Author: Henry Van Dyke
Publisher: Wildside Press LLC
ISBN: 1434489906
Category : Fiction
Languages : en
Pages : 294

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Author: Barry Simon
Publisher: American Mathematical Soc.
ISBN: 0821849883
Category : Mathematics
Languages : en
Pages : 162

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From a review of the first edition: Beautifully written and well organized ... indispensable for those interested in certain areas of mathematical physics ... for the expert and beginner alike. The author deserves to be congratulated both for his work in unifying a subject and for showing workers in the field new directions for future development. --Zentralblatt MATH This is a second edition of a well-known book on the theory of trace ideals in the algebra of operators in a Hilbert space. Because of the theory's many different applications, the book was widely used and much in demand. For this second edition, the author has added four chapters on the closely related theory of rank one perturbations of self-adjoint operators. He has also included a comprehensive index and an addendum describing some developments since the original notes were published. This book continues to be a vital source of information for those interested in the theory of trace ideals and in its applications to various areas of mathematical physics.

Author: Richard C. Penney
Publisher: John Wiley & Sons
ISBN: 1118909593
Category : Mathematics
Languages : en
Pages : 510

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Praise for the Third Edition “This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications.” – Electric Review A comprehensive introduction, Linear Algebra: Ideas and Applications, Fourth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique. The book introduces each new concept in the context of an explicit numerical example, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fourth Edition also features: Two new and independent sections on the rapidly developing subject of wavelets A thoroughly updated section on electrical circuit theory Illuminating applications of linear algebra with self-study questions for additional study End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB® code Linear Algebra: Ideas and Applications, Fourth Edition is an excellent undergraduate-level textbook for one or two semester courses for students majoring in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.

Author: Ming Li
Publisher: Springer Science & Business Media
ISBN: 1475726066
Category : Mathematics
Languages : en
Pages : 655

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Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).

Author: Thomas J. Jech
Publisher: American Mathematical Soc.
ISBN: 0821822144
Category : Mathematics
Languages : en
Pages : 77

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This work is a systematic study of ideals over uncountable sets. In particular, we investigate the role of various properties of ideals in arithmetic of cardinal numbers. We also study consequences of existence of precipitous ideals for the generalized continuum hypothesis and the singular cardinals problem.

Author: Craig Huneke
Publisher: Cambridge University Press
ISBN: 0521688604
Category : Mathematics
Languages : en
Pages : 446

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Book Description
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Author: Arkadii Slinko
Publisher: Springer
ISBN: 3319219510
Category : Mathematics
Languages : en
Pages : 336

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Book Description
This book examines the relationship between mathematics and data in the modern world. Indeed, modern societies are awash with data which must be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from an unauthorised access and transmitted over unreliable channels. All of these operations can be understood only by a person with knowledge of basics in algebra and number theory. This book provides the necessary background in arithmetic, polynomials, groups, fields and elliptic curves that is sufficient to understand such real-life applications as cryptography, secret sharing, error-correcting, fingerprinting and compression of information. It is the first to cover many recent developments in these topics. Based on a lecture course given to third-year undergraduates, it is self-contained with numerous worked examples and exercises provided to test understanding. It can additionally be used for self-study.

Author: Anna M. Bigatti
Publisher: Springer
ISBN: 364238742X
Category : Mathematics
Languages : en
Pages : 201

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Book Description
This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.

Author: Christopher Thorpe
Publisher: Routledge
ISBN: 1135985588
Category : Social Science
Languages : en
Pages : 224

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Book Description
Trying to understand how the world looks through the eyes of individuals and groups and how it shapes the ways they think and act is something social workers do all the time. It is what social theorists do too. This book identifies and explains in a highly accessible manner the absolute value of social theory for social work. Drawing on the theoretical ideas and perspectives of a wide range of classical and modern social theorists, the book demonstrates the insights their work can bring to bear on a wide range of social work practice scenarios, issues and debates. Departing with the work of the classical theorists, the book covers a diverse range of theoretical traditions including phenomenology, symbolic interactionism, Norbert Elias, Michel Foucault, Pierre Bourdieu, feminism and globalization theory. Putting to work ideas from these different perspectives, a range of social work scenarios, issues and debates are opened up and explored. The final chapter brings together the various theoretical strands, and critically considers the contribution they can make towards realizing core social work values in a rapidly globalizing world. Demonstrating exactly how and in what ways social theory can make important and enduring contributions to social work, Social Theory for Social Work is essentialial reading for social work students, practitioners and professionals alike.

Author: Myoung An
Publisher: Springer Science & Business Media
ISBN: 0817647384
Category : Technology & Engineering
Languages : en
Pages : 237

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Book Description
This book develops theory and algorithms leading to systematic waveform design in time-frequency space. The key tool employed in the work is the Zak transform, which provides a two-dimensional image for sequences, the Fourier transform, convolution, and correlation, and allows for the design of sequences directly in Zak space. Application areas covered include pulse radars and sonars, multibeam radar and sonar imaging systems, remote dielectric material identification, and code division multiple-access communication systems. This is an excellent reference text for graduate students, researchers, and engineers in radar, sonar, and communication systems.