MIT 18.100A: Real Analysis
18.100A is MIT's introductory real analysis course: the construction of the real numbers, sequences and series, continuity, differentiation, and the Riemann integral, all proved from scratch. It's most students' first fully rigorous math course, and its OCW version with full lecture videos has a devoted self-study following.
Fennie is independent and not affiliated with MIT. This is an unofficial study guide.
What makes it hard
Calculus answers stop counting; only proofs do, and epsilon-delta arguments are a genuinely new language that takes weeks of fumbling before fluency. The pace at which definitions stack (suprema, convergence, compactness, uniform continuity) means a fuzzy week two quietly sabotages week six.
What you'll cover
- • The real numbers and completeness
- • Sequences and series
- • Limits and continuity
- • Epsilon-delta arguments
- • Differentiation
- • The Riemann integral
The 18.100A study guide
How to study for MIT 18.100A, step by step.
- 1
Memorize definitions word-perfectly, then test them
Analysis definitions are precision instruments; one misplaced quantifier changes everything. Restate each from memory, then build an example and a counterexample; the counterexamples are where understanding lives.
- 2
Write epsilon-delta proofs daily through the early weeks
The notation becomes a language only through volume. One complete limit proof per day for the first month is the single highest-yield habit in the course.
- 3
Reprove the lecture theorems with the book closed
The psets are variations on lecture techniques. Reconstructing the proofs from memory, and finding where you can't, is the most honest diagnostic available.
- 4
Use OCW solutions as graders, not guides
For self-learners: attempt every assignment problem fully before reading a solution, then audit your proof line by line against it. Reading proofs is not writing proofs, and analysis exposes the difference brutally.
Today
Today's 18.100A plan
What a Fennie Daily Plan looks like for 18.100A. Yours is built from your own syllabus and adapts every day to your deadlines and progress.
First plan free, no card required. Fennie is independent and unaffiliated with your school.
FAQ
Is 18.100A hard?
It's most students' first fully rigorous course, and the adjustment to proof-only standards is real. Expect several weeks of epsilon-delta fumbling; that's the course working, not failing.
What's the difference between 18.100A and 18.100B?
Both are real analysis; 18.100B runs at greater abstraction with metric spaces throughout, while 18.100A keeps the focus on the real line. 18.100A is the gentler entry to the same destination.
Can I self-study real analysis with 18.100A on OCW?
Yes. The OCW version includes full lecture videos, notes, and assignments. Pair it with disciplined honest-attempt-first use of solutions; analysis self-study fails when reading replaces writing.
More MIT courses
18.01: Single Variable Calculus
18.01 is MIT's single-variable calculus GIR, covering limits, differentiation, integration, and infinite series, required of every MIT student without prior credit. The OCW version, including David Jerison's lectures, has taught calculus to millions of self-learners.
18.02: Multivariable Calculus
18.02 is MIT's multivariable calculus GIR: vectors, partial derivatives, multiple integrals, and vector calculus through Green's, Stokes', and the divergence theorems. It's required for every MIT student and is among the most-viewed math courses on OpenCourseWare.
18.06: Linear Algebra
18.06 is MIT's linear algebra course, made world-famous by Gilbert Strang, whose OCW lectures are arguably the most beloved math course recordings ever published. It covers systems of equations, vector spaces, orthogonality, determinants, eigenvalues, and the SVD with Strang's signature intuition-first style.
18.03: Differential Equations
18.03 is MIT's differential equations course, covering first and second order ODEs, Laplace transforms, Fourier series, and linear systems. It's required by most engineering and science majors and among the most-used math courses on OpenCourseWare, where Arthur Mattuck's lectures are a classic.