Nowadays the main academic achievements of mathematicians are related to their research, not teaching. Young people who have just started their academic career, like myself, are more focused on research results. Even though teaching has still significant importance, since it is the major source of money for mathematicians. In fact it is more than that, i.e., it is the way we can communicate with and contribute to the public.

I always consider 3 goals when I teach mathematics. The first one is to deliver mathematical facts to my students clearly and effectively. So it is my responsibility to prepare well organized lectures which start from the level of my audience. The second one is to encourage people to apply those mathematical results to various situations. It may include some demonstration of example problems during the lecture, but more importantly it should be accomplished through homework or various kinds of projects. So the design of reasonable homework problem sets or research projects is important. I know that unnecessarily hard problems may discourage people and that easy problems make them overlook the material.

My third goal of teaching mathematics is to deliver mathematical ideas which are behind the mathematical facts. Sometimes we think in this way and in other case we do things in that way. In many cases people just know it works. But we, mathematicians, can not be happy with that. There is a mathematical reason why it works and, if we can reveal it, it will be applied to more general cases.

Nowadays there are many good computational programs solving mathematical problems such as differentiations and integrations. They solve problems exactly, or approximate the solution numerically if there is no exact solution. Nowadays these programs are so reliable and almost error free. I believe that teaching mathematics is not aiming to make students compete with these things. What I believe is that the focus should be on the mathematical ideas and to encourage people to have creative mind based on those ideas.

It is clear that I can not fully deliver those ideas to students. The hard part is that most of mathematical ideas are related to the proof, which is the part most of the students do not want to try. On the other hand I am not sure if it is fair to ask my students to follow the way of arguments we do. It is clear that the public are not ready for that at all. Sometimes I try to simplify mathematical formulas in an easy way to use and demonstrate how to use them. I believe that it is a necessary thing to do. But it makes me to feel I am trying to make them compete with computers. This situation has been a puzzle since I considered my teaching job seriously. I hope I can get better solution for the issue as I continue my academic career related to teaching.