Preparation For TIFR

I’m doing preparation for Tata Institute of Fundamental Research and looking for the syllabus for that will you please help me here?

[Pathak]

Don’t worry buddy I will help you here to get the Tata Institute of Fundamental Research syllabus so that you can complete your courses easily.

Here is the syllabus
Mathematics:
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.

Physics:
Classical Mechanics
Mathematics Relevant To Physics
Electricity and Magnetism
Quantum Mechanics
Heat
Thermodynamics and Statistical Physics
General Physics
Modern Physics
Electronics And Experimental Physics

Chemistry:
Physical
Organic
Inorganic
Analytical
Electro And Quantum Chemistry
Biophysics
Thermodynamics
Spectroscopy ( NMR, Fluorescence, IR, UV And X-Ray )
Logic And Statistics And Mathematical Methods

Computer Science
Discrete Mathematics
Formal Languages, Automata Theory and Computability.
Data Structures and Algorithms
Fundamentals of Programming Languages and Compilers
Operating Systems and Concurrency
Switching Theory and Digital Circuits
Theory of Databases