Notes on Harvard's Math 55 Course

Overview

• Math 55 at Harvard University is reputedly the hardest undergraduate math course in the United States.
• The course condenses four years of math into two semesters.
• Typically half the students drop out after the first semester.
• Homework assignments can take between 24 to 60 hours to complete.
• The class is known for having students who are former international math Olympiad members.

Course Details

• Professor: Joe Harris, an esteemed mathematician in algebraic geometry.
• Structure: Math 55 consists of Math 55A and Math 55B.
  • Math 55A: Focuses on algebra, group theory; includes linear and abstract algebra with representation theory.
  • Math 55B: Covers real and complex analysis; includes algebraic topology.
• Originally, the course content varied greatly depending on the professor, but it is becoming more standardized.
• Lecture Environment:
  • The class has around 20-30 students, though enrollment is about 60.
  • The environment is friendly, with students actively engaging and asking questions.

Insights from Students

• Students come from various backgrounds, including competitive math and summer programs.
• Some students are drawn by the course's notoriety, while others develop a love for math during the course.
• Homework, or problem sets (p-sets), are said to take between 15 to 30 hours, contrary to exaggerated reports.
• The course encourages collaboration, and grading is noted to be lenient.

Historical Context and Evolution

• The reputation of high dropout rates is outdated; the rate was initially high due to the non-standardized syllabus and lack of student preparation.
• Modern Math 55 has a low dropout rate (3.5% as per recent data).
• Past students lacked the comprehensive background students have today, such as access to summer programs and competitive math experiences.

Community and Culture

• The course fosters a strong sense of community among students.
• Math 55 is challenging and demanding, yet not ruthless or cutthroat.
• The Math department at Harvard is welcoming and supportive.
• Mathematics in higher education is viewed as a community-based field, emphasizing collaboration.

Conclusion

• Math 55 is indeed one of the hardest undergraduate math courses but also highly rewarding.
• It is suitable for those interested in and motivated to learn advanced mathematics.
• The course atmosphere is supportive, cultivating both academic and interpersonal growth.