# MATHEMATICAL TRIPS

Invitations, in an educational vein, to problem solving, ideas and their history, biographical snapshots, visuals, classroom capsules, undergraduate research ideas, recreations, experiments, arts and poetry, philosophical and foundational matters and connections.

## Sunday, June 16, 2019

## Friday, May 17, 2019

### A mathematical method for calculating black-hole properties from gravitational-wave data

"Sean McWilliams, an assistant professor at West Virginia University, has developed a mathematical method for calculating black hole properties from gravitational wave data. He has written a paper describing his method and posted it on thearXivpreprint server. The paper has been accepted for publication inPhysical Review Letters."

Read on Phys.Org

## Friday, May 3, 2019

### Journal papers with ONU students co-authors

student co-author(s) in

Conference Proceedings

*italics**Nathan Baxter*and Mihai Caragiu,**Arithmetic Properties of Some Special Sums**, JP Journal of Algebra, Number Theory and Applications, 4 (3), 455-463 (December 2004);- Mihai Caragiu and
*Lisa Scheckelhoff*,**The Greatest Prime Factor and Related Sequences**, JP Journal of Algebra, Number Theory and Applications, 6 (2), 403-409 (August 2006); - Mihai Caragiu, Ronald A. Johns and
*Justin Gieseler*,**Quasi-random Structures from Elliptic Curves**, JP Journal of Algebra, Number Theory and Applications, 6 (3), 561-571 (December 2006); - Mihai Caragiu and
*Nathan Baxter*,**A note on p-adic Ducci games**, JP Journal of Algebra, Number Theory and Applications 8 (1), 115-120 (June 2007); - Mihai Caragiu and
*John Holodnak*,**On Sampling Periodic Functions**, Far East Journal of Mathematical Sciences, 29 (1), 145-149 (April 2008); - Mihai Caragiu and
*Greg Back*,**The Greatest Prime Factor and Related Magmas**, JP Journal of Algebra, Number Theory and Applications, 15(2), 127-136 (December 2009); *Greg Back*and Mihai Caragiu,**The Greatest Prime Factor and Recurrent Sequences**, Fibonacci Quarterly 48, no. 4, 358-362 (November 2010);- Mihai Caragiu and
*Ashley Risch*,**An Euler-Fibonacci Sequence**, Far East Journal of Mathematical Sciences, Volume 52, Issue 1, Pages 1-7 (May 2011); - Mihai Caragiu,
*Lauren Sutherland*and Mohammad Zaki,**Multidimensional Greatest Prime Factor Sequences**, JP Journal of Algebra, Number Theory and Applications, Volume 23, Issue 2, Pages 187-195 (December 2011); - Mihai Caragiu and
*Courtney J. Brown*,**Quadratic residues and a special class of polynomials**, Far East Journal of Mathematical Education, Volume 8, Issue 1, 43-50 (February 2012); *Lauren Cassell*and William Roger Fuller,**Guarding a Koch Fractal Art Gallery**, Open Journal of Discrete Mathematics, Vol. 2 No. 4,134-137 (November 2012);- Mihai Caragiu,
*Donald Pleshinger*and*Jonathan C. Schroeder*,**Uniform Distribution for a Class of k‑Paradoxical Oriented Graphs**, JP Journal of Algebra, Number Theory and Applications, Volume 29, Issue 2, Pages 107-117 (June 2013); *Thomas Steinberger*, Alexandru Zaharescu and Mohammad Zaki,**Arithmetic Functions on Gaussian Integers**, International Journal of Number Theory (December 2013);- Jaki Chowdhury and
*Thomas Steinberger*,**Arithmetic Functions of Several Variables over Gaussian Integers**, Mathematical Reports (accepted on 4/24/17); - Anup Lamichhane,
*Yu Wakayama*,*Alexander Shube*and Balaram K. Ghimire,**The closed-form particular solutions for the Laplace operator using oscillatory radial basis functions in 2D**, Engineering Analysis with Boundary Elements Vol. 96, 187 - 193 (November 2018) - Mihai Caragiu,
*Shannon Tefft, Aaron Kemats*and*Travis Maenle*,**A linear complexity analysis of quadratic residues and primitive roots spacings.**Far East Journal of Mathematical Education Volume 19, Issue 1, Pages 27 - 37 (February 2019) https://arxiv.org/abs/1902.07314

*Kristi Patton*, Sandra Schroeder and Richard Daquila:*An Investigation of Continued Fractions,*Electronic Proceedings of Undergraduate Mathematics Day, Volume 2, Nov. 2005.

