Reach out to Hannah Schwartz (hannah.schwartz@ncssm.edu) & Eric Taylor (eric.taylor@ncssm.edu), NCSSM Instructors of Mathematics, to learn more about Research in Math at Morganton

### About Research in Mathematics

Research in Math is a semester-long course in which students collaborate on open-ended research problems on topics in higher level mathematics. This is an application-based course.

### What would I do in the program?

Students will spend the semester understanding and working on open problems in mathematics. Throughout the semester, students will also engage with professional research mathematicians, practice reading higher level mathematical research papers, and hone their formal proof writing skills. At the end of the semester, students will package and present their original results.

### How do I know this program is a good fit for me?

Students in this course should have a very strong interest in mathematics, and have some experience with proof-writing. Students should also enjoy working collaboratively and exchanging mathematical ideas with others.

### What projects have past / current students worked on?

The Match Game

A Game on Graphs

𝒕-tone 𝒌-colorings of a Graph

Positive Triangle Game

Application Deadline

### September 29,

12:00 PM (Noon)

12:00 PM (Noon)

Scheduling

### Spring Semester

(with optional second semester continuation)

Commitment

### One Semester

(with optional second semester continuation)

Course Information

### MA4510 & MA4512, Academic Year

### Hannah Schwartz, NCSSM Morganton Instructor of Mathematics

Hannah is thrilled to be an instructor of mathematics at NCSSM-Morganton. She graduated with her PhD from Bryn Mawr College, where she researched low dimensional topology. She then traveled to Germany for a research position at the Max Planck Institute of Math, followed by a second postdoc at Princeton University. There, she began to develop courses where students could explore higher mathematics in unexpected and creative ways, regardless of their background. Her favorites included a course for Princeton freshmen on the mathematics behind circus acts, and a course on mathematics in the courtroom for incarcerated students earning their BA from Rutgers. Now, she is happy to be part of the NCSSM community where she enjoys sharing her love of mathematics, especially the aspects of her research that involve visualizing knots, surfaces, and 4-dimensional spaces! She spends her time outside of work sitting on her front porch, cooking, hiking, gardening, and exploring with her three beautiful dogs and partner Jason.

### Eric Taylor, NCSSM Morganton Interim Chair of Mathematics

Eric Taylor joined the NCSSM-Morganton team in July 2022 as an Instructor of Mathematics. He is a National Board Certified Teacher with a bachelor’s degree in mathematics and a master’s in instructional technology. Prior to joining NCSSM, he taught high school math for Burke County Public Schools for 20 years. While at Patton High School in BCPS, Eric served as the graduation coordinator and chair of the school improvement/leadership team. In addition, he has presented at the North Carolina Technology in Education Society annual conference, teaching other teachers how to utilize Canvas in the math classroom. Outside of school, Eric’s favorite pastimes include reading and traveling with his family. In April 2022, the Taylor family achieved their goal of visiting all 50 US states. Up next on their list? Only 194 more countries to go!

### Course Descriptions

### MA4510 Research in Mathematics

Prerequisite(s): MA4500 AND Research Program Application, MA4330 AND Research Program Application, or permission of the Dean of Math

Corequisite(s): None

Graduation Requirements Met: One STEM credit OR One Mathematics credit

Schedule Requirements Met: One of five courses required each semester

Meeting Times: Three periods per week and a lab

This course is designed for students who have completed calculus and would like to work on a research team investigating an unsolved problem in mathematics. Since the research questions usually arise from the fields of graph theory and complex systems, students are encouraged to complete MA4500 Graph Theory with REX Math and MA4230 Introduction to Complex Systems prior to enrolling or to have completed comparable coursework in 9th or 10th grade.

### MA4512 Research in Mathematics II

Prerequisite(s): MA4510 Research in Mathematics I OR MA4520 Advanced Mathematical Topics I OR MA4522 Advanced Mathematics Topics II

Corequisite(s): None

Graduation Requirements Met: One STEM credit OR One Mathematics credit

Schedule Requirements Met: One of five courses required each semester

Meeting Times: Three periods per week and a lab

This course continues the project begun in MA4510. Students write a formal paper presenting the background of the problem and any prior results found by other researchers. The students' results are then presented in standard mathematical form with all necessary detail in the proofs and corollaries presented. If the students' results warrant, the paper may be submitted for publication.