The book covers various topics of computer algebra methods, algorithms and software applied to scientific computing. An important topic presented in the book, which may be of interest to researchers and engineers, is the application of computer algebra methods to the development of new efficient analytic and numerical solvers, both for ordinary and partial differential equations. A specific feature of the book is an intense use of advanced software systems such as Mathematica, Maple etc. for the solution of problems as outlined above and for the industrial application of computer algebra for simulation. The book will be useful for researchers and engineers who apply advanced computer algebra methods for the solution of their problems.

The vast area of Scientific Computing, which is concerned with the computer- aided simulation of various processes in engineering, natural, economical, or social sciences, now enjoys rapid progress owing to the development of new efficient symbolic, numeric, and symbolic/numeric algorithms. There has already been for a long time a worldwide recognition of the fact that the mathematical term algorithm takes its origin from the Latin word algo- ritmi, which is in turn a Latin transliteration of the Arab name "AI Khoresmi" of the Khoresmian mathematician Moukhammad Khoresmi, who lived in the Khoresm khanate during the years 780 - 850. The Khoresm khanate took sig- nificant parts of the territories of present-day TUrkmenistan and Uzbekistan. Such towns of the Khoresm khanate as Bukhara and Marakanda (the present- day Samarkand) were the centers of mathematical science and astronomy. The great Khoresmian mathematician M. Khoresmi introduced the Indian decimal positional system into everyday's life; this system is based on using the famil- iar digits 1,2,3,4,5,6,7,8,9,0. M. Khoresmi had presented the arithmetic in the decimal positional calculus (prior to him, the Indian positional system was the subject only for jokes and witty disputes). Khoresmi's Book of Addition and Subtraction by Indian Method (Arithmetic) differs little from present-day arith- metic. This book was translated into Latin in 1150; the last reprint was produced in Rome in 1957.

This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book.

The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.

CASC 2001 continues a tradition ~ started in 1998 ~ of international con ferences on the latest advances in the application of computer algebra systems to the solution of various problems in scientific computing. The three ear (CASs) lier conferences in this sequence, CASC'98, CASC'99, and CASC 2000, were held, Petersburg, Russia, in Munich, Germany, and in Samarkand, respectively, in St. Uzbekistan, and proved to be very successful. We have to thank the program committee, listed overleaf, for a tremendous job in soliciting and providing reviews for the submitted papers. There were more than three reviews per submission on average. The result of this job is reflected in the present volume, which contains revised versions of the accepted papers. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scientific computing. In particular, five papers are devoted to the implementation of the analysis of involutive systems with the aid of CASso The specific examples include new efficient algorithms for the computation of Janet bases for monomial ideals, involutive division, involutive reduction method, etc. A number of papers deal with application of CASs for obtaining and vali dating new exact solutions to initial and boundary value problems for partial differential equations in mathematical physics. Several papers show how CASs can be used to obtain analytic solutions of initial and boundary value problems for ordinary differential equations and for studying their properties.

This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2012, held in Maribor, Slovenia, in September 2012. The 28 full papers presented were carefully reviewed and selected for inclusion in this book. One of the main themes of the CASC workshop series, namely polynomial algebra, is represented by contributions devoted to new algorithms for computing comprehensive Groebner and involutive systems, parallelization of the Groebner bases computation, the study of quasi-stable polynomial ideals, new algorithms to compute the Jacobson form of a matrix of Ore polynomials, a recursive Leverrier algorithm for inversion of dense matrices whose entries are monic polynomials, root isolation of zero-dimensional triangular polynomial systems, optimal computation of the third power of a long integer, investigation of the complexity of solving systems with few independent monomials, the study of ill-conditioned polynomial systems, a method for polynomial root-finding via eigen-solving and randomization, an algorithm for fast dense polynomial multiplication with Java using the new opaque typed method, and sparse polynomial powering using heaps.

In recent years, IT application scenarios have evolved in very innovative ways. Highly distributed networks have now become a common platform for large-scale distributed programming, high bandwidth communications are inexpensive and widespread, and most of our work tools are equipped with processors enabling us to perform a multitude of tasks. In addition, mobile computing (referring specifically to wireless devices and, more broadly, to dynamically configured systems) has made it possible to exploit interaction in novel ways. To harness the flexibility and power of these rapidly evolving, interactive systems, there is need of radically new foundational ideas and principles; there is need to develop the theoretical foundations required to design these systems and to cope with the many complex issues involved in their construction; and there is need to develop effective principles for building and analyzing such systems.

Reflecting the diverse and wide spectrum of topics and interests within the theoretical computer science community, Exploring New Frontiers of Theoretical Informatics, is presented in two distinct but interrelated tracks:

-Algorithms, Complexity and Models of Computation,
-Logic, Semantics, Specification and Verification.

Exploring New Frontiers of Theoretical Informatics contains 46 original and significant contributions addressing these foundational questions, as well as 4 papers by outstanding invited speakers. These papers were presented at the 3rd IFIP International Conference on Theoretical Computer Science (TCS 2004), which was held in conjunction with the 18th World Computer Congress in Toulouse, France in August 2004 and sponsored by the International Federation for Information Processing (IFIP).

This book constitutes the refereed proceedings of the 13th International Workshop on Computer Algebra in Scientific Computing, CASC 2011, held in Kassel, Germany, in September 2011. The 26 full papers included in the book were carefully reviewed and selected from numerous submissions. The articles are organized in topical sections on the development of object oriented computer algebra software for the modeling of algebraic structures as typed objects; matrix algorithms; the investigation with the aid of computer algebra; the development of symbolic-numerical algorithms; and the application of symbolic computations in applied problems of physics, mechanics, social science, and engineering.