- Mihai Caragiu and
*Jacob L. Johanssen*, Fibonacci-Lucas densities, math.GM/0603232

### ONU-SOLVE data

- Problem 1115 - College Mathematics Journal Vol. 49(5), November 2018, recognizes correct solution sent by Noah Pinkney
- Problem 2025 - Mathematics Magazine Vol. 91(3), June 2018
- Problem 1956 - Mathematics Magazine Vol. 89 (1), Feb. 2016
- Problem 1920 - Mathematics Magazine Vol. 87 (2), April 2014 - published solution of Tommy Steinberger
- Problem 1916 - Mathematics Magazine Vol. 87 (2), April 2014 - Tommy Steinberger recognized among those submitting correct solutions.
- Problem 1896 - Mathematics Magazine Vol. 86 (3), June 2013 - Tommy Steinberger recognized among those submitting correct solutions.
- Problems 961 and 965 (The College Mathematics Journal 43, No. 5, November 2012, 410-419) ) - Tommy Steinberger recognized among those submitting correct solutions.
- Problem B-1120 (Fibonacci Quarterly - Vol. 50.4, November 2012) - Matt Zirkle recognized in the November 2013 Issue among those submitting correct solutions.
- Problem 11596 – American Mathematical Monthly – recognized in May 2013 issue.
- Problem B-1103 (recognized in the February 2013 Issue of the Fibonacci Quarterly, which features the solution provided by ONU-Solve)
- Problems B-1101 and B-1102 (recognized in the February 2013 Issue of the Fibonacci Quarterly).
- Problems 1872 and 1873 - Mathematics Magazine, Vol. 84, No. 3, June 2011 - recognized in the June 2012 issue.
- Problem B-1074 (recognized in the August 2011 Problem Section of the Fibonacci Quarterly, which features the solution provided by ONU-Solve)
- Problem B-1078 (recognized in the November 2011 Problem Section of the Fibonacci Quarterly

