MTTS Pamphlet

8/11/2019 MTTS Pamphlet

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FUNDED BY : THE NATIONAL BOARD FOR HIGHER MATHEMATICS,DEPARTMENT OF ATOMIC ENERGY, GOVERNMENT OF INDIA

MATHEMATICSTRAININGAND TALENTSEARCHPROGRAMME

(CONDUCTED SINCE 1993)


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SOME OF THE MTTS VENUES IN THE PAST

BENEFITS OF MTTS PROGRAMME (AS PERCEIVED BY THE STUDENTS)


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INTRODUCTIONTe Mathematics raining and alent Search (M S)Programme is a four week intensive summer trainingprogramme for undergraduate and postgraduate studentsin India. Tis programme has been conducted, since 1993,at various centres in India. Te programme is funded bythe National Board for Higher Mathematics (NBHM),

an apex body of the Department of Atomic Energy,Government of India.During a Discussion Meeting on Harmonic Analysisheld at the Indian Institute of Science (I.I.Sc) Bangalorein 1992, a session was devoted for discussing the academicpreparation of the students who come for Ph.D. programmesin Mathematics to various universities and Institutions inthe country. o improve the level of the Ph.D. aspirants,it was felt that a training programme should be started atthe B.Sc. nal year level, to expose young minds to theexcitement of doing mathematics and enabling them topursue a meaningful career in mathematics (research and/orteaching). Te programme, christened as the Mathematicsraining and alent Search Programme (M S), waslaunched in 1993, with nancial support from NBHM.Since then, the programme has been organised under theDirectorship of Professor S. Kumaresan, (formerly fromUniversity of Mumbai), Department of Mathematics andStatistics, University of Hyderabad, India.

Some of the main aims of this programme are: to expose and attract young minds to the excitement

of solving problems in mathematics and choosingmathematics as a career;

to promote independent thinking; to provide a platform for talented students through

which they can interact with their peers and expertsin the eld

to improve the teaching methodology for mathematicsin the country in the long run

Te programme has three levels: Level-O, Level-I andLevel-II. Level-O is meant for rst and second year

undergraduate students of mathematics, Level-I for 2ndand third year undergraduate students and Level-II for therst year post graduate students.Te Levels I & II have lectures in the four basic streamsof Mathematics: Algebra, Analysis, Geometry and

opology. Students of Level-0 are offered courses in BasicReal Analysis, Linear Algebra, Geometry (curve tracing,sketching of surfaces and classication of quadric surfaces)and one of Discrete Probability, Combinatorics andElementary Number theory.M S is conducted every year in summer (May-June) forfour weeks, at several centres in India. Usually, there is one

main centre, where all the three levels are held. Level-O isconducted at many (about three) centres.

TEACHING METHODOLOGYTe teaching methodology adopted for this programme isdifferent from standard class room teaching. Te faculty isdiscouraged to deliver well polished lectures. Te principlefollowed in this programme is best explained by thefollowing quotesTe only instruction which a teacher can give, in my opinion,is to think in front of his students.

-- Henri Lebesgue Te art of teaching is the art of assisting discovery.

-- Mark van DorenIt is the supreme art of the teacher to awaken joy in creative expression and knowledge.

-- Albert Einstein All sessions are highly interactive and the students arediscouraged to takes notes; rather they are encouragedto think along with the teacher. Rarely a denition isintroduced to the students. Often they are given a lot

of examples and they come up with a denition, whichabstracts properties seen in the examples. With a lotof examples, leading questions and visual aids, such asdiagrams, the students are trained to observe patterns,formulate a result or a conjecture and nally look for aproof.

