top experts in the field, this book presents an excellent overview of current developments in spectral geometry.
Civil Islam tells the story of Islam and democratization in Indonesia, the world's largest Muslim nation. Challenging stereotypes of Islam as antagonistic to democracy, this study of courage and reformation in the face of state terror suggests possibilities for democracy in the Muslim world and beyond. Democratic in the early 1950s and with rich precedents for tolerance and civility, Indonesia succumbed to violence. In 1965, Muslim parties were drawn into the slaughter of half a million communists. In the aftermath of this bloodshed, a "New Order" regime came to power, suppressing democratic forces and instituting dictatorial controls that held for decades. Yet from this maelstrom of violence, repressed by the state and denounced by conservative Muslims, an Islamic democracy movement emerged, strengthened, and played a central role in the 1998 overthrow of the Soeharto regime. In 1999, Muslim leader Abdurrahman Wahid was elected President of a reformist, civilian government. In explaining how this achievement was possible, Robert Hefner emphasizes the importance of civil institutions and public civility, but argues that neither democracy nor civil society is possible without a civilized state. Against portrayals of Islam as inherently antipluralist and undemocratic, he shows that Indonesia's Islamic reform movement repudiated the goal of an Islamic state, mobilized religiously ecumenical support, promoted women's rights, and championed democratic ideals. This broadly interdisciplinary and timely work heightens our awareness of democracy's necessary pluralism, and places Indonesia at the center of our efforts to understand what makes democracy work.
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