Volume 14, Issue 1

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https://hdl.handle.net/20.500.14291/202374
Mathematics Exchange is a journal for undergraduate research in the mathematical sciences. It is a forum for student activities, which are not necessarily original research but go beyond standard classroom material. Among other information, issues contain senior thesis abstracts, extra curricular projects, and seminar and colloquium papers.

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    Mathematics Exchange Volume 14
    (2020-10)
    Complete issue of Volume 14, published in Fall 2020
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    A Word from the Editor
    (2020-10) Stankewitz, Rich
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    Exploring Bounds for the Frobenius Number
    (2020-10) El Turkey, Houssein; Shackett, Alec; Svitlik, Andrew
    Let G be a set of three natural numbers, G = {a, b, c}, such that gcd(a, b, c) = 1. The Frobenius number of G is the largest integer that cannot be written as a non-negative linear combination of elements of G. In this article, we present some experimental results on the Frobenius number.
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    AM-GM Any Baby’s BMs
    (2020-10) Trujillo, Timothy; del Valle, Vanessa; Robles, Jacob; Daniels, Elisha; Jimenez, Jacqueline; Rodriguez, Diana; Clark, Alex
    Reusable diapers are growing in popularity due to new and improved designs. The total cost associated with reusable diapers is the sum of the upfront cost of purchasing the diapers and the reoccurring cost of cleaning the diapers. With a nice application of the AM-GM inequality we show that the minimum cost to the consumer is twice the geometric mean of the upfront and cleaning costs plus the cost of a single reusable diaper. Moreover, the minimum is obtained when the upfront cost is equal to the total cleaning costs plus the cost of a single reusable diaper. We conclude with an analysis of our reusable diaper model and a cost comparison with disposable diapers.
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    Another view of the coarse invariant σ
    (2020-10) Imamura, Takuma
    Miller, Stibich and Moore developed a set-valued coarse invariant σ (X, ξ) of pointed metric spaces. DeLyser, LaBuz and Tobash provided a different way to construct σ (X, ξ) (as the set of all sequential ends). This paper provides yet another definition of σ (X, ξ). To do this, we introduce a metric on the set S (X, ξ) of coarse maps (N, 0) → (X, ξ), and prove that σ (X, ξ) is equal to the set of coarsely connected components of S (X, ξ). As a by-product, our reformulation trivialises some known theorems on σ (X, ξ), including the functoriality and the coarse invariance.