TIFR GS Syllabus 2013
TIFT GS Syllabus 2013
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.
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.
Pigeon – hole principle ( box principle ), induction, elementary properties of divisibility, elementary combinatorics ( permutations and combinations, bi¬nomial coefficients), elementary reasoning with graphs.
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 ( multiple – choice 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.
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 and Systems Science
1. Discrete Mathematics: Sets and Relations, Combinatorics ( Counting ) and Ele¬mentary Probability Theory, Graph Theory, Propositional and Predicate Logic.
2. Formal Languages, Automata Theory and Computability.
3. Data Structures and Algorithms: Arrays, Lists and Trees, Sorting and Search¬ing, Graph algorithms, Complexity of problems and NP – completeness.
4. Fundamentals of Programming Languages and Compilers : Control structures, Parameter passing mechanisms, Recursion, Parsing and type checking, Memory management.
5. Operating Systems and Concurrency.
6. Switching Theory and Digital Circuits.
7. Theory of Databases.
The test will be extremely basic and cover topics in mathematics, physics, chemistry and biology.
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