### Contributed Math/Stat talks/posters at professional meetings - Ohio Northern

###
**Contributed talks/posters at professional meetings**

- Bradley Lockhart: "Force Propagation in a Multi-Rod Drumstick" - 2019 Ohio MAA Spring Meeting - The University of Akron, April 5 – 6 [advisor Dr. William Fuller]
- Jack Raney: "Multivariable Data Fitting by Using Radial Basis Function" - 2019 Ohio MAA Spring Meeting - The University of Akron, April 5 – 6 [advisor Dr. Anup Lamichhane]
- Yu Wakayama: "Solving Poisson’s equation by using Method of particular solutions with the Oscillatory Radial Basis Function in 2D" - 2018 Ohio MAA Fall Meeting, Malone University, October 27, 2018 [advisor Dr. Anup Lamichhane]
- Aaron Kemats and Travis Maenle: "Linear Complexities of Quadratic Residues and Primitive Roots Spacings"- 2018 Ohio MAA Fall Meeting, Malone University, October 27, 2018 [advisor Dr. Mihai Caragiu]
- Shannon Tefft: "Processing Quadratic Residues with Ducci Iterations" - 2018 Ohio MAA Fall Meeting, Malone University, October 27, 2018 [advisor Dr. Mihai Caragiu]
- Rachel Liebrecht et al. : "On maximum packings of lambda-fold complete 3-uniform hypergraphs with loose 3-cycles", MCCCC 32 – Midwest Conference on Combinatorics and Combinatorial Computing, Duluth, MI, October 5-7 2018 (major peer-reviewed conference) [2018 REU at Illinois State University - group presentation]
- Dr. Tena Roepke, Addison Carter, Rachel Liebrecht and Shannon Tefft: "Combatting Mathematical Misconceptions", 68-th OCTM Annual Conference, Akron OH, October 11-12 2018 [Advisor Dr. Tena Roepke]
- Emma Talley: "With Replacement or Without Replacement or..." - 2018 Pi Mu Epsilon Student Conference, Miami University [advisor Dr. Laurence Robinson]
- Alexander Sube: "Particular Solutions for the Laplace Operator using Oscillatory Radial Basis Functions" - 2017 Ohio MAA Fall Meeting, Ohio University East, October 27, 2017 [advisor Dr. Anup Lamichhane]
- Takumi Kijima: "Naive Bayes Classifiers" - 2017 Ohio MAA Fall Meeting, Ohio University East, October 27, 2017 [advisor Dr. Mihai Caragiu]
- Aaron Kemats: "A Fibonacci-Lucas Experiment" - 2017 Ohio MAA Fall Meeting, Ohio University East, October 27, 2017 [advisor Dr. Mihai Caragiu]
- Emma Talley and Kayla Rieman: "Deal or No Deal: Can We Predict the Banker's Offer?" - 2017 Pi Mu Epsilon Student Conference, Miami University [advisor Dr. Laurence Robinson]
- Michelle Haver: "Classification of numerical sequences originating from recursive polynomial sequences", 2017 Nebraska Conference for Undergraduate Women in Mathematics, February 4, 2017 [REU in Experimental Mathematics at Michigan State]
- Michelle Haver et al.: "Classification of numerical sequences originating from recursive polynomial sequences", Joint Mathematics Meetings, Atlanta GA, January 5, 2017 [REU in Experimental Mathematics at Michigan State]
- Michelle Haver: "Closed Forms of Recursive Polynomial Sequences and Combinatorial Identities", 2016 Math Fest, Columbus, OH, August 4, 2016 [REU in Experimental Mathematics at Michigan State]
- Michelle Haver: "On the R. Lemke Oliver - K. Soundararajan recent "prime conspiracy", Spring 2016
*Centennial Meeting*of the Ohio MAA, Ohio Northern University [advisor Dr. Mihai Caragiu] - Nathan Knodel and William Fuller: "An Exact Solution for a Duffing Oscillator", Fall 2015 meeting of the Ohio MAA, Capital University [advisor Dr. William Fuller]
- Lacey Hittle: "Progression on Regression" 2014 Pi Mu Epsilon Student Conference, Miami University [advisor Dr. Ryan Rahrig]
- Zachary Soja:
*"The Case of The Disappearing Tablet"*, 2014 MAA Fall Meeting, University of Wittenberg [advisor Dr. William Fuller] - James Rader:
*"Gold Glove Winners: Baseball Statistics"*, 2014 MAA Fall Meeting, University of Wittenberg [advisor Dr. Ryan Rahrig] - Kerry DuLaney:
*"Exploring Gears and Watchmaking"*, 2014 MAA Fall Meeting, University of Wittenberg [advisor Dr. Donald Hunt] - Nathan Knodel
*:*"Scaling, Sneezes and the Elephant's Trunk" 2014 MAA Spring Meeting, Toledo, OH (April 2014) - [advisor: Dr. William Fuller] - Emily Barbee:
*Another Downfall With Using Facebook,*2013 Pi Mu Epsilon Student Conference, Miami University - [advisor: Dr. Ryan Rahrig] - Lacey Hittle:
*Living With Loans,*2013 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Ryan Rahrig] - Thomas Steinberger: Arithmetical Functions On Gaussian Integers
*(poster presentation) 2013 MAA Undergraduate Poster Session, San Diego*- [advisor: Dr. Mohammad Zaki] - Jonathan C. Schroeder: A Uniform Distribution Result for k-Paradoxical Directed Graphs
*(poster presentation) 2013 MAA Undergraduate Poster Session, San Diego*- [advisor: Dr. Mihai Caragiu] - James Rader: Gold Glove Winners
*(poster presentation) 2013 MAA Undergraduate Poster Session, San Diego*- [advisor: Dr. Ryan Rahrig] - James Rader: Quantifying Defensive ability in Baseball, 2012 Pi Mu Epsilon Student Conference, Miami University - [advisor: Dr. Ryan Rahrig]
- Emily Barbee: Are the Statistics Really Statistics? - 2012 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Ryan Rahrig]
- Johnathan Neville: What Difference Can A Single Game Make? - 2012 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Laurence D. Robinson]
- Hannah DePriest: How Much Does One Point Matter? - 2012 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Ryan Rahrig]
- Joanna Snyder: Hot Hand - 2012 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Ryan Rahrig]
- Caitlin Zook: My Relentless Struggle with a Sangaku Problem - 2012 Ohio MAA Spring Meeting, Xavier University - [advisor: Dr. Donald Hunt]
- Tommy Steinberger: On Bernoulli's Inequality, 2012 Michigan Undergraduate Mathematics Conference, March 3, Siena Heights University - [advisor: Dr. Mohammad Zaki]
