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 is among the 100 Best Number Theory Books of All Time @ https://bookauthority.org/books/best-number-theory-books at #60 (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.


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)



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:

PRIME PATTERNS

Monday, March 29, 2021

Received another endowed chair at ONU

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

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.

  1. 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);
  2. Mihai Caragiu and Lisa ScheckelhoffThe Greatest Prime Factor and Related Sequences, JP Journal of Algebra, Number Theory and Applications, 6 (2), 403-409 (August 2006);
  3. 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);
  4. 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);
  5. Mihai Caragiu and John Holodnak, On Sampling Periodic Functions, Far East Journal of Mathematical Sciences, 29 (1), 145-149 (April 2008);
  6. 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);
  7. Greg Back and Mihai Caragiu, The Greatest Prime Factor and Recurrent Sequences, Fibonacci Quarterly 48, no. 4, 358-362 (November 2010);
  8. Mihai Caragiu and Ashley Risch, An Euler-Fibonacci Sequence, Far East Journal of Mathematical Sciences, Volume 52, Issue 1, Pages 1-7 (May 2011);
  9. 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);
  10. 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);
  11. 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);
  12. 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);
  13. Thomas Steinberger, Alexandru Zaharescu and Mohammad Zaki, Arithmetic Functions on Gaussian Integers, International Journal of Number Theory (December 2013);
  14. Jaki Chowdhury and Thomas Steinberger, Arithmetic Functions of Several Variables over Gaussian Integers, Mathematical Reports (accepted on 4/24/17);
  15. 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);
  16. 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 ;
  17. 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)
Conference Proceedings
  • 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
ArXiv e-prints
  • 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.

