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Algebra --- -Machine theory --- -681.3*I1 --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Logic, Symbolic and mathematical --- Recursive functions --- Robotics --- Mathematics --- Mathematical analysis --- Data processing --- Algebraic manipulation (Computing methodologies) --- Machine theory --- Data processing. --- 681.3*I1 Algebraic manipulation (Computing methodologies) --- 681.3*I1

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This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come. The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director. More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic. Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger’s successor as director of the Research Institute for Symbolic Computation.

Algorithms. --- Computer science -- Mathematics -- Philosophy. --- Computer software. --- Information theory. --- Logic, Symbolic and mathematical. --- Logic. --- Mathematics. --- Mathematics -- Philosophy. --- Engineering & Applied Sciences --- Computer Science --- Software engineering. --- Computer software engineering --- Math --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Communication theory --- Software, Computer --- Algorism --- Computers. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Mathematical Software. --- Software Engineering/Programming and Operating Systems. --- Theory of Computation. --- Engineering --- Science --- Computer systems --- Algebra --- Arithmetic --- Foundations --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Communication --- Cybernetics --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Machine theory --- Calculators --- Cyberspace --- Philosophy.

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The theory of Gröbner bases, invented by Bruno Buchberger, is a general method by which many fundamental problems in various branches of mathematics and engineering can be solved by structurally simple algorithms. The method is now available in all major mathematical software systems. This book provides a short and easy-to-read account of the theory of Gröbner bases and its applications. It is in two parts, the first consisting of tutorial lectures, beginning with a general introduction. The subject is then developed in a further twelve tutorials, written by leading experts, on the application of Gröbner bases in various fields of mathematics. In the second part are seventeen original research papers on Gröbner bases. An appendix contains the English translations of the original German papers of Bruno Buchberger in which Gröbner bases were introduced.

Gröbner bases. --- Coding theory --- Gröbner basis theory --- Commutative algebra --- Geometry, Algebraic --- Géométrie algébrique. --- Algorithms --- Algorithmes. --- Anneaux de polynômes. --- Polynomial rings. --- Algèbres commutatives. --- Polynômes --- Polynomials --- 512.56 --- 512.56 Lattices, including Boolean rings and algebras --- Lattices, including Boolean rings and algebras --- Grobner bases. --- Géométrie algébrique --- Algorithmes --- Anneaux de polynômes. --- Algèbres commutatives. --- Polynômes

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Computer-aided engineering --- Computer-aided design --- Computer-aided engineering - Congresses --- Computer-aided design - Congresses