Download or read book Mechanical Geometry Theorem Proving written by Shang-Ching Chou and published by Springer. This book was released on 2001-11-30 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Download or read book Mechanical Theorem Proving in Geometries written by Wen-tsün Wu and published by Springer Science & Business Media. This book was released on 1994-04-14 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of Professor Wu’s seminal Chinese book of 1984 on Automated Geometric Theorem Proving. The translation was done by his former student Dongming Wang jointly with Xiaofan Jin so that authenticity is guaranteed. Meanwhile, automated geometric theorem proving based on Wu’s method of characteristic sets has become one of the fundamental, practically successful, methods in this area that has drastically enhanced the scope of what is computationally tractable in automated theorem proving. This book is a source book for students and researchers who want to study both the intuitive first ideas behind the method and the formal details together with many examples.
Download or read book Machine Proofs in Geometry written by Shang-Ching Chou and published by World Scientific. This book was released on 1994 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.
Download or read book Mechanical Theorem Proving in Geometries written by Wen-tsün Wu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: There seems to be no doubt that geometry originates from such practical activ ities as weather observation and terrain survey. But there are different manners, methods, and ways to raise the various experiences to the level of theory so that they finally constitute a science. F. Engels said, "The objective of mathematics is the study of space forms and quantitative relations of the real world. " Dur ing the time of the ancient Greeks, there were two different methods dealing with geometry: one, represented by the Euclid's "Elements," purely pursued the logical relations among geometric entities, excluding completely the quantita tive relations, as to establish the axiom system of geometry. This method has become a model of deduction methods in mathematics. The other, represented by the relevant work of Archimedes, focused on the study of quantitative re lations of geometric objects as well as their measures such as the ratio of the circumference of a circle to its diameter and the area of a spherical surface and of a parabolic sector. Though these approaches vary in style, have their own features, and reflect different viewpoints in the development of geometry, both have made great contributions to the development of mathematics. The development of geometry in China was all along concerned with quanti tative relations.
Download or read book Symbolic Logic and Mechanical Theorem Proving written by Chin-Liang Chang and published by Academic Press. This book was released on 2014-06-28 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
Download or read book Proceedings written by and published by . This book was released on 1990 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book How to Prove It written by Daniel J. Velleman and published by Cambridge University Press. This book was released on 2006-01-16 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Download or read book Selected Topics in Geometry with Classical Vs Computer Proving written by Pavel Pech and published by World Scientific. This book was released on 2007 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents various automatic techniques based on Grbner 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.
Download or read book A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton s Principia written by Jacques Fleuriot and published by Springer Science & Business Media. This book was released on 2012-09-30 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sir Isaac Newton's philosophi Naturalis Principia Mathematica'(the Principia) contains a prose-style mixture of geometric and limit reasoning that has often been viewed as logically vague. In A Combination of Geometry Theorem Proving and Nonstandard Analysis, Jacques Fleuriot presents a formalization of Lemmas and Propositions from the Principia using a combination of methods from geometry and nonstandard analysis. The mechanization of the procedures, which respects much of Newton's original reasoning, is developed within the theorem prover Isabelle. The application of this framework to the mechanization of elementary real analysis using nonstandard techniques is also discussed.
Download or read book Mathematics Mechanization written by Wu Wen-tsun and published by Springer. This book was released on 2001-04-30 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of essays centred around the subject of mathematical mechanization. It tries to deal with mathematics in a constructive and algorithmic manner so that reasoning becomes mechanical, automated and less laborious. The book is divided into three parts. Part I concerns historical developments of mathematics mechanization, especially in ancient China. Part II describes the underlying principles of polynomial equation-solving, with polynomial coefficients in fields restricted to the case of characteristic 0. Based on the general principle, some methods of solving such arbitrary polynomial systems may be found. This part also goes back to classical Chinese mathematics as well as treating modern works in this field. Finally, Part III contains applications and examples. Audience: This volume will be of interest to research and applied mathematicians, computer scientists and historians in mathematics.
Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafał Abłamowicz and published by Springer Science & Business Media. This book was released on 2000 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.
Download or read book Automated Deduction in Geometry written by Hoon Hong and published by Springer Science & Business Media. This book was released on 2006-01-25 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 5th International Workshop on Automated Deduction in Geometry, ADG 2004, held at Gainesville, FL, USA in September 2004. The 12 revised full papers presented were carefully selected from the papers accepted for the workshop after careful reviewing. All current issues in the area are addressed - theoretical and methodological topics as well as applications thereof - in particular automated geometry theorem proving, automated geometry problem solving, problems of dynamic geometry, and an object-oriented language for geometric objects.
Download or read book Applications of Geometric Algebra in Computer Science and Engineering written by Leo Dorst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.
Download or read book Learning and Geometry Computational Approaches written by David Kueker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of computational learning theory arose out of the desire to for mally understand the process of learning. As potential applications to artificial intelligence became apparent, the new field grew rapidly. The learning of geo metric objects became a natural area of study. The possibility of using learning techniques to compensate for unsolvability provided an attraction for individ uals with an immediate need to solve such difficult problems. Researchers at the Center for Night Vision were interested in solving the problem of interpreting data produced by a variety of sensors. Current vision techniques, which have a strong geometric component, can be used to extract features. However, these techniques fall short of useful recognition of the sensed objects. One potential solution is to incorporate learning techniques into the geometric manipulation of sensor data. As a first step toward realizing such a solution, the Systems Research Center at the University of Maryland, in conjunction with the Center for Night Vision, hosted a Workshop on Learning and Geometry in January of 1991. Scholars in both fields came together to learn about each others' field and to look for common ground, with the ultimate goal of providing a new model of learning from geometrical examples that would be useful in computer vision. The papers in the volume are a partial record of that meeting.
Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Download or read book Automated Deduction in Geometry written by Franz Winkler and published by Springer. This book was released on 2004-05-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Automated Deduction in Geometry, ADG 2002, held at Hagenberg Castle, Austria in September 2002. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement. Among the issues addressed are theoretical and methodological topics, such as the resolution of singularities, algebraic geometry and computer algebra; various geometric theorem proving systems are explored; and applications of automated deduction in geometry are demonstrated in fields like computer-aided design and robotics.
Download or read book Algebraic Techniques written by Hassan Aït-Kaci and published by Academic Press. This book was released on 2014-05-10 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Resolution of Equations in Algebraic Structures: Volume 1, Algebraic Techniques is a collection of papers from the "Colloquium on Resolution of Equations in Algebraic Structures" held in Texas in May 1987. The papers discuss equations and algebraic structures relevant to symbolic computation and to the foundation of programming. One paper discusses the complete lattice of simulation congruences associated with the ground atomic theory of hierarchical specification, retrieving as the lattice's maximum element Milner's strong bisimulation for CCS. Another paper explains algebraic recognizability of subsets of free T-algebras, or equational theories, and covers discrete structures like those of words, terms, finite trees, and finite graphs. One paper proposes a general theory of unification using a category theoretic framework for various substitution systems including classical unification, E-unification, and order-sorted unification. Another paper shows the universality of algebraic equations in computer science. Fixpoint theorems in ordered algebraic structures can be applied in computer science. These theorems, or their variations, include semantics and proof theory, logic programming, as well as efficient strategies for answering recursive queries in deductive data bases. The collection is suitable for programmers, mathematicians, students, and instructors involved in computer science and computer technology.
