UNDERGRADUATE MATHEMATICAL RESEARCH

AREAS OF INTEREST INCLUDE:

Send me e-mail  if you are interested in doing a capstone research with me, or if you just want to do
research in any of these topics.
Doing research and participating to conferences will greatly enrich a
student's life!
Above all, it's fun.


RECENT CAPSTONE PROJECTS ADVISED


                    1. Sara Miller: Fibonacci Numbers (2003)
                    2. Nathan Baxter: Finite Fields (2004)
                    3. Jacob L. Johanssen: Fibonacci-Lucas Densities (2006)
                    4. Allison Mackay: Elementary Number Theory and Classical Cryptography (2006)
                    5. Lisa Scheckelhoff: GPF Sequences (2006)
                    6. Brandon Bucholtz: The Euclidean Algorithm (2006)
                   
7. Andrew Homan: An Overview of Model Theory and Completeness (2007)
                    8. Joshua Somerlot: The Affine Cipher (2009)
                    9. Sharon Binkley: The One Time Pad and Text Visualization (2009)
                   10. Greg Back: The Greatest Prime Factor Function and its Applications
                   11. Jenna Brace: Traffic Flow Simulation with Cellular Automata
                   12. John Holodnak: The Perron-Frobenius Theorem and Other Results from Linear Algebra with Application to Sports Ranking

Publications with current or former ONU students as co-authors and ONU-based research:
1. Greg Back and Mihai Caragiu, The Greatest Prime Factor and Recurrent Sequences, Fibonacci Quarterly (accepted for publication - July 2010);
2. Mihai Caragiu and Greg Back, The Greatest Prime Factor and Related Magmas, JP J.of Algebra, Number Theory and Appl. 15 (2), 127-136 (December 2009);
3. Mihai Caragiu and John Holodnak, On Sampling Periodic Functions, Far East Journal of Mathematical Sciences 29(1), 145-149 (2008);
4. Mihai Caragiu and Nathan Baxter, A note on p-adic Ducci games,  JP J.of Algebra, Number Theory and Appl. 8(1), 115-120 (2007);
5. Mihai Caragiu, Ronald Johns and Justin Gieseler, Quasi-random Structures from Elliptic Curves,  JP J.of Algebra, Number Theory and Appl. 6(3), 561-571 (2006);
6. Mihai Caragiu and Lisa Scheckelhoff, The Greatest Prime Factor and Related Sequences,  JP J.of Algebra, Number Theory and Appl. 6(2), 403-409 (2006);
7. Mihai Caragiu and Nathan Baxter, Arithmetic Properties of Some Special Sums,  JP J.of Algebra, Number Theory and Appl. 4(3), 455-463 (2004).
Award-winning student posters: GPF Sequences  , Putnam "2n+1" - mod p  , Elliptic Curves Projections


            Mihai Caragiu and Jacob L. Johanssen, Fibonacci-Lucas densities, math.GM/0603232
  1. Ashley Risch:  A Phi-bonacci Sequence, 27th Annual PI MU EPSILON Student Conference, Miami University (September 24, 2010)
  2. Greg Back: The Greatest Prime Factor Function and Some Applications, 2010 Ohio MAA Spring Meeting, Kent State University
  3. 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, ONU advisor - Dr. Mihai Caragiu]
  4. Greg Back: A Prime Addition Commutative Magma (poster presentation) 2010 AMS-MAA Joint Meetings, San Francisco
  5. Sharon Binkley: One-time Pad and Text Visualization, 2009 MAA Ohio Spring Meeting, Bowling Green State University
  6. Greg Back: The Jacobi Symbol and Cryptography, 2009 MAA Ohio Spring Meeting, Bowling Green State University
  7. John Holodnak: On Sequences Not Satisfying Recurrence Relations (poster presentation) 2008 AMS-MAA Joint Meetings, San Diego
  8. Greg Back: Counting with Transfer Matrices, 2007 MAA Ohio Spring Meeting, Shawnee State University
  9. John Holodnak: Kronecker's Theorem and Linear Recurrences, 2007 MAA Ohio Spring Meeting, Shawnee State University
  10. Andrew J. Homan:  An Outline of the Completeness Theorem, 2007 MAA Ohio Spring Meeting, Shawnee State University
  11. 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
  12. 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]
  13. Andrew J. Homan: Robinson's theorem in connection with a Putnam problem (award-winning poster presentation), 2007 AMS-MAA Joint Meetings, New Orleans
  14. Andrew J. Homan:  An Extension of a Putnam problem, 2006 MAA Ohio Fall Meeting, Muskingum College
  15. Lisa Scheckelhoff: On a class of sequences related to the greatest prime factor function, 2006 MAA Ohio Spring Meeting, University of Akron
  16. Justin Gieseler:  Randomness properties of elliptic curves, 2006 MAA Ohio Spring Meeting, University of Akron
  17. Lisa Scheckelhoff: Sophie Germain Digraphs, Eighth Annual Nebraska Conference for Undergraduate Women in Mathematics, February 3-5, 2006.
  18. Jacob Johanssen: Fibonacci-Lucas densities, 2006 AMS-MAA Joint Meetings, San Antonio, TX
  19. Justin Gieseler: The Distribution of points on elliptic curves projections, 2006 AMS-MAA Joint Meetings, San Antonio, TX [advisors Dr. Mihai Caragiu and Dr. Ronald Johns]
  20. Justin Gieseler: Cubic Polynomials and Quadratic Residues, 2005 MAA Ohio Fall Meeting, Ashland University
  21. Justin Gieseler: Distribution of Points on Elliptic Curves Projections Undergraduate Mathematics Day,University of Dayton, November 5, 2005
  22. Jacob L. Johanssen: Fibonacci-Lucas densities, 2005 MAA Ohio Fall Meeting, Ashland University
  23. Nathan Baxter and Justin Gieseler: Some computer explorations in Number Theory, 2005 MAA Ohio Spring Meeting, Miami University
  24. Nathan Baxter:  Quadratic Residues: a Computer - Assisted Journey, 2004 MAA Ohio Fall Meeting, John Carroll University
  25. Kristine Patton: The Ducci Problem: a Brief Review, 2004 MAA Ohio Fall Meeting, John Carroll University
  26. Kristine Patton: On Primorial Primes, 2004 MAA Ohio Spring Meeting, University of Cincinnati
  27. Nathan Baxter:  Arithmetic Properties of Some Partial Sums,2004 MAA Ohio Spring Meeting, University of Cincinnati
  28. Nathan Baxter:  P-adic exponents and some of their applications, 2004 MAA-AMS Joint Meetings, Phoenix, AZ
  29. Nathan Baxter:  On the Partial Sums of the Harmonic Series, 2003 MAA Ohio Fall Meeting, Ohio Northern University
  30. Nathan Baxter:  An Application of Weyl's Theorem, 2003 MAA Ohio Spring Meeting, The Ohio State University
  31. Nicholas Vidovich: On a Fibonacci identity, 2002 MAA Ohio Spring Meeting, Xavier University
  32. Thomas Jonell:  A square root algorithm, 2002 MAA Ohio Spring Meeting, Xavier University
  33. Ethan Miller and Paul Pfeiffer: Cellular Automata with Finite Life Span, 2001 MAA Ohio Spring Meeting, Bowling Green


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