6.055J | Spring 2008 | Undergraduate

The Art of Approximation in Science and Engineering

Student Comments

Students comment below about course content and teaching style and their reasons for taking the course.


“I took it to learn ways to quickly perform back of the envelope calculations, and I really learned a lot. The instructor was fantastic, and did a great job of incorporating ideas from many fields, answering questions, seeking feedback, and giving good explanations.”


“This class literally changes the way you view the world. Everywhere you go, you begin to break up objects into smaller pieces or devise estimation methods for solving everyday tasks.”

“You learn how to attack problems on topics you know barely nothing. You learn to have common sense. Yes, the subject matched my expectations. The balance between application and theory is critical, the purpose of the class to learn how to deal with this balance. Strong points: it puts everyone — freshmen, seniors, grads — at the same level, and allows us all to contribute with our knowledge to solve a problem in different ways. Weak point: the problems on the problem sets sometimes aren’t repetitive enough for some strategies to stick to your mind.”

“Class discussions. Everyone in the classroom knows something about each topic — mindblowing. Whenever the professor’s assumptions/derivations are flaky, someone will come up with a better way of solving the problem. We all learn.”

“I used to be curious, naively curious. Now I am fearlessly curious. I feel ready to attack any problem that comes at me, and at least get a feel for why things happen…roughly.”


“Grading policy is fairly relaxed, as long as you show interest in class and turn in problem sets. Now, it is impossible to be in the classroom and not show interest, and not liking the problem sets would be not to be curious at all — so basically everyone does fine.”

“Grading policy is established so [that] you don’t have to worry about grades, just about the material you are supposed to be learning.”

Problem Sets

“… It is the simplest problems that will keep your brain busy most of the week.”

“Problems on problem set ranged from fairly easy to real head scratchers. I didn’t finish every problem, but supposedly they are “graded lightly” on a “made a reasonable effort”/“didn’t make a reasonable effort”/“didn’t turn in” scale. Problems generally expanded on examples from class. For the most part I did not collaborate. There are no bibles because this is a new class.”

“Problem sets are really entertaining. I wish we could have had more. They were extremely useful, although sometimes repetitive with what we saw in class. I solved them on my own, but then shared results with classmates before turning them in. We’d usually have different results (which, in this class, is completely normal) and would engage into really interesting discussions. No bible needed, brain needed.”

“The problem sets are great, but there are not really enough of them to get a lot of practice using the methods you learn in class. To get enough practice you will have to come up with thing to figure out on your own using the methods introduced in class.”


“At the beginning of the term, the professor drew for us a tree showing all the different approximation methods that we would be learning. Periodically throughout the term, he would draw it again to show us where we were.”

“At the end of every class, he has us fill out a feedback form, then at the beginning of the next class, he will spend maybe 15 minutes addressing them. Uses the blackboard a lot. A lot of times he will give us a problem to think about for a minute or so, then tell us to find a neighbor and share what we got and how we got it. I never really liked talking to my neighbor. Sometimes brings demonstrations to class, which was always fun.”

“Blackboard use was great. Things were almost always clear, and if any thing wasn’t clear, he’d go over it again. The best feel was the environment. I feel like the class was really exploring and felt comfortable to ask questions/be wrong. When exploring problems and different methods offered by the class, he presented them with an extreme non-bias that made them all seem possible to be right before giving his own method at the end. Best class in four years.”

Course Info

Learning Resource Types
Problem Sets with Solutions
Online Textbook