GRE Subject Test · GRE Mathematics

3:27 Topic 1 C.1 · Single-variable calculus and applications This unit uses limits, continuity and differentiability; derivatives, integrals and the fundamental theo… 3:05 Topic 2 C.2 · Multivariable calculus and vector analysis This unit computes partial derivatives, gradients and directional derivatives; uses multiple integrals a… 3:06 Topic 3 A.1 · Linear algebra This unit relates rank, nullity and the solutions of linear systems; analyses vector spaces and linear m… 2:13 Topic 4 A.2 · Abstract algebra and number theory This unit uses groups, subgroups, homomorphisms and quotients; distinguishes rings, integral domains and… 2:14 Topic 5 T.1 · Real analysis and topology This unit applies the limit definitions for sequences and functions; distinguishes compactness, connecte… 2:58 Topic 6 T.2 · Discrete mathematics, probability and numerical methods This unit counts, uses recurrences, graphs and logic; calculates probabilities and distribution properti… 2:40 Topic 7 T.3 · Complex analysis and residues This unit tests complex differentiability, uses contour integrals and residues, and evaluates contour in… 2:38 Topic 8 C.3 · Differential equations and initial conditions This unit solves separable first-order equations and constant-coefficient second-order equations, and us… 2:55 Topic 9 A.3 · Groups, cosets and quotient maps This unit verifies group structure and computes element orders and subgroup indices; uses kernels and im… 2:50 Topic 10 A.4 · Rings, ideals and modules This unit distinguishes units, zero divisors and integral domains; identifies ideals and interprets quot… 3:12 Topic 11 A.5 · Polynomials and field extensions This unit tests polynomial irreducibility over a specified field, constructs small finite fields, uses e… 3:36 Topic 12 A.6 · Congruences, divisibility and arithmetic functions This unit solves linear congruences using gcd conditions, combines coprime congruences with the Chinese … 2:52 Topic 13 T.4 · Sequences, series and uniform convergence This unit uses Cauchy, monotone convergence and subsequence criteria; distinguishes pointwise from unifo… 2:56 Topic 14 T.5 · Open sets, compactness and connectedness This unit computes closure, interior and boundary in a stated space, applies compactness and connectedne… 3:04 Topic 15 C.4 · Taylor expansions and power-series endpoints This unit constructs Taylor polynomials and controls their error, determines radii of convergence and te… 2:56 Topic 16 C.5 · Improper integrals and geometric applications This unit defines improper integrals by limits at each singular boundary, selects area, volume and arc-l… 2:55 Topic 17 C.6 · Multivariable extrema and constrained optimisation This unit classifies two-variable critical points with the Hessian, uses Lagrange multipliers with a reg… 2:51 Topic 18 C.7 · Coordinate changes and vector integral theorems This unit transforms double and triple integrals with their Jacobians, applies the Green, Stokes and div… 3:00 Topic 19 T.6 · Functions, inverse branches and composition This unit distinguishes injectivity and surjectivity using the stated domain and codomain, chooses and v… 3:05 Topic 20 T.7 · Set images, equivalence relations and logical negation This unit proves image identities and distinguishes inclusion from equality, checks reflexivity, symmetr… 3:14 Topic 21 T.8 · Conditioning, Bayesian inference and sampling error This unit separates conditional, joint and independent-event probabilities, calculates posterior probabi… 3:07 Topic 22 T.9 · Similarity, scaling and conic distance loci This unit matches triangle vertices by equal angles before forming a side ratio, applies length, area an… 3:17 Topic 23 C.8 · Trigonometric phase and parametric curves This unit distinguishes amplitude, angular frequency, phase angle and horizontal shift; eliminates a par… 2:58 Topic 24 T.10 · Vector geometry, projections and oriented area This unit uses dot products to classify angles and compute projections, calculates triangle area and ori… 2:54 Topic 25 C.9 · Integrating factors and nonhomogeneous differential equations This unit solves first-order linear equations with an integrating factor, builds the homogeneous and par… 3:02 Topic 26 T.11 · Weak compositions, loop invariants and flowchart tracing This unit counts indistinguishable allocations with nonnegative or positive constraints, traces a flowch… 3:12 Topic 27 C.10 · Implicit differentiation and the inverse Jacobian This unit differentiates a coupled implicit system as a linear system, uses a nonzero Jacobian determina… 2:51 Topic 28 A.7 · LU factorisation and nullity of composed maps This unit solves a factored linear system by forward and backward substitution, applies row permutations… 3:16 Topic 29 C.11 · Integration by parts, order reversal and symmetry This unit derives integration-by-parts reductions with valid endpoint limits, reverses a double integral… 3:02 Topic 30 C.12 · Related rates and removable quotient limits This unit translates a geometric rate into a derivative, derives and differentiates a spherical-cap volu… 2:43 Topic 31 T.12 · Metric completeness and closure from a basis This unit checks a pullback metric using its defining map, decides completeness through the image of an …