Integer Solutions to Optimization Problems and Modular Sequences of Nexus Numbers

<p>In this thesis, we examine the use of integers through two ideas. As mathematics teachers, we prefer students not use calculators on assessments. In order to require this, students compute the problems by hand. We take a look at the classic Calculus I optimization box problem while restricting values to integers. In addition, sticking with the integer theme, we take a new look at the nexus numbers. Nexus numbers are extensions of the hex and rhombic dodecahedral numbers. We put these numbers into a sequence, and through a few computations of modular arithmetic, we analyze the sequences and their patterns based upon the different moduli. These patterns are specific to whether the power is even or odd. Within each power, there are other properties to this set of sequences. Depending on modulus, there are some sequences that stand out more than others.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2012

Author dc:creator

• Davis, Jeremy T.

Contributors dc:contributor

• Andrew Sills
• Hua Wang

• ETD
• Integer
• Optimization
• Modular arithmetic
• Sequences
• Nexus numbers
• Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/2

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1001