The Richard V. Andree Awards are given annually to the authors of the papers, written by undergraduate students, that have been judged by the officers and councilors of Pi Mu Epsilon to be the best that have appeared in the Pi Mu Epsilon Journal in the past year.

Until his death in 1987, Richard V. Andree was Professor Emeritus of Mathematics at the University of Oklahoma. He had served Pi Mu Epsilon for many years and in a variety of capacities: as President, as Secretary-Treasurer, and as Editor of this Journal.

The following is a list of past recipients of the Richard V. Andree Award:

### 2016

Bradley Dougherty, Northwest Missouri State University – On the Average Value and the Mean Value Theorem for Integrals

**2015**

Elijah Soria, Saint Mary’s College of California – Some properties of k-Pell Sequences

### 2014

Sarah Ritchey, Youngstown State University – Points on a Circle and Integer Distances

### 2013

Kehao Li and Meng Zhu, Worcester Polytechnic Institute – Variable Continuation in Solving a Problem in Discrete Mathematics

Lauren Morey, University of Montana – An Integral Formula for Counting Perfect Matchings in Graphs

Siqi Zheng, – Necessary and Sufficient Conditions for Benford Sequences

### 2012

Austin Buscher, US Air Force Academy – Approximating Trigonometric Functions with Sums of Generalized Binomial Coefficients

Samantha Campbell, University of Richmond – From Graphs to Determinants to Matrices

Yiran Duan, University of Richmond – From Graphs to Determinants to Matrices

Hristiyan Hristov, Ernst & Young – From Graphs to Determinants to Matrices

Max Grinchenko, University of Richmond – From Graphs to Determinants to Matrices

### 2011

Robert Thijs Kozma, SUNY Stonybrook – Julia Sets of Perturbed Quadratic Maps Converging to the Filled Basilica

### 2010

Matt Alexander, Youngstown State University – A Curiously Rational Result

Dan Emmendorfer, Hope College – Classification of Geometric Spirals

Martha Precup, University of Notre Dame – Classification of Geometric Spirals

Ashley Warren, Otterbein College – Classification of Geometric Spirals

Alex Cameron, Hendrix College – Counting Ring Homomorphisms

### 2009

Giulia Fanti, Olin College of Engineering – Habitats on Costa Rican Jaguar Populations

Brian Nowatowski, Princeton University – Habitats on Costa Rican Jaguar Populations

Adam Shull, Valparaiso University – Properties of Ideal Divisors

John Holmes, Wabash College – Properties of Ideal Divisors

### 2008

Joseph David Gastenveld, Northern Kentucky University – Extensions that Yield Quasi p-Groups

Sharon J. Sternadel, Oregon State University – Circles in a One-Way Street Taxicab Model

Melissa Wasson, Hartwick College – Scaling Ratios and Self-Contact in Planar Asymmetric Trees

### 2007

Sarah Baker and Larisa Perolli The George Washington University Log concavity in lattice path matroids

### 2006

Colleen Hughes Denison University Linked Triangle Pairs in a Straight edge K_6

Sara Zasada Elmhurst College Working with Block Products

### 2005

Aja Johnson Elon University Strategies of a Sequenced Game of Chance

David Nash Santa Clara University Cayley Graphs of Symmetric Groups Generated by Reversals

Jared Williams Hendrix College Extending Wilson’s Theorem

### 2004

Stephen W. Hruska Wheaton College An Alternating Series Expansion for (ln(2))^2

Rebekah B. Johnson Wheaton College An Alternating Series Expansion for (ln(2))^2

Ryan L. Yates Wheaton College An Alternating Series Expansion for (ln(2))^2

Molly McGinty Washington & Lee University Geometric Probability for the Space-Time Plane

Peter Horn Hendrix College Modelling the Impact of Forest Fragmentation on Predator-Prey Populations

Ryan D. Westbrook Texas A&M University Modelling the Impact of Forest Fragmentation on Predator-Prey Populations

### 2003

First Place:

Patrick Hummel California Institute of Technology Solid constructions using ellipses

Second Place:

John M. Zobitz St. John’s University Pascal matrices and particular solutions to differential equations

Third Place:

Stephanie Libera St. Olaf College Some Perfect Order Subset Groups

Paul Tlucek St. Olaf College Some Perfect Order Subset Groups

### 2002

First Place:

Andrea Douglas Hope College Expected Areas of Randomly Generated Triangles

Courtney Fitzgerald Niagara University Expected Areas of Randomly Generated Triangles

Scott Mihailik University of Michigan Expected Areas of Randomly Generated Triangles

Kimberly L. Patti Saint Louis University Randomly Generating a Finite Group

### 2001

First Place:

Emilia Huerta-Sanchez Mills College Iteration of an Even-Odd Splitting Map

Aida Navarro-Lopez University of Puerto Rico in Humacao Iteration of an Even-Odd Splitting Map