When a new concept is introduced or a new result is proven,students are given typical situations or problems. Manyexamples are given as soon as new denitions are made andthe students have to verify that they are examples of the

concept just introduced. Only if the teacher is convincedthat the majority has understood s/he proceeds further.Sometimes, another teacher, who is present in the class,may try to explain things in his/her own way. Tis givesdifferent perspectives to the concept. ( o achieve this, the

Student assisted by another student during student seminar Student is assisted by a faculty during student seminars


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faculty members, who will be willing to work as a team, areselected for delivery.) Te teacher makes cross-referencesto analogous/similar results/concepts, explained by his/hercolleague for the programme.Usually, students are given an outline, strategies or the ideaof the proof and they are asked to work out the detailsin the class itself. Such exercises are to be submitted as

writing assignments, with complete details. Te studentsare encouraged to discuss among themselves before writingthe nal proof. Tis advice has two benets; (i) those whodid not understand or could not work out the completedetails will have an opportunity to learn them thoroughlyby discussing them with their peers (ii) those who didunderstand get a chance to enhance their communicationskills and consolidate their understanding, can do so whilethey explain or clarify the doubts of their friends.It is universally true that whenever a teacher asks a question,some of the bright students tend to answer it aloud. Teother students gradually comes to a stage in which they donot even try to understand the question and answer it ontheir own, as they know that some of the good students

will give the answer. o prevent this, the policy followedin the M S programme is that all students should writethe answer very briey; this will then be examined by theinstructors present in the class. Tis allows us to identifythe problem area of the students in the very beginning andtake remedial measures.Student Seminars are an integral part of this programme.

After two weeks one of the sessions is completely devotedto student seminars. Te topics of the seminars are eitherchosen by the student or assigned by the teachers, takinghis/her background into account. Tis serves manypurposes; (i) it builds the condence level of the students,(ii) it eliminates stage fear and the fear of expressingthemselves before experts.Invariably while presenting in seminars, the students followthe methodology of M S, by making it highly interactive.In fact, in some of the student seminars, hardly anything is

written on the board. Tis aspect of M S is so popularthat almost all students volunteer to conduct seminars, somuch so that it is difficult to accommodate them all.Since the last few years, after one week or so, students aredivided into groups of 4-5 and are encouraged to discuss

topics. At times, each group is assigned some topic fordiscussion, which they need to present at the end beforethe class. Tis feature has been so successful that students

want more time for group discussions.In each level, almost every day one writing assignmentis given to students, which is critically evaluated by theconcerned teacher. Te assignment is discussed either with

the entire class or individually. During the M S camp, weinsist that students discuss the days happening with theirpeers. Te faculty stay on campus and have dinner along

with them. Tis gives a chance to students, to interact withthe faculty outside the classroom, both at the professionaland personal levels. Tis results in a better rapport betweenthem.It is an avowed policy of M S not to hold any writtenexams, but to encourage students to learn mathematics forits own sake. However, the students are informed that theirperformance will be critically evaluated by the teachers. Teteachers of the particular level collectively award a grade toeach participant, which will be disclosed to a student if s/he wants to know it. It is a matter of great pride that nostudent fails. Each student feels that individual attentionis paid to him/her, thanks to the steps mentioned above.

SELECTION OF STUDENTSOut of more than 2000 applications received each year,about 230 students are selected for the programme.

About 180 actually participate. Te selection of students

depends mainly on their consistent academic record andthe recommendation letter of a teacher, closely acquainted

with the student. Te selection is highly inuencedby specics rather than by the general remarks in therecommendation letter. While selecting students, regionaland rural backgrounds are also given importance, so asto give opportunities to students from all regions and tothose, who lack exposure to good teaching, peers and goodtextbooks. In fact, due to this consideration, the Level Oof this programme is also arranged in different parts of thecountry. As a rule, not more than two students from the samecollege/institution are selected. If a former student appliesfor the next level, his/her performance in the previous levelis the most decisive factor. As there are regional imbalancesin the grading pattern, applicants of the same region are

Students Seminar, MTTS 2012, IIT Kanpur Students Seminar, MTTS 2012, IIT Kanpur


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collected and scrutinised together. We make a shortlistfrom this, which will be compared with similar shortlists.Usually, the rst two rounds are elimination rounds. Tenext two rounds are comparison with other shortlists of thesame state and states with a similar grading pattern. Tepenultimate round is at the national level. Te nal roundtakes care of regional representation.

