I visited the world's hardest math class

Overview of Math 55

• Math 55 is recognized as one of the hardest undergraduate math courses in the U.S.

• The course compresses four years of mathematics into two semesters:

  • 55A: Studies in Algebra and Group Theory

  • 55B: Studies in Real and Complex Analysis

• Historical enrollment suggests high drop-out rates, with claims that half the students drop out after the first semester.

• Homework assignments can take between 24 to 60 hours to complete.

• Notable alumni include Bill Gates and many former international math Olympiad team members.

Experience and Insights

• Joe Harris, the current professor, is noted for making complex material accessible.

• The course has no strict prerequisites, only a recommendation for familiarity with proof-based mathematics.

• Professor Denny Aru mentions that having time and a love for math is crucial for success in Math 55.

Classroom Environment

• The Science Center houses Math 55, contrasting with Harvard's traditional architecture.

• Class sizes are small (20 to 30 students) despite higher enrollment of around 60.

• There exists a casual yet intellectual environment, with students actively engaging in discussions.

Course Content

• 55A Topics:

  • Linear Algebra

  • Abstract Algebra

  • Representation Theory

• 55B Topics:

  • Real Analysis

  • Complex Analysis

  • Algebraic Topology

• The Cypher-Von Kompan theorem is one of the advanced topics discussed in class.

Student Perspectives

• Students come from diverse backgrounds:

  • Some have competitive math experience.

  • Others discover their passion for math through challenges posed by this course.

• Wan Jaya, a Math 55 student, explains that newcomers can adapt with dedication and time.

• Collaborative problem-solving is encouraged, and students often work together.

Homework Assignments

• There's a disparity in problem completion times reported:

  • Rumors suggest assignments may take 24 to 60 hours, but actual experiences indicate 15 to 30 hours may be more common with proper preparation.

• Collaboration is an essential aspect of the homework process, enhancing learning.

Drop-out Rates and Course Evolution

• The claim that half the students drop out originated decades ago; current statistics show only 3.3% of students drop out now, with high retention rates.

• Changes over the years include:

  • Standardization of the curriculum.

  • Improvement in student preparedness through prior math experiences.

• The course is often seen as a rite of passage and fosters community among math majors, dispelling the myth of a cutthroat environment.

Community and Support

• Math 55 promotes a supportive, collaborative environment:

  • Students report forming lasting bonds that extend beyond the course.

  • The overall atmosphere is described as warm and inviting, with an emphasis on mutual aid and understanding.

• The math department encourages questions, discussions, and shared exploration of concepts.

Conclusion

• While Math 55 is challenging, it's not unforgiving.

• Students motivated to learn can thrive in this environment, finding not only academic rigor but also a welcoming community.

• Participants in Math 55 are likely to join the ranks of future leaders in mathematics.