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An Introduction To Number Theory Prime Numbers And Their Applications., Crystal Lynn Anderson
An Introduction To Number Theory Prime Numbers And Their Applications., Crystal Lynn Anderson
Electronic Theses and Dissertations
The author has found, during her experience teaching students on the fourth grade level, that some concepts of number theory haven't even been introduced to the students. Some of these concepts include prime and composite numbers and their applications. Through personal research, the author has found that prime numbers are vital to the understanding of the grade level curriculum. Prime numbers are used to aide in determining divisibility, finding greatest common factors, least common multiples, and common denominators. Through experimentation, classroom examples, and homework, the author has introduced students to prime numbers and their applications.
Proven Cases Of A Generalization Of Serre's Conjecture, Jonathan H. Blackhurst
Proven Cases Of A Generalization Of Serre's Conjecture, Jonathan H. Blackhurst
Theses and Dissertations
In the 1970's Serre conjectured a correspondence between modular forms and two-dimensional Galois representations. Ash, Doud, and Pollack have extended this conjecture to a correspondence between Hecke eigenclasses in arithmetic cohomology and n-dimensional Galois representations. We present some of the first examples of proven cases of this generalized conjecture.
On Conway's Generalization Of The 3x + 1 Problem, Robin M. Givens
On Conway's Generalization Of The 3x + 1 Problem, Robin M. Givens
Honors Theses
This thesis considers a variation of the 3x+1, or Collatz, Problem involving a function we call the Conway function. The Conway function is defined by letting C3(n)=2k for n=3k and C3(n)=4k±1 for n=3k±1, where n is an integer. The iterates of this function generate a few 'short' cycles, but the s' tructural dynamics are otherwise unknown. We investigate properties of the Conway function and other related functions. We also discuss the possibility of using the Conway function to generate keys for cryptographic use based on a fast, efficient binary implemenation of the function. Questions related to the conjectured tree-like structure …