Math Really Counts
Research Projects
My passion for math and computer science has led me to conduct a number of research projects: Parametric 4D Plotting, Waring's Problem and Kissing Numbers, and Bioinformatics Interface in Yale University's Gerstein Lab.
A. Parametric 4D Plotting:
I have developed an innovative 4D plotting function ParametricPlot4D that allows a user to visualize a 4D object in the 3D world. ParametricPlot4D projects a 4D parameterization either orthogonally or stereographically to make a 3D shadow and uses Graphics3D to render it. In the orthogonal projection case, the function displays the bounding tesseract, which is analogous to Plot3D's bounding rectangular prism and Plot2D's bounding rectangle.
More details are available on the Wolfram website.
Here are some projection pictures.
B. Waring's Problem and Kissing Numbers:
I'm currently conducting this research. I plan to help solve two open math problems through computational methods. The aim for Waring's Problem is to improve the lower bound of 471,600,000 for values of k that satisfy $$ 2^k\ast\lbrace(\frac{3}{2})^k\rbrace+\lfloor(\frac{3}{2})^k\rfloor>2^k $$, or better yet, show that no such k exists. The aim for the kissing numbers problem is to either find the exact kissing number for 5-D or improve the bounds on it.
Here are some graphical representations of the kissing numbers:
C. Bioinformatics Interface in Yale University's Gerstein Lab:
I worked on a data-intensive, computational project to interpret, manipulate, and simulate genomic and biophysical data to better understand phenomena such as gene regulation and their implications in severe illnesses, such as cancer.
Thomas Jefferson High School for Science and Technology