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Master’s Thesis Defense: Nicholas Johnson
May 6, 2021 @ 11:00 am - 1:00 pm
Due to the COVID-19 Pandemic, the University has instruction to cancel all in-person events through the Spring semester to adhere to city and state orders limiting public gatherings. Events still running must now take place Online— listed events will include a link in which one may access the Online webspace:
To view Mr. Johnsons defense, enter his Online chatroom via Collaborate Ultra— it will open at 11:00am on Thursday, May 6th, 2021
Exploring the Division Algorithm in Euclidean Domains with Exploding Dots
Mr. Nicholas Johnson
University of Wisconsin-Milwaukee
Graduate Student
We will give an overview of the representation of place value and arithmetic known as Exploding Dots and use this idea to explore the division algorithm. It is well-known that the ring of integers, the ring of polynomials, and the ring of Gaussian integers are all examples of Euclidean domains and therefore possess a division algorithm. Exploding Dots beautifully illustrates how one can perform division in any base and how this naturally leads us to division of polynomials. We will show how this same idea of having a ”base machine” can be used to perform division in the Gaussian integers.
Committee Members:
Profs. Kevin McLeod (advisor), Gabriella Pinter, Suzanne Boyd, Jeb Willenbring
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