...Perhaps one of the most important things to do is to make a student smile, if they're smiling or laughing they're far more likely to commit what they learn to memory as they'll enjoy what they're learning. Its also important for students to see what mathematics does. The most common question I hear is, "Why are we learning this?" or "Why is this useful?". (read more)
...My Ph.D. dissertation involved quadratic forms and eigenvalue-based methods of analyzing interactions between the different components in a model. I also taught a course in applied linear algebra for engineers that included matrix algebra, eigenvalue and eigenvector analysis, vector spaces, and ... (read more)