  1. 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]
  2. 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]
  3. 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]
  4. Samuel Powell: "Applications of Group Theory in Chemistry" - 2019 Ohio MAA Fall Meeting - Shawnee State University [advisor Dr. Anup Lamichhane]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. Shannon Tefft: "Processing Quadratic Residues with Ducci Iterations" - 2018 Ohio MAA Fall Meeting, Malone University, October 27, 2018 [advisor Dr. Mihai Caragiu]
  10. 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]
  11. 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]
  12. Emma Talley: "With Replacement or Without Replacement or..." - 2018 Pi Mu Epsilon Student Conference, Miami University [advisor Dr. Laurence Robinson] 
  13. 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]
  14. Takumi Kijima: "Naive Bayes Classifiers" - 2017 Ohio MAA Fall Meeting, Ohio University East, October 27, 2017 [advisor Dr. Mihai Caragiu]
  15. Aaron Kemats: "A Fibonacci-Lucas Experiment" - 2017 Ohio MAA Fall Meeting, Ohio University East, October 27, 2017 [advisor Dr. Mihai Caragiu]
  16. 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] 
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  21. 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] 
  22. Lacey Hittle: "Progression on Regression" 2014 Pi Mu Epsilon Student Conference, Miami University [advisor Dr. Ryan Rahrig]
  23. Zachary Soja: "The Case of The Disappearing Tablet", 2014 MAA Fall Meeting, University of Wittenberg [advisor Dr. William Fuller]
  24. James Rader: "Gold Glove Winners: Baseball Statistics", 2014 MAA Fall Meeting, University of Wittenberg [advisor Dr. Ryan Rahrig]
  25. Kerry DuLaney: "Exploring Gears and Watchmaking", 2014 MAA Fall Meeting, University of Wittenberg [advisor Dr. Donald Hunt]
  26. Nathan Knodel: "Scaling, Sneezes and the Elephant's Trunk" 2014 MAA Spring Meeting, Toledo, OH (April 2014) - [advisor: Dr. William Fuller]
  27. Emily Barbee: Another Downfall With Using Facebook, 2013 Pi Mu Epsilon Student Conference, Miami University - [advisor: Dr. Ryan Rahrig]
  28. Lacey Hittle: Living With Loans, 2013 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Ryan Rahrig]
  29. Thomas Steinberger: Arithmetical Functions On Gaussian Integers (poster presentation) 2013 MAA Undergraduate Poster Session, San Diego- [advisor: Dr. Mohammad Zaki]
  30. 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]
  31. James Rader: Gold Glove Winners (poster presentation) 2013 MAA Undergraduate Poster Session, San Diego - [advisor: Dr. Ryan Rahrig]
  32. James Rader: Quantifying Defensive ability in Baseball, 2012 Pi Mu Epsilon Student Conference, Miami University - [advisor: Dr. Ryan Rahrig]
  33. Emily Barbee: Are the Statistics Really Statistics? - 2012 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Ryan Rahrig]
  34. Johnathan Neville: What Difference Can A Single Game Make? - 2012 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Laurence D. Robinson]
  35. Hannah DePriest: How Much Does One Point Matter? - 2012 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Ryan Rahrig]
  36. Joanna Snyder: Hot Hand - 2012 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Ryan Rahrig]
  37. Caitlin Zook: My Relentless Struggle with a Sangaku Problem - 2012 Ohio MAA Spring Meeting, Xavier University  - [advisor: Dr. Donald Hunt]
  38. Tommy Steinberger: On Bernoulli's Inequality, 2012 Michigan Undergraduate Mathematics Conference, March 3, Siena Heights University - [advisor: Dr. Mohammad Zaki]
  39. 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]
  40. 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]
  41. Joe Mileski: The Mathematical Relationship between Musical Phrases [poster presentation], MAA Undergraduate Poster Session, 2012 Joint Mathematical Meetings, Boston - [advisor: Dr. William Fuller]
  42. Lauren Cassell: Guarding a Koch Fractal Art Gallery [poster presentation] - MAA Undergraduate Poster Session, 2012 Joint Mathematical Meetings, Boston [advisor: Dr. William Fuller]
