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**BOOK INFO**

**BOOK NAME** – TIFR MATHEMATICS QUESTION & ANSWER

**AUTHOR** – P KALIKA

**SIZE** – 2.5MB

**PAGES** – 84

**About TIFR**

The Tata Institute of Fundamental Research (TIFR) was founded by the distinguished Indian Scientist Dr. Homi Bhabha in June 1945. The Institute is located at Colaba on the shores of the Arabian Sea. The faculty at TIFR is subdivided into three Schools: School of Mathematics, School of Natural Sciences and School of Technology & Computer Science and there three National Centres: National Centre for Biological Sciences (NCBS), Bangalore, the National Centre for Radio Astrophysics (NCRA), Pune and the Homi Bhabha Centre for Science Education (HBCSE), Mankhurd, Mumbai. Scientists at TIFR are world leaders in several fields and their published contributions to scientific knowledge are internationally recognized. Free download PDF TIFR Mathematics Question Papers And Answer By P Kalika.

**TIFR GS 2020 Syllabus for 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 vector spaces, matrices, determinants, ranks of linear transformations, characteristic and minimal polynomials, symmetric matrices. Integers and their basic properties. Inner products, positive definiteness
- Analysis: Basic facts about real and complex numbers, the 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), sequences and series of functions and their different types of convergence, ordinary differential equations.
- 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 probability theory, elementary reasoning with graphs.

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