- Ashley Ernst, Morgan Hammer, Mitchell Thayer and Matt Tremains : A Nice Relation in Triangle Geometry, 2012 Michigan Undergraduate Mathematics Conference, March 3, Siena Heights University - [advisor: Dr. Mihai Caragiu]
- Emily Barbee, David Kauffman, Katie Klopp and Liz Spingola: On The Product of Binomial Coefficients, 2012 Michigan Undergraduate Mathematics Conference, March 3, Siena Heights University - [advisor: Dr. Mihai Caragiu]
- Joe Mileski: The Mathematical Relationship between Musical Phrases [poster presentation], MAA Undergraduate Poster Session, 2012 Joint Mathematical Meetings, Boston - [advisor: Dr. William Fuller]
- Lauren Cassell: Guarding a Koch Fractal Art Gallery [poster presentation] - MAA Undergraduate Poster Session, 2012 Joint Mathematical Meetings, Boston [advisor: Dr. William Fuller]
- Courtney J. Brown: Special Polynomial Interpolation over Finite Fields, 2011 Undergraduate Mathematics Day, University of Dayton [advisor: Dr. Mihai Caragiu]
- Joseph Mileski: Paths of Melody Lines on Circles - 2011 Ohio MAA Fall Meeting, University of Findlay [advisor: Dr. William Fuller]
- Lauren Cassell: Guarding a Koch Fractal Art Gallery - 2011 Ohio MAA Fall Meeting, University of Findlay [advisor: Dr. William Fuller]
- Molly Eickholt: Simplifying Ford Links - 2011 Ohio MAA Spring Meeting, Youngstown State University [advisor: Dr. Donald Hunt]
- Kristin Elix: Maximizing The Product of Two Multi-Digit Numbers - 2011 Ohio MAA Spring Meeting, Youngstown State University - [advisor: Dr. Harold Putt]
- David Mangus: Ways in Which I was Wrong - 2011 Ohio MAA Spring Meeting, Youngstown State University [advisor: Dr. Donald Hunt]
- Ashley Risch: An Euler-Fibonacci Sequence - 2010 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Mihai Caragiu]
- Lauren Cassell, Joseph Mileski and Christopher Iliff: "Hyperbolic" Nine Point Circles - 2010 Ohio MAA Fall Meeting, Ursuline College [advisor: Dr. William Fuller]
- Axel Brandt and Nicholas Erickson: Efficiencies of Factorization Algorithms on RSA Encryption - (poster presentation) 2010 Posters on the Capitol, Columbus, OH [advisors: Dr. Mohammad Zaki and Dr. Nathaniel Bird]
- Greg Back: The Greatest Prime Factor Function and Some Applications - 2010 Ohio MAA Spring Meeting, Kent State University [advisor Dr. Mihai Caragiu]
- Kevin Earnest: Perturbations in the Aerospace Sequence of Attitude Determination Using Quaternions - 2010 Ohio MAA Spring Meeting, Kent State University [advisor Dr. William Fuller]
- John Holodnak: The Perron-Frobenius Theorem with Applications to Sports Ranking Models - 2010 Ohio MAA Spring Meeting, Kent State University [REU advisor Dr. Carl D. Meyer, North Carolina State University]
- Caitlin Zook: A Nonvanishing Result for Certain Sums … - 2010 Ohio MAA Spring Meeting, Kent State University [advisor Dr. Mohammad Zaki]
- John Holodnak: Rush versus Pass:Modeling the NFL
*(poster presentation) - 2010 AMS-MAA Joint Meetings, San Francisco*[REU advisor Dr. Carl D. Meyer, North Carolina State University] - Greg Back: A Prime Addition Commutative Magma
*(poster presentation) - 2010 AMS-MAA Joint Meetings, San Francisco*[advisor Dr. Mihai Caragiu] - Andrew Magyar: Edgar Structures on Manifolds (poster presentation) -
*2009 Mathfest*, Portland OR [advisor Dr. William Fuller] - John Holodnak: Rush versus Pass: Modeling the NFL
*, 2009 Ohio MAA Fall Meeting, Kenyon College*[REU advisor Dr. Carl D. Meyer, North Carolina State University] - Axel Brandt: Characterisation of Ford Links
*- Undergraduate Knot Theory Conference*, Denison University, 13-15 July 2009 [advisor Dr. Donald Hunt] - Joshua Stoffel: Maxwell's equations
*- 2009 Ohio MAA Spring Meeting, Bowling Green*[advisor Dr. Khristo Boyadzhiev] - Joshua Szekely: Annular and annular-like functions
*- 2009 Ohio MAA Spring Meeting, Bowling Green.*[advisor Dr. Donald Hunt] - Gregory Back: The Jacobi symbol and cryptography
*- 2009 Ohio MAA Spring Meeting, Bowling Green.*[advisor Dr. Mihai Caragiu] - Eric Gossett: Hailstones in tornadoes
*- 2009 Ohio MAA Spring Meeting, Bowling Green.*[advisor Dr. Bill Fuller] - Sharon Binkley: One-time pad and text visualization
*- 2009 Ohio MAA Spring Meeting, Bowling Green.*[advisor Dr. Mihai Caragiu] - John Holodnak: Sudoku and binary integer programming
*- 2009 Ohio MAA Spring Meeting, Bowling Green.*[advisor Dr. Donald Hunt] - Axel Brandt: Characterisation of Ford Links
*- 2009 Ohio MAA Spring Meeting, Bowling Green.*[advisor Dr. Donald Hunt] - Axel Brandt: Characterisation of Ford Links
*(poster presentation) - 2009 AMS-MAA Joint Meetings, Washington D.C.*[advisor Dr. Donald Hunt; co-author - Tyler Dunlap, ONU '08] - John Holodnak: A Stochastic Model of Tuberculosis
*(poster presentation) - 2009 AMS-MAA Joint Meetings, Washington D.C.*[advisors Dr.Yuliya Gorb and Dr. Jay Walton, Texas A&M; co-presenter Andrew Basinski] - Andrew Magyar: The Structure of Digroups - 2008 MAA Ohio Spring Meeting, Marietta College [REU advisor Dr. J. D. Phillips, Wabash College]
- Christopher Lemon: Markov Chains and the Ising Model, 2008 MAA Ohio Spring Meeting, Marietta College [advisor Dr. Ronald Johns]
- Andrew Magyar (ONU), Kyle Prifogle (Wabash College), David White
(Bowdoin College), and William Young (Purdue University): An
Investigation into the Structure of Digroups
*(award-winning poster presentation) - 2008 AMS-MAA Joint Meetings, San Diego*[REU advisor Dr. J. D. Phillips, Wabash College] - John Holodnak: On Sequences Not Satisfying Recurrence Relations
*(poster presentation) - 2008 AMS-MAA Joint Meetings, San Diego*[advisor Dr. Mihai Caragiu] - Charise Kazmierczak: Geometry in Rose Windows - 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Maria Raiti]