Level O students are assigned centres, which are close totheir institution or home. o encourage participation bygirl students, we make it a policy to select two students(preferably another girl) from the same institute. But forthis policy, many parents would not permit their daughtersto participate in this programme held at a far-away placefrom their home.

FACILITIESTe selected candidates are provided with sleeper classreturn train fare and free lodging and boarding. Tey arealso given reading material and a few books. M S spendsabout 15 to 20 thousand Indian rupees (approximately300-400 USD) on each student. Since several years, weprovide them an electronic version of the notes, along withsome free and open source mathematical software.

CHALLENGESTe major difficulty for this programme is to nd dedicatedfaculty, who can work as a team and who can spend theirvaluable time for all four weeks, at the M S Camp.

M S has been organised year after year, with the helpof a very small group of dedicated people, who want toimprove the scene of Mathematical teaching and researchin India. Our hope is to solve this problem, by encouragingformer M participants, who are now faculty members,at various institutes, to serve as resource persons for theprogramme.

While selecting the students for the M S programme, we have the challenge of selecting the most deservingcandidate. Many a times, the recommendation letter isvery generic, which makes it difficult to make a choice. Insuch cases, we compare the academic achievements of theshortlisted candidates and make the selection. At times,rejection is very difficult.Since the participants come from all over the country,

many students have language problems, as the mediumof instruction is English. Even though the students mighthave been taught in English in their home institute, manya times, their teachers resort to explaining the concepts intheir regional language. Te absence of this practice in theM S camp leads to some difficulties for the students.Even for those, who are reasonably comfortable withEnglish, the differences in regional accents pose problemsin understanding. However, the programme attends tothese problems. As regards the second issue, the studentsare assured that they will get used to the accents and thatthey should not be unduly bothered. Every effort is made toidentify students with language difficulties. Such studentsare assigned a teacher, who can possibly communicate withthem in their own language. Te faculty members at everylevel are carefully chosen, so that we can ensure that theycan communicate in different languages. As a result, noparticipant feels left behind, due to language barriers.

Given the innate bureaucratic nature of the academicinstitutions in India, it is difficult to nd a suitable venue,

with accommodation, to organise the programme.In spite of our best efforts, we do not think that M Shas reached every nook and corner of the country and lotmore needs to be done at the local level. Usually, we getmore applications from the same set of institutions fromthe same set of states. In fact, there are some states from

which there are hardly any applications. At times, we selecta student just based on regional consideration, even though

his/her academic records may not be comparable to others.Tis gesture serves as an advertisement for M S, so thatin future students of that region apply.In order to provide opportunities to a large numberof students at regional levels, we have launched Mini-M S programmes, which are modelled after the M SProgramme, but are of a shorter duration and they cateronly to students of the region, in which the programme isheld.In order to spread the M S methodology to large

number of students, we have started a new scheme Pedagogical raining for Mathematics eachers (P M ).Te suggestion for this came from the participants. Teparticipants of P M are introduced to the M Smethodology, so that they can adopt it in their regular

Group Discussion, MTTS 2012 (IIT Guwahati) Group Discussion, MTTS 2012 (IIT Kanpur)


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teaching.In the rst few years, some of the top performingparticipants of the M S camps were selected for veryintensive training, in a topic or two of considerable depth,in the leading institutions of the country. Tis follow-upprogramme was discontinued for the following reason- the fountain-head of the ow of the research students

to the leading departments and institutes of this countryis M S. In spite of that, the contributions from theseinstitutes, either to the main programme or to the follow-up programme is almost non-existent.

