Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 27,20 MB
Release : 2003
Category : Mathematics
ISBN : 082184377X
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author : Henri Darmon
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 20,4 MB
Release : 2004
Category : Mathematics
ISBN : 0821828681
The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
Author : Ken Ono
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 14,44 MB
Release : 2004
Category : Mathematics
ISBN : 0821833685
Chapter 1.
Author : Alain Lascoux
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 13,13 MB
Release : 2003
Category : Mathematics
ISBN : 0821828711
The theory of symmetric functions is an old topic in mathematics, which is used as an algebraic tool in many classical fields. With $\lambda$-rings, one can regard symmetric functions as operators on polynomials and reduce the theory to just a handful of fundamental formulas. One of the main goals of the book is to describe the technique of $\lambda$-rings. The main applications of this technique to the theory of symmetric functions are related to the Euclid algorithm and its occurrence in division, continued fractions, Pade approximants, and orthogonal polynomials. Putting the emphasis on the symmetric group instead of symmetric functions, one can extend the theory to non-symmetric polynomials, with Schur functions being replaced by Schubert polynomials. In two independent chapters, the author describes the main properties of these polynomials, following either the approach of Newton and interpolation methods, or the method of Cauchy and the diagonalization of a kernel generalizing the resultant. The last chapter sketches a non-commutative version of symmetric functions, with the help of Young tableaux and the plactic monoid. The book also contains numerous exercises clarifying and extending many points of the main text.
Author : Alberto Candel
Publisher : American Mathematical Soc.
Page : 562 pages
File Size : 20,71 MB
Release : 2000
Category : Mathematics
ISBN : 0821808818
This is the second of two volumes on foliations (the first is Volume 23 of this series). In this volume, three specialized topics are treated: analysis on foliated spaces, characteristic classes of foliations, and foliated three-manifolds. Each of these topics represents deep interaction between foliation theory and another highly developed area of mathematics. In each case, the goal is to provide students and other interested people with a substantial introduction to the topic leading to further study using the extensive available literature.
Author : Robert Plato
Publisher : American Mathematical Soc.
Page : 476 pages
File Size : 14,31 MB
Release : 2003
Category : Mathematics
ISBN : 9780821834145
"The book is suitable as a text for a first course in numerical methods for mathematics students or students in neighboring fields, such as engineering, physics, and computer science. In general, the author assumes only a knowledge of calculus and linear algebra."--BOOK JACKET.
Author : Hans Niels Jahnke
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 37,70 MB
Release : 2003
Category : Mathematics
ISBN : 0821826239
Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics, and one treats the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.
Author : United States. Congress. Senate. Committee on Appropriations. Subcommittee on Agriculture, Rural Development, and Related Agencies
Publisher :
Page : 854 pages
File Size : 39,56 MB
Release : 2002
Category : Political Science
ISBN :
Author : Peter W. Michor
Publisher : American Mathematical Soc.
Page : 510 pages
File Size : 48,82 MB
Release : 2008
Category : Mathematics
ISBN : 0821820036
"This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.
Author : Colin John Campbell
Publisher : multi-science publishing
Page : 428 pages
File Size : 15,50 MB
Release : 2005
Category : Business & Economics
ISBN : 9780906522394
"Colin Campbell is renowned for his lucid earlier work, 'The coming oil crisis'. Eight years on, events have proved his analysis right. Now, he argues that the oil crisis has come. The familiar technical explanation of the crisis is carefully made again : essentially, that there is no more oil to be found. That fact is beginning to manifest itself in heightened competition for the remaining resource ; which is why America invaded Iraq ; why Central Asia is in turmoil ; why oil is persistently priced above $50/barrel (and why Goldman Sachs think $100 a barrel is not too unlikely in the near future). The problem - of an oil-less world - is beyond the grasp of politicians. They can fiddle with ideas about renewables or hydrogen but they, along with most of humanity, have not really grasped that it is the oil economy that enables about a 7 billion world population to be sustained. A wholly new world is imminent. It is not likely to be very pleasant. Dr Campbell outlines our grim future." -- book cover.