This book constitutes the refereed proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing, CASC 2009, held in Kobe, Japan, in September 2009.

The 28 revised full papers presented together with 2 invited lectures were carefully reviewed and selected from numerous submissions. The topics addressed are all basic areas of scientific computing as they benefit from the application of computer algebra methods and software. The papers cover computer algebra methods and algorithms, application of symbolic and algebraic manipulation, and CA methods and results for the numerical integration of the partial differential equations of the mathematical physics.

CASC 2005 continued a tradition - started in 1998 - of international c- ferences on the latest advances in the application of computer algebra systems (CASs) and methods to the solution of various problems in scienti?c computing. The methods of scienti?c computing play an important role in research and engineering applications in the natural and the engineering sciences. The sign- icance and impact of computer algebra methods and computer algebra systems for scienti?c computing has increased considerably in recent times. Nowadays, suchgeneral-purposecomputeralgebrasystemsasMaple, Magma, Mathematica, MuPAD, Singular, CoCoA and others enable their users to solve the following three important tasks within a uniform framework: (a) symbolic manipulation; (b) numerical computation; (c) visualization. The ongoing development of such systems, including their integrationand ad- tation to modern software environments, puts them at the forefront in scienti?c computing and enables the practicalsolution of many complex applied problems in the domains of natural sciences and engineering. Greece o?ers excellent infrastructures for hosting international conferences, and this was a reason for us to choose the city of Kalamata, Greece, as the lo- tion for CASC 2005, the eighth conference in the sequenceof CASC conferences. The seven earlier CASC conferences, CASC 1998, CASC 1999, CASC 2000, CASC 2001, CASC 2002, CASC 2003, and CASC 2004 were held, respectively, in St. Petersburg, Russia, in Munich, Germany, in Samarkand, Uzbekistan, in Konstanz, Germany, in the Crimea (Ukraine), in Passau (Germany), and in St. Petersburg, Russia, and they proved to be successf

During the last few years, we have seen quite spectacular progress in the area of approximation algorithms: for several fundamental optimization problems we now actually know matching upper and lower bounds for their approximability. This textbook-like tutorial is a coherent and essentially self-contained presentation of the enormous recent progress facilitated by the interplay between the theory of probabilistically checkable proofs and aproximation algorithms. The basic concepts, methods, and results are presented in a unified way to provide a smooth introduction for newcomers. These lectures are particularly useful for advanced courses or reading groups on the topic.

This volume presents the proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science (WG '94), held in Herrsching, Germany in June 1994.
The volume contains 32 thoroughly revised papers selected from 66 submissions and provides an up-to-date snapshot of the research performed in the field. The topics addressed are graph grammars, treewidth, special graph classes, algorithms on graphs, broadcasting and architecture, planar graphs and related problems, and special graph problems.

This book presents the proceedings of the 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS 95), held in Munich, Germany in March 1995.
Besides three invited talks, the book contains revised versions of 53 research papers selected from a total of 180 submissions. The contributions address all current aspects of theoretical computer science; they are organized in sections on complexity theory, automata theory, algorithms, logic, theory of parallel computing, communication theory, graph theory and databases, and computational geometry.

This volume constitutes the proceedings of the 11th annual Symposium on Theoretical Aspects of Computer Science (STACS '94), held in Caen, France, February 24-26, 1994. Besides three prominent invited papers, the proceedings contains 60 accepted contributions chosen by the international program committee during a highly competitive reviewing process from a total of 234 submissions for 38 countries. The volume competently represents most areas of theoretical computer science with a certain emphasis on (parallel) algorithms and complexity.

The 18th International Workshop on Graph-Theoretic Concepts in Computer Science (WG '92) was held in Wiesbaden-Naurod, Germany, June 18-20, 1992. Itwas organized by the Department of Computer Science, Johann Wolfgang Goethe University, Frankfurt am Main. Contributions with original results inthe study and application of graph-theoretic concepts in various fields of computer science were solicited, and 72 papers were submitted and reviewed, from which 29 were selected for presentation at the workshop. The workshop was attended by 61 scientists from 16 countries. All 29 papers in the volume have undergone careful revision after the meeting, based on the discussions and comments from the audience and the referees. The volume is divided into parts on restricted graph classes, scheduling and related problems, parallel anbd distributed algorithms, combinatorial graph problems, graph decomposition, graph grammars and geometry, and modelling by graphs.

This book constitutes revised selected papers from the 41st International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2015, held in Garching, Germany, in June 2015. The 32 papers presented in this volume were carefully reviewed and selected from 79 submissions. They were organized in topical sections named: invited talks; computational complexity; design and analysis; computational geometry; structural graph theory; graph drawing; and fixed parameter tractability.

The development of powerful computer algebra systems has considerably ex tended the scope of problems of scientific computing which can now be solved successfully with the aid of computers. However, as the field of applications of computer algebra in scientific computing becomes broader and more complex, there is a danger of separation between theory, systems, and applications. For this reason, we felt the need to bring together the researchers who now ap ply the tools of computer algebra for the solution of problems in scientific computing, in order to foster new and closer interactions. CASC'99 is the second conference devoted to applications of computer al gebra in scientific computing. The first conference in this sequence, CASC'98, was held 20-24 April 1998 in St. Petersburg, Russia. This volume contains revised versions of the papers submitted by the par ticipants and accepted by the program committee after a thorough reviewing process. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scien tific computing: symbolic-numeric analysis and solving differential equations, efficient computations with polynomials, groups, matrices and other related objects, special purpose programming environments, application to physics, mechanics, optics and to other areas. In particular, a significant group of papers deals with applications of com puter algebra methods for the solution of current problems in group theory, which mostly arise in mathematical physics."