- Megan Reese: The Golden Section and Design, 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Maria Raiti]
- Greg Back: Counting with Transfer Matrices - 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Mihai Caragiu]
- John Holodnak: Kronecker's Theorem and Linear Recurrences, 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Mihai Caragiu]
- Andrew Homan: An Outline of the Completeness Theorem, 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Mihai Caragiu]
- Lisa Scheckelhoff: On a class of recurrent sequences based on the greatest prime factor function
*(award-winning poster presentation) 2007 AMS-MAA Joint Meetings, New Orleans*[advisor Dr. Mihai Caragiu] - Andrew J. Homan:
*Robinson's theorem in connection with a Putnam problem (award-winning poster presentation), 2007 AMS-MAA Joint Meetings, New Orleans*[advisor Dr. Mihai Caragiu] - Justin Gieseler:
*An application of elliptic curves to one-time pad cryptography (award-winning poster presentation), 2007 AMS-MAA Joint Meetings, New Orleans*[advisors Dr. Mihai Caragiu and Dr. Ronald Johns] - Andrew J. Homan:
*An Extension of a Putnam problem*, 2006 MAA Ohio Fall Meeting, Muskingum College [advisor Dr. Mihai Caragiu] - Lisa Scheckelhoff:
*On a class of sequences related to the greatest prime factor function*, 2006 MAA Ohio Spring Meeting, University of Akron [advisor Dr. Mihai Caragiu] - Justin Gieseler:
*Randomness properties of elliptic curves*, 2006 MAA Ohio Spring Meeting, University of Akron [advisors Dr. Mihai Caragiu and Dr. Ronald Johns] - Jason J. Bockey:
*Ford Circles*, 2006 MAA Ohio Spring Meeting, University of Akron [advisor Dr. Donald Hunt] - Lisa Scheckelhoff: Sophie Germain Digraphs
*(poster presentation) -*Eighth Annual Nebraska Conference for Undergraduate Women in Mathematics (university of Nebraska, Lincoln), February 3-5, 2006 [advisor Dr. Mihai Caragiu] - Kristi Patton:
*Continued Fractions (poster presentation) - 2006 AMS-MAA Joint Meetings, San Antonio, TX*[advisors Dr. Sandy Schroeder and Dr. Richard Daquila] - Jacob Johanssen:
*Fibonacci-Lucas densities (poster presentation) - 2006 AMS-MAA Joint Meetings, San Antonio, TX*[advisor Dr. Mihai Caragiu] - Justin Gieseler:
*The Distribution of points on elliptic curves projections (poster presentation) - 2006 AMS-MAA Joint Meetings, San Antonio, TX*[advisors Dr. Mihai Caragiu and Dr. Ronald Johns] - Kristi Patton:
*Continued Fractions - Undergraduate Mathematics Day,University of Dayton, November 5, 2005*[advisor Dr. Sandy Schroeder] - Justin Gieseler:
*Distribution of Points on Elliptic Curves Projections**, Undergraduate Mathematics Day,University of Dayton, November 5, 2005*[advisors Dr. Mihai Caragiu and Dr. Ronald Johns] - Justin Gieseler:
*Cubic Polynomials and Quadratic Residues*, 2005 MAA Ohio Fall Meeting, Ashland University - Jacob L. Johanssen:
*Fibonacci**-Lucas densities*, 2005 MAA Ohio Fall Meeting, Ashland University - Nathan Baxter and Justin Gieseler: Some computer explorations in Number Theory - 2005 MAA Ohio Spring Meeting, Miami University [advisor Dr. Mihai Caragiu]
- Nathan Baxter: Ultrasonic Beam-Forming with the Genetic Algorithm
*(award-winning poster presentation)*2005 Joint MAA-AMS Meetings, Atlanta [REU advisor Dr. Jerry Magnan, Florida State University] - Julie Holda: A closer look at Monte Carlo simulations
*(poster presentation)*2005 Joint MAA-AMS Meetings, Atlanta [Project developed at NASA Glenn Research Center] - Matt Katschke: San Gaku Problems and the Consequences of their Analogs
*(poster presentation)*2005 Joint MAA-AMS Meetings, Atlanta [REU advisor Dr. William Dickinson, GVSU; ONU advisor Dr. Donald Hunt] - Kara S. Lewis: Increasing the Retention Rate of Women in Sciences at Purdue University, 2005 Joint MAA-AMS Meetings, Atlanta [REU advisor Dr. George McCabe, Purdue University]
- Nathan Baxter:
*Quadratic Residues: a Computer - Assisted Journey*- 2004 MAA Ohio Fall Meeting, John Carroll University [advisor Dr. Mihai Caragiu] - Kristine Patton:
*The Ducci Problem: a Brief Review -*2004 MAA Ohio Fall Meeting, John Carroll University [advisor Dr. Mihai Caragiu] - Julie Holda: An application of Monte Carlo simulations for NASA - 2004 Pi Mu Epsilon Fall Student Conference, Miami University, Oxford, OH [Project developed in a summer internship at NASA Glenn Research Center]
- Matt Katschke: San Gaku Problems in Other Geometries
*(award-winning poster presentation)*2004 MATHFEST, Providence, RI [REU Project at Grand Valley State University] - Kristine Patton:
*On Primorial Primes -*2004 MAA Ohio Spring Meeting, University of Cincinnati [advisor Dr. Mihai Caragiu] - Mark Clausing: Advanced compass and straightedge constructions - 2004 MAA Ohio Spring Meeting, University of Cincinnati [advisor Dr. Donald Hunt]
- Nathan Baxter:
*Arithmetic Properties of Some Partial Sums*- 2004 MAA Ohio Spring Meeting, University of Cincinnati [advisor Dr. Mihai Caragiu] - Nathan Baxter:
*P-adic exponents and some of their applications*[poster presentation] - 2004 MAA-AMS Joint Meetings, Phoenix, AZ [advisor Dr. Mihai Caragiu] - Nathan Baxter:
*An Application of Weyl's Theorem*, 2003 MAA Ohio Spring Meeting, The Ohio State University [advisor Dr. Mihai Caragiu] - Matt Valerio: Fractal Exploration: A Look at Mandelbrot and Julia sets in 2 and 3 dimensions, 2002 MAA Ohio Spring Meeting, Xavier University [advisor Dr. Khristo Boyadzhiev]
- Nicholas Vidovich:
*On a Fibonacci identity*- 2002 MAA Ohio Spring Meeting, Xavier University [advisor Dr. Mihai Caragiu] - Thomas Jonell:
*A square root algorithm,*2002 MAA Ohio Spring Meeting, Xavier University [advisor Dr. Mihai Caragiu] - Ethan Miller and Paul Pfeiffer:
*Cellular Automata with Finite Life Span*, 2001 MAA Ohio Spring Meeting, Bowling Green [advisor Dr. Mihai Caragiu]