  43. Courtney J. Brown: Special Polynomial Interpolation over Finite Fields, 2011 Undergraduate Mathematics Day, University of Dayton [advisor: Dr. Mihai Caragiu]
  44. Joseph Mileski: Paths of Melody Lines on Circles - 2011 Ohio MAA Fall Meeting, University of Findlay [advisor: Dr. William Fuller]
  45. Lauren Cassell: Guarding a Koch Fractal Art Gallery - 2011 Ohio MAA Fall Meeting, University of Findlay [advisor: Dr. William Fuller]
  46. Molly Eickholt: Simplifying Ford Links - 2011 Ohio MAA Spring Meeting, Youngstown State University [advisor: Dr. Donald Hunt]
  47. Kristin Elix: Maximizing The Product of Two Multi-Digit Numbers - 2011 Ohio MAA Spring Meeting, Youngstown State University -  [advisor: Dr. Harold Putt]
  48. David Mangus: Ways in Which I was Wrong - 2011 Ohio MAA Spring Meeting, Youngstown State University [advisor: Dr. Donald Hunt]
  49. Ashley Risch: An Euler-Fibonacci Sequence - 2010 Pi Mu Epsilon Student Conference, Miami University [advisor: Dr. Mihai Caragiu]
  50. Lauren Cassell, Joseph Mileski and Christopher Iliff: "Hyperbolic" Nine Point Circles - 2010 Ohio MAA Fall Meeting, Ursuline College [advisor: Dr. William Fuller]
  51. 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]
  52. Greg Back: The Greatest Prime Factor Function and Some Applications - 2010 Ohio MAA Spring Meeting, Kent State University [advisor Dr. Mihai Caragiu]
  53. Kevin Earnest: Perturbations in the Aerospace Sequence of Attitude Determination Using Quaternions - 2010 Ohio MAA Spring Meeting, Kent State University [advisor Dr. William Fuller]
  54. 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]
  55. Caitlin Zook: A Nonvanishing Result for Certain Sums … - 2010 Ohio MAA Spring Meeting, Kent State University [advisor Dr. Mohammad Zaki]
  56. 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]
  57. Greg Back: A Prime Addition Commutative Magma (poster presentation) - 2010 AMS-MAA Joint Meetings, San Francisco [advisor Dr. Mihai Caragiu]
  58. Andrew Magyar: Edgar Structures on Manifolds (poster presentation) - 2009 Mathfest, Portland OR [advisor Dr. William Fuller]
  59. 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]
  60. Axel Brandt: Characterisation of Ford Links - Undergraduate Knot Theory Conference, Denison University, 13-15 July 2009 [advisor Dr. Donald Hunt]
  61. Joshua Stoffel: Maxwell's equations - 2009 Ohio MAA Spring Meeting, Bowling Green [advisor Dr. Khristo Boyadzhiev]
  62. Joshua Szekely: Annular and annular-like functions - 2009 Ohio MAA Spring Meeting, Bowling Green. [advisor Dr. Donald Hunt]
  63. Gregory Back: The Jacobi symbol and cryptography - 2009 Ohio MAA Spring Meeting, Bowling Green. [advisor Dr. Mihai Caragiu]
  64. Eric Gossett: Hailstones in tornadoes - 2009 Ohio MAA Spring Meeting, Bowling Green. [advisor Dr. Bill Fuller]
  65. Sharon Binkley: One-time pad and text visualization - 2009 Ohio MAA Spring Meeting, Bowling Green. [advisor Dr. Mihai Caragiu]
  66. John Holodnak: Sudoku and binary integer programming - 2009 Ohio MAA Spring Meeting, Bowling Green. [advisor Dr. Donald Hunt]
  67. Axel Brandt: Characterisation of Ford Links - 2009 Ohio MAA Spring Meeting, Bowling Green. [advisor Dr. Donald Hunt]
  68. 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]
  69. 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]
  70. Andrew Magyar: The Structure of Digroups - 2008 MAA Ohio Spring Meeting, Marietta College [REU advisor Dr. J. D. Phillips, Wabash College]
  71. Christopher Lemon: Markov Chains and the Ising Model, 2008 MAA Ohio Spring Meeting, Marietta College [advisor Dr. Ronald Johns]
  72. 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]
  73. John Holodnak: On Sequences Not Satisfying Recurrence Relations (poster presentation) - 2008 AMS-MAA Joint Meetings, San Diego [advisor Dr. Mihai Caragiu]
  74. Charise Kazmierczak: Geometry in Rose Windows - 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Maria Raiti]
  75. Megan Reese: The Golden Section and Design, 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Maria Raiti]
  76. Greg Back: Counting with Transfer Matrices - 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Mihai Caragiu]
