Analysis & Topology on the Subject GRE

GRE Math Subject · Axiom Academy

INTRO Real Analysis & Topology on the Subject GRE The largest conceptual chunk of the exam — roughly 25% of all questions Approximately 16–17 of the 66 questions come from real analysis and point-set topology. That makes this section, together with calculus, the single most important area to master. The good news: many analysis/topology questions on the GRE are definitional — they test whether you know what a concept means rather than asking you to produce a proof. If you internalize the key definitions and classic counterexamples, you can answer them quickly. Within the ~25% devoted to analysis/topology, here is roughly how the questions distribute: Percentages are approximate and vary by exam form. What You'll Master in This Unit Sequences & Series — convergence, Cauchy sequences, Bolzano–Weierstrass, all major convergence tests Continuity — epsilon-delta, uniform continuity, Intermediate Value Theorem Differentiability — Mean Value Theorem, Rolle's theorem, L'H pital's rule, Taylor's theorem Riemann Integration — Darboux sums, FTC I & II, properties of the integral Metric Spaces — open/closed sets, compactness, Heine–Borel theorem Connectedness — connected and path-connected spaces, IVT as a topological result Fundamental Group (basic) — homotopy, , simply connected spaces Core Lessons (6 modules): Rigorous definitions, key theorems, and GRE-style worked examples for each topic area.

This is the written version of the interactive lesson above. See the full GRE Math Subject course.