Prospective students

Mentoring Principles

Mentoring students is my primary reason to enter academia. I enjoy interacting with students, helping them explore their potential, and seeing them achieve their personal best. I view the MASc and PhD programs as an educational process to develop research-related skills, such as critical thinking skills, creative thinking skills, presentation skills, writing skills, professional communication skills, among others.

To train critical thinking skills, I encourage my students to become active learners rather than passive recipients of information while reading papers and learning new techniques. I will ask students to think through every detail in an argument and understand the logical connection between ideas. Taking math courses will be highly encouraged. The mathematical rigor in reasoning ideas and assumptions, as well as the fine distinction in mathematical concepts, could be excellent training to build the necessary thinking skills for a theoretical researcher. (Real analysis (Math 507) and Probability Theory (Math 544, Math 545) are typical courses my students take. Besides, courses in analysis, linear algebra, combinatorics, graph theory, statistics, optimization, group theory, and finite field, are all helpful.) 

To cultivate creative thinking, I encourage questions and stimulate discussions in group meetings and everyday conversations. I listen carefully and relevantly respond to each student’s comments considering and respecting their perspectives. While explaining an existing result, I wish to lead the students to think through the process as if they are discovering the theorems themselves. One crucial element in creating such a learning experience is the thorough preparation and carefully designed step-by-step questions. To build intuition, I encourage students to work out simple examples and guess the result from the first principles. To stimulate ideas, I strive to exemplify how to view a concept from several perspectives, and how to approach a problem from many different angles.

To build presentation skills, I follow my academic grandfather Thomas Cover's round-robin group meeting: In a round-robin fashion, each person is asked to talk for five minutes on anything that is intellectually stimulating. The content has to be self-contained and accessible to most people. Due to the time constraint, one has to think hard to distill the simplest way to set up the problem, the cleanest way to explain the ideas, and the shortest path to convey the essence of the message. Often times in theoretical research, beautiful ideas are simple and thus explainable in a short time. I believe the training to identify something suitable for five minutes and to present it in front of group members is crucial in cultivating clear thinking, clean presentation, as well as a taste of beauty. Presenting at international workshops and conferences is an important experience for practicing presentation skills. I will strive to create opportunities for students to attend conferences, so as to build their confidence on an international stage.

To develop writing skills, I will encourage my students to take academic writing courses and learn from well-written textbooks or papers. To me, writing is thinking. The development of writing skills goes hand-in-hand with organized thinking and clean presentation. Usually, paper writing is a central time for practicing writing skills. I will try to respect each student's writing style while exemplifying good practices for academic writing for them.