Nuovi arrivi ottobre 2009

An *introduction to Grobner bases / William W. Adams, Philippe Loustaunau. – Providence : American Mathematical Society, c1994. – XIII, 289 p. ; 26 cm. (*Graduate studies in mathematics ; 3)

Collocazione: Biblioteca di scienze matematiche 013/B/0520

As the primary tool for doing explicit computations in polynomial rings in many variables, Grobner bases are an important component of all computer algebra systems. They are also important in computational commutative algebra and algebraic geometry. This book provides a leisurely and fairly comprehensive introduction to Grobner bases and their applications.Adams and Loustaunau cover the following topics: the theory and construction of Grobner bases for polynomials with coefficients in a field, applications of Grobner bases to computational problems involving rings of polynomials in many variables, a method for computing syzygy modules and Grobner bases in modules, and the theory of Grobner bases for polynomials with coefficients in rings. With over 120 worked out examples and 200 exercises, this book is aimed at advanced undergraduate and graduate students. It would be suitable as a supplement to a course in commutative algebra or as a textbook for a course in computer algebra or computational commutative algebra. This book would also be appropriate for students of computer science and engineering who have some acquaintance with modern algebra.

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Nuovi arrivi agosto 2009

The *LATEX companions : revised set / Mittelbach … [et al.]. – Boston [etc.] : Addison Wesley. – 4 v. ; 25 cm. ((In custodia

Collocazione: Biblioteca di scienze matematiche

LaTeX is the text-preparation system of choice for scientists and academics, and is especially useful for typesetting technical materials. This popular book shows you how to begin using LaTeX to create high-quality documents. The book also serves as a handy reference for all LaTeX users. In this completely revised edition, the authors cover the LaTeX2ε standard and offer more details, examples, exercises, tips, and tricks. They go beyond the core installation to describe the key contributed packages that have become essential to LaTeX processing.Inside, you will find: Complete coverage of LaTeX fundamentals, including how to input text, symbols, and mathematics; how to produce lists and tables; how to include graphics and color; and how to organize and customize documentsDiscussion of more advanced concepts such as bibliographical databases and BIBTeX, math extensions with AMS-LaTeX, drawing, slides, and lettersHelpful appendices on installation, error messages, creating packages, using LaTeX with HTML and XML, and fontsAn extensive alphabetized listing of commands and their uses

New to this edition: More emphasis on LaTeX as a markup language that separates content and form–consistent with the essence of XMLDetailed discussions of contributed packages alongside relevant standard topicsIn-depth information on PDF output, including extensive coverage of how to use the hyperref package to create links, bookmarks, and active buttons

As did the three best-selling editions that preceded it, “Guide to LaTeX, Fourth Edition, will prove indispensable to anyone wishing to gain the benefits of LaTeX.

The accompanying CD-ROM is part of the TeX Live set distributed by TeX UsersGroups, containing a full LaTeX installation for Windows, MacOSX, and Linux, as well as many extensions, including those discussed in the book.

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Nuovi arrivi agosto 2009

Integrable systems in celestial mechanics / Diarmuid O Mathuna. – Boston [etc.] : Birkhauser, c2008. – X, 234 p. ; 24 cm.
(*Progress in mathematical physics ; 51)

Collocazione: Biblioteca di scienze matematiche: 070/D/0544

This work presents a unified treatment of three important integrable problems relevant to both Celestial and Quantum Mechanics. Under discussion are the Kepler (two-body) problem and the Euler (two-fixed center) problem, the latter being the more complex and more instructive, as it exhibits a richer and more varied solution structure. Further, because of the interesting investigations by the 20th century mathematical physicist J.P. Vinti, the Euler problem is now recognized as being intimately linked to the Vinti (Earth-satellite) problem.

Here the analysis of these problems is shown to follow a definite shared pattern yielding exact forms for the solutions. A central feature is the detailed treatment of the planar Euler problem where the solutions are expressed in terms of Jacobian elliptic functions, yielding analytic representations for the orbits over the entire parameter range. This exhibits the rich and varied solution patterns that emerge in the Euler problem, which are illustrated in the appendix. A comparably detailed analysis is performed for the Earth-satellite (Vinti) problem.

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Nuovi arrivi agosto 2009

Integrable hamiltonian hierarchies : spectral and geometric methods / V.S. Gerdjikov, G. Vilasi, A.B. Yanovski. – Berlin [etc.] : Springer, c2008. – XII, 643 p. ; 24 cm. (*Lecture notes in physics ; 748)

Collocazione: Biblioteca di scienze matematiche 070/D/0546

his book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform.

The book brings together the spectral and the geometric approaches and as such will be useful to a wide readership: from researchers in the field of nonlinear completely integrable evolution equations to graduate and post-graduate students.

