#### Submissions from 2010

Effective Collaborations to Support Transformative Research, Jeffrey G. Ryan and Lisette G. de Pillis

Teaching Research: Encouraging Discoveries, Francis E. Su

#### Submissions from 2009

Some Properties of Algebras of Real-valued Measurable Functions, Hassan Azadi, Melvin Henriksen, and Ehsan Momtahan

Ta Da! (A Magical Math Pop Quiz), Arthur T. Benjamin

Ted Talk: Arthur Benjamin's Formula for Changing Math Education, Arthur T. Benjamin

Compression Theorems for Periodic Tilings and Consequences, Arthur T. Benjamin, Alex K. Eustis '06, and Mark A. Shattuck

Counting on Chebyshev Polynomials, Arthur T. Benjamin and Daniel Walton '07

A Semilinear Wave Equation with Smooth Data and No Resonance Having No Continuous Solution, Jose F. Caicedo and Alfonso Castro

Voting, the Symmetric Group, and Representation Theory, Zajj Daugherty '05, Alexander K. Eustis '06, Gregory Minton '08, and Michael E. Orrison

Mathematical Model Creation for Cancer Chemo-Immunotherapy, Lisette G. de Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, and Benjamin Preskill '09

Asymptotic Dynamics of Attractive-Repulsive Swarms, Andrew J. Leverentz '08, Chad M. Topaz, and Andrew J. Bernoff

A preliminary mathematical model of skin dendritic cell trafficking and induction of T cell immunity, Amy H. Lin Erickson, Alison Wise, Stephen Fleming, Margaret Baird, Zabeen Lateef, Annette Molinaro, Miranda Teboh-Ewungkem, and Lisette G. de Pillis

Stability of Traveling Waves in Thin Liquid Films Driven by Gravity and Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, and Rachel Levy

Attribute estimation and testing quasi-symmetry, Nicholas Pippenger and Krzysztof Majewski

Sum Rules and Universality in Electron-modulated Acoustic Phonon Interaction in a Free-standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, and Nobuya Mori

Gaseous Hole Closing in a Polymer Langmuir Monolayer, Lu Zou, Andrew J. Bernoff, J. Adin Mann Jr., James C. Alexander, and Elizabeth K. Mann

#### Submissions from 2008

Uniqueness of Large Radial Solutions and Existence of Nonradial Solutions for a Superlinear Dirichlet Problem in Annulii, Hugo Aduén, Alfonso Castro, and Jorge Cossio

The 99th Fibonacci Identity, Arthur T. Benjamin, Alex K. Eustis '06, and Sean S. Plott '08

A Combinatorial Approach to Fibonomial Coefficients, Arthur T. Benjamin and Sean S. Plott '08

Tiling Proofs of Recent Sum Identities Involving Pell Numbers, Arthur T. Benjamin, Sean S. Plott '08, and James A. Sellers

Tiling Proofs of Recent Sum Identities Involving Pell Numbers, Arthur T. Benjamin, Sean S. Plott, and James A. Sellers

An Alternate Approach to Alternating Sums: A Method to DIE for, Arthur T. Benjamin and Jennifer J. Quinn

Paint it Black -- A Combinatorial Yawp, Arthur T. Benjamin, Jennifer J. Quinn, James A. Sellers, and Mark A. Shattuck

Mathematics in the Mountains: The Park City Mathematics Institute, Andrew J. Bernoff

Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers' Equation, Victor Camacho '07, Robert D. Guy, and Jon T. Jacobsen

The Art of Teaching Mathematics, Garikai Campbell, Jon T. Jacobsen, Aimee S A Johnson, and Michael E. Orrison Jr.

Are Engineering Schools Masculine and Authoriarian? The Mission Statements Say Yes, Emmeline G. de Pillis and Lisette G. de Pillis

Optimal Control of Mixed Immunotherapy and Chemotherapy of Tumors, Lisette G. de Pillis, K Renee Fister, Weiqing Gu, Tiffany Head '06, Kenny Maples '06, Todd Neal, Anand Murugan, and Kenji Kozai '08

Distribution of the Number of Encryptions in Revocation Schemes for Stateless Receivers, Christopher Eagle, Zhicheng Gao, Mohamed Omar, Daniel Panario, and Bruce Richmond

The Shapley Value of Phylogenetic Trees, Claus-Jochen Haake, Akemi Kashiwada '05, and Francis E. Su

