Raison d'être - Capstone projects

A Capstone Research project is a wonderful experience for a Mathematics educator engaged in Undergraduate Research. That's our raison d'être! Here are the Capstones that I advised at ONU. With many thanks to all those amazing students.

1.     Kaleb Swieringa, On the Alternating Sum of Divisors 2023

2.     McKinley Britton: Fibonacci Numbers and Domino Tilings 2023

3.     Alexander Hare: Experiments with Greatest Prime Factor Sequences 2023

4.     Rachael Harbaugh: Extending a Putnam Problem to Fields of Various Characteristics 2022

5.     Benjamin Morris: Fibonacci Periods 2022

6.     Greg Hassenpflug: The Golden Ratio 2021

7.     Aaron Kemats: An Investigation of the Square Grid Graph 2021

8.     Travis Maenle: A linear complexity analysis of quadratic residues and primitive roots spacings 2020

9.     Bryan Peck: Bell's Inequalities 2020

10.  Kaity Kelly: Gaussian Integers 2020

11.  Kenneth Eaton: The Fundamentals of Automated Theorem Proving 2019

12.  Megan Meyer: An Experimental Approach to Sophie Germain Sequences 2019

13.  Addison Carter: An Introduction to Partitions and Compositions 2019

14.  Rachel Liebrecht: Special Topics on Graph Theory and Ramsey Numbers 2019

15.  Shannon Tefft: Processing Quadratic Residues with Ducci Iterations 2019

16.  Jenna Holler: American Mathematics Competitions – Variations and Generalizations 2018

17.  Joseph Stomps: American Mathematics Competitions AMC 10 - analogies and generalizations 2018

18.  Matthew Golden: The Baker-Campbell-Hausdorff Formula 2017

19.  Michelle Haver: Poissonian Character and Chebyshev Bias for GPF Sequences: A Computational Analysis 2017

20.  Amanda Marco: Fibonacci Numbers and Some of Their Properties 2014

21. Matthew R. Zirkle: Finding Square Roots in a Prime Field 2013

22.  Jonathan C. Schroeder: Small Special Pairs of Primitive Roots 2013

23.  Donald J. Pleshinger: On a Congruence of Ohtsuka 2013

24.  Ashley Risch: An Euler-Fibonacci Sequence 2011

25.  Lauren Sutherland: Multidimensional Greatest Prime Factor Sequences 2011

26.  Greg Back: The Greatest Prime Factor and its Applications 2010

27.  Jenna Brace: Traffic Flow Simulation with Cellular Automata 2010

28.  John Holodnak: The Perron-Frobenius Theorem and Applications 2010

29.  Sharon Binkley: The One Time Pad and Text Visualization 2009

30.  Joshua Somerlot: The Affine Cipher 2009

31.  Andrew Homan: An Overview of Model Theory and Completeness 2007

32.  Allison Mackay: Elementary Number Theory and Classical Cryptography 2006

33.  Lisa Scheckelhoff: GPF Sequences 2006

34.  Brandon Bucholtz: The Euclidean Algorithm 2006

35.  Jacob L. Johanssen: Fibonacci-Lucas Densities 2006

36.  Nathan Baxter: Finite Fields 2005

37.  Sara Miller: Fibonacci Numbers 2003

 

Ada, Ohio - brief historical highlights

 Brief history Ada, OH, from https://en.wikipedia.org/wiki/Ada,_Ohio

"Ada is a village in Hardin County, Ohio, United States, located about 69 miles (111 km) southwest of Toledo. The population was 5,334 at the 2020 census. It is the home of Ohio Northern University and Ada High School. 

History 

Following the 1817 Treaty of Fort Meigs, the Shawnee Indians held reservation land at Hog Creek near Ada. Ada itself was originally called Johnstown, platted in 1853 by S. M. Johnson when the railroad was extended to that point. When a post office was established it was called Ada Post Office, named after the postmaster's daughter, Ada. The post office has been in operation since 1854.The growth of the village is due in large part to the founding of the Ohio Normal School, now known as Ohio Northern University. The University was founded in 1871 by Henry Solomon Lehr, just eighteen years after Ada was first settled. Today, Ada is the second largest incorporated community in Hardin County. In 1910, President William Howard Taft visited Ada, to give the fall commencement speech at Ohio Northern University. To date, Taft is the only president to visit the village. Ada welcomed Martin Luther King Jr. to the village in January of 1968, just three months before his assassination. Ada has been noted for having one of the shortest place names in Ohio. The National Arbor Day Foundation has qualified Ada as a Tree City USA since 1981."

Brief history of Kenton, Ohio

Brief history of the local county seat - Kenton, OH, from https://en.wikipedia.org/wiki/Kenton,_Ohio

"Kenton is a city in and the county seat of Hardin County, Ohio, United States, located in the west-central part of Ohio about 57 mi (92 km) northwest of Columbus and 70 mi (113 km) south of Toledo. Its population was 7,947 at the 2020 census. The city was named for frontiersman Simon Kenton of Kentucky and Ohio. 

History

Kenton was originally the site of Fort McArthur, erected in 1812 by Colonel Duncan McArthur as one of the forts along the line of General William Hull's march against the British headquarters at Fort Detroit during the War of 1812. 

In 1845, Kenton was incorporated as a village; it became a city in 1886. The city was named after frontiersman Simon Kenton. The city began as a center for agricultural trade, then in the late 19th century, developed industry common to America of the time.

From 1890 to 1952, Kenton was home to the Kenton Hardware Company, manufacturers of locks, cast-iron toys, and the very popular Gene Autry toy cap guns. International Car Company, a manufacturer of rail cabooses, operated in Kenton for many years. In 1975, it was purchased by Paccar, a manufacturer of medium- and heavy-duty trucks. In 1983, Paccar closed down the business, noting a decrease in demand for rail equipment. The 2001 CSX 8888 incident involving an unmanned freight train ended in Kenton."

 

Math Education: "more than good grades and test scores..."

An interesting article at The Conversation:

Real equity in math education is about more than good grades and test scores - by Megan Staples, Associate Professor of Mathematics Education, University of Connecticut

"With more than three decades of experience as a researcher, math teacher and teacher educator, I advocate for expanding what equity means in mathematics education. I believe policymakers and educators should focus less on test scores and grades and more on developing students’ confidence and ability to use math to make smart personal and professional decisions. This is mathematical power – and true equity."

Read the full article at  

https://theconversation.com/real-equity-in-math-education-is-about-more-than-good-grades-and-test-scores-215518