Harvard University

Mathematics 55

The most rigorous undergraduate mathematics course in America. A year-long journey through abstract algebra, real analysis, and complex analysis.

1965 First Offered
2 Semesters
Possibilities

Two Semesters of Pure Mathematics

Fall Semester 55A

Studies in Algebra

Group theory, ring theory, linear algebra, and the foundations of abstract algebraic structures.

Groups Rings Fields Linear Maps
Spring Semester 55B

Real & Complex Analysis

Metric topology, measure theory, integration, and the beautiful world of complex variables.

Topology Integration Complex Analysis Fourier

Legendary. Rigorous. Transformative.

Math 55 is not just a course—it's a rite of passage. Known as "probably the most difficult undergraduate math class in the country," it covers in two semesters what most programs spread across four years.

Students emerge not just with knowledge, but with a fundamentally different way of thinking about mathematics and problem-solving.

Proof-Based

Every concept rigorously proven from first principles

Intensive

20-30 hours per week of focused study

Collaborative

Learn alongside brilliant peers

∀ε>0, ∃δ>0
G/H ≅ Im(φ)
∮ f(z)dz = 2πi·Res
∫∫ = ∫∫