Instructor Insights

Instructor Insights pages are part of the OCW Educator initiative, which seeks to enhance the value of OCW for educators.

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.

Connecting class materials with real-world applications is critical to the success of a student's experience in this course.

— Chengzhao “Richard” Zhang

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.

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Curriculum Information


Requirements Satisfied

18.085 can be applied toward a Bachelor’s of Science in Mathematics, but is not required.


Every semester

Student Information

21 students took this course when it was taught in Summer 2020.


21 students took this course.

Typical Student Background

As noted above, the students enrolled in this iteration of 18.085 were active duty Marine and Coast Guard officers studying to become naval engineers.



Grade Breakdown

Each student’s overall grade for the course is based on the higher of the grades generated by the following two grading schemes:

Scheme 1

  • 50% Homework; two lowest scores discarded
  • 25% Midterm exam
  • 25% Final exam

Scheme 2

  • 70% Homework; lowest score dropped
  • 15% Midterm exam
  • 15% Final exam

How Student Time Was Spent

During an average week, students were expected to spend 12 hours on the course, roughly divided as follows:

In class: 3 hours

Met 3 times per week for 1 hour per session; 29 sessions total; mandatory attendance

Out of class: 9 hours

Outside of class, students completed problem sets and studied for exams.