  77. John Holodnak: Kronecker's Theorem and Linear Recurrences, 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Mihai Caragiu]
  78. Andrew Homan: An Outline of the Completeness Theorem, 2007 MAA Ohio Spring Meeting, Shawnee State University [advisor Dr. Mihai Caragiu]
  79. 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]
  80. 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]
  81. 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]
  82. Andrew J. Homan: An Extension of a Putnam problem, 2006 MAA Ohio Fall Meeting, Muskingum College [advisor Dr. Mihai Caragiu]
  83. 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]
  84. Justin Gieseler: Randomness properties of elliptic curves, 2006 MAA Ohio Spring Meeting, University of Akron [advisors Dr. Mihai Caragiu and Dr. Ronald Johns]
  85. Jason J. Bockey: Ford Circles, 2006 MAA Ohio Spring Meeting, University of Akron [advisor Dr. Donald Hunt]
  86. 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]
  87. Kristi Patton: Continued Fractions (poster presentation) - 2006 AMS-MAA Joint Meetings, San Antonio, TX [advisors Dr. Sandy Schroeder and Dr. Richard Daquila]
  88. Jacob Johanssen: Fibonacci-Lucas densities (poster presentation) - 2006 AMS-MAA Joint Meetings, San Antonio, TX [advisor Dr. Mihai Caragiu]
  89. 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]
  90. Kristi Patton: Continued Fractions - Undergraduate Mathematics Day,University of Dayton, November 5, 2005  [advisor Dr. Sandy Schroeder]
  91. 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]
  92. Justin Gieseler: Cubic Polynomials and Quadratic Residues, 2005 MAA Ohio Fall Meeting, Ashland University  [advisor Dr. Mihai Caragiu]
  93. Jacob L. Johanssen: Fibonacci-Lucas densities, 2005 MAA Ohio Fall Meeting, Ashland University  [advisor Dr. Mihai Caragiu]
  94. Nathan Baxter and Justin Gieseler: Some computer explorations in Number Theory - 2005 MAA Ohio Spring Meeting, Miami University [advisor Dr. Mihai Caragiu]
  95. 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]
  96. Julie Holda: A closer look at Monte Carlo simulations (poster presentation) 2005 Joint MAA-AMS Meetings, Atlanta  [Project developed at NASA Glenn Research Center]
  97. 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]
  98. 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]
  99. Nathan Baxter: Quadratic Residues: a Computer - Assisted Journey - 2004 MAA Ohio Fall Meeting, John Carroll University  [advisor Dr. Mihai Caragiu]
  100. Kristine Patton: The Ducci Problem: a Brief Review -  2004 MAA Ohio Fall Meeting, John Carroll University  [advisor Dr. Mihai Caragiu]
  101. 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]
  102. Matt Katschke: San Gaku Problems in Other Geometries (award-winning poster presentation) 2004 MATHFEST, Providence, RI  [REU Project at Grand Valley State University]
  103. Kristine Patton: On Primorial Primes -  2004 MAA Ohio Spring Meeting, University of Cincinnati  [advisor Dr. Mihai Caragiu]
  104. Mark Clausing: Advanced compass and straightedge constructions - 2004 MAA Ohio Spring Meeting, University of Cincinnati  [advisor Dr. Donald Hunt]
  105. Nathan Baxter: Arithmetic Properties of Some Partial Sums - 2004 MAA Ohio Spring Meeting, University of Cincinnati  [advisor Dr. Mihai Caragiu]
  106. Nathan Baxter: P-adic exponents and some of their applications [poster presentation]  - 2004 MAA-AMS Joint Meetings, Phoenix, AZ  [advisor Dr. Mihai Caragiu]
  107. Nathan Baxter: An Application of Weyl's Theorem, 2003 MAA Ohio Spring Meeting, The Ohio State University  [advisor Dr. Mihai Caragiu]
  108. 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]
  109. Nicholas Vidovich: On a Fibonacci identity - 2002 MAA Ohio Spring Meeting, Xavier University  [advisor Dr. Mihai Caragiu]
  110. Thomas Jonell: A square root algorithm, 2002 MAA Ohio Spring Meeting, Xavier University  [advisor Dr. Mihai Caragiu]
  111. Ethan Miller and Paul Pfeiffer: Cellular Automata with Finite Life Span, 2001 MAA Ohio Spring Meeting, Bowling Green [advisor Dr. Mihai Caragiu]
https://www.onu.edu/arts_sciences/mathematics_statistics/undergraduate_research

