Mathematics at the undergraduate level is often treated as merely a tool for other sciences. In my opinion, this is the wrong approach to teaching mathematics. Rather, mathematics is a fantastic field for the development of intellectual skills. With the growth of AI tools, such skills are of rising importance. It is according to this principle that I conduct my teaching. There are two areas that I pay particular attention to:
I believe that learning the process of problem-solving is more important than learning facts or techniques. To promote such learning, I give students questions that are slightly above their standard curriculum level, while breaking them into manageable steps, and leading them through these steps. I often ask them to work in small groups to promote collaboration.
I believe that motivating mathematical concepts is important for learning. There are two ways through which I implement this:
When introducing an abstract mathematical concept, I often start with a real-world problem where this concept could be useful, and introduce it as an important step to solving the problem.
To help students deepen their understanding, I give them applications of the mathematical concepts in other areas like biology, chemistry or physics.
Mixed opinions exist regarding the usage of AI tools in education. I believe that it can be helpful as long as the usage is directed and with purpose. Based on the above principle, the usage of AI must support the exercise of intellect, rather than diminishing it. Although I haven't implemented this, I plan to let students work on problems in classes without the help of AI, and discuss their answers with AI to improve them.
NSERC undergraduate research program. Mentee: T. Karabela. Topic: Quantum groups and quantization of symplectic reductions.
Summer 2020: Calculus MAT 021C
Summer 2021: Calculus MAT 021C
Fall 2021: Calculus MAT 021D
Summer 2022: Real Analysis MAT 127B
Various TA duties for both lower and upper division courses at UC Davis.