TIFR Syllabus & Sample Question Papers GS-2014 : Graduate School Admissions

Name of the Organization : Tata Institute of Fundamental Research Deemed University (univ.tifr.res.in)
Name of the Paper : Graduate School Admissions GS-2014 Syllabus & Sample Question Papers
Location : Mumbai

Website : http://univ.tifr.res.in/gs2022/

TIFR GS Syllabus

Graduate School Admissions GS-2014 Syllabus & Sample Question Papers

Related / Similar Syllabus : TIFR GS-2021 Syllabus

Syllabus & Sample Question Papers :
** Mathematics
** Physics
** Chemistry
** Biology
** Computer & Systems Sciences

Mathematics :
Syllabus for Screening Test and Sample Questions :
The screening test is mainly based on mathematics covered in a reason- able B.Sc. course. The interviev need not be confined to this.

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 vith real or formations. Integers and their b complex coeÆcients in l variable.

Analysis :
Basic facts about real and complex numbers, convergence of sequences and series of real and complex numbers, continuity, diferentiability 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 spaces (of any dimension), connectedness, compactness. Cmetric 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 coeÆcients)) elementary reasoning vith graphs.

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