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.


  1. Kaleigh Cummins: The Birthday Problem - an Expanded Look [Rahrig] 2020
  2. John Mullin: What Makes a Successful Hire for A College Library [Wang] 2020
  3. Hannah Ray: Heel Spur Surgery: Evaluating the Outcomes [Wang] 2020
  4. Travis Maenle: A linear complexity analysis of quadratic residues and primitive roots spacings [Caragiu] 2020
  5. Bryan Peck: Bell's Inequalities [Caragiu] 2020
  6. Kenneth Eaton: The Fundamentals of Automated Theorem Proving [Caragiu] 2019
  7. Megan Meyer: An Experimental Approach to Sophie Germain Sequences [Caragiu] 2019
  8. Corey Thrush: Two Person Zero Sum Games [Robinson] 2019
  9. Kayla Rieman:  Flipping Coins [Rahrig] 2019
  10. Bradley Lockhart: Force Propagation in Multi-Rod Drumsticks [Fuller] 2019
  11. Takumi Kijima: Naive Bayes Classifier [Wang] 2019
  12. Addison Carter: An Introduction to Partitions and Compositions [Caragiu] 2019
  13. Emma Talley: Multivariate Analysis of Variance [Wang] 2019
  14. Rachel Liebrecht: Special Topics on Graph Theory and Ramsey Numbers [Caragiu] 2019
  15. Grant McConnel: Problem Posing Using the Mathematical Game Qubic [Robinson] 2019
  16. Dylan Battison: SAS Base Programmer Certification [Rahrig] 2019
  17. Shannon Tefft: Processing Quadratic Residues with Ducci Iterations [Caragiu] 2019
  18. Andrew Kurdys: The Autoregressive Model and Real Life Time Series Applications [Rahrig] 2019
  19. Jenna Holler: American Mathematics Competitions – Variations and Generalizations [Caragiu] 2018
  20. Joseph Stomps: American Mathematics Competitions AMC 10 - analogies and generalizations [Caragiu] 2018
  21. Ian Simpson: Passive Scalar Transport of Contaminants via Traveling Waves [Fuller] 2018
  22. Andrew Tomkins: Statistical Analysis of Library Surveys Using SAS [Wang] 2018
  23. Gia Saturday: Myth Busting the Sophomore Slump [Wang] 2018
  24. Zachary Goodchild: Three Dichotomous Variables: There is more to it than you think [Robinson] 2018
  25. Lindsely Black: Player Efficiency Ratings for Basketball Players [Rahrig] 2018
  26. Jennifer Point: Brownian Motion & Its Application to Stock Evaluation [Rahrig] 2017
  27. Kyle Thomas: Performance Evaluation of Selected Normality Tests, a Simulation Study [Wang] 2017
  28. Jessica Lewe: Analysis of Fall Preventions Outreach Survey Using Nonparametric Statistical Methods" [Wang] 2017
  29. Meredith Eichenlaub: Variation of Probability: Baseball and the Binomial Distribution [Robinson] 2017
  30. Matthew Golden: The Baker-Campbell-Hausdorff Formula [Caragiu] 2017
  31. Michelle Haver: Poissonian Character and Chebyshev Bias for Greatest Prime Factor Sequences: a Computational Analysis [Caragiu] 2017
  32. Andrew Harden: The Capital Asset Pricing Model & Markowitz Problem" [Jaki] 2017
  33. David Zirkle: The Lognormal Distribution as a Model for Stock Prices [Rahrig] 2017
  34. Kaila Bollinger: Kruskal-Wallis versus Classical One-Way Analysis of Variance: Who's the Winner? [Rahrig] 2016
  35. Brandon Wilson: Black-Scholes Formula [Jaki] 2016
  36. Jeffrey Hancock:  Optimal Strategy for an Obscure Game Show" [Robinson] 2016
  37. Nathan Knodel: Exact Solutions of Cubic-Quintic Duffing Oscillators [Fuller] 2016
  38. Abigail Thayer: Computer Solutions of the One Dimensional Diffusion Equation [Johns] 2015
  39. Brian Slabe: Contingent Payment Methods [Rahrig] 2015
  40. James Rader: Analysis of Points After Touchdown in the NFL [Putt] 2015
  41. Ashley Ernst: A Group Theoretic Development of Isospin and Low Isospin Multiplets [Fuller] 2015
  42. Benjamin McKinnis: The Square Wheel Problem [Hunt] 2014
  43. Brandon Guillen: A Look at Bayesian Statistics [Robinson] 2014
  44. Amanda Marco: Fibonacci Numbers and Some of Their Properties [Caragiu] 2014
  45. Kerry DuLaney: Exploring Gears and Watchmaking [Hunt] 2014
  46. Kate Klopp: Wheel of Fortune: From a Statistical Standpoint [Robinson] 2014
