571 research outputs found
A Primer on the Tools and Concepts of Computable Economics
Computability theory came into being as a result of Hilbert's attempts to meet Brouwer's challenges, from an intuitionistc and constructive standpoint, to formalism as a foundation for mathematical practice. Viewed this way, constructive mathematics should be one vision of computability theory. However, there are fundamental differences between computability theory and constructive mathematics: the Church-Turing thesis is a disciplining criterion in the former and not in the latter; and classical logic - particularly, the law of the excluded middle - is not accepted in the latter but freely invoked in the former, especially in proving universal negative propositions. In Computable Economic an eclectic approach is adopted where the main criterion is numerical content for economic entities. In this sense both the computable and the constructive traditions are freely and indiscriminately invoked and utilised in the formalization of economic entities. Some of the mathematical methods and concepts of computable economics are surveyed in a pedagogical mode. The context is that of a digital economy embedded in an information society
Computability and Algorithmic Complexity in Economics
This is an outline of the origins and development of the way computability theory and algorithmic complexity theory were incorporated into economic and finance theories. We try to place, in the context of the development of computable economics, some of the classics of the subject as well as those that have, from time to time, been credited with having contributed to the advancement of the field. Speculative thoughts on where the frontiers of computable economics are, and how to move towards them, conclude the paper. In a precise sense - both historically and analytically - it would not be an exaggeration to claim that both the origins of computable economics and its frontiers are defined by two classics, both by Banach and Mazur: that one page masterpiece by Banach and Mazur ([5]), built on the foundations of Turing’s own classic, and the unpublished Mazur conjecture of 1928, and its unpublished proof by Banach ([38], ch. 6 & [68], ch. 1, #6). For the undisputed original classic of computable economics is Rabinís effectivization of the Gale-Stewart game ([42];[16]); the frontiers, as I see them, are defined by recursive analysis and constructive mathematics, underpinning computability over the computable and constructive reals and providing computable foundations for the economist’s Marshallian penchant for curve-sketching ([9]; [19]; and, in general, the contents of Theoretical Computer Science, Vol. 219, Issue 1-2). The former work has its roots in the Banach-Mazur game (cf. [38], especially p.30), at least in one reading of it; the latter in ([5]), as well as other, earlier, contributions, not least by Brouwer.
Іншомовна компетентність – платформа професійного розвитку в ХХІ столітті : збірник матеріалів ІV Міжнародної науково-практичної студентської конференції для студентів немовних спеціальностей
У збірнику представлені матеріали ІV Міжнародної науково-практичної студентської конференції для студентів немовних спеціальностей, що висвітлюють питання філології, психології, педагогіки, методики викладання іноземних мов, історії, політології, екології, інформатики, менеджменту та економіки.
Для студентів вищих навчальних закладів, аспірантів, наукових та педагогічних працівників
Economics and the Complexity Vision: Chimerical Partners or Elysian Adventurers?
This work began as a review article of: "Complexity and the History of Economic Thought", edited by David Colander, Routledge, London,UK, 2000; & "The Complexity Vision and the Teaching of Economics", edited by David Colander, Edward Elgar, Cheltenham, UK, 2000. It has, in the writing, developed into my own vision of complexity economics
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