The Eleventh Annual Western Washington Community College Student Mathematics Conference
Green River College
Saturday, February 25, 2017

• Check-in will begin at approximately 9:30 a.m. in Cedar Hall.
• Light refreshments will be available in Room 316.
• Sessions will be held in Room 214.

10:00 Welcome
Cathy Wells, Dean of Green River’s Mathematics Division and Science Division

10:05 Art and Abstract Algebra
Dr. Luke Rawlings, Bellevue College

Art can illuminate mathematical principles; we’ll see how, and investigate some drawings.

10:35 Modeling Voyager II’s Gravity Assist Using Differential Equations
Seong Hoon (Alex) Lee, Green River College

The purpose of this model is to analyze a gravity assist maneuver by using a second order ordinary differential equation (ODE). Researching and studying Differential Equations has enabled us to come up with a solution to the differential equation, solving it numerically using the Runge-Kutta method. Resulting from many factors affecting the spacecraft’s motion during a gravity assist maneuver, this model will make some assumptions in order to perform calculations that will explain the theory.

10:55 Calculus-based Studies of Volume and Surface Area of Three-Dimensional Objects
Stephen Scharkov, Alexey Sinitsin, and Narayani Choudhury, Lake Washington Institute of Technology

We derive parametric equations to model a three-dimensional flower vase. The volume and surface area of the vase is computed using calculus-based techniques employing cylindrical coordinates. Numerical multidimensional Riemann sums and regression-based methods are required for calculating the volume of the flower vase and objects having complex shapes. The project presents hands-on experience with data modeling, visualization and real life applications of calculus.

11:15 Knot Fertility and Lineage
Briana Zimmer, Green River College

Is your favorite knot fertile? We define a knot K  to be a parent knot of a knot H  if some number of crossings in a minimal crossing projection of K  can be resolved to produce a diagram of H. We say that K  is fertile if it is a parent of every knot with a smaller crossing number than itself. We explore families of knots and their relative fertility. We also explore ways to find the trefoil in every knot.

12:00 Lunch (Room 316)

12:45 Vector Fields, Divergence, and Circulation
Aidan Hahn, Cesar Campos, and Narayani Choudhury, Lake Washington Institute of Technology

We discuss the role of data visualization in elucidating the critical points of a multivariable function. The local and absolute maximum, minimum, and saddle points can be derived analytically using multivariable calculus. We employ surface plots, contour plots and vector gradient fields to study the local maxima and minima, divergence, curl, and circulation. The plots provide key insights into identifying whether a vector field is conservative or not.   Quiver and Streamline integral plots provide visual solutions of differential equations. Data visualization enhances critical understanding and aids in the study of functions of many variables.

1:05 The Cantor Set and Infinite Series
Kyle Airis, Kevin Airis, Anthony Thorn, and Elise Dunning, Green River College

A short introduction to Georg Cantor and the Cantor Set, with techniques from Calculus III. Sierpinski’s Carpet and the Menger Sponge will be presented, including handmade models.

1:20 Hard Problems from my Calculus Class
Levan Jikiya, Clark College

Short solutions to some seemingly hard problems.

1:35 A Freeway Traffic Model
Kristiana Soranaka, Natasha Braunstein, and Alyssa Leano, Green River College

An attempt to model the flow of traffic and how self-driving cars may affect that flow, including concepts like headway and capacity. This problem was from the 2017 Mathematical Contest in Modeling (MCM).

1:50 Building a Better Toll Plaza
Gavin Liu, Briana Zimmer, and Chase Lee, Green River College

Tolled highways allow government agencies to collect money in the form of tickets. For this year's MCM contest, we took on the challenge of designing a safe, efficient, and cost effective toll plaza.

2:15 48 = 47
Nathan Williams, Green River College

A discussion of a “proof” without words of a surprising result.

2:30 Some Applications in Electrical Engineering
Vi Ho, Highline College

Some applications of mathematics to electrical engineering, especially operational amplifiers.

2:40 Conclusion and Door Prizes

The 2017 Western Washington Community College Student Mathematics Conference is supported by a generous grant from the Washington Mathematical Association of Two-Year Colleges (WAMATYC).