Selected Topics In Geometry With Classical Vs. Computer Proving PDF Download

Author: Pavel Pech
Publisher: World Scientific Publishing Company
ISBN: 9813107030
Category : Mathematics
Languages : en
Pages : 252

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Book Description
This textbook presents various automatic techniques based on Gröbner bases elimination to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects — which cannot be easily done with a ruler and compass.Each problem is firstly solved by an automatic theorem proving method. Secondly, problems are solved classically — without using computer where possible — so that readers can compare the strengths and weaknesses of both approaches.

Author: Pavel Pech
Publisher: World Scientific
ISBN: 9812709428
Category : Mathematics
Languages : en
Pages : 252

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Book Description
This textbook presents various automatic techniques based on Gr”bner bases elimination to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects ? which cannot be easily done with a ruler and compass.Each problem is firstly solved by an automatic theorem proving method. Secondly, problems are solved classically ? without using computer where possible ? so that readers can compare the strengths and weaknesses of both approaches.

Author: Vladimir P. Gerdt
Publisher: Springer
ISBN: 3319022970
Category : Computers
Languages : en
Pages : 457

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Book Description
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.

Author: Beniamino Murgante
Publisher: Springer
ISBN: 3642218989
Category : Computers
Languages : en
Pages : 712

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Book Description
The five-volume set LNCS 6782 - 6786 constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2011, held in Santander, Spain, in June 2011. The five volumes contain papers presenting a wealth of original research results in the field of computational science, from foundational issues in computer science and mathematics to advanced applications in virtually all sciences making use of computational techniques. The topics of the fully refereed papers are structured according to the five major conference themes: geographical analysis, urban modeling, spatial statistics; cities, technologies and planning; computational geometry and applications; computer aided modeling, simulation, and analysis; and mobile communications.

Author: Ulrich Langer
Publisher: Springer Science & Business Media
ISBN: 3709107946
Category : Mathematics
Languages : en
Pages : 361

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Book Description
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.

Author: Pascal Schreck
Publisher: Springer Science & Business Media
ISBN: 3642250696
Category : Computers
Languages : en
Pages : 268

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Book Description
This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on Automated Deduction in Geometry, ADG 2010, held in Munich, Germany in July 2010. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement from the lectures given at the workshop. Topics addressed by the papers are incidence geometry using some kind of combinatoric argument; computer algebra; software implementation; as well as logic and proof assistants.

Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 0387255303
Category : Mathematics
Languages : en
Pages : 240

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Book Description
This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises

Author: Dana Ferguson
Publisher: Book Review Index Cumulation
ISBN: 9781414419121
Category : Language Arts & Disciplines
Languages : en
Pages : 1304

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Book Description
Book Review Index provides quick access to reviews of books, periodicals, books on tape and electronic media representing a wide range of popular, academic and professional interests. The up-to-date coverage, wide scope and inclusion of citations for both newly published and older materials make Book Review Index an exceptionally useful reference tool. More than 600 publications are indexed, including journals and national general interest publications and newspapers. Book Review Index is available in a three-issue subscription covering the current year or as an annual cumulation covering the past year.

Author: Arthur Baragar
Publisher: Pearson
ISBN:
Category : Mathematics
Languages : en
Pages : 392

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Book Description
This book emphasizes the beauty of geometry using a modern approach. Models & computer exercises help readers to cultivate geometric intuition. Topics include Euclidean Geometry, Hand Constructions, Geometer's Sketch Pad, Hyperbolic Geometry, Tilings & Lattices, Spherical Geometry, Projective Geometry, Finite Geometry, and Modern Geometry Research. Ideal for geometry at an intermediate level.

Author: Joel David Hamkins
Publisher: MIT Press
ISBN: 0262542234
Category : Mathematics
Languages : en
Pages : 350

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Book Description
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.