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The Contraction Mapping Principle, Elaine Rosenbloom
The Contraction Mapping Principle, Elaine Rosenbloom
Honors Capstones
In the world of mathematics, it is often necessary to approximate the solution to a problem by using an iterative method. One such method, not totally dependent on the initial guess, is the contraction mapping method. This paper will explore the contraction mapping principle for the real line, some extensions of it, and the principle in other contexts.
Expanding Horizons In Intermediate Mathematics, Sheri Pindel
Expanding Horizons In Intermediate Mathematics, Sheri Pindel
Honors Capstones
This project is aimed at providing teachers with activities that could be used to increase students’ understanding of mathematics. The activities listed are aimed for students in fifth through eighth grade. Many of the concepts presented have strong upper level mathematical background, but a complete understanding of the background of the material is not necessary to effectively present the material to students. A teacher who understands the material that is presented to the students in the everyday textbooks should find these supplement activities interesting and enjoyable to teach their students.
Some Insights Into Partitioning And Repartioning Behaviors, Gina Marie Conner
Some Insights Into Partitioning And Repartioning Behaviors, Gina Marie Conner
Honors Capstones
Recently, in mathematical educational research, there has been quite a bit of work focusing on the acquisition of rational numbers concepts by school age children. It is believed that partitioning, the act of dividing a quantity into a given number of parts which are quantitatively equal, is one of the necessary behaviors for students to obtain in order to fully understand the rational numbers. The first part of this paper will discuss the research that has examined the partitioning behaviors of school age children. The latter part of this paper will contain an analysis of data collected from videotapes of …
Qualitative Theory Of Differential Equations, Sheri Homeyer
Qualitative Theory Of Differential Equations, Sheri Homeyer
Honors Capstones
The problem of stability is of primary concern in the qualitative theory of differential equations and has occupied mathematicians for the past century. The problem appears when considering solutions to the differential equation x-f(t,x) where x=( x1(t),…,xn(t) )T and f(t,x) is a nonlinear function of x1,…,xn. While no known method of solving this equation explicitly exists even for the case n=2, it is possible to discuss the qualitative properties of x1(t) and x2(t) where x1(t) and x2(t) denote, for example, the populations, at time t, of two competing species. The qualitative attributes under consideration include points of equilibrium and the …
Selection In Genetics : A Mathematical Model, Sarah J. Blean
Selection In Genetics : A Mathematical Model, Sarah J. Blean
Honors Capstones
There are many areas of study in the field of genetics which continually affect our highly technological society. In particular, the idea of being able to predict the time when, given the current distribution of a population, a specific inherited trait might disappear from the population is one important question that is being raised. In order to accurately make such a prediction, a mathematical model will be built. Since there are several variables that enter into such a model, certain assumptions will initially be made. After studying the original model, a selected group of the variables and their corresponding assumptions …