Borda Meets Pascal, Marie K. Jameson, Gregory Minton '08, and Michael E. Orrison

The Cooperating and Competitive Strategy Research of Tianjin Port, Tianxia Li and Weiqing Gu

Systematic mistakes are likely in bounded optimal decision-making systems, Nicholas Pippenger and Adi Livnat

Fault Tolerance in Cellular Automata at High Fault Rates, Nicholas Pippenger and Mark McCann

A Model for Rolling Swarms of Locusts, Chad M. Topaz, Andrew J. Bernoff, Sheldon Logan '06, and Wyatt Toolson '07

Mathematics of Voting, Darryl H. Yong

Imagine Math Day: Encouraging Secondary School Students and Teachers to Engage in Authentic Mathematical Discovery, Darryl H. Yong and Michael E. Orrison Jr.

#### Submissions from 2007

Domain Relaxation in Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Jacob R. Wintersmith '06, and Lu Zou

Ways in which C(X) mod a Prime Ideal Can be a Valuation Domain; Something Old and Something New, Bikram Banerjee and Melvin Henriksen

The Probability of Relatively Prime Polynomials, Arthur T. Benjamin and Curtis D. Bennet

The Probability of Relatively Prime Polynomials, Arthur T. Benjamin and Curtis D. Bennett

Fibonacci Deteminants - A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, and Jennifer J. Quinn

Solution to Problem 1751, A Combinatorial Identity, Arthur T. Benjamin and Andrew Carman '09

A Combinatorial Proof of Vandermonde's Determinant, Arthur T. Benjamin and Gregory P. Dresden

A Combinatorial Solution to Intertwined Recurrences, Arthur T. Benjamin and Michael D. Hirschhorn

Recounting Determinants for a Class of Hessenberg Matrices, Arthur T. Benjamin and Mark A. Shattuck

Positive Solutions for Classes of Multiparameter Elliptic Semipositone Problems, Scott Caldwell, Alfonso Castro, Ratnasingham Shivaji, and Sumalee Unsurangsie

Infinitely Many Radial Solutions for a Sub-Super Critical Dirichlet Boundary Value Problem in a Ball, Alfonso Castro, John Kwon, and Chee Meng Tan '07

Seeking Bang-Bang Solutions of Mixed Immuno-Chemotherapy of Tumors, Lisette G. de Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, and Benjamin Preskill '09

Chemotherapy for Tumors: An Analysis of the Dynamics and a Study of Quadratic and Linear Optimal Controls, Lisette G. de Pillis, Weiqing Gu, K Renee Fister, Tiffany Head '06, Kenny Maples '06, Anand Murugan, Todd Neal, and Kenji Yoshida '08

Teaching Time Savers: Is Homework Grading on Your Nerves?, Lisette G. de Pillis and Michael E. Orrison Jr.

Comment on: A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth, Lisette G. de Pillis, Ami E. Radunskaya, and Charles L. Wiseman

Turing Patterns on Growing Spheres: The Exponential Case, Julijana Gjorgjieva and Jon T. Jacobsen

Removing Sets from Connected Spaces While Preserving Connectedness, Melvin Henriksen and Amir Nikou

SP-Scattered Spaces: A New Generalization of Scattered Spaces, Melvin Henriksen, Robert M. Raphael, and R. G. Woods

As Flat As Possible, Jon T. Jacobsen

Approximations of Continuous Newton's Method: An Extension of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, and Bradley Tennis '06

Automated Review of Prerequisite Material for Intermediate-Level Undergraduate Mathematics, Rachel Levy, Michael Shearer, and Padraic Taylor

Gravity-driven Thin Liquid Films with Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, and Thomas P. Witelski

Teaching Time Savers: The Exam Practically Wrote Itself!, Michael E. Orrison Jr.

A Fixed Point Theorem for the Infinite-Dimensional Simplex, Douglas Rizzolo '08 and Francis E. Su

Estimating Winning Probabilities in Backgammon Races, Andrew M. Ross, Arthur T. Benjamin, and Michael Munson '94

The LSB Theorem Implies the KKM Lemma, Gwen Spencer '05 and Francis E. Su

Applying Risk Assessment to Secure the Containerized Supply Chain, Maarten van de Voort, Henry H. Willis, David S. Ortiz, and Susan E. Martonosi

Determination of Interphase Line Tension in Langmuir Films, Jacob R. Wintersmith '06, Lu Zou, Andrew J. Bernoff, James C. Alexander, and J. Adin Mann Jr.

