The advent of mathematical software has been one of the most important events in mathematics. Mathematical software systems are used to construct examples, to prove theorems, and to find new mathematical phenomena. On the other hand, mathematical research often motivates developments of new algorithms and new systems.This volume contains the papers presented at the First International Congress of Mathematical Software, which aimed at a coherent study of mathematical software systems from a wide variety of branches of mathematics. The book discusses more than one hundred mathematical software systems. Readers can get an overview of the current status of the arts of mathematical software and algorithms.The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings (ISTP ROM version / ISI Proceedings)Contents: The Experimental Mathematician: A Computational Guide to the Mathematical Unknown (J M Borwein)Computer Algebra and Finite Groups (G-M Greuel & G Pfister)Software Integration and Computer Proofs (M Joswig)LinBox: A Generic Library for Exact Linear Algebra (B D Saunders et al.)An Efficient Modular Algorithm for Computing the Global b-Function (M Noro)D-Modules for Macaulay 2 (A Leykin)Computer Graphics in Mathematical ResearchFrom Helsinki 1978 to Beijing 2002 (T F Banchoff)Making the Move: The Next Version of Cinderella (U Kortenkamp & J Richter-Gebert)Algorithmic Constructions of Elliptic Curves with Complex Multiplication (A Enge)Parallel Implementation of Polyhedral Continuation Methods for Systems of Polynomial Equations (M Kojima et al)Minimal Sets of Critical Pairs (L Robbiano et al)A Study in the Integration of Computer Algebra Systems: Memory Management in a Maple–Aldor Environment (S M Watt)Σit — An Aldor Library for Linear Differential and Difference Equations (M Bronstein)ALLTYPES: An Algebraic Language and TYPE System (F Schwarz)and other papersReadership: Graduate students, researchers and industrialists in numerical and computational mathematics.Key Features:Unique combination of introductory/review material on quantum-dot physics and most advanced research results in this rapidly developing fieldStrong and continuous link between nanodevice fabrication/characterization and theoretical modeling/simulationCohesive and selfcontained treatment of diverse issues related to semiconductor-device physics and nanotechnologyMost of the scientific activity presented in the book is the result of a number of cross-collaborations within a large-scale European Project, thus the volume offers a cohesive perspective on the many research areas involved