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Since their discovery hundreds of years ago, people have been fascinated by the wondrous properties of Fibonacci numbers. Being of mathematical significance in their own right, Fibonacci numbers have had an impact on areas like art and architecture, and their traces can be found in nature and even the behavior of the stock market. Starting with the basic properties of Fibonacci numbers, the present book explores their relevance in number theory, the theory of continued fractions, geometry and approximation theory. Rather than giving a complete account of the subject, a few chosen examples are treated exhaustively. They not only reveal the bearing of Fibonacci numbers on mathematics, but also provide very readable marvels of mathematical reasoning. This book is the translation of the 6th Russian edition (the first edition appeared in the early fifties and became a standard source of information on the subject).
Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate.
Structuring Sense explores the difference between words however defined and structures however constructed. It sets out to demonstrate over three volumes that the explanation of linguistic competence should be shifted from lexical entry to syntactic structure, from memory of words to manipulation of rules. Its reformulation of how grammar and lexicon interact has profound implications for linguistic, philosophical, and psychological theories about human mind and language. Hagit Borer departs from language specific constructional approaches and from lexicalist approaches to argue that universal hierarchical structures determine interpretation, and that language variation emerges from the morphological and phonological properties of inflectional material. Taking Form, the third and final volume of Structuring Sense, applies this radical approach to the construction of complex words. Integrating research in syntax and morphology, the author develops a new model of word formation, arguing that on the one hand the basic building blocks of language are rigid semantic and syntactic functions, while on the other hand they are roots, which in themselves are but packets of phonological information, and are devoid of both meaning and grammatical properties of any kind. Within such a model, syntactic category, syntactic selection and argument structure are all mediated through syntactic structures projected from rigid functions, or alternatively, constructed through general combinatorial principles of syntax, such as Chomsky's Merge. The meaning of 'words', in turn, does not involve the existence of lexemes, but rather the matching of a well-defined and phonologically articulated syntactic domain with conceptual Content, itself outside the domain of language as such. In a departure from most current models of syntax but in line with many philosophical traditions, then, the Exo-Skeletal model partitions 'meaning' into formal functions, on the one hand, and Content, on the other hand. While the former are read off syntactico-semantic structures as is usually assumed, Content is crucially read off syntactico-phonological structures.
Accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Topics include classes and sets, functions, natural and cardinal numbers, arithmetic of ordinal numbers, and more. 1971 edition with new material by author.
Helping current and future system designers take a more productive approach in the field, Communication System Security shows how to apply security principles to state-of-the-art communication systems. The authors use previous design failures and security flaws to explain common pitfalls in security design.Divided into four parts, the book begins w
With most services and products now being offered through digital communications, new challenges have emerged for information security specialists. A Multidisciplinary Introduction to Information Security presents a range of topics on the security, privacy, and safety of information and communication technology. It brings together methods in pure m
