Mathematics And Plausible Reasoning V1 2
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Mathematics And Plausible Reasoning V1 2
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Author : George Polya
language : en
Publisher:
Release Date : 2012-07-01
Mathematics And Plausible Reasoning V1 2 written by George Polya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-01 with Analogy categories.
Artificial Mathematical Intelligence
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Author : Danny A. J. Gómez Ramírez
language : en
Publisher: Springer Nature
Release Date : 2020-10-23
Artificial Mathematical Intelligence written by Danny A. J. Gómez Ramírez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-23 with Mathematics categories.
This volume discusses the theoretical foundations of a new inter- and intra-disciplinary meta-research discipline, which can be succinctly called cognitive metamathematics, with the ultimate goal of achieving a global instance of concrete Artificial Mathematical Intelligence (AMI). In other words, AMI looks for the construction of an (ideal) global artificial agent being able to (co-)solve interactively formal problems with a conceptual mathematical description in a human-style way. It first gives formal guidelines from the philosophical, logical, meta-mathematical, cognitive, and computational points of view supporting the formal existence of such a global AMI framework, examining how much of current mathematics can be completely generated by an interactive computer program and how close we are to constructing a machine that would be able to simulate the way a modern working mathematician handles solvable mathematical conjectures from a conceptual point of view. The thesis that it is possible to meta-model the intellectual job of a working mathematician is heuristically supported by the computational theory of mind, which posits that the mind is in fact a computational system, and by the meta-fact that genuine mathematical proofs are, in principle, algorithmically verifiable, at least theoretically. The introduction to this volume provides then the grounding multifaceted principles of cognitive metamathematics, and, at the same time gives an overview of some of the most outstanding results in this direction, keeping in mind that the main focus is human-style proofs, and not simply formal verification. The first part of the book presents the new cognitive foundations of mathematics’ program dealing with the construction of formal refinements of seminal (meta-)mathematical notions and facts. The second develops positions and formalizations of a global taxonomy of classic and new cognitive abilities, and computational tools allowing for calculation of formal conceptual blends are described. In particular, a new cognitive characterization of the Church-Turing Thesis is presented. In the last part, classic and new results concerning the co-generation of a vast amount of old and new mathematical concepts and the key parts of several standard proofs in Hilbert-style deductive systems are shown as well, filling explicitly a well-known gap in the mechanization of mathematics concerning artificial conceptual generation.
Automated Theory Formation In Pure Mathematics
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Author : Simon Colton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Automated Theory Formation In Pure Mathematics written by Simon Colton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.
The Stanford Mathematics Problem Book
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Author : George Polya
language : en
Publisher: Courier Corporation
Release Date : 2013-04-09
The Stanford Mathematics Problem Book written by George Polya and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.
Nurturing Reflective Learners In Mathematics
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Author : Berinderjeet Kaur
language : en
Publisher: World Scientific
Release Date : 2013
Nurturing Reflective Learners In Mathematics written by Berinderjeet Kaur and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This annual volume focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reflection among students and teachers in mathematics classrooms. Published jointly with the Association of Mathematics Educators in Singapore.
The Mathematics Curriculum 9 12
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Author : Donald L. Chambers
language : en
Publisher:
Release Date : 1980
The Mathematics Curriculum 9 12 written by Donald L. Chambers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Crc Concise Encyclopedia Of Mathematics
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Author : Eric W. Weisstein
language : en
Publisher: CRC Press
Release Date : 2002-12-12
Crc Concise Encyclopedia Of Mathematics written by Eric W. Weisstein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-12 with Mathematics categories.
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Mathematics And Plausible Reasoning 2 Patterns Of Plausible Inference
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Author : George Pólya
language : en
Publisher:
Release Date : 1954
Mathematics And Plausible Reasoning 2 Patterns Of Plausible Inference written by George Pólya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Logic, Symbolic and mathematical categories.
A New Automatic Processing Technique For Satellite Imagery Analysis
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Author : R. S. Hawkins
language : en
Publisher:
Release Date : 1977
A New Automatic Processing Technique For Satellite Imagery Analysis written by R. S. Hawkins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Image processing categories.
A new approach to the analysis of satellite imagery is presented. The central part of this approach is an algorithm which compresses information stored in the ordinary six or eight bits per picture element into only one bit. The quality of this compression is demonstrated by examples of its application to high resolution visual imagery. Both visual inspection and rms difference criterion are used for this evaluation. There are four objectives of this report which are: to review the status of processing techniques which remove redundant information, to show the need for redundance reduction in the processing of satellite images, to present the development of an algorithm for reducing it, and to show results obtained by application of the algorithm to visual imagery. Also, comments are made on needed developments of the technique and its potential application to problems of analysis of satellite imagery data. (Author).
Mathematics In Middle And Secondary School
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Author : Alexander Karp
language : en
Publisher: IAP
Release Date : 2014-11-01
Mathematics In Middle And Secondary School written by Alexander Karp and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-01 with Education categories.
The experience and knowledge acquired in teacher education courses should build important fundamentals for the future teaching of mathematics. In particular, experience in mathematical problem solving, and in planning lessons devoted to problem solving, is an essential component of teacher preparation. This book develops a problem solving approach and is intended to be a text used in mathematics education courses (or professional development) for pre-service or in-service middle and secondary school teachers. It can be used both in graduate and undergraduate courses, in accordance with the focus of teacher preparation programs. The content of the book is suited especially for those students who are further along in their mathematics education preparation, as the text is more involved with mathematical ideas and problem solving, and discusses some of the intricate pedagogical considerations that arise in teaching. The text is written not as an introduction to mathematics education (a first course), but rather as a second, or probably, third course. The book deals both with general methodology issues in mathematics education incorporating a problem solving approach (Chapters 1-6) and with more concrete applications within the context of specific topics – algebra, geometry, and discrete mathematics (Chapters 7-13). The book provides opportunities for teachers to engage in authentic mathematical thinking. The mathematical ideas under consideration build on specific middle and secondary school content while simultaneously pushing the teacher to consider more advanced topics, as well as various connections across mathematical domains. The book strives to preserve the spirit of discussion, and at times even argument, typical of collaborative work on a lesson plan. Based on the accumulated experience of work with future and current teachers, the book assumes that students have some background in lesson planning, and extends their thinking further. Specifically, this book aims to provide a discussion of how a lesson plan is constructed, including the ways in which problems are selected or invented, rather than the compilation of prepared lesson plans. This approach reflects the authors’ view that the process of searching for an answer is often more important than the formal result.