"*Three’s a crowd: an exploration of subprime tribonacci sequences*" - *College Mathematics Journal* 54, No. 5, 464-475 (2023) - by Sara Barrows, Emily Noye, Sarah Uttormark, and Matthew Wright.

"*Three’s a crowd: an exploration of subprime tribonacci sequences*" - *College Mathematics Journal* 54, No. 5, 464-475 (2023) - by Sara Barrows, Emily Noye, Sarah Uttormark, and Matthew Wright.

A wonderful article by Laurie Wurth-Pressel (**source**)

2024 marks the 130th anniversary of The American Mathematical Monthly.

The trailblazer who launched this premier academic journal in 1894
and inspired the establishment of the American Mathematical Association
(AMA) graduated from Ohio Northern University in the late 1800s—**Benjamin Franklin Finkel,** BS 1888, BA 1896.

Mathematical problems fascinated Finkel from a young age, and his eagerness to solve them impelled his ambition to “publish a journal devoted solely to mathematics and suitable to the needs of teachers of mathematics.”

He once stated: “Many dormant minds have been aroused into activity through the mastery of a single problem.”

Over a century later, Finkel’s statement still rings true.

While much has changed at Ohio Northern since Finkel’s days, the University continues to attract brilliant problem-solvers molded in Finkel’s character who graduate to become leading mathematicians and physicists.

Read about three outstanding alumni from ONU’s School of Science, Technology, and Mathematics, housed in the Getty College of Arts & Sciences, who are making a mark in the world of physics and mathematics.

**Thomas (Tommy) Steinberger**, BS ’14, Ph.D., is breaking new ground in experimental plasma physics at West Virginia University in Morgantown, W.V.

A research assistant professor in the Department of Physics and Astronomy, he explores charged gas systems (plasmas), investigating gas particle motion and temperature. His work aims to enhance electronics manufacturing, space travel, and our understanding of space phenomena, such as magnetic reconnection.

“I come into the lab and can work on 10 different projects before lunch,” he said. “I have a lot of ongoing projects that are unique. Most of my effort is helping all these projects move forward.”

Steinberger’s journey began in freshman Algebra class in high school. While his classmates bellyached about having to solve 50 of the 100 algebra problems listed in the final exam, he felt a burst of excitement.

“I completed nearly all 100 in a couple of days, almost obsessively,” he recalled.

His ONU experience further ignited his passion for problem solving. He joined ONU-SOLVE, a problem-solving group of students that tackle the challenging problems found in leading math magazines such as Fibonacci Quarterly, Mathematics Magazine, The College Mathematics Journal, and Finkel’s own The American Mathematical Monthly.

ONU-SOLVE has been recognized multiple times in recent years for submitting correct solutions, and several have been published in leading journals as the most well-written solutions, according to Mihai Caragiu, Ph.D., professor of mathematics.

According to Steinberger, several solutions he worked on with the assistance of ONU professors received honorable mentions in academic magazines.

“My time at ONU really fostered my interest in math and its application to other fields,” he said. “I received fantastic instruction from professors who truly cared about their students.”

After graduating from ONU with a double major in mathematics and physics, and minor in astronomy, Steinberger received a master’s degree in physics and astronomy, and a Ph.D. in experimental plasma physics from West Virginia University.

“The challenge of the subjects (math and physics) resonates with my stubborn nature,” he added. “It leads me to be ever more persistent in my studies.”

**Ashley Ernst,** BS ’15, Ph.D., is a senior physicist
at Arcfield in Colorado Springs, Colo, where she helps to solve complex
challenges in support of the United States’ most critical national
security missions.

Arcfield is a leading provider of mission-focused systems engineering and integration capabilities to the U.S. Intelligence Community, Department of Defense, and other agencies.

Ernst is currently working primarily with simulation and modeling of radiation in both vacuum and in atmosphere or material. She develops technical documentation, presents work to clients, and performs calculations with the aid of software.

“There is always another problem on the horizon,” she says. “The quest for the solution to the next problem is what drives me every day.”

Growing up, Ernst loved to solve jigsaw puzzles with her mom. As her skill increased, so did her hunger for harder challenges.

“They became larger in puzzle number, smaller in puzzle piece size, and more complex in shape and design,” she said. “When that wasn’t enough, I started solving puzzles without guide pictures.”