EVOLUTION OF MTTSTe programme continuously evolves, thanks to theextensive feedback sought from the faculty and theparticipants.o begin with, the M S programme was started onlyfor Level-I and Level-II students, at only one centre. Teneed for starting the training even earlier was realised andLevel-O was launched in the year 1995. Since then, LevelO is simultaneously conducted at different places, in orderto enable students from different parts of the country toparticipate in the programme.In the beginning, morning sessions were devoted toinstruction, whereas afternoon sessions were for problemsolving. In order to make the session more interactive, thelecture and problem solving sessions are now combined.Tis also ensures that the teachers are more interactive inthe classroom and keep a certain pace, so that students canfollow the course.o provide a proper grounding in fundamentals, weintroduced a course in foundation in Level-O, whichmainly deals with logic, concept of a proof and a rigorousacquaintance with sets and function etc. Tis also servesthe purpose of introducing standard examples, which arisenaturally in mathematics, rather than giving contrived/articial examples. We have started giving daily writingassignments, which gradually increase in difficulty, as the

programme progresses. Tis trains the students in writing/solving mathematics on their own, rather depending uponnotes and books.

As, mentioned earlier, since several years, one session

is completely devoted to student seminars and nocompromise is made on this account. Tis has been highlysuccessful and appreciated by one and all.

We have also introduced group discussion sessions, at allthe levels, so that the students interact among themselvesand discuss the days happenings. At times, each group isassigned some topic for discussion, which they need to

present at the end, before the entire class. Tis feature hasbeen so successful that students want more time for groupdiscussion.Since the last few years, on the inaugural day, a questionnaireis circulated to Level-I and Level-II students. Based ontheir answers, the students are counselled and appropriatecourses are suggested to them. It is possible that a studentmay have to attend one subject with one level and anothersubject with another level. o make this feasible, the timetable is suitably framed.Moreover, students are given a feedback form at the end ofthe rst week. Te idea behind this is that students assesstheir own efforts and involvement in the programme.Tis has resulted in some of the laggards getting theiract together and performing better, as seen by their ownadmission in the nal feedback form.o keep pace with the changing mode of communication,

we have introduced online applications. However, we stillcontinue to accept applications submitted in the traditional

way. We also encourage many activities, shorter in duration,modelled after M S, to be organised at many places, inthe country.

FEEDBACK FROMSTUDENTS AND TEACHERSM S is a great programme to channel mathematics talentfrom all over India, by exposing bright young studentsto rigorous mathematics, terric teachers and a chargedenvironment. Te M S experience is memorable,creating numerous opportunities for students andmotivating them to choose their careers in mathematics.

In addition to propelling students towards research careers,it has inuenced a generation of mathematics teachers allover India.

--Dr. Abhijit Champanerkar, City University of NewYork, MTTS 95 & 96

Students Discussing with Faculty in the Guest room on Sunday Team work of teachers


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I think attending M S was one of the turning points forme, it helped me gain clarity in thinking and also helpedme to gain a broader attitude towards life.

--Saurabh S. Bhangaonkar, Connizant TechnologySoluttions Ltd. Pune, MTTS 2000

It was very helpful in kindling my individual thinking,through which I realised the joy of mathematics, which in

turn motivated me to aspire for a career in mathematics.--- Lakshmi Priya ME, MTTS 2007-2009

When I look at myself as I was three years ago, I see radicalchange in myself. Te way M S teaches its students, the

way it motivates them to study on their own, and effectivelyat that, is really amazing. Tis is the only programme in thecountry at the undergraduate level, which helps studentscoming from various parts of the country, with variousbackgrounds, to reach a specic level, from which they cancarry on.

--Anand P. Sawant, MTTS 2006-08.I am back to my routine after M S2010 at HRI. I havereally gained a lot from the programme. I can feel that myapproach towards mathematics has changed. Now that mycollege has started, I can see that I can do whatever is beingdone in the class without a pen and paper. I have startedthinking along with the teacher and I clear my doubts thenand there. It was a very useful programme. I could also feelthat my interest in the subject and condence level haveincreased.

--- Nethra Neelakandan, Level O, MTTS 2010, HRI. After attending M S, each and every class, I attend inmy college is very different from the class I attended till lastyear. Every single problem I solve, I am able to think aboutit and then solve it.

---Padmaja G., Level O, MTTS 2010, Mysore

M S is a programme, where emphasis is laid ondeveloping thinking ability in mathematics. Althoughpresently I am not directly working in Maths, the thinkingability that I could develop during the M S programme,

always helps me solve problems (both mathematical andnon-mathematical).

