Math 55 at Harvard University

Overview

• Math 55 is regarded as one of the hardest undergraduate math courses in the country.
• It condenses four years of mathematics into two semesters.
• Allegedly, half the students drop out after the first semester.
• Homework assignments can take between 24 to 60 hours weekly.
• Notable alumni include Bill Gates.
• Class mainly consists of exceptional math students and former members of international math Olympiads.

Course Structure

• Math 55 is divided into two classes:
  • Math 55A: Studies in Algebra and Group Theory
  • Math 55B: Studies in Real and Complex Analysis
• Recent changes have led to a more standardized curriculum.
• Course content includes:
  • 55A Topics: Linear and abstract algebra, representation theory.
  • 55B Topics: Real and complex analysis, algebraic topology.

Classroom Experience

• Classes are held in the Science Center, a modern building for STEM disciplines.
• Class size is small, typically 20-30 students despite higher enrollment numbers (around 60).
• Professor Joe Harris is friendly and approachable, fostering an open discussion environment.
• Example topic discussed: Cohomology Theorem related to algebraic topology.

Student Backgrounds

• Students come from diverse mathematical backgrounds:
  • Competitive math experience (e.g., Olympiads)
  • Exposure to math through summer programs
  • Some take university courses during high school
• Others enroll just for the challenge and fall in love with math during the course.

Challenges and Misconceptions

• Rumors of a 50% dropout rate stem from outdated information (from the 1970s).
• Current dropout rate is about 3.3%.
• The course has evolved and now has a standardized syllabus.
• Modern students generally have more math experience compared to past cohorts.

Community and Support

• Students emphasize a strong sense of community within Math 55.
• Collaboration is encouraged; grading is reportedly lenient.
• Students support each other and create lasting bonds that carry through their time at Harvard.
• Math 55 is described as challenging but rewarding, with a welcoming environment.

Conclusion

• Math 55 is challenging and likely the hardest math course for many students.
• However, it is not as cutthroat or unforgiving as some suggest.
• Motivation and a willingness to learn are key to succeeding in the course.