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Realms: A Structure for Consolidating Knowledge about Mathematical Theories [article]

Jacques Carette, William M. Farmer, Michael Kohlhase
2014 arXiv   pre-print
We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed.  ...  Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics  ...  A realm R of the real numbers could be used to consolidate and organize all the knowledge about the real numbers that resides in a UDLM.  ... 
arXiv:1405.5956v1 fatcat:wl7jhafgcfelziasv6bmunzynq

Realms: A Structure for Consolidating Knowledge about Mathematical Theories [chapter]

Jacques Carette, William M. Farmer, Michael Kohlhase
2014 Lecture Notes in Computer Science  
We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed.  ...  Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics  ...  A realm R of the real numbers could be used to consolidate and organize all the knowledge about the real numbers that resides in a UDLM.  ... 
doi:10.1007/978-3-319-08434-3_19 fatcat:vbuytxhm7ja6farniiuitmmpoa

Practising Mathematics Teacher Education: Expanding The Realm of Possibilities [chapter]

Uwe Gellert, S. Amato, M. Bairral, L. Zanette, I. Bloch, G. Gadanidis, I. Namukasa, G. Krummheuer, B. Grevholm, C. Bergsten, D. Miller, A. Peter-Koop (+5 others)
2009 New ICMI Studies Series  
This is particularly important for "the communication about shape, number and structure in the primary mathematics classroom.  ...  For them, a theorem has to get a proof, but no justification in terms of problem solving, it is seen as a part of a mathematical theory which its own justification."  ... 
doi:10.1007/978-0-387-09601-8_5 fatcat:iw5oonnomvflhi2vsqxy3ilvki

Explorations in the realm of organization theory. IV: The simulation of social organization

Richard L. Meier
2007 Behavioral Science  
IN THE REALM OF ORGANIZATION THEORY.  ...  Some of these models may reflect in great detail a theory about the behavior of their real-life counterparts and be useful for testing hypotheses about its behavior.  ... 
doi:10.1002/bs.3830060308 fatcat:lug5il7slrgclo6ujsgwb2waeq

An Analytical Insight to Investigate the Research Patterns in the Realm of Type-2 Fuzzy Logic

Amita Jain, Devendra Tayal, Oscar Castillo
2018 Journal of Automation, Mobile Robotics & Intelligent Systems  
and also it is consolidating in countries that already have research on type 2.  ...  However, there are limitations and challenges in this area, for example: how to optimally design the structure of the type-2 fuzzy systems, how to find the optimal parameter values for a particular application  ... 
doi:10.14313/jamris_2-2018/8 fatcat:67vugsfh2jcrdmgcihjqjkzlke

Continuities in State–Society Interactions across Broad Spatio-temporal Realms: Gong Tingxian as Both an Author of Popular Medical Texts and an Imperial Medical Secretary in Early Modern China

Sare Aricanli
2022 Social history of medicine  
Moreover, Gong's texts were not only transmitted in China, but reached Japan and Korea, and even found a place within a European collection by the early eighteenth century.  ...  These continuities crossed political, linguistic and cultural lines as Gong's popular texts were translated to Manchu and housed in a state medical library of the ensuing dynasty.  ...  Chinese Medicine in Comparative Perspective', colleagues from the Durham University History Department reading group, as well as Professor Yu Xinzhong, Dr Martina Siebert, and the anonymous reviewers for  ... 
doi:10.1093/shm/hkab036 pmid:35264907 pmcid:PMC8902002 fatcat:pih2oqyhxfa5heb23ah6yjbgem

In the Realm of Opportunity: The Kaiser Wilhelm Institute for Anthropology, Human Heredity and Eugenics during World War II, 1938/42–1945 [chapter]

2008 The Kaiser Wilhelm Institute for Anthropology, Human Heredity, and Eugenics, 1927–1945  
of the KWI-A into the second half of the 1930s, twin research had the function of a scientific paradigm for the institute, providing an ensemble of axioms and premises, concepts, theories and models,  ...  The point is to fill in the quite significant gaps and deepen our knowledge.  ...  Hillmann [Günther Hillmann (1919-1976)], a staff member of the Kaiser Wilhelm Institute for Biochemistry. Dr. Hillmann is a biochemical specialist for protein research.  ... 
doi:10.1007/978-1-4020-6600-9_5 fatcat:z4lelstryvg2jlikklbfvkx3yi

On the Science of Embodied Cognition in the 2010s: Research Questions, Appropriate Reductionism, and Testable Explanations

Rafael Núñez
2012 The Journal of the Learning Sciences  
Journal of the Learning Sciences Publication details, including instructions for authors and subscription information:  ...  the conditions for a testable theory of the mind.  ...  Many of the claims about embodied mathematical cognition in Where Mathematics Comes From remain theoretically plausible but for the moment empirically untested.  ... 
doi:10.1080/10508406.2011.614325 fatcat:3yruu5qegnav3fslujcrqk2tra

