#1
January 19th, 2016, 11:28 AM
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TIFR Mathematics Syllabus
I am interested in the field of Mathematics and for this I have decided to take admission in Tata Institute of Fundamental Research (TIFR). Will you please provide me TIFR Mathematics Syllabus of entrance exam so that I get to know lists of topics I have to cover in exam?
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#2
January 19th, 2016, 11:29 AM
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Re: TIFR Mathematics Syllabus
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 |
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