Do not take Math 113 as your first proof-based course. You need to be comfortable with:
Math 113 is a foundational undergraduate course in the Department of Mathematics at Harvard University. Officially titled "Abstract Algebra," it serves as a rigorous introduction to the core algebraic structures that underpin much of modern mathematics.
One of the most common surprises for students enrolling in is the heavy reliance on Linear Algebra. While the prerequisites list Linear Algebra (usually Math 22b, 23b, 25b, or 55b), Math 113 demands a fluency that goes beyond solving systems of equations.
While the title "Analytic Mechanics and Classical Geometry" sounds like a physics course, the content is distinctly mathematical. The syllabus generally revolves around the study of curves and surfaces using the tools of differential geometry. However, unlike a standard differential geometry course that might jump straight into Riemannian manifolds, Math 113 roots itself in the "Classical" aspect. math 113 harvard
: The development of functions into Power series (Taylor series) and Laurent series , the latter of which is used to study functions near singular points.
). It is often described as "Introductory Complex Analysis" and is designed to provide fluency in the language of modern mathematics. Harvard University Core Topics Complex differentiability and entire functions. Cauchy’s Integral Formula and the calculus of residues. Power series and Laurent series expansions. Conformal mappings and the Maximum Modulus Principle
| Course | Focus | Difficulty | Audience | | --- | --- | --- | --- | | | Abstract Algebra (Groups, Rings, Fields) | High | Standard math concentrators | | Math 122 | Advanced Abstract Algebra (more depth, Galois theory) | Very High | Potential PhD students | | Math 112 | Intro to Proofs & Number Theory | Medium | Those not ready for 113 | | CS 121 | Intro to Theory of Computation (discrete math) | Medium | Computer science focus | Do not take Math 113 as your first proof-based course
This forces students to engage in "vertical thinking"—building upon concepts layer by layer. It is common for students to spend 10 to 15 hours a week on a single problem set. This struggle is intentional. It is in the wrestling with the proofs that the intuition is forged. The satisfaction of solving a multi-step geometry problem, where the final result clicks into place like a puzzle, is the defining reward of the course.
: Studying Conformal Mappings —functions that preserve angles—which have significant applications in fluid dynamics and electrostatics.
The course often uses Abstract Algebra by Dummit and Foote (chapters 1–7 and 9–14) or A First Course in Abstract Algebra by John B. Fraleigh. One of the most common surprises for students
The lifeblood of Math 113 is the weekly problem set. These are notorious for their difficulty. They are not mere regurgitations of lecture material; they require synthesis. A typical problem might ask a student to prove that a surface of revolution has specific curvature properties, requiring them to construct a parameterization, derive the fundamental forms, and interpret the results.
Math 113 is essential for any student considering graduate school in mathematics, theoretical physics, or computer science (especially cryptography and coding theory). It is also the prerequisite for advanced courses like Math 114 (Lie Groups), Math 123 (Number Theory), and Math 124 (Advanced Galois Theory).