## Saturday, May 20, 2023

## Thursday, May 11, 2023

### Senior Capstone presentations - May 10, 2023

Session of Senior Capstone presentations today at ONU, featuring topics on Partial Differential Equations and Number Theory. It was definitely a success, with a lively attendance. Many thanks to these awesome students!

## Monday, May 1, 2023

## Wednesday, March 1, 2023

## Wednesday, February 1, 2023

### Number theory and cryptography class - chalkboard pictures

Today, the topic was the Euclidean algorithm...

Just before erasing this number theoretic Tibetan mandala :)

## Friday, December 16, 2022

### Undergraduate research - a post pandemic restart

My first post-pandemic faculty-student paper and the 14-th overall (written with Rachael Harbaugh, ONU '23, a talented Mathematics Education major). Glad for this "restart". Students need confidence, need to be exposed to interesting math topics, and then we hope for the best in their future timelines.

## Friday, December 9, 2022

### Senior Capstone Colloquium - Fall 2022

Mathematics Capstone Colloquium - December 7, 2022 @ohionorthern (from L to R: Dr. Chowdhury, Joelena Brown, Rachael Harbaugh, and Dr. Caragiu)

Joelena Brown: "Rectangular Donut Numbers" (advisor Dr. Chowdhury)

Rachael Harbaugh: "Extending a Putnam Problem to Fields of Various Characteristics" (advisor Dr. Caragiu)

## Monday, November 7, 2022

## Thursday, November 3, 2022

## Wednesday, June 29, 2022

## Monday, June 20, 2022

### The random Fibonacci sequence and the Viswanath's constant

Random Fibonacci recursion

https://en.wikipedia.org/wiki/Random_Fibonacci_sequence

In mathematics, therandom Fibonacci sequenceis a stochastic analogue of the Fibonacci sequence defined by the recurrence relation $f_{n}=f_{n-1}\pm f_{n-2}$, where the signs + or − are chosen at random with equal probability ${\tfrac {1}{2}}$, independently for different $n$. By a theorem of Harry Kesten and Hillel Furstenberg, random recurrent sequences of this kind grow at a certain exponential rate, but it is difficult to compute the rate explicitly. In 1999, Divakar Viswanath showed that the growth rate of the random Fibonacci sequence is equal to 1.1319882487943...(sequence A078416 in the OEIS), a mathematical constant that was later named Viswanath's constant.

## Tuesday, May 31, 2022

## Saturday, May 21, 2022

## Friday, April 22, 2022

## Sunday, March 27, 2022

## Wednesday, March 23, 2022

## Friday, March 18, 2022

### A nice application of Calculus 2

Via @10kdiver

*Take 2 random numbers X and Y between 0 and 1. What's the probability that the integer nearest to X/Y is even?*

Prove that said probability is (5-Pi)/4.

## Monday, February 28, 2022

### Experimental math fantasy 1

In my classes I often try to communicate the specific sense of wonder arising from mathematical experimentation, to the benefit of undergraduates. Here "phi" represents the Euler's totient function, in a serendipitous trigonometric (albeit nonlinear) mix.

## Saturday, February 26, 2022

## Friday, February 25, 2022

# What is chaos? A complex systems scientist explains

Mitchell Newberry,*University of Michigan*

Chaos evokes images of the dinosaurs running wild in Jurassic Park, or my friend’s toddler ravaging the living room.

In a chaotic world, you never know what to expect. Stuff is happening all the time, driven by any kind of random impulse.

But chaos has a deeper meaning in connection to physics and climate science, related to how certain systems – like the weather or the behavior of a toddler – are fundamentally unpredictable.

Scientists define chaos as the amplified effects of tiny changes in the present moment that lead to long-term unpredictability. Picture two almost identical storylines. In one version, two people bump into each other in a train station; but in the other, the train arrives 10 seconds earlier and the meeting never happens. From then on, the two plot lines might be totally different.

Usually those little details don’t matter, but sometimes tiny differences have consequences that keep compounding. And that compounding is what leads to chaos.

A shocking series of discoveries in the 1960s and ‘70s showed just how easy it is to create chaos. Nothing could be more predictable than the swinging pendulum of a grandfather clock. But if you separate a pendulum halfway down by adding another axle, the swinging becomes wildly unpredictable.

## Chaos is different from random

As a complex systems scientist, I think a lot about what is random.

What’s the difference between a pack of cards and the weather?