### Senior Capstone Presentations in Math/Stat at Ohio Northern

###
**Recent capstone presentations by ONU math/stat majors**

- Bradley Lockhart: Force Propagation in Multi-Rod Drumsticks [Fuller] 2019
- Takumi Kijima: Naive Bayes Classifier [Wang] 2019
- Addison Carter: An Introduction to Partitions and Compositions [Caragiu] 2019
- Emma Talley: Multivariate Analysis of Variance [Wang] 2019
- Rachel Liebrecht: Special Topics on Graph Theory and Ramsey Numbers [Caragiu] 2019
- Grant McConnel: Problem Posing Using the Mathematical Game Qubic [Robinson] 2019
- Dylan Battison: SAS Base Programmer Certification [Rahrig] 2019
- Shannon Tefft: Processing Quadratic Residues with Ducci Iterations [Caragiu] 2019
- Andrew Kurdys: The Autoregressive Model and Real Life Time Series Applications [Rahrig] 2019
- Jenna Holler: American Mathematics Competitions – Variations and Generalizations [Caragiu] 2018
- Joseph Stomps: American Mathematics Competitions AMC 10 - analogies and generalizations [Caragiu] 2018
- Ian Simpson: Passive Scalar Transport of Contaminants via Traveling Waves [Fuller] 2018
- Andrew Tomkins: Statistical Analysis of Library Surveys Using SAS [Wang] 2018
- Gia Saturday: Myth Busting the Sophomore Slump [Wang] 2018
- Zachary Goodchild: Three Dichotomous Variables: There is more to it than you think [Robinson] 2018
- Lindsely Black: Player Efficiency Ratings for Basketball Players [Rahrig] 2018
- Jennifer Point: Brownian Motion & Its Application to Stock Evaluation [Rahrig] 2017
- Kyle Thomas: Performance Evaluation of Selected Normality Tests, a Simulation Study [Wang] 2017
- Jessica Lewe: Analysis of Fall Preventions Outreach Survey Using Nonparametric Statistical Methods" [Wang] 2017
- Meredith Eichenlaub: Variation of Probability: Baseball and the Binomial Distribution [Robinson] 2017
- Matthew Golden: The Baker-Campbell-Hausdorff Formula [Caragiu] 2017
- Michelle Haver: Poissonian Character and Chebyshev Bias for Greatest Prime Factor Sequences: a Computational Analysis [Caragiu] 2017
- Andrew Harden: The Capital Asset Pricing Model & Markowitz Problem" [Jaki] 2017
- David Zirkle: The Lognormal Distribution as a Model for Stock Prices [Rahrig] 2017
- Kaila Bollinger: Kruskal-Wallis versus Classical One-Way Analysis of Variance: Who's the Winner? [Rahrig] 2016
- Brandon Wilson: Black-Scholes Formula [Jaki] 2016
- Jeffrey Hancock: Optimal Strategy for an Obscure Game Show" [Robinson] 2016
- Nathan Knodel: Exact Solutions of Cubic-Quintic Duffing Oscillators [Fuller] 2016
- Abigail Thayer: Computer Solutions of the One Dimensional Diffusion Equation [Johns] 2015
- Brian Slabe: Contingent Payment Methods [Rahrig] 2015
- James Rader: Analysis of Points After Touchdown in the NFL [Putt] 2015
- Ashley Ernst: A Group Theoretic Development of Isospin and Low Isospin Multiplets [Fuller] 2015
- Benjamin McKinnis: The Square Wheel Problem [Hunt] 2014
- Brandon Guillen: A Look at Bayesian Statistics [Robinson] 2014
- Amanda Marco: Fibonacci Numbers and Some of Their Properties [Caragiu] 2014
- Kerry DuLaney: Exploring Gears and Watchmaking [Hunt] 2014
- Lacey Hittle: Progression on Regression: A Look at Multicollinearity [Rahrig] 2014
- Matthew R. Zirkle: Finding Square Roots in a Prime Field [Caragiu] 2013
- Thomas E. Steinberger: Arithmetic Functions of Several Variables on the Gaussian Integers [Jaki] 2013
- Jonathan C. Schroeder: Small Special Pairs of Primnitive Roots [Caragiu] 2013
- Devin F. Kisor: Eploration of the Regression to the Mean Phenomenon [Robinson] 2013
- Morgan Hammer: Applications of Direct Products to Molecular Spectroscopy [Putt] 2013
- Kelsie E. Zumberger: Did You Cheat In School This Year? [Robinson] 2013
- Donald J. Pleshinger: On a Congruence of Ohtsuka [Caragiu] 2013
- Matthew J. McCandless: Picturing Eigenfaces [Retterer] 2013
- Joanna Snyder: Analyzing the "Hot Hand" Effect [Rahrig] 2012
- Jennifer Krauss: In the World of a Taxicab Driver: an Exploration of Conic Sections in Taxicab Geometry [Putt] 2012
- Hannah (DePriest) Barnaba: How Much Does One Point Matter: A Study on the Probability of Winning a Tennis Match and the Generalized Case of Winning by n [Rahrig] 2012
- Lauren Cassell: Guarding a Koch Fractal Art Gallery [Fuller] 2012
- Ashley Risch: An Euler-Fibonacci Sequence. [Caragiu] 2011
- Molly Eickholt: Simplifying Ford Links [Hunt] 2011
- Lauren Sutherland: Multidimensional Greatest Prime Factor Sequences [Caragiu] 2011
- Lucas Witt: Sometimes Two Wrongs Do Make a Right [Robinson] 2011
- Lindsey Miller Walch: Chordal Geometries and Their Axioms [Fuller] 2011
- Joshua Szekely: The Quantum Harmonic Oscillator and the Hermite Polynomials [Boyadzhiev] 2011
- Greg Back: The Greatest Prime Factor and its Applications [Caragiu] 2010
- Jenna Brace: Traffic Flow Simulation with Cellular Automata [Caragiu] 2010
- Josh Caldwell: Misuses of Statistics [Robinson] 2010
- Kevin Earnest: Perturbations in the Aerospace Sequence of Attitude Determination Using Quaternions [Fuller] 2010
- John Holodnak: The Perron-Frobenius Theorem and Applications [Caragiu] 2010
- Kyle Meyer: Parity in Professional Sports [Robinson] 2010
- Matt Rader: Quantifying Defensive Ability in Baseball [Putt] 2010
- Sharon Binkley: The One Time Pad and Text Visualization [Caragiu] 2009
