Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly re...
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ISBN:
(数字)9780817682569
ISBN:
(纸本)9780817682552
Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a noisy channel. Despite frequent use in a range of contexts, the subject still contains interesting unsolved problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing Sagea free open-source mathematics software systemto illustrateideas, this bookis intended for graduate students and researchers in algebraic coding theory. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.
This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically c...
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ISBN:
(数字)9780817649807
ISBN:
(纸本)9780817649791
This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. A central theme of the book is the structure of various vector spacesmost importantly, Hilbert spacesand expansions of elements in these spaces in terms of bases. Key topics and features include: * More than 150 exercises * Abstract and normed vector spaces * Approximation in normed vector spaces * Hilbert and Banach spaces * General bases and orthonormal bases * Linear operators on various normed spaces * The Fourier transform, including the discrete Fourier transform * Wavelets and multiresolution analysis * B-splines * SturmLiouville problems As a textbook that provides a deep understanding of central issues in mathematical analysis, Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.
Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be ...
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ISBN:
(数字)9780817646837
ISBN:
(纸本)9780817646820
Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions. Contributors: C. Benson, M. Bownik, V. Furst, V. W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang.
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