1-57146-049-7

0-8218-0828-1

3-7643-5900-5

Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Center de Recerca Mathematica in Bellaterra organized the Summer School on Commutative Algebra 1996. Lecture Series were presented by six high-level specialists, L. Avramov (Purdue), M. K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W. V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research.

3-7643-5951-X

The author set out to present the solution of a problem posed by Wolfgang Krull in 1932. He asked whether what is now called the "Krull-Schmidt Theorem" hold for artinian modules. A negative answer was published only in 1995 by Facchini, Herbera, Levy and Vlmos. Second, the author presents the answer to a question posed Warfieldin 1975, namely, whether the Krull-Schmidt-Theorem holds for serial modules. Facchini published a negative answer in 1966. The solution to the Warfield problem shows an interesting behavior; in fact, it is a phenomena so rare in the history of Krull-Schmidt type theorems that its presentation to a wider mathematical audience provides the third incentive for modules. When it does hold, any two in decomposable decompositions are uniquely determined up to one permutation.

3-7643-5908-0

0-521-64558-1

0-521-57587-7

A coherent modern account of the computational methods used to solve diophantine equations, this book's emphasis is on approaches with wide ranging applications. After a brief introduction, the first section considers basic techniques. The second section explores problems which can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves. Useful exercise and a detailed bibliography are include. Requiring a basic knowledge of number theory, this book will appeal to graduate students and research workers. Oct. 1998 245 pp. 0-521-64156-X/64633-2 13,480./5,040.(Paper ed.)

0-521-62462-2

The notion of solitons arose with the study of partial differential equations at the end of the 19th century. In more recent times their study has involved ideas from other areas of mathematics such as algebraic geometry, topology, and in particular infinite dimensional Lie algebras, and it this approach that is the main theme of this book.

0-521-56161-2

This introduction to classical logic emphasises computational aspects. The authors treat issues of complexity and algorithmic analysis that have traditionally not been considered the realm of mathematical logic, but which are vital in areas such as automated reasoning, knowledge engineering, logic programming and AI. In order to make the book suited for teaching and for self-study, the book includes a systematic account of theoretical results, as well as an exposition of those appropriate algorithms which incorporate them.

0-521-63017-7

3-540-98491-7

3-540-98431-3

Based on a translation of the 6th edition of Gewohnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed. July 1998 375 pp. 3-540-98459-3

3-540-98491-7

3-540-98431-3

Based on a translation of the 6th edition of Gewohnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed. July 1998 375 pp. 3-540-98459-3 11,270.