TIFR / NBHM / ISI / I.I.Sc.
The National Board for Higher Mathematics (NBHM) was set up by the Government of India under the Department of Atomic Energy (DAE), in the year 1983, to foster the development of higher mathematics in the country, to formulate policies for the development of mathematics, help in the establishment and development of mathematical centres and give financial assistance to research projects and to doctoral and postdoctoral scholars. The NBHM functions essentially autonomously framing its own budget taking into account the funds made available by DAE.
The NBHM normally provides financial support only to Indian nationals and institutions. Currently the NBHM grants postdoctoral fellowships, Ph. D. scholarships, M.A. / M.Sc. scholarships for research / education in mathematics
EDUCATIONAL QUALIFICATION
Applicants must be motivated B.A./B.Sc./B.Tech. /B.E./M.A./M.Sc. degree holders or final year students of these degree courses. They must have a good academic record (1st Class or equivalent grade in all years from +2 level) to the present. B.Sc (Honors) students with second class may also apply.
SCHOLARSHIP
Successful candidates will be eligible to receive a scholarship amount of Rs. 16,000/- (Rs Sixteen thousand only) per month for the first and second year and Rs. 18,000/- (Rs Eighteen thousands only) per month for subsequent years, a contingency grant of Rs. 20,000/- (Rs. Twenty thousand only) per year and house rent allowance as per central government norms wherever applicable. The scholarships are normally for a total period of four years, sanctioned for one year at a time and renewable at the end of the year, subject to satisfactory progress. The enhanced amount of scholarship may be offered after evaluation by the board at the end of the second year. If deemed fit, the scholarship may be extended to five years at the discretion of NBHM.
To avail of the scholarship the students have to enrol in an appropriate institution for a Ph.D. degree in mathematics. The scholarship will be paid through the institution they join.
SELECTION PROCEDURE
A written test will be held based on questions in topics normally covered in Master’s degree programmes in mathematics. The test will be for two and half hours and involve questions with short answers. Selection will be made on the basis of a written test followed by interview of short-listed candidates.
EXAMINATION STRUCTURE
There are five sections, containing ten questions each, entitled Algebra, Analysis, Topology, Applied Mathematics and Miscellaneous. Answer as many questions as possible. The assessment of the paper will be based on the best four sections. Each question carries one point and the maximum possible score is forty.
THERE ARE TWO TYPES OF QUESTIONS :
(1) Subjective answer type
(2) MCQ answer type
MARKING SCHEME : Points will be awarded for questions involving more than one answer only if all the correct answers are given. There will be no partial credit.
NBHM Ph.D. Syllabus
Since this is a Ph.D. Course, the syllabus is not well structured and predefined, instead, it covers topics from UG and PG levels of Mathematics. The question paper is divided into three sections. To know more about the outline of the syllabus and its sections check below :
Section A : Algebra Syllabus
NBHM Algebra syllabus covers multiple subtopics as mentioned below:
1. Abstract Algebra
2. Set Theory
3. Binary Operations
4. Matrix Theory
5. Groups Algebra
6. Rings and Fields Polynomials (Calculus, Matrix Polynomials, Roots)
Section B : Analysis Syllabus
Mathematics – Analysis Syllabus covers majorly three sections such as Complex, Functional, Real. Candidates are suggested to cover these topics thoroughly, as they are vast. Below mentioned is the NBHM Analysis Syllabus in detail :
Complex Analysis Syllabus
- Polar Coordinates
- Poles and Residues
Real Analysis Syllabus
Sequence and Limits
Metric Spaces
Series (Infinite Series Expansion, Taylor Series Expansion)
Functional Analysis Syllabus
- Continuous Function
- Maxima and Minima
- Differential Function
- Defining Function
Section C : Geometry Syllabus
NBHM Geometry Syllabus contains mainly two sub-topics. Check below to know more :
Plane Algebraic Syllabus
- Line
- Circle
- Ellipses
- Elliptical Curve
- Cubic Curves
- Spheres (3D Shapes)
Algebraic Geometry Syllabus
- Polar Coordinates
- Cartesian Coordinates
