They are an elite among the elite, and they can achieve wonders with only a writing instrument and a surface to write on.

They are the students of Mathematics 55a, "Honors Advanced.

Calculus and Linear Algebra," a course intended for students, primarily first-years, who have had, according to the Courses of Instruction, substantial experience with abstract mathematics.

"The theory behind Math 55 is that we wanted to design a course that helps [students] mature as mathematicians rather than as course takers," Professor of Mathematics Clifford H. Taubes says. "People can do wonderfully at passing math but not being good mathematicians."

With a drop rate of slightly over 50 percent, Math 55 seems to be more of a challenge than most entering students expect. According to Assistant Professor of Mathematics Pavel Etingof, who teaches the course, 23 of the 43 people originally in the class dropped out, bringing the number of students down to 20 Harvard students and one MIT student.

But many of those who remain say the course--which scores 4.7 out of a possible 5.0 in the CUE guide--is difficult but ultimately rewarding.

Etingof says the course is difficult but is intended to be that way.

"Unless the students have lots of experience in math, it's not surprising that it's not easy," he says. "It's a select group of people. We don't start from scratch."

An Overwhelming Challenge

Joshua P. Nichols-Barrer '00, one of the two course assistants for the class, says that Math 55 is more difficult than most undergraduate mathematics courses.

"Math 55 covers the content of Math 21 with maximal generality and rigor," he says. "It is comparable to a graduate course. The types of assumptions it makes about students are more akin to graduate level than 100-level courses, which you can walk in on with no background on the material."

Daniel A. Stronger '01 took the class last year and ended up scarred by the experience.

"[Math 55] pretty much destroyed my year last year," he says. "I was doing more work for Math 55 than for all my other classes combined, and I wasn't even completing all the work. It was really painful and just too hard."

Eleanor E. Williams '02 started out in Math 55 this semester but dropped out after the first problem set was returned.

"[I took it] for the challenge, because several of my friends are taking it, and probably because my sister had taken it," Williams says. "It's also a bit of a `status'thing as far as math majors here are concerned."

Williams says she found the course extremelydifficult, challenging and work-intensive.