Probabilistic Knowledge as Objective Knowledge in Quantum Mechanics: Potential Powers Instead of Actual Properties [article]

Christian de Ronde
2016 arXiv   pre-print
We propose instead a metaphysical scheme in terms of powers with definite potentia which allows us to consider quantum probability in a new light, namely, as providing objective knowledge about a potential  ...  In classical physics, probabilistic or statistical knowledge has been always related to ignorance or inaccurate subjective knowledge about an actual state of affairs.  ...  Graffigna for a careful reading of previous versions of this manuscript. Their many insightful comments and suggestions have been valuable for revising and improving our manuscript.  ... 
arXiv:1506.07378v2 fatcat:faigaf7rxjdqfdvy2rny6vjs2y

Theory usage and theoretical trends in Europe: a survey and preliminary analysis of CERME4 research reports

Bharath Sriraman, Gabriele Kaiser
2006 ZDM: Mathematics Education  
In order to convey trends in theory usage in Europe we compile, survey and analyze a large subset of the research papers from the 4 th European Congress on Mathematics Education (CERME4).  ...  The 29th PME research forum on theories included only one European perspective on mathematics education.  ...  While the notions of Skemp and Hiebert were invoked to argue for a consolidation and the linking of new ideas with prior ones, there was no evidence of attempts to inform current theories on how structural  ... 
doi:10.1007/s11858-007-0056-x fatcat:rdte2ji235gmpe3vm5ve4kqgd4

Cognitive Structures of the Gifted: Theoretical Perspectives, Factor Analysis, Triarchic Theories of Intelligence, and Insight Issues

Michael F. Shaughnessy
1990 Gifted Education International  
Summary and Conclusion Drawing upon a number of realms, the present paper has endeavored to investigate the cognitive structures of the gifted and his proposed a six realm domain for the understanding  ...  Thus, the "gifted child" is better able to cope with divergent tasks and acquires knowledge more rapidly, both in the word realm (vocabulary) and in the world realm (general informa- tion and world knowledge  ... 
doi:10.1177/026142949000600305 fatcat:gtsfx2mhq5grxmj6m4w4jj2sr4

Characteristic features of relationships between intelligence and imagination in the synthesis of conceptualized forms of knowledge

Andrey Kuznetsov, Alexander Zhikharev, Olga Kurganskaya, Alina Kuznetsova, B. Yazyev
2019 SHS Web of Conferences  
Two fundamental capacities of the subject that accomplish a constructive function in conceptualization of theoretical forms of knowledge are distinguished.  ...  distinct structure comprising the previous findings as fundamental constructs.  ...  While the main task for a scientist consists in acquisition of the true knowledge about an object, for a "methodologist it is the knowledge of linguistic reconstruction, organizing scientific knowledge  ... 
doi:10.1051/shsconf/20197201020 fatcat:73wwzc27n5b2hn6m2oh5c6opyu

The Big Other and Sentimentalism: A Sexual Critique of Mathematics, Its Education, and the Disavowed Fetish of Technology

Alexander S. Moore
2022 Zenodo  
Mathematics functions as a particularly egregious agent of this mechanism because, in late capitalism, mathematics occupies the position of l'Autre (the Big Other), the nonexistent Symbolic position that  ...  In this paper, I use Lacanian psychoanalytic theory to first introduce and develop the notion of the psychotic position of mathematics and its connection to Lacan's maxim, "There is no sexual relationship  ...  Because of its synthetic nature, humans engaged in mathematics do not experience it as a psychosis that structures their entire existence, for other parts of their knowledge and life are not subjected  ... 
doi:10.5281/zenodo.6385155 fatcat:ir2jugfx7val3b2mbxkvirqfy4

Introduction [chapter]

James B. Glattfelder
2019 Zum Performativen des frühen Dialogs  
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material.  ...  which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a  ...  For string theory to be mathematically consistent, it requires esoteric postulations about the nature of reality.  ... 
doi:10.1007/978-3-030-03633-1_1 fatcat:anej4bw4kfe3payq6zwirak3t4

Exploring Selected Theories Applicable to Educational Disciplines and Social Sciences Research

2019 International Journal of Humanities Social Sciences and Education  
The article concludes that there is a lot of room for theoretical mapping of educational research efforts.  ...  The authors conducted a search on academic institutional repositories for dissertations, theses and research papers across the globe.  ...  In the educational realm, research is widely recognized as playing a critical role in discovering knowledge, testing hypotheses and uncovering new relationships, associations or causal imperatives about  ... 
doi:10.20431/2349-0381.0612008 fatcat:mdqwlyytzjdw5e3mrpgpz6qvpe
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