When she first arrived at ONU, however, she lacked focus and felt extremely homesick. Her ONU professors noticed her struggles and made special efforts to engage her in math conferences and ONU-SOLVE. Professor Caragiu spurred her mind into action by exposing her to Graph Theory and Discrete mathematics.

“Having a direction for my mental energy definitely helped me,” she said.

Within a short time, she says, she was on a better path forward. “I would not be where I am today without their help. The math and physics programs at ONU nurture the search for knowledge. No matter the level, the program meets the student at that level and pushes them to the next level.”

After graduating from ONU with a double major in physics and applied mathematics, Ernst earned a master’s degree in physics and a Ph.D. in hadronic physics from Florida State University. Her second year of graduate school, she received a highly-competitive National Science Foundation (NSF) Graduate Research Fellowship, which she credits to the quality of education and one-on-one mentoring she received at ONU.

“Each student that passes through the math program at ONU is instilled with a sense of excitement regarding a problem. While that problem may change, that excitement stays,” she said.

**Matthew Golden,** BS ’17, Ph.D., is a postdoctoral
fellow at the Georgia Institute of Technology in the Xtreme Astrophysics
group. The group is led by two founding members of the Event Horizon
Telescope Collaboration, which released the first image of a black hole
in 2019.

“I am a full-time researcher,” he said. “My research focuses on the interface of machine learning and physics. Specifically, I work on using machine learning to accelerate human learning. Our goal is to produce physics equations directly from complex data with minimal human intervention.” His recent publication in Science Advances showed how machine learning learned the equations of a living fluid directly from a video of the experiment.

In high school, Golden became enthralled with solving “twisty puzzles”—think Rubik’s cube, only the more complicated versions. He had puzzles of every platonic solid and with hundreds of pieces. Some would take him mere minutes to solve, others weeks.

“I eventually went on to solve the four-dimensional 3x3x3x3 Rubik’s cube,” he said. “You can find my name in the 4D Hall of Fame as solver #196.”

At ONU, his obsession switched to General Relativity. He spent many late nights in the Mathile Center for the Natural Sciences working through derivations. Then, he’d head to the third floor of Heterick Memorial Library, pull a random math or physics book from the shelf, and read until he was “hopelessly confused.”

“My schooling was significantly accelerated compared to the usual undergraduate,” he said. “That’s because the physics department was small and the teachers eager to teach at any pace.”

His professors allowed him to take courses in any order he desired. He completed Quantum Mechanics his first semester, then continued to grow his knowledge in leaps and bounds. He’ll never forget being the only student in Dr. Khristo Boyadzhiev’s Real Analysis class. Dr. Boyadzhiev, who obtained YouTube fame for his consistent classroom outfit and greeting, passed away in June 2023.

“It feels like half the people my age know Dr. Khristo Boyadzhiev because of his lovable appearance on Vine,” said Golden. “He was a micro celebrity, and I still remember him laughing about it in the hall.”

Golden also recalls leading a small group of students to first place in the 2017 Ohio MAA Leo Schneider Team Math Competition, dethroning Case Western Reserve University for the first time in many years.

With accelerated learning and one-on-one attention, Golden says he was way ahead of his peers in graduate school.

“The education I received was passionate and tailored to me,” he said. “There is no math program in the Midwest that could compete with the personal attention I received at ONU, and it paid off.”

He’s ecstatic that his professional career is centered on gravity research.

“I love that every day I get to think about machine learning and extreme astrophysical environments,” he said. “I get to interact with some of the greatest minds in physics.”

Topic: Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions

Speaker: Florian Richter, Northwestern University

June 4, 2020

"A1Dcellular automaton,Rule 110(bottom), being fed as input to a 2D cellular automaton,Conway’s Game of Life(top)"

**https://www.cde.ca.gov/nr/ne/yr23/yr23rel54.asp **

CDE/SBE Joint Release: #23-54

July 12, 2023

July 12, 2023

SACRAMENTO—The California State Board of Education today approved the *2023* *Mathematics Framework for California Public Schools, *instructional
guidance for educators that affirms California’s commitment to
ensuring equity and excellence in math learning for all students.

“I’m thankful for everyone who worked tirelessly to develop this framework to ensure California’s students have equitable access to rigorous and high-quality math instruction that will prepare them for the future. The framework has struck a great balance in new ways to engage students in developing a love for math while supporting those on an accelerated path,” said Mary Nicely, Chief Deputy Superintendent of Public Instruction. “Our State Superintendent is a champion of equity and excellence, and it is our core mission that every child—regardless of race, ZIP code, or background—has access to a quality education. The approval of the revised Math Framework is one more step forward to meeting the needs of all California’s students.”

The vote today concludes four years of work to update math instructional guidance aligned with the California Common Core State Standards for Mathematics (PDF), which are rigorous learning standards that detail what every student should know and be able to do at every grade level. The framework approved today is the third iteration and reflects revisions responsive to thousands of public comments fielded over two 60-day public comment periods and two public hearings.

The draft was presented by Dr. Mike Torres, Executive Director of the Instructional Quality Commission and a former high school math teacher. Others who participated in the presentation include Dr. Kyndall Brown, Executive Director of the California Mathematics Project at the University of California, Los Angeles; Omowale Moses, Founder and Chief Executive Officer of Math Talks; Dr. Adrian Mims, Founder of The Calculus Project; Ellen Barger, Chair of the Curricular and Improvement Support Committee of the California County Superintendents; and Dr. Linsey Gotanda, Vice Chair of the Instructional Quality Commission.

“This framework provides strategies to challenge, engage, and support all students in deep and relevant math learning by building on successful approaches used in nations that produce high and equitable achievement in math,” said State Board President Linda Darling-Hammond. “It also draws on the experiences of educators who have worked for a decade to develop successful strategies for teaching California’s rigorous standards, carrying those lessons to others across the state. This framework provides teachers and schools with a path to greater excellence with greater equity.”

The guidance includes strategies to:

- Structure the teaching of the state’s math standards around “big ideas” that integrate rather than isolate math concepts—a best practice in high-performing countries.
- Increase focus on developing student mathematical expertise as described in California’s Standards for Mathematical Practice, which include the ability to make sense of problems and persevere to solve them; to reason abstractly and quantitively; to attend to precision; and to apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.
- Connect learning to the “real world” through authentic examples and use of data, prompting students to ask and answer meaningful questions. Adding authenticity to lessons helps teachers answer students’ questions around “why do I need to learn this?”
- Allow students to “see themselves” in curriculum and in math-related careers by making math instruction culturally relevant and empowering.
- Stimulate deep learning by sparking student curiosity through lessons that encourage inquiry and problem-solving.
- Ensure that students develop both appreciation of math concepts and fluency in using math efficiently through the productive use of algorithms and mastery of math facts they have come to understand.
- Integrate and align math concepts taught at the elementary, middle, and high school levels.
- Ensure that all high school math pathways are open to all students.
- Support multiple ways to get more students to higher level mathematics—ranging from successful acceleration to differentiated instruction, personalized supports, extra lab sections, and additional coursework offered at multiple junctures—augmenting more effective core instruction.
- Expand high school math course options to encourage more students to go beyond minimum course requirements.
- Encourage students across age spans to become proficient at understanding and using data—a key skill in the 21st century job market.
- Help students to identify misleading uses of data and use data to make decisions in their roles as global citizens.
- Develop in students a “growth mindset” about mathematics, in line with the groundbreaking research of Stanford’s Dr. Carol Dweck, that supports effort and perseverance.
- Instill confidence in learners by dispelling myths about who can and cannot learn math.
- Develop instruction and curriculum that is “multi-dimensional” and employs the use of visuals, graphics, and words in addition to numbers and equations.

More information is available on the California Department of Education's Mathematics Frameworks web page, which includes frequently asked questions, an overview, and a timeline of events in the framework’s development.

# # # #

Tony Thurmond —
State Superintendent of Public Instruction

Communications Division, Room 5602, 916-319-0818, Fax 916-319-0100

Last Reviewed: Wednesday, July 12, 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!

Today, the topic was the Euclidean algorithm...

Just before erasing this number theoretic Tibetan mandala :)

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.

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)

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.

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.

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.

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.

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.

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.

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

**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."

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

**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.

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."

“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?**

**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

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

(via Steven Strogatz)

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

Received the 5th endowed chair of my career at ONU: the 2021-2022 Mary Reichelderfer Chair of Mathematics from Ohio Northern University.

student co-author(s) in *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 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

- 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]

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