"Unit Circle" Animation
"Parabola" Animation
These animiations show what the unit ball in R^2 and a
parabola with vertex at the origin look like
under different norms. The unit ball starts as a diamond in the 1-norm (also
known as the Taxicab norm), rounds out to the familiar unit circle (achieved by
the Euclidean norm) and approaches the unit square (achieved by the max-norm).
Pi Day Presentation - I gave this talk as a Pi Day presentation to a local MENSA chapter.
My research interests range from theoretical areas in functional analysis and differential equations to applied areas in cancer research and mathematical modeling. I am currently studying sufficiency conditions for unique solutions to Sturm-Liouville problems with nonlinear boundary conditions. I also am working with four undergraduates to mathematically model the effects of colorectal cancer. Below is a list of publications along with works in progress. If you're interested in my work, would like to look at a preprint, or are an undergraduate thinking about research in mathematics, please send me an email!
Functional Analysis/Differential Equations
Cancer Research/Mathematical Modeling
NetLogo Models
Netlogo website
- Link will take you to the program's website where you can download
NetLogo and explore other user generated models.
Colorectal cancer model
The purposes of this model are to compare a healthy colon crypt to a
mutated colon crypt and demonstrate the effects of mutated stem cells on polyp
growth. This model specifically focuses on bottom-up morphogenesis, which occurs
when the stem cells have a mutation that causes the production of abnormal
daughter cells. This model was created as part of an undergraduate research
program during the summer of 2012 at Winthrop University. Authors of this
program and accompaning lesson plans and worksheets include Winthrop faculty
Kristen Abernathy, Zachary Abernathy, and Joseph Rusinko, and student
researchers Katrina Harmon, Anna Johnson, Johnakin Martin, and Kirsten
Stallings. Any questions should be directed to Kristen Abernathy at
abernathyk@winthrop.edu.
NetLogo file for colorectal cancer
model
Picture needed for program - Download the
colon cancer program and picture to the same folder. Open NetLogo and choose to
open the colon cancer program. As long as the colon cancer program and picture
are in the same
file, the program will work.
Lesson plans and worksheets to accompany cancer model:
1. Middle level mathematics course
Lesson plan
Worksheet
2. Algebra I course
Lesson plan
Worksheet
3. Introductory to Data Analysis course
Lesson plan
Worksheet
Breast cancer model
This agent-based model illustrates the application of chemotherapy to
breast cancer. This model was created as part of Winthrop's Initiative for STEM
Educators summer intern program, funded by the National Science Foundation
10-513, Robert Noyce Teacher Scholarship Program under award #1035322. Authors
of this program include Winthrop faculty Zachary Abernathy and Joseph Rusinko,
and student researchers Tyler Brooks, Courtney Cabaniss, Michelle Humphrey,
Taylor McGee, and Katherine Rigby. Any questions should be directed to Joseph
Rusikno at rusinkoj@winthrop.edu
NetLogo file for breast
cancer model
Picture
needed for program - Download the breast cancer program and picture to the
same folder. Open NetLogo and choose to open the breast cancer program.
As long as the breast cancer program and picture are in the same file, the
program will work.
