To Be Presented in the 11th Asian Technology Conference in Mathematics December 1216, 2006, Hong Kong SAR, China 

Reformation Through Merging Higher Algebra and Analytic GeometrySchool of Mathematics and Statistics Southwest University China
AbstractFor undergraduates majoring in mathematics and applied mathematics and even computer science, linear algebra and analytic geometry are two required courses in all Chinese universities and Colleges. Actually, the course "higher algebra" is used instead of ``linear algebra" in China. The most important difference is the theory of polynomials on number fields added in higher algebra. And in some textbooks of higher algebra in China contains the theory of $\lambda$Matrices, such as textbooks used in Beijing University and Southwest University, in which some versions contain introductions to number theory and use the terms of "ring" and "field" as well, of coursed, this is helpful for students conceive of the idea of modern algebra and number theory, but the practical reason to introduce such concepts to first year students is to make the system more general. For example, after students understand concepts of "ring" and "field", we can make the definition of a vector space and a polynomial over an arbitrary number fields not only rational, real and complex number field. In SWU, we use this kind of system many years, it is successful, especially it looks better connected to modern algebra.
Generally, in linear algebra, discussion of diagonalizing matrices
stops after giving the (necessary and) sufficient conditions on
diagonalizability of matrices. So there is a question how about
the matrices who cannot be diagonalized, if they are similar to
some kinds of simpler matrices, especially if we can make criteria
for similarity of matrices through pure matrices language. This
is done by introduce the theory of $\lambda $matrices, which some
textbook named ``Jordan Canonical Form", which is introduced by
few textbook "linear algebra". Reformation Through Merging
Higher Algebra and Analytic Geometry: About 6 years ago, a new round
reformation of system of curriculums started in universities with
purpose to promote the quality of teaching and studying through
shorten teaching time and make each curriculum adapted to both theoretical
and practical usage. In such background, several universities, such
as Nankai University, East China Normal University and Southwest
China Normal University, made experimental reform to merging higher
algebra and analytic geometry. This reform was started in 1998 in
SWU by the section of algebra of School of Mathematics and Finance(former
name, now is School of Mathematics and Statistics), and teaching
material was first used in 1999, the textbook named "higher
algebra and analytic geometry" was published in 2002. Now I would
like to introduce the system of this book.


close window  Electronic Proceedings of ATCM 
© ATCM,
Inc. 2006 