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Algorithmic information theory / Gregory J Chaitin
Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987
x, 175 pages. ; 25 cm.
Ký hiệu phân loại (DDC): 006.31
Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Goedel's incompleteness theorem, using an information theoretic approach based on the size of computer programs.
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2
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Analysis for computer scientists : foundations, methods, and algorithms / Michael Oberguggenberger; Alexander Ostermann; Elisabeth Bradley Translator
Cham, Switzerland : Springer, 2018
372 pages. : illustrations
Ký hiệu phân loại (DDC): 004.0151
This textbook/reference presents a concise introduction to mathematical analysis from an algorithmic point of view, with a particular focus on applications of analysis and aspects of mathematical modelling. The text describes the mathematical theory alongside the basic concepts and methods of numerical analysis, enriched by computer experiments using MATLAB, Python, Maple, and Java applets. This fully updated and expanded new edition also features an even greater number of programming exercises. Topics and features : Describes the fundamental concepts in analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives, integrals, and curves; Discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations; Presents tools from vector and matrix algebra in the appendices, together with further information on continuity; Includes added material on hyperbolic functions, curves and surfaces in space, second-order differential equations, and the pendulum equation (NEW); Contains experiments, exercises, definitions, and propositions throughout the text; Supplies programming examples in Python, in addition to MATLAB (NEW); Provides supplementary resources at an associated website, including Java applets, code source files, and links to interactive online learning material.
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Combinatorial optimization : algorithms and complexity / Christos H Papadimitriou; Kenneth Steiglitz
Mineola, N.Y. : Dover Publications, 1998
496 p. : illustrations ; 22 cm.
Ký hiệu phân loại (DDC): 511.6
A text for a range of graduate courses, with some of the material suitable for students of computer science with a background in the theory of algorithms and some suitable for those with a background in operations research. Corrected and unabridged from the 1982 publication by Prentice-Hall, with a new preface. Annotation copyrighted by Book News, Inc., Portland, OR.
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5
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Communication complexity / Eyal Kushilevitz, Noam Nisan
Cambridge : Cambridge University Press, 1997
189 p. ; 24 cm.
Ký hiệu phân loại (DDC): 004.6
Many aspects of the internal and external workings of computers can be viewed as a series of communication processes. Communication complexity is the mathematical theory of such communication processes. It is also often used as an abstract model of other aspects of computation. This book surveys this mathematical theory, concentrating on the question of how much communication is necessary for any particular process. The first part of the book is devoted to the simple two-party model introduced by Yao in 1979, which is still the most widely studied model. The second part treats newer models developed to deal with more complicated communication processes. Finally, applications of these models, including computer networks, VLSI circuits, and data structures, are treated in the third part of the book. This is an essential resource for graduate students and researchers in theoretical computer science, circuits, networks and information theory.
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