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**TIFR GS Syllabus**

TIFR GS Syllabuses are given in the below,

- Mathematics
- Physics
- Chemistry
- Computer & Systems Sciences
- Biology

**Mathematics**

**Algebra**: Definitions and examples of group (finite and infinite, commutative and non-commutative),cyclic groups, subgroups, homomorphisms, quotients. Definitions and example of rings and fields. Basic facts about finite dimensional vector spaces, matrices, determinants, ranks of linear transformations, characteristic and minimal polynomials, symmetric matrices. Integers and their basic properties. Polynomials with real or complex coefficients in one 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 subset 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, binomial coefficients), elementary reasoning with graphs.

**Physics**

In general, the syllabus for the Admissions Tests in Physics (Written and Interview) is typically a course of studies in Physics as the main subject in the Undergraduate and Masters levels in an Indian University. The questions in the written test (multiplechoice type) and the interviews are distributed over the following areas: 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**

The syllabus for the Written test in Chemistry is similar to the typical standard syllabus followed in any Indian university for the B.Sc. and M.Sc. degree course. The questions are aimed at testing the basic understanding and knowledge in the areas of 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 & Systems Sciences**

**Computer Sciences**

- Discrete Mathematics: Sets and Relations, Combinatorics (Counting) and Ele- mentary Probability Theory, Graph Theory, Propositional and Predicate
- Formal Languages, Automata Theory and Computability.
- Data Structures and Algorithms: Arrays, Lists and Trees, Sorting and Search- ing, Graph algorithms, Complexity of problems and NP-completeness.
- Fundamentals of Programming Languages and Compilers: Control structures, Parameter passing mechanisms, Recursion, Parsing and type checking, Memory managemen
- Operating Systems and Concurrency
- Switching Theory and Digital Circuits
- Theory of Databases

**System Sciences**

- Engineering Mathematics: Complex Analysis, Linear Algebra, Elementary Nu-merical Analysis, Basic Optimization Theory and Algorithms, Introduction to Probability Theory and Statistics.
- Electrical and Computer Sciences: Introduction to Signals and Linear Systems Analysis, Control Systems, Digital Signal Processing, Basic Circuit Theory, Introduction to Digital Communications, Digital Computer Fundamentals, In- troduction to Computer Programming.

**Biology**

The test will be extremely basic and cover topics in mathematics, physics, chemistry and biology.

#### JEE Main

Application Form Submission 16 Dec 2020 to 16 Jan 2021.