  47. Lacey Hittle: Progression on Regression: A Look at Multicollinearity [Rahrig] 2014
  48. Matthew R. Zirkle: Finding Square Roots in a Prime Field [Caragiu] 2013
  49. Thomas E. Steinberger: Arithmetic Functions of Several Variables on the Gaussian Integers  [Jaki] 2013
  50. Jonathan C. Schroeder: Small Special Pairs of Primnitive Roots [Caragiu] 2013
  51. Devin F. Kisor: Eploration of the Regression to the Mean Phenomenon [Robinson] 2013
  52. Morgan Hammer: Applications of Direct Products to Molecular Spectroscopy [Putt] 2013
  53. Kelsie E. Zumberger: Did You Cheat In School This Year? [Robinson] 2013
  54. Donald J. Pleshinger: On a Congruence of Ohtsuka [Caragiu] 2013
  55. Matthew J. McCandless: Picturing Eigenfaces [Retterer] 2013
  56. Joanna Snyder: Analyzing the "Hot Hand" Effect [Rahrig] 2012
  57. David Mangus: "Let's Get Paradoxical: A Statistical Major's Quest to Solve Some Common Problems [Robinson] 2012
  58. Jennifer Krauss: In the World of a Taxicab Driver: an Exploration of Conic Sections in Taxicab Geometry [Putt] 2012
  59. 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
  60. Lauren Cassell: Guarding a Koch Fractal Art Gallery [Fuller] 2012
  61. Ashley Risch: An Euler-Fibonacci Sequence. [Caragiu] 2011
  62. Molly Eickholt: Simplifying Ford Links [Hunt] 2011
  63. Lauren Sutherland: Multidimensional Greatest Prime Factor Sequences [Caragiu] 2011
  64. Lucas Witt: Sometimes Two Wrongs Do Make a Right [Robinson] 2011
  65. Lindsey Miller Walch: Chordal Geometries and Their Axioms [Fuller] 2011
  66. Joshua Szekely: The Quantum Harmonic Oscillator and the Hermite Polynomials [Boyadzhiev] 2011
  67. Greg Back: The Greatest Prime Factor and its Applications [Caragiu] 2010
  68. Jenna Brace: Traffic Flow Simulation with Cellular Automata [Caragiu] 2010
  69. Andrew Caldwell: Misuses of Statistics [Robinson] 2010
  70. Kevin Earnest: Perturbations in the Aerospace Sequence of Attitude Determination Using Quaternions [Fuller] 2010
  71. John Holodnak: The Perron-Frobenius Theorem and Applications [Caragiu] 2010
  72. Kyle Meyer: Parity in Professional Sports [Robinson] 2010
  73. Matt Rader: Quantifying Defensive Ability in Baseball [Putt] 2010
  74. Sharon Binkley: The One Time Pad and Text Visualization [Caragiu] 2009
  75. Joshua Stoffel: Maxwell's Equations through the Major Vector Theorems [Boyadzhiev] 2009
  76. Joshua Somerlot: The Affine Cipher [Caragiu] 2009
  77. Brock Prater: Transmission and Reflection Holograms [Hovis] 2009
  78. Eric Gossett: Behavior of Particles in Circular Vertical Floe with Magnus Effect" [Fuller] 2009
  79. Axel Brandt: Classification of Ford Links [Hunt] 2009
  80. Andrew Magyar: The Einstein's Field Equations [Fuller] 2009
  81. Amanda Stype: Holy Voley! How Should We Allocate Those Traps? [Robinson] 2009
  82. Michael Gabrieli: The Exploration of Time Series and Forecasting [Robinson] 2009
  83. Michael Garee: Solitary Waves and KdV Theory [Fuller] 2008
  84. Steven Garofalo: Relational Model for Database Management [Retterer] 2008
  85. Brittany Metz: Latin Squares, Probability, and their involvement in the Sudoku [Robinson] 2008
  86. Heather Schimmoeller: B2 or not B2. That is the Question [Robinson] 2008
  87. Ashley Yontz: Mathematics and Stocks: Risk Analysis of a Portfolio [Putt] 2008
  88. Lorelei Rautsaw: The Geometry of Flowers [Raiti] 2008
  89. Christopher Lemon: Markov Chains and the Heat Bath Monte Carlo Algorithm for the Ising Model of Ferromagnetism [Johns] 2008
  90. Stacy Nagel: Symmetry and Quilting [Raiti] 2008
  91. Brian Henderson: A Probability Distribution Associated with the Minehunt Game [Hovis] 2008
  92. Katie Milligan: The Underlying Mathematical Patterns of Tessellations [Schroeder] 2008
  93. Gretchen Deeg: Projective Geometry and the Art of Perspective [Hovis] 2008
  94. Rachel Fye: An Analysis of Stock Portfolios: Random vs. Non-Random [Putt] 2007
  95. Tyler Dunlap: Ford Links [Hunt] 2007
