Lectures On Fundamental Concepts of Algebra And Geometry
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In our eReader you can find the full English version of the book. Read Lectures On Fundamental Concepts of Algebra And Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Lectures On Fundamental Concepts of Algebra And Geometry
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— The real number system of algebra has now been character- ized by two methods. The first, given at the end of Lecture IX, described this number system at one stroke, as it were, by a set of assumptions concerniag the undefined terms, number, <, 4-, X . The other, the discussion of which we have just completed, followed a more historical line of de- velopment, and showed how it was possible to build up this system by successive extensions of the number concept, be- ginning with that of the positive integer. It could now be LECTURE XI 115 shown without serious difficulty that the two characteriza- tions of the real number system which have been given are abstractly equivalent. Bearing on Elementary Teaching. — It will be well now to ask ourselves what bearing this discussion has on the prob- lems of elementary teaching. Should either of these meth- ods be applied in making the pupil, at the first approach to the study of algebra, familiar with its conceptions and its processes ? Should we begin by placing before him a set of assumptions characterizing real algebra, or should we at- tempt to make clear to him the notions involved by succes- sively extending the number system in the way described above ?
What to read after Lectures On Fundamental Concepts of Algebra And Geometry?
You can find similar books in the "Read Also" column, or choose other free books by John Wesley Young to read online
To quickly assess the difficulty of the text, read a short excerpt:
— The real number system of algebra has now been character- ized by two methods. The first, given at the end of Lecture IX, described this number system at one stroke, as it were, by a set of assumptions concerniag the undefined terms, number, <, 4-, X . The other, the discussion of which we have just completed, followed a more historical line of de- velopment, and showed how it was possible to build up this system by successive extensions of the number concept, be- ginning with that of the positive integer. It could now be LECTURE XI 115 shown without serious difficulty that the two characteriza- tions of the real number system which have been given are abstractly equivalent. Bearing on Elementary Teaching. — It will be well now to ask ourselves what bearing this discussion has on the prob- lems of elementary teaching. Should either of these meth- ods be applied in making the pupil, at the first approach to the study of algebra, familiar with its conceptions and its processes ? Should we begin by placing before him a set of assumptions characterizing real algebra, or should we at- tempt to make clear to him the notions involved by succes- sively extending the number system in the way described above ?
What to read after Lectures On Fundamental Concepts of Algebra And Geometry?
You can find similar books in the "Read Also" column, or choose other free books by John Wesley Young to read online
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