**About TIFR**

TIFR Stands For **Tata Institute of Fundamental Research**. TIFR is a nationwide entrance exam conducted by **Tata Institute of Fundamental Research (TIFR)** in order to provide admission to candidates in postgraduate Science courses offered by it.

**Subjects Under TIFR**

- Mathematics
- Physics
- Chemistry
- Biology
- Computer & Systems Sciences (including Communications and Applied Probability)
- Science Education

**Eligibility Criteria for TIFR**

- Candidates in the final year of qualifying degree can also apply.

**TIFR Mathematics:**

**For Ph.D.:**M.A./M.Sc./M.Tech.**For I-Ph.D.**: B.A./B.Sc./B.E./B.Tech. (Students already having/completing an M.Sc. degree by July 2020 are not eligible for I-Ph.D.).

**Exam Centers for TIFR**

Agartala |
Mangalore |

Jaipur |
Kolkata |

Kanpur |
Nagpur |

Ahmedabad |
Mangalore |

Jammu |
Delhi |

Bengaluru |
Pune |

Visakhapatnam |
Hyderabad |

Varanasi |
Guwahati |

Bhubaneshwar |
Cochin |

Chennai |
Mangalore |

**Exam Pattern for** **TIFR ****Mathematics**

The candidates who will be appearing for the admission to the various programs in Mathematics in TIFR, namely the Ph.D. and Integrated Ph.D. programs at TIFR, Mumbai and TIFR CAM, Bengaluru and Ph.D. at ICTS, Bengaluru, there has been a change in the exam pattern. The exam pattern is as follows:

**Duration of the exam:**The test is now of 3 hours duration**Type of Questions:**There are 2 types of questions in the test which are Objective type MCQ and true/false questions.**Number of Questions:**There are 20 true/false and 20 multiple-choice questions.**Standard of the test:**It is mainly based on mathematics covered in a reasonable B.Sc. course in Mathematics.

**Syllabus of TIFR Mathematics**

**Algebra:**Definitions and examples of groups (finite and infinite, commutative and non-commutative), cyclic groups, subgroups, Homomorphism’s, 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, 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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