GATE MA study plan

Reconstruct the full GATE MA syllabus topic list from memory, then verify it against the official syllabus page and mark every subtopic as Strong, Shaky, or Unknown to build a personal gap map.

Derive and prove the core results of linear algebra (rank-nullity, Cayley-Hamilton, spectral theorem for real symmetric matrices, diagonalisability criteria) without consulting notes.

Solve 15 eigenvalue and Jordan-form style problems, writing each solution in exam format with justified steps.

Set up a single error log spreadsheet with columns for topic, error type, root cause, and revisit date, and seed it with this week's mistakes.

Compute limits, continuity, and differentiability classifications for multivariable functions, including directional and partial derivative counterexamples.

Apply the inverse and implicit function theorems to decide local invertibility and solve for derivatives of implicitly defined maps.

Work through 20 problems on maxima-minima, Lagrange multipliers, and constrained optimisation under a 90-minute timer.

Summarise in your own words the three theorems you found hardest, with a worked example each.

Prove convergence or divergence of sequences and series using comparison, ratio, root, and integral tests, and distinguish absolute from conditional convergence.

Determine uniform versus pointwise convergence of function sequences and series, invoking the Weierstrass M-test where appropriate.

Compute Riemann integrals and apply the fundamental theorem, mean value theorems, and interchange-of-limit results correctly.

Solve 18 real-analysis problems and tag each by the theorem it depends on.

Classify groups up to isomorphism for small orders and apply Lagrange, Sylow, and the isomorphism theorems to concrete examples.

Identify rings, ideals, quotient rings, and check field and integral-domain properties; verify polynomial irreducibility over Q and finite fields.

Solve 15 abstract-algebra problems mixing group and ring arguments, writing complete proofs.

Re-attempt every error-log item from weeks 1-3 and mark each as resolved or still open.

Establish countability, separability, compactness, connectedness, and completeness properties of metric spaces and Euclidean spaces with proofs.

Apply the contraction mapping theorem and Baire category theorem to standard existence and density arguments.

Solve 15 topology and functional-analysis-flavoured problems, including normed space and inner product space basics.

Write a half-page comparison of compactness in metric versus general topological settings.

Solve first-order ODEs (separable, exact, linear, Bernoulli) and second-order linear equations with constant and variable coefficients.

Use Laplace transforms and power-series methods to solve initial value problems, and check answers by substitution.

Analyse existence, uniqueness, and stability for linear systems, computing eigenvalues of the coefficient matrix.

Solve 15 ODE problems under timed conditions and log every algebraic slip.

Compute partial differential equations solutions for first-order linear PDEs by characteristics and for the heat, wave, and Laplace equations by separation of variables.

State and apply maximum principles and energy methods to argue uniqueness of PDE solutions.

Solve 12 PDE problems, including at least three Fourier-series boundary value problems.

Compile a formula sheet limited to one A4 side covering the whole MA syllabus.

Take three full-length timed mock papers under exam conditions and score each strictly.

Diagnose every wrong answer to a root cause and re-solve it without notes within 48 hours.

Drill your 20 weakest error-log items until each is solved correctly twice in a row.

Rehearse exam-day logistics: section order, time per question, and a skip-and-return rule.