# 2017 Conference Program

**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).*