- Joshua Stoffel: Maxwell's Equations through the Major Vector Theorems [Boyadzhiev] 2009
- Joshua Somerlot: The Affine Cipher [Caragiu] 2009
- Brock Prater: Transmission and Reflection Holograms [Hovis] 2009
- Eric Gossett: Behavior of Particles in Circular Vertical Floe with Magnus Effect" [Fuller] 2009
- Axel Brandt: Classification of Ford Links [Hunt] 2009
- Andrew Magyar: The Einstein's Field Equations [Fuller] 2009
- Amanda Stype: Holy Voley! How Should We Allocate Those Traps? [Robinson] 2009
- Michael Gabrieli: The Exploration of Time Series and Forecasting [Robinson] 2009
- Michael Garee: Solitary Waves and KdV Theory [Fuller] 2008
- Steven Garofalo: Relational Model for Database Management [Retterer] 2008
- Brittany Metz: Latin Squares, Probability, and their involvement in the Sudoku [Robinson] 2008
- Heather Schimmoeller: B2 or not B2. That is the Question [Robinson] 2008
- Ashley Yontz: Mathematics and Stocks: Risk Analysis of a Portfolio [Putt] 2008
- Lorelei Rautsaw: The Geometry of Flowers [Raiti] 2008
- Christopher Lemon: Markov Chains and the Heat Bath Monte Carlo Algorithm for the Ising Model of Ferromagnetism [Johns] 2008
- Stacy Nagel: Symmetry and Quilting [Raiti] 2008
- Brian Henderson: A Probability Distribution Associated with the Minehunt Game [Hovis] 2008
- Katie Milligan: The Underlying Mathematical Patterns of Tessellations [Schroeder] 2008
- Gretchen Deeg: Projective Geometry and the Art of Perspective [Hovis] 2008
- Rachel Fye: An Analysis of Stock Portfolios: Random vs. Non-Random [Putt] 2007
- Tyler Dunlap: Ford Links [Hunt] 2007
- Andrew Homan: An Overview of Model Theory and Completeness [Caragiu] 2007
- Aaron Piper: Given two fractions, what is the fraction between the two that has the smallest denominator? [Robinson] 2007
- Greg Snyder: March Madness Probabilities [Robinson] 2007
- Mark Bierkan: To Deal or Not to Deal - is that the Question? [Robinson] 2007
- Matthew Shonkwiler: Conflict: A Game Theory Approach [Putt] 2007
- Megan Reese: The Golden Section and Design [Raiti] 2007
- Charise Kazmierczak: Geometry of Rose Windows [Raiti] 2007
- Katie Miklovic: The Truth Behind the Witch of Agnesi [Schroeder] 2007
- Anthony Gerdeman: A Venture Into the World of Obstructed Random Walks [Robinson] 2006
- Allison Mackay: Elementary Number Theory and Classical Cryptography [Caragiu] 2006
- Lisa Scheckelhoff: GPF Sequences [Caragiu] 2006
- Brandon Bucholtz: The Euclidean Algorithm [Caragiu] 2006
- Kara Stechschulte: Braids and Music [Fuller] 2006
- Michael Paulus: Predicting Winning Percentage: An Application of Mathematics to Sports [Putt] 2006
- Adam Hibbard: Predicting Movie Ratings [Robinson] 2006
- Dan Gudorf: Mary Had a Little Paradox: Whose fleece was and was not as white as snow... [Fuller] 2006
- Jason Bockey: Ford Circles [Hunt] 2006
- Jacob L. Johanssen: Fibonacci-Lucas Densities [Caragiu] 2006
- Kristine Patton: An investigation of Continued Fractions [Schroeder] 2006
- Kara S. Lewis: A look at Confounding [Robinson] 2005
- Matt Katschke: San Gaku Problems in Hyperbolic and Spherical Geometry [Hunt] 2005
- Nathan Baxter: Finite Fields [Caragiu] 2005
- Jennifer Szippl: Platonic solids [Raiti] 2004
- Julie Holda: Monte Carlo simulations [Robinson] 2004
- Tyler Betts: Applications of Group Theory in Chemistry [Putt] 2004
- Clinton Louiso: Tic-Tac-Toe: an in-depth analysis [Robinson] 2004
- Molly Neer: Mathematics and Arts at Ohio Northern University [Fuller] 2004
- Mark Clausing: Advanced Compass and Straightedge Constructions [Hunt] 2004
- Michael Hewit: The Ehrenfest Model, Analysis via Markov Chains and Recurrent Events [Johns] 2004
- Sara Miller: Fibonacci Numbers [Caragiu] 2003
- Julia Gould: Fear of Crime, An Investigative Analysis [Putt] 2003
- Matthew Suchan: Is Hitter Performance Affected by Free Agency? [Putt] 2003
- Ann Boerger: The Value of a Bond [Putt] 2002
- Reid Moore: Analysis of Interest and Basic Annuities [Putt] 2002
- Stacey Stillion: Covariates of Pancreas Transplant Survival in Recipients of Combined Kidney-Pancreas Grafts [Putt] 2002
- Laura DiMarco: Classification of Compact, Connected Topological Surfaces Without Boundary [Raiti] 2001
- Kimberly Myers: Bond Valuation [Putt] 2001
- Stephanie Osgood: Statistics Reveal the True "Best Hitters" in Baseball [Putt] 2001
- Ivan Tornes: The Circular Vibrating Membrane [Boyadzhiev] 2001
- Jason Kline: The Fourier Series and Some Applications [Boyadzhiev] 2000
- Rachel Kahlenberg: Confidence Intervals for One Pupulation Mean [Song] 2000
- Ryan Snivley: Analysis of Categorical Data [Song] 2000
- Sarah Ruppert: Rubik's Cube [Retterer] 2000
- Lindsay Nicholson: Fourier Series [Lahmon] 2000
- Tim Thompson: Solutions to the Shortest Path Problem [Putt] 1999
- Nathan Hyatt: Hypothesis Testing [Song] 1999
- William Anthony: Recurrent Events [Hovis] 1999
- Justin Reckner: Differential Geometry of Curves in 3-Space [Raiti] 1999
- Bodi Kauffman: The Stieltjes Integral [Boyadzhiev] 1999
- Chris Finney: The Mathematics of Annuity Valuation [Putt] 1999
- James Conine: Fuzzy Sets [Hovis] 1998
- Lee Koratich: Functions of Matrices [Boyadzhiev] 1998
- Jason McCartney: Game Theory [Shult] 1998
- Amanda Pater: Regression Analysis [Song] 1998
- Michelle Schlauch: Random Walks [Roepke] 1998

