Product Description
Provides a self-contained representation of the local version of the Atiyah-Singer index theorem. For researchers and graduate students in mathematics. ... Read more

Product Description
The question of estimating the number of minimal surfaces that bound a prescribed contour has been open since Douglas's solution of the Plateau problem in 1931. In this book, the authors formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. The Index Theorem for Minimal Surfaces of Higher Genus describes, in terms of Fredholm Index, a rough measure on the set of curves bounding minimal surfaces of prescribed branching type and genus. ... Read more

Product Description
This book develops a method to obtain limit theorems for variousfunctionals of random graphs. The method is based on a certainorthogonal decomposition. Janson's results include limittheorems for the two standard random graph models, $G_{n,p}$ and$G_{n,m}$, as well as functional limit theorems for theevolution of a random graph and results on the maximum of afunction during the evolution. Janson obtains both normal andnonnormal limits, and the method provides an explanation for theappearance of nonnormal limits. Applications to subgraph countsand to vertex degrees are presented as examples. ... Read more

Product Description
The Novikov conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds.These two volumes give a snapshot of the status of work on the Novikov conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry, and analysis. Volume 1 contains a detailed historical survey and bibliography of the Novikov conjecture and of related subsequent developments, including an annotated reprint (both in the original Russian and in English translation) of Novikov's original 1970 statement of his conjecture; an annotated problem list; the texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and research/survey papers on the Novikov conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg.Volume 2 contains fundamental long research papers by G. Carlsson on "Bounded K-theory and the assembly map in algebraic K-theory" and by S. Ferry and E. Pedersen on "Epsilon surgery theory"; and shorter research and survey papers on various topics related to the Novikov conjecture, by Bekka, Cherix, Valette, Eichhorn, and others. These volumes will appeal to researchers interested in learning more about this intriguing area. ... Read more

Product Description
Chapters: Frobenius Theorem, Contact Geometry, Integrability Conditions for Differential Systems, Darboux's Theorem, Differential Ideal. Source: Wikipedia. Pages: 32. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, the theorem gives necessary and sufficient conditions for the existence of a foliation by maximal integral manifolds each of whose tangent bundles are spanned by a given family of vector fields (satisfying an integrability condition) in much the same way as an integral curve may be assigned to a single vector field. The theorem is foundational in differential topology and calculus on manifolds. In its most elementary form, the theorem addresses the problem of finding a maximal set of independent solutions of a regular system of first-order linear homogeneous partial differential equations. Suppose that fk(x) are a collection of real-valued C functions on R, for i = 1, 2, ..., n, and k = 1, 2, ..., r, where r ... Read more

Product Description
Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Faltings' Theorem, Glossary of Arithmetic and Diophantine Geometry, Field of Definition, Principal Homogeneous Space, Birch and Swinnerton-Dyer Conjecture, Arakelov Theory, Local Zeta-Function, Arithmetic of Abelian Varieties, Thin Set, Chevalley-warning Theorem, Mordell-weil Theorem, Quasi-Algebraically Closed Field, Approximation in Algebraic Groups, Erdős-diophantine Graph, Semistable Abelian Variety, Tate Conjecture, Weil Conjecture on Tamagawa Numbers, Siegel's Lemma, Igusa Zeta-Function, Conductor of an Abelian Variety, Integer Lattice, Severi-Brauer Variety, Fermat Curve, Rational Point, Manin Obstruction, Bogomolov Conjecture, Mazur's Torsion Theorem. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: This is a glossary of arithmetic and Diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality. Diophantine geometry in general is the study of algebraic varieties V over fields K that are finitely generated over their prime fields including as of special interest number fields and finite fields and over local fields. Of those, only the complex numbers are algebraically closed; over any other K the existence of points of V with co-ordinates in K is something to be proved and studied as an extra topic, even knowing the geometry of V. Arithmetical or arithmetic (algebraic) geometry is a field with a less elementary definition. After the advent of scheme theory it could reasonably be defined as the study of Alexander Grothendieck's schemes of finite type over the spectrum of the ring of integers Z. This point of view has been very influentia...More: http://booksllc.net/?id=3141761 ... Read more

Product Description
This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University.The purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. Contributors to this volume include: B. Conrad, H. Darmon, E. de Shalit, B. de Smit, F. Diamond, S. J. Edixhoven, G. Frey, S. Gelbart, K. Kramer, H. W. Lenstra, Jr. , B. Mazur, K. Ribet, D. E. Rohrlich, M. Rosen, K. Rubin, R. Schoof, A. Silverberg, J. H. Silverman, P. Stevenhagen, G. Stevens, J. Tate, J. Tilouine, and L. Washington. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem. ... Read more

Customer Reviews (3)

Yet another application of elliptic curves...
The successful proof of Fermat's Last Theorem by Andrew Wiles was probably the most widely publicized mathematical result of the 20th century. And once again, among their numerous other applications, elliptic curves are employed in the proof. The book is a compilation of articles written by first-class mathematicians, the reading of which will give one a thorough understanding of the proof, along with an overview of some very interesting topics in number theory and algebraic geometry. The reader who undertakes an understanding of the proof already no doubt has a substantial amount of 'mathematical maturity', and no review, no matter how complete, would influence greatly such a reader. Suffice it to say then that this book is excellent, and even a reader interested solely in elliptic curves and modular forms could benefit greatly from the reading of this book.

