{"id":{"repo_id":"arizona-thes","oai_identifier":"oai:repository.arizona.edu:10150/282664"},"canonical_url":"https://search.dev.ndltd.org/etd/arizona-thes/oai:repository.arizona.edu:10150/282664","repository":{"repo_id":"arizona-thes","name":"University of Arizona","base_url":"https://repository.arizona.edu/oai/request"},"display":{"title":"Design considerations in manufacturing composite conductors: An exposition of Percolation Theory","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Gillis, Gregory Nelson, 1965-"],"institution":"The University of Arizona.","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":"Graduate College","degree_department":null,"school":null,"contributors":[],"advisors":["Gay, David A."],"committee_chairs":[],"committee_members":[],"year":1998,"date_issued":"1998","date_published":"1998","updated_at":"2026-07-24T00:57:34Z","subjects":["Education, Mathematics.","Mathematics.","Education, Curriculum and Instruction."],"languages":["en_US"],"rights":["Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10150/282664","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Gay, David A."]},{"key":"dc:creator","label":"Author","values":["Gillis, Gregory Nelson, 1965-"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-04-18T09:57:29Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-04-18T09:57:29Z"]},{"key":"dc:date.issued","label":"Date","values":["1998"]},{"key":"dc:publisher","label":"Institution","values":["The University of Arizona."]},{"key":"dc:type","label":"Dc Type","values":["text","Dissertation-Reproduction (electronic)"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Graduate College","Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Arizona"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Education, Mathematics.","Mathematics.","Education, Curriculum and Instruction."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10150/282664"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Design considerations in manufacturing composite conductors: An exposition of Percolation Theory"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gay, David A."],"dc:creator":["Gillis, Gregory Nelson, 1965-"],"dc:date.accessioned":["2013-04-18T09:57:29Z"],"dc:date.available":["2013-04-18T09:57:29Z"],"dc:date.issued":["1998"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/10150/282664"],"dc:language.iso":["en_US"],"dc:publisher":["The University of Arizona."],"dc:rights":["Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author."],"dc:subject":["Education, Mathematics.","Mathematics.","Education, Curriculum and Instruction."],"dc:title":["Design considerations in manufacturing composite conductors: An exposition of Percolation Theory"],"dc:type":["text","Dissertation-Reproduction (electronic)"],"thesis:degree_discipline":["Graduate College","Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Arizona"]},"updated_at":"2026-07-24T00:57:34Z"}