## Wednesday, April 25, 2018

### Repeat a number of 3011 digits

If we repeat twice a number of 3011 digits, the resulting number is divisible by the prime number
9090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909091
(the prime factors of 10^3011+1 are 11 and the above number - MAPLE verification).

## Wednesday, February 7, 2018

### Partitions, Dyson, and Ramanujan - George Andrews

In 2013, Freeman Dyson celebrates his ninetieth birthday and also marks his sixtieth year as a Professor at the Institute for Advanced Study. Dreams of Earth and Sky, conceived by Dyson’s colleagues in the School of Natural Sciences, was an opportunity to provide a perspective on his work and impact across the sciences and humanities. Held on the Institute campus from September 27-28, the program featured a range of talks on mathematics, physics, astronomy, and public affairs that reflect both the diversity of Dyson’s interests and his ability to open new dialogues and inspire generations of scholars. https://video.ias.edu/dyson-dreams

Partitions, Dyson, and Ramanujan - George Andrews

Introduction by Peter Sarnak

Partitions, Dyson, and Ramanujan - George Andrews

Introduction by Peter Sarnak

## Friday, February 2, 2018

## Tuesday, September 19, 2017

### Mathematicians...

“Mathematicians are finite, flawed beings who spend their lives trying to understand the infinite and perfect.” (Bruce Schechter, My Brain is Open: The Mathematical Journeys of Paul Erdős)

## Friday, August 25, 2017

### Lectures on Gravity

*February 14 - 28, 2015 Winter School on Gravity and Light*

*Johannes Kepler University, Linz, Austria*

*100th anniversary of Einstein's theory of general relativity*

Great set of YouTube video lectures -

**HERE**

### Plimpton 322

Mathematical mystery of ancient Babylonian clay tablet solved - PHYS.ORG - August 24, 2017

Photo source: Plimpton 322, Babylonian tablet listing pythagorean triples - Wikimedia commons

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