#### Submissions from 2007

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

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

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

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

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

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

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

Ted Talk: Arthur Benjamin Does "Mathemagic", Arthur T. Benjamin

Q.954 and A.954, Quickie Problem and Solution, Arthur T. Benjamin and Michel Bataille

Recounting the Odds of an Even Derangement, Arthur T. Benjamin, Curtis D. Bennet, and Florence Newberger

Counting on Determinants, Arthur T. Benjamin and Naiomi T. Cameron

Pythagorean Primes and Palindromic Continued Fractions, Arthur T. Benjamin and Doron Zeilberger

Lower Bounds for Simplicial Covers and Triangulations of Cubes, Adam Bliss '03 and Francis E. Su

Upper Estimates for the Energy of Solutions of Nonhomogeneous Boundary Value Problems, Alfonso Castro and Mónica Clapp

Construction of a Radial Solution to a Superlinear Dirichlet Problem that Changes Sign Exactly Once, Alfonso Castro and Jorge Cossio

Determinants and Polynomial Root Structure, Lisette G. de Pillis

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

Using Ultrasonic Atomization to Produce an Aerosol of Micron-scale Particles, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, M. Schubmehl '02, N. Schommer '04, Andrew J. Bernoff, S. Dasnurkar, and T. Ditmire

Properties of One-Point Completions of a Noncompact Metrizable Space, Melvin Henriksen, Ludvík Janoš, and R. G. Woods

C(X) Can Sometimes Determine X Without X Being Realcompact, Melvin Henriksen and Biswajit Mitra

Two-Dimensional Self-Assembly in Diblock Copolymers, Anette E. Hosoi, Dmitriy Kogan '03, Caitlin E. Devereaux '02, Andrew J. Bernoff, and Shenda M. Baker

Looking Beyond the Curriculum in Jamaica, Jon T. Jacobsen and Michael E. Orrison Jr.

Kinetics and Nucleation for Driven Thin Film Flow, Rachel Levy and Michael Shearer

Evaluating the Viability of 100 Per Cent Container Inspection at America’s Ports, Susan E. Martonosi, David S. Ortiz, and Henry H. Willis

SRT Division Algorithms As Dynamical Systems, Mark McCann and Nicholas Pippenger

A Mathematical Model for Treatment-Resistant Mutations of HIV, Helen Moore and Weiqing Gu

The Average Amount of Information Lost in Multiplication, Nicholas Pippenger

The Boolean Functions Computed by Random Boolean Formulas OR How to Grow the Right Function, Nicholas Pippenger and Alex Brodsky

A Constructive Proof of Ky Fan's Generalization of Tucker's Lemma, Timothy Prescott '02 and Francis E. Su

#### Submissions from 2004

A (not so) Complex Solution to a² + b² = cⁿ, Arnold M. Adelberg, Arthur T. Benjamin, and David I. Rudel '99

Mathematical Magic, Arthur T. Benjamin

Putnam, Pizza & Problem Solving, Andrew J. Bernoff and Francis E. Su

Semilinear Equations with Discrete Spectrum, Alfonso Castro

An Existence Result for a Class of Sublinear Semipositone Systems, Alfonso Castro, C. Maya, and Ratnasingham Shivaji

An Experimental Study of Micron-scale Droplet Aerosols Produced via Ultrasonic Atomization, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, N. Schommer '04, M. Schubmehl '02, Andrew J. Bernoff, and B. Forrest '02

Examples of Cayley 4-Manifolds, Weiqing Gu and Christopher Pries

Cozero Complemented Spaces; When the Space of Minimal Prime Ideals of a C(X) is Compact, Melvin Henriksen and R. G. Woods

A Liouville-Gelfand Equation for k-Hessian Operators, Jon T. Jacobsen

Radial Solutions of Quasilinear Elliptic Differential Equations, Jon T. Jacobsen and Klaus Schmitt

Comparison of Two Dynamic Contact Line Models for Driven Thin Liquid Films, Rachel Levy and Michael Shearer

Terror is in the Air, Susan E. Martonosi and Arnold Barnett

Computing Isotypic Projections with the Lanczos Iteration, David K. Maslen, Michael E. Orrison Jr., and Daniel N. Rockmore

Rooted Trees and Iterated Wreath Products of Cyclic Groups, Rosa C. Orellana, Michael E. Orrison Jr., and Daniel N. Rockmore

Radon Transforms and the Finite General Linear Groups, Michael E. Orrison

Essential P-Spaces: A Generalization of Door Spaces, Emad Abu Osba and Melvin Henriksen

Combining Local and Von Neumann Regular Rings, Emad Abu Osba, Melvin Henriksen, and Osama Alkan

Entropy and Expected Acceptance Counts for Finite Automata, Nicholas Pippenger

Random Walks on the Torus with Several Generators, Timothy Prescott '02 and Francis E. Su

Blowup and Dissipation in a Critical-Case Unstable Thin Film Equation, Thomas P. Witelski, Andrew J. Bernoff, and Andrea L. Bertozzi

#### Submissions from 2003

A Combinatorial Approach to Hyperharmonic Numbers, Arthur T. Benjamin, David Gaebler '04, and Robert Gaebler '04

A Probabilistic View of Certain Weighted Fibonacci Sums, Arthur T. Benjamin, Judson D. Neer, Daniel T. Otero, and James A. Sellers