The Tata Institute of Fundamental Research is a research institution in Mumbai and Hyderabad, India, dedicated to basic research in mathematics and the sciences.

TIFR conducts GS Entrance Examination for admission in various courses like Ph.D in Mathematics, Physics, Chemistry, Biology, Computer & Systems Sciences and Science Education, Integrated M.Sc Ph.D program in Mathematics, Physics and Biology.

TIFR 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 dimensional vector spaces, matrices, determinants and ranks of linear transformations. 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. Definition 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.

Address:

Tata Institute of Fundamental Research (TIFR)
Dr. Homi Bhabha Road, Navy Nagar, Near Navy Canteen, Mandir Marg
Colaba, Mumbai, Maharashtra 400005
Phone: 022 2278 2000