Computer Algebra In Science And Engineering
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Linear Algebra for Computational Sciences and Engineering
This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory. It is structured to be accessible to everybody, from students of pure mathematics who are approaching algebra for the first time to researchers and graduate students in applied sciences who needa theoretical manual of algebra to successfully perform their research. Most importantly, this book is designed to be ideal for both theoretical and practical minds and to offer to both alternative and complementary perspectives to study and understand linear algebra.
Computer Algebra in Science and Engineering
Systems and tools of computer algebra (Like AXIOM, Derive, FORM, Mathematica, Maple, Mupad, REDUCE, Macsyma...) let us manipulate extremely complex algebraic formulae symbolically on a computer. Contrary to numerics these computations are exact and there is no loss of accuracy. After decades of research and development, these tools are now becoming as indispensable in Science and Engineering as traditional number crunching already is.The ZiF'94 workshop is amongst the first devoted specifically to applications of computer algebra (CA) in Science and Engineering. The book documents the state of the art in this area and serves as an important reference for future work.
Algorithmic Algebra
Author: Bhubaneswar Mishra
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.