#### Submissions from 2006

The Maximal Regular Ideal of Some Commutative Rings, Emad Abu Osba, Melvin Henriksen, Osama Alkam, and Frank A. Smith

Hole Dynamics in Polymer Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., and Lu Zou

Double Birthday Magic Square, Arthur T. Benjamin

Self-Avoiding Walks and Fibonacci Numbers, Arthur T. Benjamin

Revisiting Fibonacci and Related Sequences, Arthur T. Benjamin and Jennifer J. Quinn

Summing Cubes by Counting Rectangles, Arthur T. Benjamin, Jennifer J. Quinn, and Calyssa Wurtz

Combinatorial Interpretations of Spanning Tree Identities, Arthur T. Benjamin and Carl R. Yerger

Mean Field Effects for Counterpropagating Traveling Wave Solutions of Reaction-Diffusion Systems, Andrew J. Bernoff, R. Kuske, B. J. Matkowsky, and V. Volpert

Dead Heat: The 2006 Public Choice Society Election, Steven J. Brams, Michael W. Hansen '07, and Michael E. Orrison Jr.

Mixed Immunotherapy and Chemotherapy of Tumors: Modeling Applications and Biological Interpretations, Lisette G. de Pillis, Weiqing Gu, and Ami E. Radunskaya

Spatial Tumor-Immune Modeling, Lisette G. de Pillis, D G. Mallet, and Ami E. Radunskaya

Some Promising Approaches to Tumor-Immune Modeling, Lisette G. de Pillis and Ami E. Radunskaya

Communicating Applied Mathematics: Four Examples, Daniel E. Finkel, Christopher Kuster, Matthew Lasater, Rachel Levy, Jill P. Reese, and Ilse C. F. Ipsen

Residue Class Rings of Real-Analytic and Entire Functions, Marek Golasiński and Melvin Henriksen

Optimal Therapy Regimens for Treatment-Resistant Mutations of HIV, Weiqing Gu and Helen Moore

The Local Gromov–Witten Invariants of Configurations of Rational Curves, Dagan Karp, Chiu-Chu Melissa Liu, and Marcos Mariño

Spectral Analysis of the Supreme Court, Brian L. Lawson, Michael E. Orrison, and David T. Uminsky

An Optimal Brain Can Be Composed of Conflicting Agents, Adi Livnat and Nicholas Pippenger

A Cellular Automata Model of Tumor–Immune System Interactions, D G. Mallet and Lisette G. de Pillis

How Effective Is Security Screening of Airline Passengers?, Susan E. Martonosi and Arnold Barnett

The Linear Complexity of a Graph, David L. Neel and Michael E. Orrison Jr.

Asymptotics of Largest Components in Combinatorial Structures, Mohamed Omar, Daniel Panario, Bruce Richmond, and Jacki Whitely

Reflections Acting Efficiently on a Building, Michael E. Orrison

Teaching Time Savers: A Recommendation for Recommendations, Michael E. Orrison Jr.

Teaching Time Savers: Some Advice on Giving Advice, Michael E. Orrison Jr.

Teaching Time Savers: Style Points, Michael E. Orrison Jr.

The Linking Probability of Deep Spider-Web Networks, Nicholas Pippenger

Topological characteristics of random triangulated surfaces, Nicholas Pippenger and Kristin Schleich

A Framework for Inclusive Teaching in STEM Disciplines, Lois Reddick, Wayne Jacobson, Angela Linse, and Darryl Yong

The Motion of a Thin Liquid Film Driven by Surfactant and Gravity, Michael Shearer and Rachel Levy

Growing Surfactant Waves in Thin Liquid Films Driven by Gravity, Thomas P. Witelski, Michael Shearer, and Rachel Levy

Strings, Chains, and Ropes, Darryl H. Yong

#### Submissions from 2005

Combinatorial Proofs of Fermat's, Lucas's, and Wilson's Theorems, Peter G. Anderson, Arthur T. Benjamin, and Jeremy A. Rouse

Book Review: Across the Board: The Mathematics of Chessboard Problems by John J. Watkins, Arthur T. Benjamin

Proof Without Words: Alternating Sums of Odd Numbers, Arthur T. Benjamin