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The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega,nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can be done in what is essentially a two dimensional vector space, have been dropped in favor of n-dimens...
Data Structures & Theory of Computation
Cryptography, as done in this century, is heavily mathematical. But it also has roots in what is computationally feasible. This unique textbook text balances the theorems of mathematics against the feasibility of computation. Cryptography is something one actually “does”, not a mathematical game one proves theorems about. There is deep math; there are some theorems that must be proved; and there is a need to recognize the brilliant work done by those who focus on theory. But at the level of an undergraduate course, the emphasis should be first on knowing and understanding the algorithms and how to implement them, and also to be aware that the algorithms must be implemented carefully to avoid the “easy” ways to break the cryptography. This text covers the algorithmic foundations and is complemented by core mathematics and arithmetic.
"Will be welcomed by many communities--academic, federal, and industrial. With new and little-known information on high-performance computing, it is the great compendium describing the last seven years of activities and looking to the future."--Charles Bender, Director, The Ohio Supercomputer Center "A valuable resource and an important contribution to thinking in this area. . . . I am impressed with the scope and coherence of this material, ranging from technical projections to the political context to market and user perspectives on supercomputers and supercomputing."--James G. Glimm, State University of New York at Stonybrook
This highly-anticipated CS2 text from Dr. D.S. Malik is ideal for a one-semester course focused on data structures. Clearly written with the student in mind, this text focuses on Data Structures and includes advanced topics in Java such as Linked Lists and the Standard Template Library (STL). This student-friendly text features abundant Programming Examples and extensive use of visual diagrams to reinforce difficult topics. Students will find Dr. Malik's use of complete programming code and clear display of syntax, explanation, and example easy to read and conducive to learning.
Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.
Through sheer determination and courage, Kahn has researched the nature of concrete in the form of precast, cast in place or blocks. Each of his renowned works in exposed concrete, such as the Yale Art Gallery, the Richards Laboratories, the Bath House, the Salk Institute, the National Assembly, the Kimbell Museum, the Exeter Library and the Yale Center for British Art, is itself an important chapter in the history of architecture for the exploration into concrete’s formal expression, beyond the lesson of Le Corbusier. Kahn’s obsession on concrete fabrication processes, on the formwork and the mix design, is systematically examined in two volumes. The authors illustrate Kahn’s vision w...
Original articles on all aspects of numerical mathematics, book reviews, mathematical tables, and technical notes. Covers advances in numerical analysis, application of computer methods, high speed calculating, and other aids to computation.