Unpredictability and Modular Variations of the Collatz Conjecture
Location
Access Type
Open Access
Entry Number
37
Start Date
4-7-2021 4:45 PM
End Date
4-7-2021 5:00 PM
Department
Mathematics
Abstract
This presentation will go over modular variations of the Collatz Conjecture, also known as the 3n+1 problem, and how they interact with a theorem proven by John Conway on finding whether a function behaves unpredictably. The presentation will go over how the modular variations of the Collatz conjecture are constructed, the properties that make these variations interesting to work with, and their connection with the standard Collatz Conjecture. It will cover why the John Conway theorem was chosen to work with these modular variations, and what was hoped to be found by using the theorem. It will then cover which modular variations will not give results with Conway's theorem, and what properties they have that causes them to not work. It will show how technological restrains prevent concrete answers from being obtainable with other modular variations. It will cover the specific causes of the technological restraints and how they may be overcome in the future.
Faculty Mentor(s)
Dr. Danny ClineDr. Kevin PetersonDr. Jennifer Styrsky
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Unpredictability and Modular Variations of the Collatz Conjecture
This presentation will go over modular variations of the Collatz Conjecture, also known as the 3n+1 problem, and how they interact with a theorem proven by John Conway on finding whether a function behaves unpredictably. The presentation will go over how the modular variations of the Collatz conjecture are constructed, the properties that make these variations interesting to work with, and their connection with the standard Collatz Conjecture. It will cover why the John Conway theorem was chosen to work with these modular variations, and what was hoped to be found by using the theorem. It will then cover which modular variations will not give results with Conway's theorem, and what properties they have that causes them to not work. It will show how technological restrains prevent concrete answers from being obtainable with other modular variations. It will cover the specific causes of the technological restraints and how they may be overcome in the future.