**Tata Institute of Fundamental Research PhD & Int. PhD Admissions (GS-2022)**

**GS2022** information has been updated. The **“Apply Online”** link will be activated on or before October 8, 2021.

**Important Dates:**

- Examination Date: Sunday, December 12, 2021
- Online application starts: October 8, 2021
- Last date for application:
**November 7, 2021** - Downloading of Hall Tickets: November 22, 2021

**Note:** Candidates in the final year of their qualifying degree can also apply.

**Admission Procedure**:

The admissions procedure (in all subjects, except Science Education) consists of an online test at one of the several nationwide centres, followed by interviews and/or second written test of shortlisted candidates depending on the subject/programme. (Read More)

Shortlisted candidates will be called for interviews to be held during March-May 2022. Exact dates would be announced later.

**Results of the entrance examination will be announced by end-January, 2022 **and students shortlisted for interview will be intimated by email.

**More details:** http://univ.tifr.res.in/gs2022/index.html

### GS2022: Selection Process for Mathematics

Selection process for admission in 2022 to the various programs in Mathematics at the TIFR centers – namely, the PhD and Integrated PhD programs at TIFR, Mumbai as well as the programs conducted by TIFR CAM, Bengaluru and ICTS, Bengaluru – will be held in two stages.**Stage I.** A nation-wide test will be conducted in various centers on December 12, 2021. For the PhD and Integrated PhD programs at the Mumbai Center, this test will comprise the entirety of Stage I of the evaluation process. For more precise details about Stage I of the selection process at other centers (TIFR CAM, Bengaluru, and ICTS, Bengaluru) we refer you to the websites of those centers.

The nation-wide test on December 12 will be an objective test of three hours duration, with 20 multiple choice questions and 20 true/false questions. The score in this test will serve as qualification marks for a student to progress to the second step of the evaluation process. The cut-off marks for a particular program will be decided by the TIFR center handling that program. Additionally, some or all of the centers may consider the score in Stage I (in addition to the score in Stage II) towards making the final selection for the graduate program in 2022.**Stage II.** The second stage of the selection process varies according to the program and the center. More details about this stage will be provided at a later date.

### Syllabus for Stage I

**Stage I **of the selection process is mainly based on mathematics covered in a reasonable B.Sc. course. This includes:**Algebra: **Definitions and examples of groups (finite and infinite, commutative and non-commutative), cyclic groups, subgroups, homomorphisms, quotients. Group actions and Sylow theorems. Definitions and examples of rings and fields. Integers, polynomial rings and their basic properties. Basic facts about vector spaces, matrices, determinants, ranks of linear transformations, characteristic and minimal polynomials, symmetric matrices. Inner products, positive definiteness. (Study Materials)**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 (Study Materials).**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, elementary probability theory.

### Application Fee & Payment

**Application Fee (Non-Refundable):**

**Male Candidates : Rs 1200/-Female Candidates : Rs 600/- Others : Rs 600/-**

Application fee can only be paid ONLINE through Internet banking/Debit Card/Credit Card/UPI or other modes as available on our payment gateway.

**Online Payment:**

After the online payment transaction is successful, please login to your account on the application portal by using your Application Sequence Number and password you set as your user id and check the payment status of your application. Normally, online payments are received within 2 working days and a auto email is sent by the system acknowledging the payment. If your transaction has been successful and your account has been debited and you do not receive the acknowledgement email within 2 working days, neither your payment status is updated in the application portal, you may write to gsch@tifr.res.in

**Please note:**Instructions for downloading/ printing of Hall tickets will be intimated by email, only after receipt of application fee/approval of fee waiver. Downloading of hall tickets will begin on from November 22, 2021.