GATE Mathematics Syllabus

Functions of two or more variables, continuity, directional derivatives, maxima and minima, vector calculus.

Finite dimensional vector spaces, linear transformations, eigenvalues and eigenvectors.

Metric spaces, compactness, completeness.

Functions of a complex variable, complex integration.

Existence and uniqueness theorems, higher order ordinary differential equations.

Groups, rings, fields, polynomial rings.

Normed linear spaces, Banach spaces, spectral theorem.

Systems of linear equations, numerical differentiation, integration.

Classification and canonical forms, method of separation of variables.

Basic concepts of topology, connectedness, compactness.

Linear programming models, duality theory.