Graduation Year
2016
Date of Submission
4-2016
Document Type
Campus Only Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Reader 1
Lenny Fukshansky
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Rights Information
© 2016 Michelle L Goodwin
Abstract
Lattices are an easy and clean class of periodic arrangements that are not only discrete but associated with algebraic structures. We will specifically discuss applying lattices theory to computing the area of polygons in the plane and some optimization problems. This thesis will details information about Pick's Theorem and the higher-dimensional cases of Ehrhart Theory. Closely related to Pick's Theorem and Ehrhart Theory is the Frobenius Problem and Integer Knapsack Problem. Both of these problems have higher-dimension applications, where the difficulties are similar to those of Pick's Theorem and Ehrhart Theory. We will directly relate these problems to optimization problems and operations research.
Recommended Citation
Goodwin, Michelle, "Lattices and Their Application: A Senior Thesis" (2016). CMC Senior Theses. 1317.
https://scholarship.claremont.edu/cmc_theses/1317
This thesis is restricted to the Claremont Colleges current faculty, students, and staff.