David Uminsky Harvey Mudd College Iteration of an Even-Odd Splitting Map

John Griesmer Miami University Results Involving Continuity of the Derivative

### 2000

First Place:

Nitish Dass St. Olaf College The Determinant of a (m,n) Pretzel

Jonathan McGrath St. Olaf College The Determinant of a (m,n) Pretzel

Erin Urbanski St. Olaf College The Determinant of a (m,n) Pretzel

Brett Alan Enge James Madison University The Search for Tri-Operate Fields

Matthew J. Hale St. Xavier High School Circular Functions of Multiple Integral Angles

### 1999

First Place:

Xiaolong Ron Yu Worcester Polytechnic Institute Curious Numbers

Second Place:

Jack Samuel Calcut III Michigan State University Single Rational Arctangent Identities for Pi

Third Place:

Gina Garza Western Michigan University Which Graphs Have Planar Shadow Graphs?

Natascha Shinkel Western Michigan University Which Graphs Have Planar Shadow Graphs?

### 1998

First Place:

Johanna Miller Duke University Mauldin-Williams Graphs with Unique Dimension

C. Ryan Vinroot North Carolina State University Mauldin-Williams Graphs with Unique Dimension

Tricia Stone John Carroll University Where Do My Sequences Lead?

Loi Nguyen University of North Florida Seeing is Not Always Believing

Tu Tran University of North Florida Seeing is Not Always Believing

### 1997

1 Marc Fusaro University of Scranton A Visual Representation of the Sequence Space

1 Danica A. Nowosielski Russell Sage College Change Ringing: A Connection Between Mathematics and Music

1 Kerry Smith Seton Hall University Rearrangement of Series

### 1996

1 Rick Mohr Rose-Hulman Institute of Technology Nearness of Normals

2 Ryan Bennink Hope College Red Light, Green Light: A Model of Traffic Signal Systems

3 Carolyn Farruggia University of Scranton The Elimination of a Family of Periodic Parity Vectors in the 3x+1 Problem

3 Michael Lawrence University of Scranton The Elimination of a Family of Periodic Parity Vectors in the 3x+1 Problem

3 Brian Waterhouse University of Scranton The Elimination of a Family of Periodic Parity Vectors in the 3x+1 Problem

3 Mark Tomforde Gustavus Adolphus College Self-Similarity and Fractal Dimension of Certain Generalized Arthimetical Triangles

### 1995

1 Scott M. Wagner Hendrix College Group Generators and Subgroup Lattices

2 Kevin Dennis Michigan State University Sierpinski n-Gons

2 Julie Varbalow University of Kentucky An Application of Partitions to the Factorization of Polynomials over Finite Fields

2 Lars Seme Hendrix College Automorphisms of Hasse Subgroup Diagrams for Cyclic Groups

### 1994

1 Gina Aurello Seton Hall University On the Rearrangement of Infinite Series

2 Rychard J. Bouwens Hope College Who Gets the Washers? A Problem in Dividing Resources

3 Michael J. Reske Carthage College The Secret Santa Problem

### 1993

1 Jennifer DeBoer Michigan Technological University Non-Existence of Certain Unitary Perfect Numbers

2 James R. Murphy Michigan State University Uniform Embeddings of Graphs

2 Mohammad P. Shaikh Western Michigan University Uniform Embeddings of Graphs

3 Carol Clifton Middle Tennessee State University Some Operations on Matrix-Valued Expressions

3 Jeremy M. Dover Worcester Polytechinic Institute and The University of Delaware Outerplanar Graphs and Matroid Isomorphism

### 1992

1 Nataniel S. Greene Yeshiva University Fractorial!

2 Michael H. Lin Stanford University Rings of Small Order

3 Mark J. Lancaster Hendrix College On the Number of Invertible Matrices Over Zpe

### 1991

1 Amy Pinegar Middle Tennessee State University Inversions and Adjacent Transpositions

2 Shannon Spittler Miami University A Math Problem Within an Antique Clock Label

3 Judy Marie Kenney College of St. Benedict Turning Triangles into Circles

### 1990

1 Amy Dykstra Western Michigan University A Generalization of Odd and Even Vertices in Graphs

1 Michelle Shultz Western Michigan University A Generalization of Odd and Even Vertices in Graphs

2 Eric Berg A Family of Fields

3 Joel Atkins Rose-Hulman Institute of Technology Regular Polygon Targets

### 1988

1 James E. Georges California Polytechnic State University Maximal Polygons for Equitransitive Periodic Tilings

1 Annette M. Matthews Portland State University Maximal Polygons for Equitransitive Periodic Tilings

2 Melanie L. Butt Middle Tennessee State University Automorphism Groups of Hasse Subgroup Diagrams for Groups of Low Order