  96. Andrew Homan: An Overview of Model Theory and Completeness [Caragiu] 2007
  97. Aaron Piper: Given two fractions, what is the fraction between the two that has the smallest denominator? [Robinson] 2007
  98. Greg Snyder: March Madness Probabilities [Robinson] 2007
  99. Mark Bierkan: To Deal or Not to Deal - is that the Question? [Robinson] 2007
  100. Matthew Shonkwiler: Conflict: A Game Theory Approach [Putt] 2007
  101. Megan Reese: The Golden Section and Design [Raiti] 2007
  102. Charise Kazmierczak: Geometry of Rose Windows [Raiti] 2007
  103. Katie Miklovic: The Truth Behind the Witch of Agnesi [Schroeder] 2007
  104. Anthony Gerdeman: A Venture Into the World of Obstructed Random Walks [Robinson] 2006
  105. Allison Mackay: Elementary Number Theory and Classical Cryptography [Caragiu] 2006
  106. Lisa Scheckelhoff: GPF Sequences  [Caragiu] 2006
  107. Brandon Bucholtz: The Euclidean Algorithm [Caragiu] 2006
  108. Kara Stechschulte: Braids and Music [Fuller] 2006
  109. Michael Paulus: Predicting Winning Percentage: An Application of Mathematics to Sports [Putt] 2006
  110. Adam Hibbard: Predicting Movie Ratings [Robinson] 2006
  111. Dan Gudorf: Mary Had a Little Paradox: Whose fleece was and was not as white as snow... [Fuller] 2006
  112. Jason Bockey: Ford Circles [Hunt] 2006
  113. Jacob L. Johanssen: Fibonacci-Lucas Densities [Caragiu] 2006
  114. Kristine Patton: An investigation of Continued Fractions [Schroeder] 2006
  115. Kara S. Lewis: A look at Confounding [Robinson] 2005
  116. Matt Katschke: San Gaku Problems in Hyperbolic and Spherical Geometry [Hunt] 2005
  117. Nathan Baxter: Finite Fields [Caragiu] 2005
  118. Jennifer Szippl: Platonic solids [Raiti] 2004
  119. Julie Holda: Monte Carlo simulations [Robinson] 2004
  120. Tyler Betts: Applications of Group Theory in Chemistry [Putt] 2004
  121. Clinton Louiso: Tic-Tac-Toe: an in-depth analysis [Robinson] 2004
  122. Molly Neer: Mathematics and Arts at Ohio Northern University [Fuller] 2004
  123. Mark Clausing: Advanced Compass and Straightedge Constructions [Hunt] 2004
  124. Michael Hewit: The Ehrenfest Model, Analysis via Markov Chains and Recurrent Events [Johns] 2004
  125. Sara Miller: Fibonacci Numbers [Caragiu] 2003
  126. Julia Gould: Fear of Crime, An Investigative Analysis [Putt] 2003
  127. Matthew Suchan: Is Hitter Performance Affected by Free Agency? [Putt] 2003
  128. Ann Boerger: The Value of a Bond [Putt] 2002
  129. Reid Moore: Analysis of Interest and Basic Annuities [Putt] 2002
  130. Stacey Stillion: Covariates of Pancreas Transplant Survival in Recipients of Combined Kidney-Pancreas Grafts [Putt] 2002
  131. Laura DiMarco: Classification of Compact, Connected Topological Surfaces Without Boundary [Raiti] 2001
  132. Kimberly Myers: Bond Valuation [Putt] 2001
  133. Stephanie Osgood: Statistics Reveal the True "Best Hitters" in Baseball [Putt] 2001
  134. Ivan Tornes: The Circular Vibrating Membrane [Boyadzhiev] 2001
  135. Jason Kline: The Fourier Series and Some Applications [Boyadzhiev] 2000
  136. Rachel Kahlenberg: Confidence Intervals for One Pupulation Mean [Song] 2000
  137. Ryan Snivley: Analysis of Categorical Data [Song] 2000
  138. Sarah Ruppert: Rubik's Cube [Retterer] 2000
  139. Lindsay Nicholson: Fourier Series [Lhamon] 2000
  140. Tim Thompson: Solutions to the Shortest Path Problem [Putt] 1999
  141. Nathan Hyatt: Hypothesis Testing [Song] 1999
  142. William Anthony: Recurrent Events [Hovis] 1999
  143. Justin Reckner: Differential Geometry of Curves in 3-Space [Raiti] 1999
  144. Bodi Kauffman: The Stieltjes Integral [Boyadzhiev] 1999
  145. Chris Finney: The Mathematics of Annuity Valuation [Putt] 1999
  146. James Conine: Fuzzy Sets [Hovis] 1998
  147. Lee Koratich: Functions of Matrices [Boyadzhiev] 1998
  148. Jason McCartney: Game Theory [Shult] 1998
  149. Amanda Pater: Regression Analysis [Song] 1998
  150. 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

