Bøger i Algorithms and Computation in Mathematics serien

Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory.

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Groebner bases) and geometry (via quiver theory).

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Groebner bases) and geometry (via quiver theory).

This book is divided into two parts, one theoretical and one focusing on applications, and offers a complete description of the Canonical Groebner Cover, the most accurate algebraic method for discussing parametric polynomial systems.

This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation.

The book deals with algorithmic problems related to binary quadratic forms. It uniquely focuses on the algorithmic aspects of the theory. The book introduces the reader to important areas of number theory such as diophantine equations, reduction theory of quadratic forms, geometry of numbers and algebraic number theory.

Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory.

A number of original research results are contained in the book, and many open problems are raised for future research in this rapidly growing area of computational mathematics.

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications.

Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. One last remark: The last chapter explains the relation between entropy and data compression, which belongs to information theory and not to ergodic theory.

This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry.

Accessible to anyone with a good general background in mathematics, but it nonetheless gets right to the cutting edge of active research. Some results appear here for the first time, while others have hitherto only been given in preprints.

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations.

This text offers an introduction to error-correcting linear codes. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The book is based on the successful German edition.

Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form.

This acclaimed book examines the topic of symbolic integration in comprehensive detail, incorporating new results along the way. The second edition offers a new chapter on parallel integration, and a number of other improvements including additional exercises.

This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity;

This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation.

One of the most remarkable theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. This book develops a new theory which is powerful enough to include all the earlier generalizations. It is also in part an extensive encyclopedia listing the different types of self-dual codes and their properties.

From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. Mathematical Reviews

This comprehensive book covers both long-standing results in the theory of polynomials and recent developments. After initial chapters on the location and separation of roots and on irreducibility criteria, the book covers more specialized polynomials.

A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15].

Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. This accessible book summarizes the present knowledge about the computational properties of Julia sets in a self-contained way.

This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. The main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects.

From the reviews of the 1st edition:"This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds.

Triangulations presents the first comprehensive treatment of the theory of secondary polytopes and related topics. The text discusses the geometric structure behind the algorithms and shows new emerging applications, including hundreds of illustrations, examples, and exercises.

Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics.

This is the third edition of the classic textbook on the subject. With its clear writing, strong organization, and comprehensive coverage of essential theory it is like a personal guide through this important topic, and now has lots of extra material.