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Nuovi arrivi agosto 2009

Symplectic invariants and Hamiltonian dynamics / Helmut Hofer, Eduard Zehnder. – Basel \etc.! : Birkhauser, c1994. – XIII, 341 p. ; 24 cm. (*Birkhauser advanced texts)

Collocazione: Biblioteca di scienze matematiche 070/D/0545

The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: sympletic topology. Surprising rigidity phenomena demonstrate that the nature of sympletic mappings is very different from that of volume preserving mappings. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. One of the links is a class of sympletic invariants, called sympletic capacities. These invariants are the main theme of this book, which includes such topics as basic sympletic geometry, sympletic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the sympletic diffeomorphism group and its geometry, sympletic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and sympletic homology.

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Nuovi arrivi agosto 2009

*Geometric fundamentals of robotics / J. M. Selig. – 2. ed. -  New York [etc.] : Springer, c2005. – XV, 398 p. ; 24 cm.
(*Monographs in computer science)

Collocazione: Biblioteca di scienze matematiche 093/C/0516

Geometric Fundamentals of Robotics provides an elegant introduction to the geometric concepts that are important to applications in robotics. This second edition is still unique in providing a deep understanding of the subject: rather than focusing on computational results in kinematics and robotics, it includes significant state-of-the art material that reflects important advances in the field, connecting robotics back to mathematical fundamentals in group theory and geometry.

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Nuovi arrivi agosto 2009

Geometry and topology in Hamiltonian dynamics and statistical mechanics /
Marco Pettini. – New York : Springer, c2007. – XVI, 451 p. : ill. ; 24 cm.
(*Interdisciplinary applied mathematics ; 33)

Collocazione: Biblioteca di scienze matematiche 070/D/0543

This book explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transition, from the point of view of geometry and topology. A broad participation of topology in these fields has been lacking and this book will provide a welcome overview of the current research in the area, in which the author himself is a pioneer. Using geometrical thinking to solve fundamental problems in these areas, compared to the purely analytical methods usually used in physics could be highly productive. The author skillfully guides the reader, whether mathematician or physicists through the background needed to understand and use these techniques.

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Nuovi arrivi agosto 2009

Geometric mechanics : toward a unification of classical physics / Richard Talman. – 2. revised and enlarged ed. – Weinheim : Wiley-VCH Verlag, c2007. – xv, 587 p. ; 24 cm.

Collocazione: Biblioteca di scienze matematiche 070/D/0542

For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for non-mathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, the author treats Lagrangian, Hamiltonian, and Newtonian mechanics separately — exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. This second, fully revised edition has been expanded to include new chapters on electromagnetic theory, general relativity, and string theory. ‘Geometric Mechanics’ features illustrative examples and assumes only basic knowledge of Lagrangian mechanics.

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Nuovi arrivi agosto 2009

La *matematica e l’esistenza di Dio / Antonio Ambrosetti. – Torino : Lindau, 2009. – 88 p. ; 21 cm.

Collocazione: Biblioteca di scienze matematiche

Come può un matematico credere in Dio? Un luogo comune nato con l’illuminismo vuole che gli scienziati siano atei o agnostici. La ricerca della verità perseguita attraverso la scienza sarebbe infatti incompatibile con qualunque convinzione di tipo religioso. Per Antonio Ambrosetti, scienziato di grande e riconosciuto valore e cristiano dichiarato, la matematica e la religione appartengono a due sfere distinte dell’esperienza umana, che possono coesistere modo proficuo e reciprocamente stimolante, come è dimostrato da illustri matematici credenti come i cattolici Giovanni Prodi ed Ennio De Giorgi, o gli ebrei Paul Rabinowitz e Haim Brezis. In particolare l’autore discute la pretesa onnipotenza della matematica, in base alla quale molti ritengono di poter dimostrare matematicamente tutto. La matematica ha molti limiti e, comunque, non può essere usata né per dimostrare né tanto meno per negare l’esistenza di Dio. Anche se forse può aiutarci ad avvicinare il suo mistero e a coglierne la grandezza.

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Nuovi arrivi agosto 2009

*Galileo Galilei e la cultura scientifica nell’età della Controriforma / Michele Camerota. – Roma : Salerno, 2004. – 703 p., [4] c. di tav. : ill. ; 24 cm.

Collocazione: Biblioteca di scienze matematiche 001/D / 0538

Il volume ripercorre l’itinerario biografico e intellettuale di Galileo, soffermandosi a illustrarne il pensiero così come consegnato alle diverse opere redatte nel corso della lunga carriera scientifica. Sono confrontati, con rigore scientifico e agevole leggibilità, i risultati conseguiti dal grande scienziato pisano e le posizioni espresse dalla cultura della sua epoca, al fine di far emergere i caratteri assolutamente originali della lezione galileiana. Il fondamentale contributo di Galileo alla storia della scienza consiste nel modello d’indagine naturalistica nel cui solco si è poi sviluppata la moderna scienza matematica e sperimentale (“provando e riprovando”).

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