Harvard MATH 1A: Introduction to Calculus
Math 1A is Harvard's introductory calculus course, covering limits, derivatives, integrals, and the Fundamental Theorem of Calculus, for students who didn't take or don't have credit for calculus before college. It leads into Math 1B and the rest of the math sequence.
Fennie is independent and not affiliated with Harvard University. This is an unofficial study guide.
What makes it hard
The material is standard first-semester calculus, but Harvard's pacing and problem sets emphasize conceptual understanding and word problems over rote computation. Students placed into 1A often have uneven precalculus backgrounds, and shaky algebra is the most common source of lost points.
What you'll cover
- • Limits and continuity
- • Derivatives and applications
- • Optimization and related rates
- • Integrals
- • The Fundamental Theorem of Calculus
- • Modeling with calculus
The MATH 1A study guide
How to study for Harvard MATH 1A, step by step.
- 1
Shore up precalculus in the first two weeks
Most points lost in Math 1A are algebra points, not calculus points. Audit your factoring, exponents, logs, and trig early, because the course assumes them even when your background didn't cover them evenly.
- 2
Do a few problems every day
Math 1A emphasizes conceptual understanding, and concepts solidify through daily contact. Twenty minutes of problems daily beats a long pre-pset scramble.
- 3
Practice word-problem setups separately
Optimization and related-rates problems are translation exercises first. Practice converting the words into a function and a constraint. Once the setup is right, the calculus is routine.
- 4
Self-test before each exam
Work problems from a blank page under light time pressure rather than rereading notes. The gap between following a solution and producing one is exactly what exams measure.
Today's MATH 1A plan
What a Fennie Daily Plan looks like for MATH 1A. Yours is built from your syllabus and adapts every day to your deadlines and progress.
- Review: IntegralsReview · 25 min
Work back through the MATH 1A material on integrals. In the app, Fennie builds this from your own notes and syllabus.
- Practice: The Fundamental Theorem of CalculusPractice · 20 min
Targeted problems on the fundamental theorem of calculus, the kind MATH 1A actually tests.
- Quick quiz: Modeling with calculusQuiz · 10 min
Five generated questions to expose weak spots on modeling with calculus before the exam does.
- Preview: Limits and continuityPreview · 10 min
A first pass over limits and continuity so the next session starts from familiar ground.
First plan free, no card required. Fennie is independent and unaffiliated with your school.
FAQ
Is Math 1A hard at Harvard?
It's the gentlest entry point in Harvard's math sequence, but it still moves briskly and tests understanding over memorization. Students with algebra gaps feel it most.
Should I take Math 1A or 1B?
Harvard's math placement process sorts this: 1A if you're new to calculus, 1B if you've seen derivatives and basic integrals. When in doubt, the placement recommendation is usually right.
What comes after Math 1A?
Math 1B (integration, series, and differential equations), then typically Math 21A/21B for multivariable calculus and linear algebra.
More Harvard courses
MATH 55: Studies in Algebra and Group Theory / Real and Complex Analysis
Math 55 (55A in fall, 55B in spring) is Harvard's legendary honors freshman math sequence, covering proof-based abstract algebra, group theory, and real and complex analysis at extraordinary speed and depth. It's widely described as the hardest undergraduate math class in the country.
MATH 21A: Multivariable Calculus
Math 21A covers multivariable calculus (vectors, partial derivatives, multiple integrals, and vector fields) and is the standard math course for Harvard students in sciences, economics, and pre-med tracks who arrive with single-variable calculus done.
MATH 21B: Linear Algebra and Differential Equations
Math 21B covers linear algebra (systems, matrices, eigenvalues, orthogonality) and applies it to differential equations and Fourier series. It's a workhorse requirement for applied math, economics, CS, and science concentrators.
MATH 25: Theoretical Linear Algebra and Real Analysis
Math 25 (25A in fall, 25B in spring) is Harvard's honors first-year sequence in proof-based linear algebra and real analysis, the rigorous track below the legendary Math 55. It's the standard landing spot for strong students who want real mathematics at a survivable pace.