Guys, can you provide me the TIFR Graduate School Admissions Mathematics Syllabus???

As per your request I am sharing the TIFR Graduate School Admissions Mathematics Syllabus:

Algebra
Definitions and examples of groups (finite and infinite, commutative and
non-commutative), cyclic groups, subgroups, homomorphisms, quotients.
Definitions and examples of rings and fields. Basic facts about finite di-
mensional vector spaces, matrices, determinants, and ranks of linear trans-
formations. Integers and their basic properties. Polynomials with real or
complex coefficients in 1 variable.

Analysis
Basic facts about real and complex numbers, convergence of sequences and
series of real and complex numbers, continuity, differentiability and Riemann
integration of real valued functions defined on an interval (finite or infinite),
elementary functions (polynomial functions, rational functions, exponential
and log, trigonometric functions).
Geometry/Topology
Elementary geometric properties of common shapes and figures in 2 and
3 dimensional Euclidean spaces (e.g. triangles, circles, discs, spheres, etc.).
Plane analytic geometry (= coordinate geometry) and trigonometry. Defini-
tion and basic properties of metric spaces, examples of subsets of Euclidean
spaces (of any dimension), connectedness, compactness. Convergence in
metric spaces, continuity of functions between metric spaces.

General
Pigeon-hole principle (box principle), induction, elementary properties of
divisibility, elementary combinatorics (permutations and combinations, bi-
nomial coefficients), elementary reasoning with graphs