The Math 51 roadblock

A student studies with his Math 51 textbooks close at hand. Over the years, students have debated whether or not AP Calculus would be an adequate replacement for Math 51. (MASARU OKA/Staff Photographer)

Correction: In an earlier version of this story, The Daily incorrectly reported that the math department recommends that students who earn a score of four on the Advanced Placement AB Calculus test, or three on BC Calculus, take Math 51.  In fact, the department recommends that students who earn a score of five on the AB test, or four or five on the BC test, take Math 51.

Math 51, Linear Algebra and Differential Calculus of Several Variables: not only a mouthful of a course title, but also one of the most widely taken classes on campus, with about 400 students enrolled in the fall.

But the 50 series, which was created only ten years ago, juggles multiple responsibilities. In the space of one quarter, Math 51 is charged with bringing students with varying backgrounds up to speed, introducing abstract mathematic skills and adequately covering the needs of other technical majors, including chemistry, economics, engineering and physics.

Yet few students give deeper consideration to the introductory math classes, seeing Math 51 as no more than a requirement to get out of the way, or a stepping stone to more advanced math classes. Its place in undergraduate education, however, is more complex.

Brian White, a professor who teaches Math 51, explained that when the 50 series was created, the math department talked to many other departments about its design, conscious of its role in providing students with essential skills and knowledge.
“We were aware that the majority of people taking the 50 series would not be math majors, and we wanted to take into account the departments that these people would eventually go to,” White said.

However, the math department chose not to create major-specific introductory math classes because they wanted to give students more flexibility.

“Freshmen don’t necessarily know what major they’re going into, and we don’t want to force a choice on them too soon,” White said, saying that was the same reason that the math department does not offer a “fuzzy” math class.

For those who are not planning on a math major, Math 51 meets the math portion of the five General Education Requirements that all students need to fulfill in order to graduate. This contributes to its status as the most commonly-taken course in the department.

Currently, guidelines recommend that students who who earn a score of five on the Advanced Placement AB Calculus test, or four or five on the BC test, take Math 51.

However, some students question whether the math requirement is necessary, arguing that a high score on the AP Calculus test should allow students to waive the math requirement in the same way a high score in AP Spanish would allow a student to waive the language requirement.

“Calculus is already pretty advanced if you’re not using it in your major or career,” said Maia Peirce ’13, who is a prospective English major. She explained that she would only take Math 51 to fulfill the math requirement, and did not plan to take any more classes afterwards.

However, others argue that the point of the math requirement is not to force students to go beyond calculus, but rather to experience a college-level math course.

“In high school, AP Calculus can be taught really differently and there is a huge range of rigor,” said Elliott Jin ’12. “AP Calculus is very computational, but college mathematics teaches you how to deal with abstraction.”
Professor Rafe Mazzeo, chair of the math department, agreed with Jin.

“Typically the classes cover more material, and cover it more deeply and abstractly,” Mazzeo said.
He said that one of the most common misconceptions among incoming freshmen was the belief that success in math came from memorizing the formulas. Mazzeo believes this is not enough.

“Students need to understand how things fit together as a big organic whole, ” he said, “and few high school classes do that.”

Lauren Janas ’12 felt that AP Calculus gives students the background knowledge they need to handle the material found in Math 51, but argued that it often does not prepare students for the pace of the 50 series.

“I had a year and a half of calculus, and there’s not so much to learn so it’s very spread out,” said Janas, who is considering majoring in physics or symbolic systems.

Of the AP test, she said, “You can sleep through that test and still get a five” — by no means a universally-held opinion.
The math requirement is also thought to cause difficulties for aspiring “techie” majors who didn’t take AP Calculus before coming to Stanford. Though the math major could be easily completed if one started in the 40 series, it would be more difficult to complete some other majors, such as physics.

“The 40 series for physics is calculus-based,” Janas explained. “So if you didn’t take AP Calculus, you’d have to do the entire physics major in three years — you’d be really screwed.”

“That’s a tricky situation,” White conceded. “There’s a limit to how fast people can absorb material, but we try to be flexible. For example, if you want to take calculus faster, you can take the 40 series instead of the 19-20-21 series.”

White also emphasized that the math department has no strict prerequisites for Math 51 and that the recommendations are only guidelines.

“If a student didn’t get a five on AB Calc, but really wanted to take 51, I would tell him to go ahead and try it,” White said.

“Ultimately, we just want people to be in the course that’s the best fit for them.”
Then, there is the question of which math classes non-math majors should take. The math department does not offer introductory math classes tailored for any of the “techie” majors; only some higher levels classes are geared towards physics or engineering majors.

“You need all of the 50 series for physics, plus lots of stuff they don’t teach you,” Janas said. “You’re expected to learn a lot of math on the fly.”

On the other hand, Hang Hong, a professor and the director of undergraduate study for the economics department, admitted that not all of Math 51 would be useful to an economics major, though it is a prerequisite for Econ 50.

Today, the math department continues to solicit feedback from students and is constantly reviewing the curriculum. Both Mazzeo and White stressed the importance of hiring professors who are not only researchers, but also good teachers, especially for introductory courses.

Mazzeo believes that the 50 series is working well for the time being, but he added, smiling, “Above all, we must be ever vigilant.”