You can’t predict your next poker hand – if you could, they’d throw you out of the casino – whereas you can probably guess tomorrow’s weather. But what about the weather two weeks from now? Or a year from now?

Randomness, like cards or dice, is unpredictable because we just don’t have the right information. Chaos is somewhere between random and predictable. A hallmark of chaotic systems is predictability in the short term that breaks down quickly over time, as in river rapids or ecosystems.

## Why chaos theory matters

Isaac Newton envisioned physics as a set of rules governing a clockwork universe – rules that, once set in motion, would lead to a predetermined outcome. But chaos theory proves that even the strictest rules and nearly perfect information can lead to unpredictable outcomes.

This realization has practical applications for deciding what kinds of things are predictable at all. Chaos is why no weather app can tell you the weather two weeks from now – it’s just impossible to know.

On the other hand, broader predictions can still be possible. We can’t forecast the weather a year from now, but we still know what the weather is like this time of year. That’s how climate can be predictable even when the weather isn’t. Theories of chaos and randomness help scientists sort out which kinds of predictions make sense and which don’t.

*Read other short accessible explanations of newsworthy subjects written by academics in their areas of expertise for The Conversation U.S. here.*

Mitchell Newberry, Assistant Professor of Complex Systems, *University of Michigan*

This article is republished from The Conversation under a Creative Commons license. Read the original article.

## Sunday, February 13, 2022

## Saturday, January 15, 2022

## Tuesday, January 4, 2022

## Tuesday, December 28, 2021

## Tuesday, December 14, 2021

## Monday, November 22, 2021

### Charles W. Trigg - Geometric Proof of a Result of Lehmer's

**See https://www.fq.math.ca/Scanned/11-5/trigg.pdf** - Fibonacci Quarterly Vol. 11 No. 5 (Dec. 1973)

## Sunday, October 24, 2021

## Wednesday, September 1, 2021

### Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

**https://www.youtube.com/playlist?list=PLbN57C5Zdl6j_qJA-pARJnKsmROzPnO9V**

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering."

## Friday, August 27, 2021

### New paper

AN ELEMENTARY NOTE ON THE GREATEST PRIME FACTORS OF LINEARLY RELATED INTEGERS

JP Journal of Algebra, Number Theory and Applications

Volume 52, Issue 1, Pages 95 - 100 (October 2021)

http://dx.doi.org/10.17654/NT052010095

## Thursday, August 5, 2021

### My Top 100 book as a jazz of numbers

**Sequential Experiments with Primes** got into the 100 Best Number Theory Books of All Time @ https://bookauthority.org/books/best-number-theory-books As an undergraduate college faculty member, I am happy. Thank you! :-)

I believe the attractiveness of the book lies not only on the novelty of certain ideas, but also in the style in which said novelty is attained. It's a sort of "jazz" with numbers (unfolding as a sustained creative piece not unlike the free development of a jazz gig). A jazz with no particular rigid/studied reverence to other established theoretical
approaches. Just free self-sustained jazz discovering new facts. In its way, it's structured as a sort of "*dessins d'enfants*" leading to a different look on the mystery of prime numbers.

## Monday, August 2, 2021

## Wednesday, July 28, 2021

### Computer Scientists Attempt to Corner the Collatz Conjecture

Quanta Magazine: *Computer Scientists Attempt to Corner the Collatz Conjecture*

"A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot."

### Francis Su: How does mathematics contribute to human flourishing?

“Those of us who do math for a living actually are drawn to math often because of this exploratory nature, and we love the creativity,” Su said. “The argument that I make is that these virtues carry over to other areas of your life.”

Read** ****Francis Su: How does mathematics contribute to human flourishing?**

## Sunday, July 4, 2021

### New paper on the friendship paradox

**The friendship paradox in real and model networks **

George T Cantwell, Alec Kirkley, and M E J Newman

*Journal of Complex Networks*, Volume 9, Issue 2, April 2021

https://doi.org/10.1093/comnet/cnab011

Published: 27 May 2021

## Monday, May 24, 2021

### Deep focus

“*I work on things nobody cares about, and I’m quite happy that way.*” - L. Mahadevan

(via Steven Strogatz)

## Thursday, May 20, 2021

## Wednesday, May 19, 2021

## Wednesday, May 12, 2021

### Stirring the pot

On a related note, a page on patterns with primes, with contributors including Charles W. Trigg and Martin Gardner:

## Sunday, May 9, 2021

## Friday, April 30, 2021

## Monday, March 29, 2021

### Received another endowed chair at ONU

## Thursday, March 25, 2021

### Journal papers with ONU students co-authors UPDATE

student co-author(s) in *italics*

**NOTE:** *Starting
Fall 2020, the Mathematics and Statistics Department is replaced by two
programs in the School of Science, Technology, and Mathematics: the
Mathematics program, and the Statistics program. The records for **The Mathematics and Statistics Department cease here. From here on, our records will involve the Mathematics program only.*

*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 Vol 19, Issue 1, 27 - 37 (February 2019) https://arxiv.org/abs/1902.07314 ; - Mihai Caragiu and
*Addison Carter*,**Random Compositions for the Undergraduate Classroom.**Far East Journal of Mathematical Education Vol 19, Issue 2, 129 - 139 (June 2019)

*Kristi Patton*, Sandra Schroeder and Richard Daquila:*An Investigation of Continued Fractions,*Electronic Proceedings of Undergraduate Mathematics Day, Volume 2, Nov. 2005.- Steven Manns, Anup R. Lamichhane,
**Derivation of the (Closed-Form) Particular Solution of the Poisson Equation in 3D Using the Oscillatory Radial Basis Function**, Electronic proceedings of Undergraduate Mathematics Day, 2020

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

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

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

**NOTE:** *Starting
Fall 2020, the Mathematics and Statistics Department is replaced by two
programs in the School of Science, Technology, and Mathematics: the
Mathematics program, and the Statistics program. The records for **The Mathematics and Statistics Department cease here. From here on, our records will involve the Mathematics program only.*

- Steven Manns: "Derivation of the (Closed-Form) Particular Solution of the Poisson’s Equation in 3D Using Oscillatory Radial Basis Function", 2019 Undergraduate Math Day, Dayton, OH [advisor Dr. Anup Lamichhane]
- Dr. Todd France, Kaity Kelly, Megan Meyer, Will Sierzputowski and Dr. Tena Roepke: “Bridging the Span between Math and Engineering with Spaghetti” (OCTM 2019 Conference, Sandusky, OH) [advisors Dr. Todd France and Dr. Tena Roepke]
- Steven Manns: "A (Closed-Form) Particular Solution of the Poisson Equation in 3D" - 2019 Ohio MAA Fall Meeting - Shawnee State University [advisor Dr. Anup Lamichhane]
- Samuel Powell: "Applications of Group Theory in Chemistry" - 2019 Ohio MAA Fall Meeting - Shawnee State University [advisor Dr. Anup Lamichhane]
- 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 UPDATE

###
**Capstone presentations by ONU math/stat majors 1998 - Spring 2020**

**NOTE:** *Starting Fall 2020, the Mathematics and Statistics Department is replaced by two programs in the School of Science, Technology, and Mathematics: the Mathematics program, and the Statistics program. The records for **The Mathematics and Statistics Department cease here. From here on, our records will involve the Mathematics program only.*

- Kaleigh Cummins: The Birthday Problem - an Expanded Look [Rahrig] 2020
- John Mullin: What Makes a Successful Hire for A College Library [Wang] 2020
- Hannah Ray: Heel Spur Surgery: Evaluating the Outcomes [Wang] 2020
- Travis Maenle: A linear complexity analysis of quadratic residues and primitive roots spacings [Caragiu] 2020
- Bryan Peck: Bell's Inequalities [Caragiu] 2020
- Kenneth Eaton: The Fundamentals of Automated Theorem Proving [Caragiu] 2019
- Megan Meyer: An Experimental Approach to Sophie Germain Sequences [Caragiu] 2019
- Corey Thrush: Two Person Zero Sum Games [Robinson] 2019
- Kayla Rieman: Flipping Coins [Rahrig] 2019
- 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
- Kate Klopp: Wheel of Fortune: From a Statistical Standpoint [Robinson] 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
- David Mangus: "Let's Get Paradoxical: A Statistical Major's Quest to Solve Some Common Problems [Robinson] 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
- Andrew 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 [Lhamon] 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

**ADVISING 5 OR MORE CAPSTONE PROJECTS (1998 - Spring 2020)**:

- Caragiu 29
- Robinson 25
- Putt 18
- Fuller 13
- Rahrig 12
- Hunt 8
- Wang 8
- Raiti 7
- Boyadzhiev 6
- Hovis 5