    Wednesday, March 24, 2021

    Matrix Models

    Journeys into Theoretical Physics - 2019, Speaker: Pedro Vieira (Perimeter/ICTP-SAIFR/IFT-UNESP) 

      

      

      

      

     

     

    Saturday, March 20, 2021

    ONU-SOLVE data (UPDATE MARCH 2021)

    1. Problem 12126 The American Mathematical Monthly Vol. 128 (3), March 2021, recognizes correct solution of ONU-SOLVE
    2. Problem 1126 – College Mathematics Journal Vol. 50 (3), May 2019, recognizes correct solution of Shannon Tefft. 
    3. Problem 1115 – College Mathematics Journal Vol. 49 (5), November 2018, recognizes correct solution of Noah Pinkney.
    4. Problem 2025 – Mathematics Magazine Vol. 91 (3), June 2018, recognizes correct solution of ONU-SOLVE.
    5. Problem B-1166 – The Fibonacci Quarterly Vol. 54 (2), May 2016, recognizes correct solution of ONU-SOLVE. 
    6. Problem 1956 – Mathematics Magazine Vol. 89 (1), February 2016, recognizes correct solution of ONU-SOLVE. 
    7. Problem 1951 – Mathematics Magazine Vol. 88 (5), December 2016, recognizes correct solution of Ashley Ernst and Matthew Golden.
    8. Problem 1921 – Mathematics Magazine Vol. 87 (3), June 2014, recognizes correct solution of ONU-SOLVE.
    9. Problem 1920 – Mathematics Magazine Vol. 87 (2), April 2014, published solution of Tommy Steinberger. 
    10. Problem 1916 – Mathematics Magazine Vol. 87 (2), April 2014 - recognizes correct solution of Tommy Steinberger.
    11. Problem 1896 – Mathematics Magazine Vol. 86 (3), June 2013 - recognizes correct solution of Tommy Steinberger.
    12. Problem 965 – College Mathematics Journal Vol. 43 (5), November 2012, recognizes correct solution of Tommy Steinberger. 
    13. Problem 961 – College Mathematics Journal Vol. 43 (5), November 2012, recognizes correct solution of Tommy Steinberger.
    14. Problem B-1120 – The Fibonacci Quarterly Vol. 50 (4), November 2012, recognizes correct solution of Matt Zirkle
    15. Problem B-1106 – The Fibonacci Quarterly Vol. 51 (2), May 2013, recognizes correct solution of ONU-SOLVE. 
    16. Problem 11596 – The American Mathematical Monthly Vol. 120 (5), May 2013, recognizes correct solution of ONU-SOLVE
    17. Problem B-1103 – The Fibonacci Quarterly Vol. 51 (1), February 2013, publishes solution of ONU-SOLVE  
    18. Problem B-1102 – The Fibonacci Quarterly Vol. 51 (1), February 2013, recognizes correct solution of ONU-SOLVE. 
    19. Problem B-1101 – The Fibonacci Quarterly Vol. 51 (1), February 2013, recognizes correct solution of ONU-SOLVE.  
    20. Problem 1873 – Mathematics Magazine, Vol. 84 (3), June 2011, recognizes correct solution of ONU-SOLVE. 
    21. Problem 1872 – Mathematics Magazine, Vol. 84 (3), June 2011, recognizes correct solution of ONU-SOLVE. 
    22. Problem B-1078 – The Fibonacci Quarterly Vol. 49 (4), November 2011, recognizes correct solution of ONU-SOLVE. 
    23. Problem B-1074 – The Fibonacci Quarterly Vol. 49 (3), August 2011, publishes solution of ONU-SOLVE.

    Mihai Caragiu CV

     See here