Instructor Insights

Below, Dr. Chengzhao “Richard” Zhang describes various aspects of how he taught the summer 2020 iteration of 18.085 Computational Science and Engineering I.

OCW: For the uninitiated, what is computational science and engineering? What kind of “big picture” understandings do you hope students will learn in the course?

Richard Zhang: In essence, computational science and engineering combines the rigor of mathematics, the power of computation, and the practical mindset of engineering. It’s a playground for theoretical mathematicians, an ideal stage of implementation for computer scientists, and a low-cost simulation tool to aid scientists and engineers in their research.

My philosophy of the subject is one of “practical rigor.” I want students to build first-principled thinking of mathematics and computation, while never losing sight of the applications and connections to their respective engineering disciplines. Students should know why the center-difference method for numerical differentiation is second-order. At the same time, they should be aware of how it’s applied in modern-day research in atmospheric science.

This philosophy follows very closely that of Professor Gil Strang and President Rafael Reif in his recent founding of MIT’s Schwarzman College of Computing. My respected mentor Prof. Strang is one of the frontrunners of modern computational science and engineering research and education. He’s a strong advocate of developing his teaching of rigorous mathematics around practical subjects, as is evident in his course 18.065: Matrix Methods in Data Analysis, Signal Processing, and Machine Learning. At the same time, President Reif, in forming the Schwarzman College, emphasizes the importance of training “bilingual” students, who are well-versed both in their own studies and in AI and computation.

OCW: Tell us about the unique student population that enrolled in this course. How did their professional orientation shape how they approached the material?

Richard Zhang: The students who enrolled 18.085 over the summer—active duty Marine and Coast Guard officers who come to MIT to become naval engineers—are some of the most disciplined, professional, and communicative students that I've ever taught. Because of their non-academic background, they tended to approach the materials with practical, engineering insight, trying to relate the fundamental mathematics to their prior engineering experiences. These experiences helped deepen their appreciation and understanding of mathematics.

OCW: You mentioned Professor Gil Strang as one of your teaching mentors. What have you learned from him that you’ll take with you into future teaching positions?

Richard Zhang: Professor Strang is a model of dedication, passion, and lifelong commitment towards teaching mathematics and connecting math with various scientific and engineering disciplines. Even at the age of 86, he still drove forward to write a book and create the course 18.065 that connects machine learning with linear algebra. All of these qualities of Professor Strang's are what I aspire to be as an instructor.

Most importantly though, Professor Strang truly cares about students. This is a rare quality of a mentor and instructor, and something that we deeply need. Society overemphasizes brilliance. But everyone is brilliant in a place like MIT; brilliance is a cheap commodity that’s no longer the sole judging criterion for a mentor. To quote Prof. Allan Adams from MIT Physics, “Find the mentors that are good to you, not just brilliant. Because brilliance is cheap, and good is special.”

I want to be as good a teacher as Professor Strang.