Discovering Mathematics with Magma: Reducing the Abstract to the Concrete: 19 (Algorithms and Computation in Mathematics, 19) - Hardcover

Hardcover

ISBN 10: 3540376321 ISBN 13: 9783540376323

Publisher: Springer, 2006

Synopsis

The appearance of this volume celebrates the ?rst decade of Magma, a new computeralgebrasystemlaunchedattheFirstMagmaConferenceonCom- tational Algebra held at Queen Mary and West?eld College, London, August 1993. This book introduces the reader to the role Magma plays in advanced mathematical research. Each paper examines how the computer can be used to gain insight into either a single problem or a small group of closely related problems. The intention is to present su?cient detail so that a reader can (a), gain insight into the mathematical questions that are the origin of the problems,and(b),developanunderstandingastohowsuchcomputations are speci?edinMagma.Itishopedthatthereaderwillcometoarealisationofthe important rolethatcomputational algebracanplayinmathematical research. Readers not primarily interested in using Magma will easily acquire the skills needed to undertake basic programming in Magma, while experienced Magma users can learn both mathematics and advanced computational methods in areas related to their own. The core of the volume comprises 14 papers. The authors were invited to submit articles on designated topics and these articles were then reviewed by referees. Although by no means exhaustive, the topics range over a consid- ablepartofMagma’scoverageofalgorithmicalgebra:fromnumbertheoryand algebraicgeometry,viarepresentationtheoryandcomputationalgrouptheory to some branches of discrete mathematics and graph theory. The papers are preceded by an outline of the Magma project, a brief summary of the papers and some instructions on reading the Magma code. A basic introduction to the Magma language is given in an appendix. Theeditorsexpresstheirgratitudetothecontributorstothisvolume,both for the work put into producing the papers and for theirpatience.

About this title

About the Author

Cannon:

1) Principal designer of the Magma system

2) Extensive contributions to the field of group theory algorithms

3) Awards:

• 1993 CSIRO Medal (for Computer Algebra)
• 2001 ATSE Clunies Ross Award (for Cryptography and Computer Algebra)
• 2006 Richard D. Jenks Memorial Prize for Excellence in Software Engineering Applied to Computer Algebra.

 

Bosma: co-designer of Magma, active in computational number theory and computer algebra

From the Back Cover

This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the reader to the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning new theoretical results. The authors of the chapters were chosen both for their expertise in the particular field and for their innovative use of Magma. Although by no means exhaustive, the topics range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.

Edition details

• Publisher: Springer
• Publication date: 2006
• Language: English
• ISBN 10: 3540376321
• ISBN 13: 9783540376323
• Binding: Hardcover
• Number of pages: 388
• Editor: Bosma Wieb, Cannon John