GATE — Mathematics (MA) Preparation

Vector spaces, linear transformations, eigenvalues, diagonalization, inner product spaces, canonical forms.

Sequences, series, continuity, differentiability, Riemann integration, metric spaces, uniform convergence.

Analytic functions, Cauchy's theorem, Laurent series, residue calculus, conformal mappings.

First/second order ODEs, systems of ODEs, series solutions, boundary value problems, Sturm-Liouville.

Classification, wave/heat/Laplace equations, method of characteristics, separation of variables.

Interpolation, numerical integration, root finding, Newton-Raphson, finite differences, splines.

Random variables, distributions, limit theorems, estimation, hypothesis testing, regression.

Groups, rings, fields, ideals, quotient structures, homomorphisms, Sylow theorems.

Topological spaces, compactness, connectedness, separation axioms, product topology.

Normed spaces, Banach spaces, Hilbert spaces, bounded operators, spectral theory.

Euler-Lagrange equation, isoperimetric problems, Hamilton's principle.

Simplex method, duality, transportation, assignment problems.