### About Research in Mathematics ("RMath")

In Mathematics, we have several opportunities for students to engage in research activities: RMath semester course, Graph Theory and REX Math, and Rmath during J-Term. Our program emphasizes opportunities for students to solve open-ended research questions in collaborative groups with rigorous expectations and creativity in approaches encouraged.

### Current Student to Contact

### What is the difference between the Academic Year RMath Program, J-Term RMath Course, and REX Math?

In Graph Theory and REX Math, offered in both the Fall and Spring semesters, students learn formal proof techniques throughout the semester, and in the final two-three weeks of the semester, students engage in solving an open-ended Graph Theory problem. They do this in collaborative groups and present their findings during finals week, along with submitting a final paper.

In our RMath semester course, students engage in solving open-ended research problems in collaborative groups over the series of weeks throughout the semester. Along the way, students present their benchmark results and engage in rigorous problem-solving and proof technique throughout. This is an application-based course.

In RMath Jterm, students focus all of their attention on one open-ended problem of their interest and engage in collaborative work throughout. As a culminating project, students both present their findings to the class and write a formal paper to communicate their research. There is no prerequisite for this opportunity.

In all of our research opportunities, students gain fluency in formal proof writing, developing and testing conjectures, and constructing logical arguments.

### What would I do in the program?

In our RMath semester course, students engage in solving open-ended research problems in collaborative groups over the series of weeks throughout the semester. Along the way, students present their benchmark results and engage in rigorous problem-solving and proof technique throughout. This is an application-based course.

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

Students in this program have a very strong interest in mathematics and focusing on one long-term, open-ended research problem. Students also enjoy working collaboratively and exchanging thoughts and ideas with others. They are interested in strengthening their skills in constructing logical arguments, communicating their thinking in various ways and developing and testing conjectures.

### 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

Commitment

### One Semester

Course Information

### MA4510,

Academic Year

Academic Year

### Tamar Avineri, NCSSM Durham Chair of Mathematics

Tamar Avineri grew up just outside of Los Angeles, completing her bachelor's degree in applied mathematics at the University of California at San Diego and her master's in mathematics at the University of California at Los Angeles. Tamar moved to North Carolina in 2004 and began teaching at NCSSM that same year. She has taught a variety of courses, including Precalculus and Modeling, Finite Mathematics, Calculus AB and BC, Modeling with Differential Equations, Graph Theory and REX Math, Combinatorics and Game Theory, Number Theory, Topics in Theoretical Mathematics, Research in Mathematics and Multivariable Calculus. Tamar received National Board Certification in 2008 and completed her Ph.D. in mathematics education at North Carolina State University in 2016, focusing her research on professional development for mathematics teachers. She also became part of the 100kin10 Teacher Forum in 2019. Tamar is most passionate about teaching, working with students inside and outside of the classroom, learning from and collaborating with colleagues and other educators, and thinking hard about mathematics. She has co-developed and taught courses in Finite Mathematics and Multivariable Calculus for the Online Program and has taught students across North Carolina for a number of years through videoconference. Tamar has served as a member and officer of the Faculty Senate and on the school re-accreditation and Math Department curriculum review writing teams, and is currently a co-chair of the UNC Math Pathways Task Force.

### Michael Lavigne, NCSSM Durham Instructor of Mathematics

Michael Lavigne joined the math faculty at NCSSM's Durham campus in August 2022 after four years of teaching at the undergraduate level. A native of New Orleans, he came to North Carolina in 2015 to pursue a Ph.D. in applied mathematics at NCSU after earning his bachelor's degree in mathematics and Spanish at Tulane University. He then served as Visiting Assistant Professor at Georgia Institute of Technology from 2020-2022. During that time Michael also served as Assistant Director for the Southeast Center for Mathematics and Biology (SCMB), where he was lead organizer for the Center’s annual symposium, undergraduate Modeling Accelerator, and community outreach initiatives. His work focuses on the mathematical modeling of complex bio-systems and espouses a philosophy of math-bio storytelling—using mathematics to narrate the “why” of a well-described biological “what”. His original Mathematical Biology course at GT was one of two in the College of Sciences to receive the Student Recognition in Teaching Excellence award. Outside of the classroom, Michael is an avid pianist, a lover of languages, and an amateur florist.

### Course Descriptions

### BI4920 Research in Biology I (*R*)

Meeting Times: Two week intensive January Term

This is an advanced course for January Term junior students with the maturity, independence, and motivation necessary to conduct their own research project. Students learn the scientific method and experimental design before conducting a trial experiment on a small scale. Students then write a mini- literature review on the topic of interest to them. Throughout the term students read from the primary scientific literature and participate in discussion groups on current issues in biological research. Students with a final grade of P or higher are expected to continue in Research in Biology II. This course includes a significant research component.

### BI4921 Research in Biology II (*R*)

Meeting Times: Seven periods per week and three labs

This is an advanced course for second semester junior students. Students write a detailed research proposal and defend it to a panel of their peers. Students begin to learn techniques and to gather data for their experiments. Based on the outcomes of the term's work, students may be given an opportunity to participate in summer research programs on campus. Students with a final grade of B or higher are expected to continue in Research in Biology III. This course includes a significant research component.

### BI4922 Research in Biology III (*R*)

Meeting Times: Seven periods per week and three labs

Students continue work on their previous research to produce additional data and conduct statistical analysis, as needed. They may research extension questions based on their original work. Students write a formal research paper and prepare a formal presentation. Students are required to present their results at the NCSSM Research Symposium in the spring and are encouraged to present their research at the North Carolina Student Academy of Science competition and other competitions. This course includes a significant research component.