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For instance, classical mathematicians by definition rely on Plato's theory of forms as the underlying basis of their mathematical worldview. The Platonist assumes the existence of true, immutable, and universal forms and structures that the mathematician approaches through the language of numbers and equations. For instance, the classical mathematician holds to the Platonic belief in the expansion of pi; to approach the expansion of pi from any other perspective "would require a restructuring of all of mathematical analysis," (p. 414). The paradigm would have to change; a most likely candidate for the restructured mathematical analysis would be constructivism, which relies more exclusively on the number system. The very existence of varied paradigms in mathematics points to the essentially "soft" core underlying all mathematical pursuits.
Finally, the growth of mathematics depends partly on the evolution of technology as well as the evolution of thinking. Paper and pencil has largely given way...
Yet many mathematicians criticize the dependency on computers to generate complex strings or to approximate answers. Computer hardware and software are not infallible. Yet human reason is also fallible (p. 418). Appel & Haken's proof of the four color conjecture relied on computers some mathematicians note that the use of the computer undermined its rigor (p. 425).
Mathematics changes as the overall body of human knowledge changes, via continual questioning and the revisiting of old ideas. Mathematics changes through evolution of technology, the evolution of paradigm, and the temporal evolution of mathematical ideas. In each case, mathematics changes by a continual transformation of soft knowledge such as intuition into hard knowledge such as a proof or theory. An idea need not be proven formally to become working knowledge. In time, however, proof becomes possible as mathematicians can avail themselves of new technologies or ways…
achievement of a teaching task. Despite of the different approach that teachers and instructors used, there is a part in teaching that allows the learners to gain knowledge, or better, to gain skills. The different methods of teaching, since the past years up to the present times, have shown and demonstrated their respective means of imparting knowledge. Each method provides ways of capturing the abilities of the learners, as well
mathematics curricula and takes a broader look at the use of Internet technology in mathematical learning. The aim of this paper is to explain the position that the Internet is on the brink to play in sustaining inquiry-based mathematical classrooms, as well as to caution educators away from guidelines that have established unprofitable. The paper begins by unfolding wide themes that have surfaced from the work in relation to
This therefore renders the bifurcation point instability null and void for the cable strayed as well as suspension bridges (Ren,1999). Cheng, Jiang, Xiao and Xiang (2001) pointed out that in theory, the analysis of the aerostatic stability of such kinds of bridges should be regarded as a limit point instability challenge. In their paper, which is based on the limit point instability concept; Cheng, Jiang, Xiao and Xiang (2001)
Macroeconomics Factors that lead to Growth There are several factors that lead to economic growth. They are physical capital, human capital, natural capital and technological change. Physical capital refers to the infrastructure that a nation has, for example transportation and communication infrastructure, and manufacturing capacity. Human capital refers to the number of people, and their skill level. Natural capital reflects natural resources that can be exploited. Technological change reflects the increases in
Null Hypothesis and an Alternate Hypothesis Hypothesizing in business assists leadership in deciding which avenue to take for the overall health of the organization. This is done by allowing the business managers to make decisions after having full research. Business leaders have had to employ hypothesizing to facilitate the implementation of right decisions in their lines of duty. This is an important process because organizations are made or destroyed by the
structure the research, to show how all of the major parts of the research project -- the samples or groups, measures, treatments or programs, and methods of assignment -- work together to try to address the central research. Creating an effective research design is likely to be one of the most difficult and eminently useful tasks in drafting a proposal. An effective research design links abstract and stylized concepts