In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2dimensional surfaces in 3space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.
About John A. Thorpe
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Author  :  John A. Thorpe 
Publisher  :  SpringerVerlag New York Inc. 
Data Published  :  12 October 2011 
ISBN  :  1461261554 
EAN  :  9781461261551 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  256 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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