Math 55

Description

The Harvard University Department of Mathematics claims that "This [Math 55] is probably the most difficult undergraduate math class in the country". Formerly, students would begin the year in Math 25 (which was created in 1983 as a lower-level Math 55) and, after three weeks of point-set topology and special topics (for instance, in 1994, p-adic analysis was taught by Wilfried Schmid), students would take a quiz. As of 2012, students may choose to enroll in either Math 25 or Math 55 but are advised to "shop" both courses and have five weeks to decide on one. Depending on the professor teaching the class, the diagnostic exam may still be given after three weeks to help students with their decision.

In 1994, 89 students took the test given after three weeks: students scoring more than 50% on the quiz could enroll in Wilfried Schmid's Math 55 (15 students), students scoring between 10 and 50% could stay in Benedict Gross's Math 25 (55 students), and students scoring less than 10% were advised to enroll in a lower-level course such as Math 21, multivariate calculus (19 students).

Historical retention rate

In 1970, this demanding course covered almost four years worth of mathematics classes in two semesters, and therefore drew only the most dedicated students. In the class of 1970, only 20 of the 75 students who began the class finished it due to its difficulty. Similar drop-out rates were true for the class of 1976: "Seventy started it, 20 finished it, and only 10 understood it." and for the class of 2009: "[...] we had 51 students the first day, 31 students the second day, 24 for the next four days, 23 for two more weeks, and then 21 for the rest of the first semester after the fifth Monday," said Scott Duke Kominers.

Course content

Through 2006, the instructor had broad latitude in choosing the content of the course, and the course bore the title "Honors Advanced Calculus and Linear Algebra". For example, in 1970 by the second semester, students were learning about the differential geometry of Banach manifolds. In 1994, students of Math 25 learned differential geometry using Manfredo do Carmo's book and calculus of variations using C.H. Edwards' book.

From 2007 onwards, the scope of the course was changed to more strictly cover the content of four existing semester-long courses in two semesters: Math 25a (linear algebra) and Math 122 (group theory) in Math 55a; and Math 25b (calculus, real analysis) and Math 113 (complex analysis) in Math 55b. The name was changed to "Honors Abstract Algebra" and "Honors Real and Complex Analysis" to reflect this.

Notable alumni

Problem sets are expected to take from 24 to 60 hours per week to complete, although some claim that it is closer to 20 hours. Of those students who could handle the workload, some became math or physics professors, including members of the Harvard Math Department such as Benedict Gross and Joe Harris; also, Harvard physics professor Lisa Randall '84 and Harvard economics professor Andrei Shleifer '82. Although a 2006 Harvard Crimson article alleged that only 17 women completed the class between 1990 and 2006, in fact 39 women completed 55a (the first of the two semesters), and 26 completed 55b. Math 25 has more women: in 1994–95, Math 55 had no women, while Math 25 had about 10 women in the 55 person course.

There are also Math 55 alumni who went on to be professors in other universities. These include Fields-medalist Manjul Bhargava, who is now a professor at Princeton University, as well as Kiran Kedlaya, now at the University of California, San Diego.

In addition to these professors, past students of Math 55 include Bill Gates and Richard Stallman.

Demographics of students taking this course over the years has been used to study causes of gender and race differences in the fields of mathematics and technology.