## 08. Research topics for Sophomores

### Sophomore students

Sophomore students refine their research skills of observation, experimentation, classification, organization and conjecturing, through analysis of models and algorithms a range of scientific disciplines. Sophomore students on the computational mathematics option have completed coursework in calculus I and II, discrete structures I and II, and object-oriented programming. They begin their sophomore year studying calculus III, linear algebra, and differential equations. In the linear algebra course sequence, Sophomore students receive additional preparation for research projects which introduces them to the process of experimentation, conjecture, and proof. Sophomore students will continue working on research projects described above for freshman research projects, and additionally may tackle new projects such as the following:

- Roots of Taylor polynomials of non-zero functions
- Graph energy
- Computing approximate eigenvectors
- Lonely runner problem
- Walks with memory
- Periodic knot solutions to the Lorenz equations
- Wrapping a sphere