Partial Differential Equation Methods in Control and Shape Analysis

Giuseppe Da Prato, Jean-Paul Zolesio "Partial Differential Equation Methods in Control and Shape Analysis"
CRC | 1997-02-20 | ISBN: 0824798376 | 352 pages | Djvu | 9,3 MB

"Based on the International Federatiojn for Information Processing WG 7.2 Conference, held recently in Pisa, Italy. Provides recent results as well as entirely new material on control theory and shape analysis. Written by leading authorities from various desciplines."

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Elliptic Curves: Number Theory and Cryptography, Second Edition

Lawrence C. Washington “Elliptic Curves: Number Theory and Cryptography, Second Edition"
Chapman & Hall/CRC | 2008-04-03 | ISBN: 1420071467 | 32 pages | PDF | 8,7 MB

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves.

New to the Second Edition
· Chapters on isogenies and hyperelliptic curves
· A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues
· A more complete treatment of the Weil and Tate–Lichtenbaum pairings
· Doud’s analytic method for computing torsion on elliptic curves over Q
· An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems
Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.

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Group Theory Birdtracks, Lie’s, and Exceptional Groups

Predrag Cvitanović “Group Theory Birdtracks, Lie’s, and Exceptional Groups "
Princeton University Press | 2008 | PDF | 285 pages | 2,8 Mb

Classical Lie groups preserve bilinear vector norms —what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanović takes the reader on the amazing, four thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional. The invariant tensors are presented in a somewhat unconventional, but in recent years widely used, “birdtracks” notation inspired by the Feynman diagrams of quantum field theory. Notably, invariant tensor diagrams replace algebraic reasoning in carrying out all group-theoretic computations. The diagrammatic approach is particularly effective in evaluating complicated coefficients and group weights, and revealing symmetries hidden by conventional algebraic or index notations.

The book covers most topics needed in applications from this new perspective: permutations, Young projections operators, spinorial representations, Casimir operators, and Dynkin indices. Beyond this well-traveled territory, more exotic vistas open up, such as “negative dimensional” relations between various groups and their representations. The most intriguing result of classifying primitive invariants is the emergence of all exceptional Lie groups in a single family, and the attendant pattern of exceptional and classical Lie groups, the so-called Magic Triangle. Written in a lively and personable style, the book is aimed at researchers and graduate students in theoretical physics and mathematics

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How to Solve It: Modern Heuristics

Zbigniew Michalewicz, David B. Fogel "How to Solve It: Modern Heuristics"
Springer | 2004-03-01 | ISBN:3540660615 | 467 pages | Djvu | 10,5Mb

This book is the only source that provides comprehensive, current, and detailed information on problem solving using modern heuristics. It covers classic methods of optimization, including dynamic programming, the simplex method, and gradient techniques, as well as recent innovations such as simulated annealing, tabu search, and evolutionary computation. Integrated into the discourse is a series of problems and puzzles to challenge the reader. The book is written in a lively, engaging style and is intended for students and practitioners alike. Anyone who reads and understands the material in the book will be armed with the most powerful problem solving tools currently known.

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