Учебное пособие по английскому языку для студентов 2 курса факультета математики и информационных технологий Уфа риц башгу 2020
Reading History of Mathematics (Part II)
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- Mathematics of the Renaissance
- The Transition to Calculus
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History of Mathematics (Part II) Medieval Mathematics The medieval period was a period of great philosophical shifts, not so much on the surface as the Roman Church dominated much of philosophy and all of religion but underneath, the old Aristotelian views began to erode. The rise of the mercantile class required mathematical training. A subculture of mathematicians was needed to train the sons of the wealthy merchants. Mathematics of the Renaissance Following the medieval period, mathematics begins to make formidable advances in the 15th century. Mercantile forces demanded the creation of an exceptionally wealthy class of individuals. To sustain such wealth required an infrastructure that required mathematical education as an important component. The first country to be impacted were the Italians. Unhampered by previous eras of mathematical prohibitions, they freely entered the world of algebra, imprinting it with their own style. Symbolism and the hindu-arabic arithmetic began to take roots, very slowly at first and not at all uniformly. The most profound changes were philosophical. The Copernican revolution toward a heliocentric planetary system meant the destruction of a powerful Greek tradition. The Transition to Calculus The sixteenth and early seventeenth centuries provided the tradition of experience with symbolism that would allow the calculus to flourish. Beginning with Francois Viete, who invented symbolic systems, the mathematicians of this period made great gains on the past. Unfettered by tradition, unhampered by political or economic issues, the mathematicians of this period were able to create a new mathematics into which ideas, not just new results, could be inserted. Mathematicians such as Descartes and Fermat were of such a caliber, that their efforts proved to be the "philosophical" base of mathematics and science whose fruits would be realized only a century later. Mathematicians of the early seventeenth century provided a wealth of analysis infinite and infinitesimal methods, in algebraic methods, and in functional concepts upon which the invention and development of calculus was based. Among the major players were Christian Huygens, Bonaventura Cavalieri, and John Wallis. Most readers of mathematical history are surprised by how much calculus was actually invented before Newton and Leibnitz took their turn. It should be noted that by this time symbolism is well developed and its implications are well under development. With symbols, many expressions take on a compact form that reveal structure such as symmetries and formulas. Moreover, the addition, multiplication and division of polynomials become transparently simple. What Newton and Leibnitz accomplished, both nearly the same, essentially independently, and at the most extreme level, must remain one of the truly remarkable achievements of all time. жүктеу/скачать 0.59 Mb. Достарыңызбен бөлісу:
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