TIFR Syllabus

From where, I can get the TIFR M.Sc syllabus? I failed to take admission in TIFR, Mumbai. I am doing the M.Sc from the other university now. If I can know the syllabus of the it then I will do the additional topics at my end. Thanks for the help.

I want to do Integrated Ph.D Program in Mathematics from TIFR Mumbai. So I have to appear in Entrance Exam conducted by TIFR. I need syllabus of this Entrance Exam, so someone is here who will provide link to download syllabus of Entrance Exam conducted by TIFR for Integrated Ph.D Program in Mathematics?

[pooja]

As you are looking for syllabus of Entrance Exam conducted by TIFR for admission in Integrated Ph.D Program in Mathematics, so I am providing complete syllabus:

TIFR Integrated Ph.D Entrance Exam Syllabus for 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.

Sample Questions for TIFR Integrated Ph.D (Mathematics) Exam:

Part A
Answer whether the following statements are True or False. Mark your answer on the machine checkable answer sheet that is provided.

1. If A and B are 3 3 matrices and A is invertible, then there exists an integer n such that
A+nB is invertible.

2. Let P be a degree 3 polynomial with complex coefficients such that the constant term is
2010. Then P has a root α with |α| > 10.

3. The symmetric group S5 consisting of permutations on 5 symbols has an element of order 6.

4. Suppose fn() is a sequence of continuous functions on the closed interval [0;1] converging
to 0 pointwise. Then the integral

5. There are n homomorphisms from the group Z/nZ to the additive group of rationals Q.

6. A bounded continuous function on R is uniformly continuous.

TIFR Integrated Ph.D Entrance Exam Syllabus and Question Paper for Mathematics: