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Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics. Contributors in the second volume: M. Harris, D. Kaledin, M. Kapranov, N.M. Katz, R.M. Kaufmann, J. Kollár, M. Kontsevich, M. Larsen, M. Markl, L. Merel, S.A. Merkulov, M.V. Movshev, E. Mukhin, J. Nekovár, V.V. Nikulin, O. Ogievetsky, F. Oort, D. Orlov, A. Panchishkin, I. Penkov, A. Polishchuk, P. Sarnak, V. Schechtman, V. Tarasov, A.S. Tikhomirov, J. Tsimerman, K. Vankov, A. Varchenko, A. Vishik, A.A. Voronov, Yu. Zarhin, Th. Zink.

Algebra. --- Arithmetic. --- Geometry. --- Elementary Mathematics & Arithmetic --- Algebra --- Mathematics Teaching & Research --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Algebraic geometry. --- Algebraic Geometry. --- Set theory --- Calculators --- Numbers, Real --- Geometry, algebraic. --- Algebraic geometry --- Geometry --- Euclid's Elements --- Mathematical analysis

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A collection of selected papers from the 18th WIRN workshop, the annual meeting of the Italian Neural Networks Society (SIREN). It is divided in two general subjects, 'models' and 'applications' and two specific ones, 'economy and complexity' and 'remote sensing image processing'.

Neural networks (Computer science) --- Computers. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- E-books --- Réseaux neuronaux (informatique)

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The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the Mordell–Weil theorem giving finite generation of the group of rational points and Siegel's theorem on finiteness of integral points. For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra's factorization algorithm, Schoof's point counting algorithm, Miller's algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro's conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics.

Arithmetic. --- Curves, Algebraic. --- Curves, Elliptic. --- Curves, Elliptic --- Curves, Algebraic --- Arithmetic --- Mathematics --- Geometry --- Physical Sciences & Mathematics --- Algebraic curves --- Elliptic curves --- Mathematics. --- Algebra. --- Algebraic geometry. --- Number theory. --- Algebraic Geometry. --- Number Theory. --- Set theory --- Calculators --- Numbers, Real --- Algebraic varieties --- Geometry, algebraic. --- Number study --- Numbers, Theory of --- Algebra --- Mathematical analysis --- Algebraic geometry --- Corbes el·líptiques --- Geometry, Algebraic.

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Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics. Contributors in the first volume include: K. Behrend, V.G. Berkovich, J.-B. Bost, P. Bressler, D. Calaque, J.F. Carlson, A. Chambert-Loir, E. Colombo, A. Connes, C. Consani, A. Da˛browski, C. Deninger, I.V. Dolgachev, S.K. Donaldson, T. Ekedahl, A.-S. Elsenhans, B. Enriquez, P. Etingof, B. Fantechi, V.V. Fock, E.M. Friedlander, B. van Geemen, G. van der Geer, E. Getzler, A.B. Goncharov, V.A. Iskovskikh, J. Jahnel, M. Kapranov, E. Looijenga, M. Marcolli, B. Tsygan, E. Vasserot, M. Wodzicki.

Algebra. --- Arithmetic. --- Geometry. --- Arithmetic --- Algebra --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Elementary Mathematics & Arithmetic --- Mathematics Teaching & Research --- Mathematics. --- Algebraic geometry. --- Number theory. --- Physics. --- Number Theory. --- Mathematical Methods in Physics. --- Algebraic Geometry. --- Euclid's Elements --- Mathematical analysis --- Set theory --- Calculators --- Numbers, Real --- Mathematical physics. --- Geometry, algebraic. --- Algebraic geometry --- Physical mathematics --- Physics --- Number study --- Numbers, Theory of --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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This text identifies, examines, and illustrates fundamental concepts in computer system design that are common across operating systems, networks, database systems, distributed systems, programming languages, software engineering, security, fault tolerance, and architecture. Through carefully analyzed case studies from each of these disciplines, it demonstrates how to apply these concepts to tackle practical system design problems. To support the focus on design, the text identifies and explains abstractions that have proven successful in practice such as, remote procedure call, client

System Design --- Computer systems --- Ordinateur --- Computers --- Application des ordinateurs --- computer applications --- Logiciel --- Computer software --- design --- Matériel informatique --- Computer hardware --- Technologie de l'information --- information technology --- Internet --- Information Technology --- General and Others --- Computer architecture. --- Computer organization. --- Software engineering. --- Computer software engineering --- Engineering --- Organization, Computer --- Electronic digital computers --- Architecture, Computer --- Automatic computers --- Automatic data processors --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Design.