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University of Arizona

1. Gillis, Gregory Nelson, 1965-. Design considerations in manufacturing composite conductors: An exposition of Percolation Theory .

Degree: 1998, University of Arizona

URL: http://hdl.handle.net/10150/282664

This dissertation is an exposition of Percolation Theory, directed to the audience of beginning undergraduate mathematics students, though this can include gifted high school students. The vehicle by which the theory is taught is that of problem solving. The reader of the dissertation is invited into a web of mathematical exploration and inquiry by attempting to solve the real real-world problem of designing composite conductors. By making real composite conductors, carrying out various experiments, using computers to do data collecting, and using calculators for subsequent data analysis the reader can participate in the creation of mathematics, the development of mathematical techniques, and in the discovery of new and unexpected connections. The mathematics of Percolation Theory are in this way constructed with the reader. The necessity and importance of this work are many-fold. It is the first such treatise on Percolation Theory that makes the theory accessible to a larger audience than mathematics graduate or senior college students. It will be of interest to high school and beginning college students who desire to know in what real-world contexts some of the mathematics they know can be put. This work will be of interest to educators for the hands-on way in which it reinforces the student's current mathematical ability, while enriching the student's understanding of problem solving, mathematical modeling, use of technology, and probability.
*Advisors/Committee Members: Gay, David A (advisor).*

Subjects/Keywords: Education, Mathematics.; Mathematics.; Education, Curriculum and Instruction.

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Gillis, Gregory Nelson, 1. (1998). Design considerations in manufacturing composite conductors: An exposition of Percolation Theory . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/282664

Chicago Manual of Style (16^{th} Edition):

Gillis, Gregory Nelson, 1965-. “Design considerations in manufacturing composite conductors: An exposition of Percolation Theory .” 1998. Doctoral Dissertation, University of Arizona. Accessed January 22, 2021. http://hdl.handle.net/10150/282664.

MLA Handbook (7^{th} Edition):

Gillis, Gregory Nelson, 1965-. “Design considerations in manufacturing composite conductors: An exposition of Percolation Theory .” 1998. Web. 22 Jan 2021.

Vancouver:

Gillis, Gregory Nelson 1. Design considerations in manufacturing composite conductors: An exposition of Percolation Theory . [Internet] [Doctoral dissertation]. University of Arizona; 1998. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10150/282664.

Council of Science Editors:

Gillis, Gregory Nelson 1. Design considerations in manufacturing composite conductors: An exposition of Percolation Theory . [Doctoral Dissertation]. University of Arizona; 1998. Available from: http://hdl.handle.net/10150/282664

University of Arizona

2. Ke, Wen-Fong. Structures of circular planar nearrings .

Degree: 1992, University of Arizona

URL: http://hdl.handle.net/10150/185884

The family of planar nearrings enjoys quite a few geometric and combinatoric properties. Circular planar nearrings are members of this family which have the character of circles of the complex plane. On the other hand, they also have some properties which one may not find among the circles of the complex plane. In this dissertation, we first review the definition and characterization of a planar nearring, and some various ways of constructing planar nearrings, as well as various ways of constructing BIBD's from a planar nearring. Circularity of a planar nearring is then introduced, and examples of circularity planar nearrings are given. Then, some nonisomorphic BIBD's arising from the same additive group of a planar nearring are examined. To provide examples of nonabelian planar nearrings, the structures of Frobenius groups with kernel of order 64 are completely determined and described. On the other hand, examples of Ferrero pairs (N, Φ)'s with nonabelian Φ, which produce circular planar nearrings, are provided. Finally, we study the structures of circular planar nearrings generated from the finite prime fields from geometric and combinatoric points of view. This study is then carried back to the complex plane. In turn, it gives a good reason for calling a block from a circular planar nearring a "circle."
*Advisors/Committee Members: Clay, James R (advisor), Gay, David A. (committeemember), Stevenson, Frederick W. (committeemember).*

Subjects/Keywords: Rings (Algebra); Near-rings.

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Ke, W. (1992). Structures of circular planar nearrings . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/185884

Chicago Manual of Style (16^{th} Edition):

Ke, Wen-Fong. “Structures of circular planar nearrings .” 1992. Doctoral Dissertation, University of Arizona. Accessed January 22, 2021. http://hdl.handle.net/10150/185884.

MLA Handbook (7^{th} Edition):

Ke, Wen-Fong. “Structures of circular planar nearrings .” 1992. Web. 22 Jan 2021.

Vancouver:

Ke W. Structures of circular planar nearrings . [Internet] [Doctoral dissertation]. University of Arizona; 1992. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10150/185884.

Council of Science Editors:

Ke W. Structures of circular planar nearrings . [Doctoral Dissertation]. University of Arizona; 1992. Available from: http://hdl.handle.net/10150/185884