NCSI: Computational Research in Number Theory: Initial and Middle Sums & FLT

Status	Completed
Mentor Name	Stephen Harnish
Mentor's XSEDE Affiliation	I have received 3 Education Allocations through the BWSIP program and am presently guiding one intern. I have participated in various NCSI workshop opportunities since 2003.
Mentor Has Been in XSEDE Community	4-5 years
Project Title	Computational Research in Number Theory: Initial and Middle Sums & FLT
Summary	Analyzing initial and middle sums of sequences dates back to antiquity--including examples from Leonardo Fibonacci. For about a decade, we have developed a series of related number theoretic research questions that led to well-received conference presentations--four regional, two national and one at an international venue. This internship extends the research by applying naturally parallelizable algorithms for our Mathematica programs and dynamic Excel spreadsheets that have yielded insight into FLT via modulo m analysis of initial and middle sums of sequences based on Stirling numbers of the second kind.
Job Description	The apprentice's duties include: a) Reading and reporting on at least three number theoretic questions amenable to experimentation via computational research. b) Using Python or C to generate small-scale code on campus computers to develop or test several number theoretic conjectures. c) Extending the work relating FLT and modular analysis of initial and middle sums by generating naturally parallelized versions of Mathematica code and Excel spreadsheets. d) Porting and rescaling the above code to larger Linux clusters such as our campus' LittleFe cluster, the Ohio Supercomputer Center's clusters or those available through a new allocation on another XSEDE partnering institution.
Computational Resources	The mentor has an active academic account at the Ohio Supercomputer Center. However, for this spring semester work, an additional academic classroom project will be applied for. The apprentice will be exposed to several and then required to use at least one XSEDE online training class--likely for visualization of the extensive data generated in these number theoretic computational experiments.
Contribution to Community
Position Type	Apprentice
Training Plan	The successful applicant should have taken an introductory computer programming course as well as a data structures course in Python or C++. Several text books in my library (as well as online resources) will allow the student to extend their programming skills in Python for the purpose of programming in C and C++. As noted above, the apprentice will be exposed to several and then required to use at least one XSEDE online training class--likely for visualization of the extensive data generated in these number theoretic computational experiments. At this time, I do not anticipate needing assistance in the development of a training plan.
Student Prerequisites/Conditions/Qualifications	The student must thrive on independent study and researching new questions. Jarod Siekman is an excellent candidate for that reason. I know he has self-taught himself advanced mathematics material and presented a number theoretic topic with ease during this past fall's Miami University mathematics conference.
Duration	Semester
Start Date	01/09/2019
End Date	05/02/2019