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Physical Sciences and Mathematics Commons™
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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Random Motion And The Diffusion Of Brine Shrimp: A Project Based Learning Unit, Rebecca Atkins
Random Motion And The Diffusion Of Brine Shrimp: A Project Based Learning Unit, Rebecca Atkins
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Over the years, there have been several trends, philosophies, and ideas about how mathematics should be taught. These have included progressive movements, essentialist movements, drill and practice, teacher-centered methodologies, student-centered methodologies, and others. However, despite these various instructional trends, research has found that mathematics teachers have basically taught the same way for years, with little or no variation with respect to the changing trends (Ward, 2001). For many students, the traditional teaching method employed in their mathematics classes is typically centered on the teacher and includes lecture in which the teacher provides the necessary definitions and notations and does several …
Teaching Probability Through Use Of An Applet, Melissa Gregory Jackson
Teaching Probability Through Use Of An Applet, Melissa Gregory Jackson
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
The use of technology in the classroom is an ongoing debate by educators. Many teachers consider it to be a valuable teaching tool. Despite the many advantages, there are also drawbacks in using technology. A Java applet is a particular kind of multimedia technology proven to be useful in education. Because of students' struggles with learning basic probability in Statistics 1040, I have created a probability applet to reinforce the concept of probability. The applet was tested with two Statistics 1040 classes. The majority of students agreed that they learned more about probability from using the applet. Several of the …
Logistic Models With Missing Categorical Covariates, Jeremiah Rounds
Logistic Models With Missing Categorical Covariates, Jeremiah Rounds
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
We present an EM based solution to missing categorical covariates in Binomial models with logit links using an assumption that experimental units are drawn from a Multinomial population of infinite size. We further address the problem of separation of points inducing large variances on parameter estimates by the use of a novel score-modification based on Firth's bias-reduction score-modification. We simulate to address questions about estimate bias, distribution, and appropriate parameter coverage by Wald intervals.
An Investigation Of The Ends Of Finitely Generated Groups, Daniel T. Murphree
An Investigation Of The Ends Of Finitely Generated Groups, Daniel T. Murphree
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Geometric group theory is a relatively new branch of mathematics, studied as a distinct area since the 1990's. It explores invariant properties of groups based on group actions defined on topological or geometrical spaces. One of the pioneering works in geometric group theory is the article "Topological Methods in Group Theory" by Peter Scott and Terry Wall, written in 1977. This article was an overview of revised notes from an advanced course give in Liverpool in the same year. This report is an attempt to make these notes more accessible to lower level graduate students in the fields of topology …
The Classification Of Simple Lie Algebras In Maple, D. Russell Sadler
The Classification Of Simple Lie Algebras In Maple, D. Russell Sadler
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Lie algebras are invaluable tools in mathematics and physics as they enable us to study certain geometric objects such as Lie groups and differentiable manifolds. The computer algebra system Maple has several tools in its Lie Algebras package to work with Lie algebras and Lie groups. The purpose of this paper is to supplement the existing software with tools that are essential for the classification of simple Lie algebras over C.
In particular, we use a method to find a Cartan subalgebra of a Lie algebra in polynomial time. From the Cartan subalgebra we can compute the corresponding root system. …