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The Mathematics Teacher, 1946
During the past four or five years volumes have been written on the reasons for adding general mathematics to the curriculum. Much has been written in general terms on the content of such courses. We are making little progress. We have had years of war with its emphasis on the need for mathematics but relatively little of a fundamental nature has been ...
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During the past four or five years volumes have been written on the reasons for adding general mathematics to the curriculum. Much has been written in general terms on the content of such courses. We are making little progress. We have had years of war with its emphasis on the need for mathematics but relatively little of a fundamental nature has been ...
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Mathematical Generative Models
2021As mentioned in the previous chapter, the second criterion of (Stumpf, Michael P. H. and Porter, Mason A. (2012). Science, 335, 665–666) on the validity of a power law is that there should be a generative process that produces it. A rigorous mathematical methodology for our purposes is to use a generative stochastic process to produce a sequence that ...
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Mathematical Models of Generalized Diffusion
Physica Scripta, 2001Summary: The authors discuss equations describing processes involving nonlinear and higher-order diffusion. They focus on a particular case \((u_t=2\lambda_2(uu_x)_x+\lambda_2u_{xxxx})\), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing ...
Kraenkel, Roberto André +1 more
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Let's Put the Mathematics in General Mathematics
The Mathematics Teacher, 1992As larger numbers of teenagers entered high school early in this century, many of these students were judged not able or willing to take traditional academic mathematics. Thus, a new course was introduced to reinforce the basic-arithmetic skills of this group of students.
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Mathematical General Relativity
2018General Relativity is one of the triumphs of twentieth century physics. Its spectacular predictions include gravitational waves, black holes, and spacetime singularities. The mathematical study of this theory leads to deep problems connecting the areas of partial differential equations, geometry and topology with physics.
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CIRCUMSCRIPTION AND GENERIC MATHEMATICAL OBJECTS
Fundamenta Informaticae, 1994We investigate the possibility of using circumscription for characterizing the concept of a generic object in the context of a formalized mathematical theory. We show that conventional circumscriptive policies do not give the intuitively expected results for elementary geometry, and that there is a common explanation for this failure and the failure of
Bertossi, Leopoldo E., Reiter, Raymond
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Generative Mathematics: Mathematically Described and Calculated Visual Art
Leonardo, 1992One of the main functions of the computer is the graphic display of results. Through the use of the computer, the visualization of mathematical relations can lead to new ways of comprehending mathematics. In addition, the resulting images can be remarkably attractive.
Herbert W. Franke, Horst S. Helbig
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Mathematics Exercise Generator
2020Nowadays, the process of teaching and learning is changing from a traditional model in which teachers were the source of information to a model in which teachers appear as advisors who carefully observe students, assist in the selection of information by identifying their learning needs, and support students in their autonomous study.
Maria Paula Oliveira, Paula Carvalho
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Civic Mathematics: A Real-Life General Mathematics Course
The Mathematics Teacher, 1994Our hopes for education coincide with those for our children: we want to help them grow into adults who will make the world an even better place for future generations. This goal may be a lofty one for a high school mathematics teacher, but it is important to keep our ideals clearly in mind as we develop ways to equip our students to live full lives ...
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