Personal Teaching philosophy Mathematics, on its own, is a highly beautiful subject, and various branches of mathematics are often closely inter-related. On a more global perspective, mathematical thinking and methods play an important role in many disciplines such as engineering, economics and other branches of science such as physics, chemistry and biology. Some of my major goals in teaching mathematics are to make students appreciate the beauty as well as the power of mathematics. Along this line of thought, my teaching philosophy can be summarized by my following beliefs: It is important to make students understand the motivations behind the mathematical concepts that they learnt in the lectures. Teachers should help students develop their problem-solving skills, their presentation skills, independent learning habits as well as their ability in critical thinking. Teachers should make the students learning process enjoyable and thereby foster their interest in learning. Teachers should also be passionate about their students as well as what they teach, be approachable to students, provide timely feedback to queries of students, and be responsive to the feedback and needs of the students. Based on my teaching philosophy, my teaching is featured by the following practices: In my lectures, some proofs of the theorems and many of the examples are worked out on the spot (instead of being pre-typed in the lecture notes). I believe this is the most effective way in helping students grasp the mathematical concepts and develop their mathematical thinking. In my lectures, I always like to draw parallels and contrasts with what the students learnt in other modules so as to help students understand the course content better and acquire an overall picture of the realm of mathematics. As an example, in the module MA3111 Complex Analysis I (2008/09 Semester 2), the similarities and the differences between calculus of functions of a complex variable (MA3111) and calculus of functions of one and two real variables (in other modules) are stressed. At numerous places in my lecture notes, some details are left as exercises for students, or students are referred to the textbook for details. Also, I give the students a problem list as supplementary exercises, and the problem list only contains the question numbers in the textbook. These are measures to encourage the students to read the textbook (rather than solely relying on lecture notes) and be more independent in learning. In homework and assessment, I always set some problems which require deeper understanding of the course content. This will help students develop their ability to apply familiar information and knowledge in less familiar situations. In tutorial classes, students are regularly asked to present their solutions to homework problems. Not only does this train the students presentation skills, students also get opportunities to learn from their fellow students alternative viewpoints, or even mistakes. Also this will help students develop their ability in critical thinking, their ability to look for alternative solutions and answers, and their ability to articulate their ideas and arguments precisely and clearly. I do not set specific consultation hours, and students are welcomed to drop by my office anytime during office hours to discuss mathematics with me. Students are welcomed to discuss any mathematics with me whether it is related to the modules I teach or not.