Undergraduate Research

Math Student Undegraduate Research at LWTech

UGR Highline 2019At Lake Washington Institute of Technology, students have the option of doing undergraduate research in the Math Department. Through undergraduate research, students obtain experience in hands-on exploration and real world problem-solving using technology and data visualization. Students who choose this option, work with Professor Narayani Choudhury to pursue projects in their areas of interest and present their findings at math conferences.

On February 23, 2019, students presented their undergraduate research at the Western Washington Community College Student Mathematics Conference at Highline College. In May, math students will also be presenting at the University of Washington Undergraduate Research Symposium and the Research Rendezvous at the University of Washington Bothell campus. The abstracts for this year's projects can be found below.

Recent Research Abstracts

Past Research Abstracts

2018 Undergraduate Research Abstracts

Vector Calculus studies of fullerenes

Iuliia Dmitrieva, Tom Skoczylas, Rami Manad, Narayani Choudhury
Lake Washington Institute of Technology

MATH Conference at Bellevue College, Feb. 19, 2018
UW Undergraduate Research conference, May, 2018

Polymer based fullerenes are used as photovoltaics in solar panels. Fullerene C60 molecules have
icosahedral based structures resembling geodesic domes. The mathematics of fullerenes have aroused much interest as their novel structures involve Golden ratios. Fullerenes have convex polyhedra which obey Euler’s topological rules. Here we use vector calculus methods to calculate bond lengths and bond angles and provide estimates for the volume of the molecule. We compare our results with reported numerical calculations of Van der Waals volume in fullerenes. To understand the critical effect of dimensionality on volume, we examine the volume of a hypersphere in n-dimensions. The project provides hands on exploration of real world problems and data visualization.

Multivariable calculus studies for environmental sciences and Engineering

Morgan Wolf, Sam Wolf, Narayani Choudhury
Lake Washington Institute of Technology

MATH Conference at Bellevue College, Feb. 19, 2018
UW Undergraduate Research conference, May, 2018

We explore applications of multivariable calculus for studying three dimensional wave media in our
environment. We use multivariable optimization methods to study the maxima and minima of three
dimensional functions. We use advanced data visualization and applications of divergence and curl to study ocean waves, including their divergence, curl, and circulation. Real world manifestations of scalar and vector fields in our environment are presented.

Monte Carlo simulations and the value of Pi

Sam Wolf, Narayani Choudhury
Lake Washington Institute of Technology

UW Undergraduate Research conference, May, 2018

Monte Carlo methods involve computational algorithms that rely on random sampling to obtain numerical results. Here we employ Monte Carlo simulations to estimate the numerical value of pi. The use of Monte Carlo methods for numerical integration and calculation of area and volumes of complex solids will be discussed. We will also discuss alternate numerical approaches including three dimensional Riemann sums and other strategies for derivation of volumes of complex solids.

2017 Undergraduate Research Abstracts

Calculus-based Studies of Volume and Surface Area of Three-Dimensional Objects

Stephen Scharkov, Alexey Sinitsin, Narayani Choudhury
Lake Washington Institute of Technology

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

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.

Vector Fields, Divergence, and Circulation

Aidan Hahn, Cesar Campos, Narayani Choudhury
Lake Washington Institute of Technology

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

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.

2016 Undergraduate Research Abstracts

Robotic Arm Kinematics using Trigonometry and Matrix algebra

Sierra Bonilla, Narayani Choudhury
Lake Washington Institute of Technology

Math Conference at Edmonds Community College, Feb. 20, 2016

The kinematics for two and three dimensional robotic arms are studied using basic trigonometry. We use linear algebra to derive the transformation matrices for simple translations and rotations in three dimensions to derive the robotic arm coordinates for complex motions. Our studies use Matrix algebra and trigonometric methods effectively to study the kinematics and transformed coordinates of the robotic arm. A small computer code is being developed to derive the coordinates of the robotic arm for a range of motions. This research project serves as an elegant platform for hands on application of mathematical and computational methods for real life solutions.

Flightpath optimization and Dynamics of a Glider

Evvan Land, Tyler Goolsby, Lisa Camire, Narayani Choudhury
Lake Washington Institute of Technology

Math Conference at Edmonds Community College, Feb. 20, 2016

The flightpath of a hang glider is modeled using a polynomial function and its parameters optimized to minimize turbulence. We have also visualized the reported glider velocity data from University of Washington and analyzed it using calculus based methods to derive the instantaneous and average acceleration. This research project provides a novel avenue for hands on exploration and application of key mathematical concepts and data visualization.