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Mathematical Aspects Of Quantum Computing 2007

This book provides a comprehensive overview of the mathematical aspects of quantum computing. It will be useful for graduate students and researchers interested in quantum computing from different areas of physics, mathematics, informatics and computer science. The lecture notes in this volume are written in a self-contained style, and hence are accessible for graduate students and researchers with even less background in the topics....

Introduction to Pattern Recognition

Statistical, Structural, Neural and Fuzzy Logic Approaches

An introduction to pattern recognition, this text is meant for students in computer science and related fields in science and technology. Algorithms and real world applications accompany most of the topics in the text. In addition to statistical and structural approaches, novel topics such as fuzzy pattern recognition and pattern recognition via neural networks are also reviewed. Each topic is followed by several examples solved in detail....

Information, Randomness and Incompleteness

Papers on Algorithmic Information Theory

2nd Edition

God not only plays dice in quantum mechanics, but even with the whole numbers! The discovery of randomness in arithmetic is presented in my book Algorithmic Information Theory published by Cambridge University Press. There I show that to decide if an algebraic equation in integers has finitely or infinitely many solutions is in some cases absolutely intractable. I exhibit an infinite series of such arithmetical assertions that are random arithmetical facts, and for which it is essentially the case that the only way to prove them is to assume them as axioms. This extreme form of Gdel incompleteness theorem shows that some arithmetical truths are totally...