Discovering Mathematics With Magma
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Discovering Mathematics with Magma
Author: Wieb Bosma
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-07-10
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.
Mathematical Software - ICMS 2010
This book constitutes the refereed proceedings of the Third International Congress on Mathematical Software, ICMS 2010, held in Kobe, Japan in September 2010. The 49 revised full papers presented were carefully reviewed and selected for presentation. The papers are organized in topical sections on computational group theory, computation of special functions, computer algebra and reliable computing, computer tools for mathematical editing and scientific visualization, exact numeric computation for algebraic and geometric computation, formal proof, geometry and visualization, Groebner bases and applications, number theoretical software as well as software for optimization and polyhedral computation.
Modular Forms: A Classical And Computational Introduction
Author: Lloyd James Peter Kilford
language: en
Publisher: World Scientific
Release Date: 2008-08-11
This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat's last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it.