3 Robert A. Coury University of Washington A Continued Fraction Approach for Factoring Large Numbers

### 1987

1 Wah Keung Chan McGill University On the Largest RAT-Free Subset of a Finite Set of Points

2 Jennifer Zobitz College of St. Benedict Fractals: Mathematical Monsters

3 Kelley Ann Chambers University of Dayton The Isomorphism of the Lattice of Congruence Relations on a Group and the Lattice of Normal Subgroups of a Group

### 1986

1 Kirk Weller Hope College Lattices of Periodic Functions

2 John Reid Perkins Oakland University The Adequacy of { ~ , Æ,?} for Gödel Many-Valued Logics

3 Janet Eckoff Albion College Random Cantor Sets

### 1985

1 Donald John Nicholson Iowa State University A Ubiquitous Partition of Subsets of Rn

2 Ruth Brisbin Plant H.S. Taxicab Trigonometry

2 Paul Artola University of South Florida Taxicab Trigonometry

3 Julie Yancey Fort Lewis College Edge-Labelled Trees

### 1982

1 Bradley D. Strand Carleton College Vector Subspaces of Magic Squares

2 Karen Cunningham University of Texas at Arlington A Simple Model for Two Interacting Species and the Principle of Competitive Exclusion

3 Ravi Salgia Loyola University of Chicago Volume of An n-Dimensional Unit Sphere

### 1981

1 Gary Ricard South Dakota School of Mines and Technology A Comparison of Computer Algorithms to Solve for Knight’s Tour

2 Sandra L. Cousins Hendrix College Singular Functions

3 Michael L. Orrick, Jr. Macalester College The Area of a Triangle Formed by Three Lines

### 1980

1 Ziad Haddad UCLA Two Remarks on the Quaternions

2 Robert C. Smith University of Arkansas Uniform Algebras and Scattered Spaces

3 Alma E. Posey Hendrix College Rolling Cones

### 1979

1 Deborah L. Massari University of Akron The Probability of Generating A Cyclic Group

2 Julie D. Anderson Hendrix College Non-linear Additive Functions

3 Michael J. Young Portland State University A Matrix Model for Use in Population Ecology

### 1978

1 Robert Antol Iowa State University The Perfect Numbers and Pascal’s Triangle

2 Debra Lea Gutridge Muskingum College Mathematical Curiosities

3 Jackie L. Lawrence Western Kentucky University Numerical Integration by Polynomial Interpolation

### 1976

1 Brent Hailpern University of Denver Continuous Non-differentiable Functions

2 Philip D. Olivier Texas Tech University Two Applications of Pseudoinverses

3 Karen M. Lesko Central Missouri State University A Generalization to Almost Divisible Groups

### 1975

1 Daniel Minoli & Robert Bear Polytechnic Institute of New York Hyperperfect Numbers

2 Mary Zimmerman Western Michigan State University Matrix Multiplication as an Application of the Principle of Combinatorial Analysis

3 Lonnie J. Kuss Texas Tech University A Conformal Group on an n-Dimensional Euclidean Space

### 1974

1 Charles D. Keys Lousiana State University Graphs Critical for Maximal Bookthickness

2 S. Brent Morris Duke University The Basic Mathematics of the Faro Shuffle

3 H. Joseph Straight Western Michigan University Applications of Finite Differences to the Summation of Series

### 1973

1 S. W. Talley Western Kentucky University Niceness of the Socle and a Characterization of Groups of Bounded Order

2 Daniel Minoli Polytechnic Institute of New York Use of Matrices in the Four Color Problem

3 Roseann Moriello Seton Hall University Partial Differentiation on a Metric Space

### 1972

1 Sidney Graham The University of Oklahoma On “Almost Unitary Perfect” Numbers

1 Christopher Scussel Michigan State University Goldbach’s Conjecture

2 Joseph J. Buff New York University Characterization of an Analytic Function of a Quaternion Variable

3 Lee Ratzan Courant Institute of Mathematical Sciences Comments on the Properties of Odd Perfect Numbers

3 Frank L. Capobianco College of the Holy Cross Spec (R) for a Particular R

### 1971

2 Martin Swiatkowski John Carroll University Wronskian Identities

3 Thomas R. Bingham State University of the New York College at Fredonia Newton and the Development of the Calculus

### 1969

1 Robert L. Devaney College of the Holy Cross Lens Spaces as Coset Spaces

2 Michael Kopkas John Carroll University Partial Sums of Certain Infinite Series of Polygonal Numbers

3 Douglas Townsend Ohio State University A Generalization of Subnet with Some Resulting Improvements in Moore-Smith Convergence Theory

3 George Benkart Ohio State University A Generalization of Subnet with Some Resulting Improvements in Moore-Smith Convergence Theory

### 1968

1 Daniel E. Putnam University of Illinois An Easier Condition Than Total Boundedness

2 Jerome M. Katz Brooklyn College An Interesting Mapping of Two Fields

### 1967

3 Dennis Spellman Temple University On Hula Hoops

### 1966

1 James Williams Carleton College A Multiplication-Free Characterization of Reciprocal Addition