The Department of Mathematical Sciences Undergraduate Research Problems
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Here are a few of the research problems our undergraduate students worked on recently.
Problems this summer would be on similar topics.
What makes a number Lucky? Skyler Addy and Zachary Parker explored what makes a number lucky. Lucky numbers are obtained by eliminating the second, third, fifth, etc. numbers from the set of natural numbers in successive iterations.
What makes a number Lucky? Skyler Addy and Zachary Parker explored what makes a number lucky. Lucky numbers are obtained by eliminating the second, third, fifth, etc. numbers from the set of natural numbers in successive iterations.
Honeycombs in the Hosoya Triangle: Matthew Blair discovered that the patterns of numbers obtained while constructing paths in a honeycomb in the Hosoya triangle gave rise to identities for Fibonacci numbers.
Honeycombs in the Hosoya Triangle: Matthew Blair discovered that the patterns of numbers obtained while constructing paths in a honeycomb in the Hosoya triangle gave rise to identities for Fibonacci numbers.
Ulam Numbers: Aaron Reynolds is currently studying patterns of consecutive positive integers in Ulam number sequences starting with 1 and 4; 1 and 5; 1 and 6 etc.
Ulam Numbers: Aaron Reynolds is currently studying patterns of consecutive positive integers in Ulam number sequences starting with 1 and 4; 1 and 5; 1 and 6 etc.
American Mathematical Monthly Problem : Freshmen math majors solved the problem to find sequences of positive integers such that the sum of consecutive members of the sequence is a power of two. This also includes the sum of the first and last members of the sequence.
Fibonacci Quarterly Problem: Ben Race and Ernest James proved an identity for balancing numbers. They used Binet's formula and derivatives of a geometric series to solve this problem.
Prime Progressions: Aaron Fannin found that there is a high density of prime numbers in progressions of the form {ap+b} where p is a prime number and a and b are specific positive integers.
If you want to know more about these problems, please send an email to math_faculty@citadel.edu.
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