UNDERGRADUATE MATHEMATICAL RESEARCH

AREAS OF INTEREST INCLUDE:

- discrete mathematics
- number
theory (divisibility, prime
numbers, algorithms, etc)

- coding
theory and cryptography

- sequences (linear recurrences, Fibonacci and Lucas numbers, etc.)
- geometry
- combinatorics
- calculus

- abstract and applied algebra
- logic
and foundations

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:

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:

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).

- ArXiv e-prints authored/coauthored by students advised by me:

- Students
advised or co-advised by myself who presented
*contributed talks/posters at professional meetings*:

- Ashley
Risch: A Phi-bonacci Sequence, 27th
Annual PI MU EPSILON Student Conference, Miami
University (September 24, 2010)

**Greg Back: The Greatest Prime Factor Function and Some Applications***, 2010 Ohio MAA Spring Meeting, Kent State University*

**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]****Greg Back:****A Prime Addition Commutative Magma***(poster presentation)**2010 AMS-MAA Joint Meetings, San Francisco*

- Sharon Binkley: One-time Pad and
Text Visualization
**, 2009 MAA Ohio Spring Meeting, Bowling Green State University**

- Greg Back: The Jacobi Symbol
and Cryptography
**, 2009 MAA Ohio Spring Meeting, Bowling Green State University**

**John Holodnak: On Sequences Not Satisfying Recurrence Relations***(poster presentation)**2008 AMS-MAA Joint Meetings, San Diego*

- Greg Back: Counting with
Transfer Matrices
**, 2007 MAA Ohio Spring Meeting, Shawnee State University**

- John Holodnak: Kronecker's Theorem
and Linear
Recurrences
**, 2007 MAA Ohio Spring Meeting, Shawnee State University** **Andrew J. Homan:***An Outline of the Completeness Theorem***, 2007 MAA Ohio Spring Meeting, Shawnee State University**

**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*

**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:****Robinson's theorem in connection with a Putnam problem**(award-winning poster presentation), 2007*AMS-MAA Joint Meetings, New Orleans*

**Andrew J. Homan:***An Extension of a Putnam problem*, 2006 MAA Ohio Fall Meeting, Muskingum College

**Lisa Scheckelhoff:***On a class of sequences related to the greatest prime factor function,***2006 MAA Ohio Spring Meeting, University of Akron****Justin Gieseler:***Randomness properties of elliptic curves,***2006 MAA Ohio Spring Meeting, University of Akron****Lisa Scheckelhoff: Sophie Germain Digraphs,**Eighth Annual Nebraska Conference for Undergraduate Women in Mathematics, February 3-5, 2006.**Jacob Johanssen:***Fibonacci-Lucas densities,**2006 AMS-MAA Joint Meetings, San Antonio, TX***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]****Justin Gieseler:***Cubic Polynomials and Quadratic Residues, 2005 MAA Ohio Fall Meeting, Ashland University***Justin Gieseler:***Distribution of Points on Elliptic Curves Projections**,**Undergraduate Mathematics Day,University of Dayton, November 5, 2005***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****Nathan Baxter:****Quadratic Residues: a Computer - Assisted Journey****, 2004 MAA Ohio Fall Meeting, John Carroll University****Kristine Patton:***The Ducci Problem: a Brief Review,*2004 MAA Ohio Fall Meeting, John Carroll University**Kristine Patton:***On Primorial Primes,*2004 MAA Ohio Spring Meeting, University of Cincinnati**Nathan Baxter:****Arithmetic Properties of Some Partial Sums**,**2004 MAA Ohio Spring Meeting, University of Cincinnati****Nathan Baxter:**,*P-adic exponents and some of their applications***2004 MAA-AMS Joint Meetings, Phoenix, AZ****Nathan Baxter:**,*On the Partial Sums of the Harmonic Series***2003 MAA Ohio Fall Meeting, Ohio Northern University****Nathan Baxter:**,*An Application of Weyl's Theorem***2003 MAA Ohio Spring Meeting, The Ohio State University****Nicholas Vidovich:***On a Fibonacci identity,*2002 MAA Ohio Spring Meeting, Xavier University**Thomas Jonell:***A square root algorithm,*2002 MAA Ohio Spring Meeting, Xavier University**Ethan Miller and Paul Pfeiffer:**,*Cellular Automata with Finite Life Span***2001 MAA Ohio Spring Meeting, Bowling Green**

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