During the ``Discussion Meeting on
Harmonic Analysis'' held at I.I.Sc. Bangalore in
1992, a session was devoted to discuss the academic
preparation of the students who come for Ph.D. programmes
in Mathematics in various Universities and Institutions
in the country. In order to improve he level of Ph.D.
aspirants it was felt that a training programme should be
started (starting at the B.Sc. level itself) which should
expose bright young minds to the excitement of doing
mathematics. The National Board for Higher Mathematics
(NBHM) was approached with the proposal and it agreed to
fund the programme. The first programme was held in the
summer of 1993. This programme has been on since 1993
with funds from NBHM.
The programme was highly
appreciated by the participants. We receive letters of
appreciation from both teachers and the
participants.
The success of this programme
depends mainly on a very small group of mathematicians
committed to the improvement of the mathematical scene in
our country and as such lacks man-power and
infrastructure.
The aims of this programme are as
follows:
1. To teach mathematics in an
interactive way rather than the usual passive
presentation. To promote active learning, the teachers
usually ask questions and try to develop the theory based
on the answers and typical examples. At every level the
participants are encouraged to explore, guess and
formulate definitions and results.
2. To promote independent thinking
in mathematics.
3. To provide a platform for the
talented students so that they can interact with their
peers and experts in the field. This serves two purposes:
i) the participants come to know where they stand
academically and what they have to do to bring out their
full potential and ii) they establish a rapport with
other participants and teachers which help them shape
their career in mathematics.
The daily programme consists of
lectures in the morning (from 9.30 a.m. to 1.00 p.m.) and
problem sessions in the afternoon (from 2.00 p.m. to 5.00
p.m.)
Each level (I and II) has lectures
in the four basic streams of Mathematics: Algebra,
Analysis, Geometry and Topology. Students of Level O are
offered courses in Basic Real Analysis, Linear Algebra,
Geometry (curve tracing, sketching of surfaces,
classification of quadric surfaces) and one of Discrete
Probability, Combinatorics and Elementary Number
theory.
The faculty is from various
leading institutions of the country and is not confined
to the institute of the venue. People who are experts in
the field, who are known for their teaching and who have
a commitment towards betterment of mathematics in India
are chosen to give the courses. As a rule each course is
taught by a single expert. This paves the way for better
interaction (over a period of 4 weeks) between the
faculty and students and also imparts a perspective of
the field among the students. The faculty is requested to
be present for all the sessions --- not for their
sessions only! In the problem sessions all students are
asked to do problems. All the four teachers of a level
will actively help the students during the problem
sessions. The teachers identify the difficulties of the
individual students. Giving individual attention is one
of the unique features of this programme which makes the
programme successful. Some reading material is also
provided. There are no tests at the end of the programme
as we want to make it clear that the students should
learn mathematics for the pleasure of doing it and not
for examinations
The programme is advertised in the
newspapers every year sometime in the month of December.
For the last several years, we are directly mailing the
posters to colleges which offer B.Sc.(Mathematics),
universities and institutes.
In the past we
received about 1500 applications for all levels and
centres. The screening depends very much upon the
recommendations of the teacher. So we request the
teachers to be very particular while recommending the
students. Even if one student applies from each college
we will receive about 5000 applications. We do not have
the man power to screen such a large number of
applications. Unless you, as a teacher, are convinced
that there is some spark in the candidate and that the
student wishes to pursue a research/teaching career in
mathematics, please do not encourage him/her to apply for
the programme. The programme is quite demanding and
the student should be prepared to work under
pressure.
How does one know whether the
student is the kind we are looking for? One rule of thumb
is that he reminds you of some of the top students whom
you know of or that he does some independent thinking
such as formulating problems, solving problems on his
own.
We also look for the following
traits as mentioned in the Recommendation form:
Motivation, Capacity to grasp new concepts and
perseverance, determination and grit.
Your cooperation, help and
suggestions will help us make the programme
successful.
Please feel free to write to me if
you have any specific questions and to send your valuable
suggestions to the Director
of this Programme.
Postscript or pdf format of the this document
can be downloaded.