--Rajesh Kumar, Directorate of Forensic Science, MHA, Govt. of India, New Delhi, Level I, 2003

I feel that the most important contribution of M Sis that it brings out a signicant change in the studentsperspective about learning mathematics. I have seen adrastic, positive change in my students after they returnfrom M S. Tey develop an outlook towards learningthe subject and the condence that they can learn thesubject on their own. Most of the M S students, frommy college, are performing exceedingly well, in their elds,including teaching, research, math education, industry,etc.; and a large share of their creative working goes toM S.

As a teacher, I am immensely beneted by the programmeand always got more insights in teaching-learning processesfrom my colleagues and students. Te programme hasbrought out a revolution in undergraduate mathematics inIndia and I am sure that it will continue to do the great

work. My Best Wishes !--Prof. V. M. Sholapurkar , S.P. College, Pune

IMPACT OF MTTS At the end of the programme one can see remarkableimprovement in a students independent thinking abilityand mathematics writing and problem solving ability. Te

whole approach of these students towards mathematicschanges, after four weeks of extensive training in thisprogramme. Students feedback taken at the end is areection of these effects.Over 2500 students have gone through the M S

programme, of which about 300 students have goneon to obtain their Ph.D. degree or are in the process ofcompleting the degree. Many of them have gone on to dotheir doctorate at prestigious research institutes in India andabroad. More than 1200 would have gone on to becomemathematics teachers at various levels, starting from highschool to the university level.Tis programme has created a great impact onthe mathematical scene in India. o quote seniormathematicians, attached to research institutes in India,Earlier, when we interviewed candidates for Ph.D., we

would be happy to nd 2 or 3 out of 100. Due to theefforts of the M S programme, we now interview about30 to 40; none of them is a dud; we can see that they arecondent of tackling unseen problems and have a clear

Group Photograph, MTTS 2012 (IIT Guwahati)

Group Photograph, MTTS 2012 (Tiruchirappalli)


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Mini-MTTS 2012 at Kerala ICM 2010, Hyderabad, MTTS alumni

understanding of the concepts and all of them can betraced back to M S.If one visits any elite institute or university in the country,one can nd a few M S students, pursuing their Ph.D.in mathematics or those, who have become faculty. In fact,in most of the leading mathematics departments of thecountry, the lineage of many new recruits can be traced

back to the M S Programme.So too, when the participants return to their homeinstitution after the Programme, their teachers areimpressed with the radical changes in the students attitudetowards mathematics and their problem solving skills. Teteachers evince a keen interest in learning and adoptingthe teaching methodology of the programme. o attend tothese requests and also to reach a large number of studentsacross the country, we have recently begun conducting theP M programme, as mentioned earlier.

M S has also helped improve and sharpen teaching skillsof many of the M S faculty members.Other science disciplines, especially Physics, have showninterest to start programmes embracing the principles ofM S.

Many students after attending just one level of M S getselected for the Visiting Students Research Programme(VSRP) of leading research institutions, in the country.Tis just shows the condence that these institutes reectas regards M S training.Te largest alumni group in the International Congressof Mathematicians (ICM) 2010 was possibly that of the

participants and faculty members of M S Programmes.Tis speaks volumes about the contribution of thisprogramme to Mathematics in India.

References:M S Website: http://www.mtts.org.in/P M Website: http://www.ptmt.mtts.org.in/NBHM Website: http://www.nbhm.dae.gov.in/

Programme Director:S. KumaresanDepartment of Mathematics and StatisticsUniversity of Hyderabad, Central University P.O.,Hyderabad 500046 (India),Email: [email protected]

Believe nothing,

Merely because you have been told it.Or because it is traditional.Or because you yourself have imagined it.Do not believe what your teacher tells you,Merely out of respect for the teacher.But whatever, after due examinationand analysis,You find to be conducive to the good,The benefit, the welfare of all beings,That doctrine believe and cling to,

And take it as your guide.

---Gautam Buddha

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MTTS Pamphlet