GATE Mathematics (MA) — which book for which section

Multivariable and vector calculus — a UG-level foundation not covered by a standalone title in our M.Sc range.

Finite-dimensional vector spaces, canonical forms and quadratic forms — not yet a standalone title in our range.

One of the largest sections — and directly covered.

Real Analysis

Covers: The whole section — metric spaces, compactness & completeness, uniform convergence, the Weierstrass and Ascoli–Arzelà theorems, and Lebesgue measure & integration up to the Lp spaces.

Analytic functions through to residues and conformal maps — directly covered.

Complex Analysis

Covers: The full section — analytic & harmonic functions, Cauchy’s theorem & formula, Taylor/Laurent series, the residue theorem with real-integral applications, Rouché & the argument principle, and conformal & Möbius maps.

First- and higher-order ODEs, Laplace & series solutions, Sturm–Liouville and stability — directly covered.

Advanced Ordinary Differential Equations

Covers: The core of the section — existence & uniqueness, higher-order & variable-coefficient linear ODEs, Cauchy–Euler, Laplace transforms, series/Frobenius solutions, Sturm–Liouville problems and systems.

Special Functions

Covers: The Legendre and Bessel functions and their orthogonal properties called out in this section.

Group, ring and field theory — directly covered.

Advanced Abstract Algebra

Covers: The whole section — groups & Sylow theory, finite abelian groups, rings & ideals, UFD/PID/Euclidean domains, polynomial rings & Eisenstein, and fields, finite fields & extensions.

Banach & Hilbert space theory and the classical theorems — directly covered.

Functional Analysis

Covers: The full section — normed & Banach spaces, bounded & compact operators, Hahn–Banach, the open mapping / closed graph / uniform boundedness theorems, Hilbert spaces, Riesz representation and the spectral theorem.

Direct & iterative solvers, interpolation and numerical integration — not yet a standalone title in our range.

First- and second-order PDEs, separation of variables and transform methods — directly covered.

Partial Differential Equations

Covers: The full section — method of characteristics, classification & canonical forms, separation of variables for Laplace/heat/wave, d’Alembert’s formula and Laplace/Fourier transform methods.

Point-set topology through to Urysohn and Tietze — directly covered.

Topology

Covers: The whole section — bases & subbases, the subspace/order/product/quotient topologies, connectedness & compactness, Tychonoff, and the countability & separation axioms up to Urysohn & Tietze.

LP, transportation and assignment — directly covered by Operations Research.

Operations Research

Covers: The full section — LP models & convex sets, the simplex / two-phase / revised-simplex methods, duality, transportation problems (NW-corner, least-cost, Vogel, MODI) and the assignment problem (Hungarian method).