Great?!?!
This book might be good if you like number theory. But if you're an analyst who hates number theory or a brick-layer, then this book is probably not meant for you. I hope you found this review helpful. Have a nice day.

Highly recommended
This item is very instructively, not only for "real"mathematicians. Of course, sometimes it's very difficult to"read". It gives me pleasure to own the proof of FLT. ... Read more

Product Description
Chapters: Minkowski's Theorem, Mahler's Compactness Theorem, Minkowski-hlawka Theorem. Source: Wikipedia. Pages: 20. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space. The geometry of numbers was initiated by Hermann Minkowski. The geometry of numbers has a close relationship with other fields of mathematics, especially functional analysis and Diophantine approximation, the problem of finding rational numbers that approximate an irrational quantity. Minkowski's first theorem states that a convex body with sufficient volume that is symmetric around the origin contains a nonzero vector with integer coordinates. Minkwoski's second theorem states that a convex body with sufficient volume (and with the same symmetry requirement) contains a basis of vectors, each having integer coordinates. In 1930-1960 research on the geometry of numbers was conducted by many number theorists (including Louis Mordell, Harold Davenport and Carl Ludwig Siegel). Contemporary research has been done by many authors, some of whose works are listed in the selective bibliography. In recent years, Lenstra, Brion, and Barvinok have developed combinatorial theories that enumerate the lattice points in some convex bodies. In the geometry of numbers, the subspace theorem was obtained by Wolfgang M. Schmidt in 1972. It states that if L1,...,Ln are linearly independent linear forms in n variables with algebraic coefficients and if ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
Symmetric space. List of simple Lie groups, Holonomy, Hermitian symmetric space, Quaternion-Kahler symmetric space, Bott periodicity theorem, Isometry, Differential geometry, Representation theory, Differentiable manifold, Pseudo-Riemannian manifold ... Read more

Product Description
This digital document is an article from UXL Encyclopedia of Science, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 145 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.This collection of entries covers major areas of science including: biology, genetics, microbiology, astronomy, chemistry, physics, engineering, technology, geology, weather, archaeology, psychology, mathematics, and medicine, and provides readers with a wide range of up-to-date, relevant, and accurate information. ... Read more

Product Description
A collection of definitions, questions, and theorems edited by M. L. Perez, such as Smarandache type conjectures, problems, numerical bases, T-numbers, progressions, series, functions, Non-Euclidean geometries, paradoxes (such as Smarandache Sorites Paradox that our visible world is composed by a totality of invisible particles), linguistic tautologies, Smarandache hypothesis that there is no speed barrier in the universe - which has been extended to SRM-theory. ... Read more

Customer Reviews (1)

A collection of very hard problems
Florentin Smarandache is one of the most prolific creators of mathematics problems in the world today. I have written three books on his problems and am currently writing a fourth. Many others also regularly work on the problems he has posed, which are collectively called Smarandache Notions. However, this still leaves a tremendous number of problems unexamined and unresolved.
Smarandache is best known for presenting problems rather than resolving them and that is also the case in this book. Basically, it is a collection of problems where each is listed and followed by a short blurb and references to what work has been done. While some of the problems have been solved, most are very difficult and may never be resolved. For many, a resolution would lead to a great deal of fame, as it would require some extremely original mathematics. No less a mathematical powerhouse than the late Pal Erdos has stated that some of these problems may never be resolved.
Mathematicians live, die and build their careers by finding and resolving problems. Thus collection contains many that are hard, perhaps impossible, but certainly worth examining if you are looking for new challenges. ... Read more

Product Description
The manifolds investigated in this monograph are generalizations of (XX)-rank one locally symmetric spaces. In the first part of the book the author develops spectral theory for the differential Laplacian operator associated to the so-called generalized Dirac operators on manifolds with cusps of rank one. This includes the case of spinor Laplacians on (XX)-rank one locally symmetric spaces. The time-dependent approach to scattering theory is taken to derive the main results about the spectral resolution of these operators. The second part of the book deals with the derivation of an index formula for generalized Dirac operators on manifolds with cusps of rank one. This index formula is used to prove a conjecture of Hirzebruch concerning the relation of signature defects of cusps of Hilbert modular varieties and special values of L-series. This book is intended for readers working in the field of automorphic forms and analysis on non-compact Riemannian manifolds, and assumes a knowledge of PDE, scattering theory and harmonic analysis on semisimple Lie groups. ... Read more