Applications of a sequence of points in teaching linear algebra, numerical methods and discrete mathematics

Abstract

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, Using a sequence of number pairs as an example in teaching mathematics. Math. Comput. Educ., 39 (2005), pp. 198–205; Y. Shi, Case study projects for college mathematics courses based on a particular function of two variables. Int. J. Math. Educ. Sci. Techn., 38 (2007), pp. 555–566) have presented some interesting examples which can be used in teaching high school and college mathematics classes. In this article, we further discuss a few interesting ways to apply this sequence of points in teaching college mathematics courses such as linear algebra, numerical methods in computing, and discrete mathematics. In addition to using them in individual courses, these studies may also be combined together to offer seminars or workshops to college mathematics students. Studies like these are likely to promote student interests and get students more involved in the learning process, and therefore make the learning process more effective.

Keywords:

• sequence of points
• binary numbers
• matrix series
• long division
• mathematical induction
• difference equation