Mathematics training course: Think, ask, then solve!

Illustration: Anshul Sharma

Shubham Dwivedi wants to pursue a research career in Mathematics. So, while scouting for learning options on the National Board for Higher Mathematics (NBHM) website, he stumbled across the Mathematical Training and Talent Search programme (MTTS), an intensive summer course in pure Mathematics. “MTTS has changed my way of understanding a problem.

Now I can solve most of them on my own. It has taught me to be disciplined and organised in my work,” he shares. ”The course also introduced me to different cultures through people,” says Shubham who adds that several MTTS alumni work as researchers at prominent institutes like TIFR, ISI, IISc, CMI, IITs, and University of Wisconsin, today.

About the programme 
The main aim of MTTS is to groom and produce future Mathematicians. Conducted every year for four weeks during vacation time in May and June (so as to encourage attendance), students are expected to ask more questions and work along with their teachers to solve problems.

The programme is conducted at three levels (view box for eligibility and courses) at different centres pan-India and comprises a group of 35-40 students per level. MTTS spends about Rs. 15,000-20,000 on each student. Students are provided with sleeper class return fare along with free lodging.


Prof S Kumaresan,
Programme Director, MTTS

Not all Toppers can “think Mathematics!

Q: How does MTTS promote independent thinking in Mathematics?
A: From Day 1, students are asked a lot of questions. The teachers while they teach show how they think. So, the participants learn that solving a problem starts from asking questions and gradually arrive at an answer.

Q: How do toppers fare at the camp?
A: Many students (along with their parents, teachers) think they are good in Maths just because they scored well. When they attend the MTTS camp they are rattled by their performance. We counsel them but if they want to leave after three days, they may. Till now, none of them have left as they enjoy the newfound confidence. If they leave in between, they don’t get any certificate.

Q: During selection, any chance of bias through recommendation letter?
A: We keep a ''mental record’ of teachers and their students. If their recommendation is corroborated by the participants’ performance, his recommendations next time are accorded a priority. There are chances of bias but we look at other parameters while comparing students of the same teacher.

Q: How do you ensure good faculty?
A: We handpick good mathematicians who are teaching and are committed to improve the status of Mathematics education in our country. In India, the problem is that the number of good mathematicians is not enough for a country of this size.

Q: What are the other challenges?
A: Finding suitable venues and good caterers. The institutes want to charge us money for everything. The main ''culprits’ here are the elite ones. There are about 200 young students (19-22 years old) and about 20 faculties who need to be offered nutritious and reasonably tasty food. Initially the caterers accept our menu but they do not deliver.


Shubham Dwivedi
Final year student,
BSc (H) Mathematics, Banaras HinduUniversity

“GDs among students help those who hesitate to discuss their difficulties within the class. They take place without any interference from the teacher”


STUDENT SEMINARS helps students overcome their fear of facing live audiences and express their ideas and approach towards a specific topic.

Programme schedule
Classes are conducted every day from 9.30 am to 1 pm Problem sessions and student seminars are held in the afternoon from 2 to 5 pm. Such a hectic schedule prepares a student to work under pressure. The programme’s USP – a rigorous approach to solving mathematical problems - is the biggest challenge for students. It takes time for students to switch from familiar methods of learning to the MTTS way. On student demand, soft copy of notes are made available and some reading material is provided to the students free of cost.

Getting selected

The selection committee follows a unique five-round process that kicks off in the second half of December and ends by the third Saturday of February of the following year:
Round 1&2: Elimination rounds on the basis of application and other documents submitted.
Round 3 & 4: Comparison rounds to select from among shortlisted candidates of the same state, and states with a similar grading pattern.
Round 5: National-level round that ensures regional representation.

How to apply
The application package comprises application form and recommendation letter from a teacher. Traits like motivation levels, capacity to grasp, perseverance and determination, are judged through the letter. Another specific is regional and rural background of the student. As a rule, not more than two students from the same institution are selected.

Shubham shares that five students were selected from his university in 2011, and four students in 2012. Since he realises the importance of the programme, he requests that students merely looking for a vacation should not apply for the course as it can hinder a deserving candidate from participating. To encourage girl student participation, special efforts are made to select them. If an alumnus applies for next level, his or her performance in the previous level becomes the decisive factor.

Harshvardhan Reddy Pinninty
Fourth year BSc student
Hyderabad University

“I gradually improved my performance in understanding, efficiency of giving seminar and answering questions in Mathematics.”


GROUP DISCUSSIONS help in enhancing team spirit among students.

Individual attention
Faculty comprise field experts from different institutes. They stay on campus, giving students a chance to better interact with the faculty, both at professional and personal levels. Shubham shares that his problem-solving sessions helped him in shaping his geometric and intuitive thinking due to which he realised that each and every step in a problem is so natural.

“Teachers are ready to clear doubts even during tea breaks, lunch or dinner. On Sundays, students are allowed to go to faculty guest house for individual problems,” he adds.

Student seminar
At the end of week 2, students must give a presentation on topics they have learnt using the MTTS teaching method i.e., ask questions to the audience (comprising fellow students and teachers) and give them breaks to ponder over the concept. This helps students overcome their fear of facing live audiences and to express their ideas and approach towards a specific topic. What’s more. it enhances teaching efficiency of a student.

Harshvardhan Reddy Pinninty, fourth year BSc student shares his experience of giving a talk on “A proof that e is irrational by using Nested Intervals: A geometrical way”.

He was happy when his friends and teachers appreciated his effort. “I gradually improved my performance in understanding, efficiency of giving seminar and answering questions,” he says. Shubham adds that presentation helps in understanding the concepts in depth as during preparation students have to understand all aspects of a problem as they will be cross-questioned on the same.

Facilities and infrastructure

Typically, all three levels are conducted at one main centre. But Level O is conducted at around three centres as the number of students are more. Separate hostels are arranged for girls and boys. Sometimes picnics are organised on Sundays.

Though infrastructure facilities vary from centre to centre, Harshvardhan feels that they need to be improved. “At RIE Mysore centre, the food provided was south Indian. Few of my friends from north India found it difficult to adjust and fell ill,” he shares. Despite logistical issues, for those who love Mathematics the MTTS programme is an enriching experience. 


Salient features

Level 0: 1st and 2nd-year students of Maths
Level I: For 2nd and 3rd year UG students
Level II: First year PG students

Level 0: Basic Real Analysis, Linear Algebra, Geometry (curve tracing, sketching of surfaces and classification of quadric surfaces) and Discrete Probability, Combinatorics and Elementary Number theory
The Levels I & II: Algebra, Analysis, Geometry and Topology The MTTS way: Learn through examples

  • A new topic is introduced using examples, leading questions and visual aids like diagrams instead of straight definition.
  • Students observe patterns, formulate a result or a conjecture and finally look for a proof.
  • After the result is proven, students are posed questions in form of examples and they have to verify that they belong to the concept proven.

No exam after training! 
Students’ performances are evaluated during classes. The teachers collectively award a grade to each participant, which are disclosed to students if they wish so.