Annual Foundation Schools Part I - (2014 IIT Madras)

Venue: IIT, Madras
1st to 27th Dec ,2014


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name A.V. Jayanthan T.E. Venkata Balaji
Mailing Address Department of Mathematics,
I.I.T. Madras, Chennai – 600036.
Department of Mathematics,
I.I.T. Madras, Chennai – 600036.


Speakers and Syllabus 

Advanced Training in Mathematics (ATM) Schools are a joint effort of a large number of mathematicians across the country, with support from the National Board of Higher Mathematics. The programmes are conducted in reputed mathematics departments in the Summer and Winter every year. The emphasis in these Schools is on solving problems, and on the relations between basic areas of mathematics. The schools are intended mainly for Ph.D. students and lecturers.

Applications are now invited for participation in the following school

Annual Foundation School – I

Basic knowledge in algebra analysis and topology forms the core of all advanced instructional schools organized in this programme. The objectives of Annual Foundation Schools (AFS), are to bring up students with diverse background to a common level. Any student who wishes to attend advanced instructional schools is strongly encouraged to enroll in the AFS first. The courses in AFS-I will cover basic topics Group Theory, Analysis and Topology.

Name of the Speaker Affiliation No. of Lectures
(1.5hrs duration)
Detailed Syllabus
Dr. V. Uma IIT Madras 4 Basic examples of groups such as cyclic groups, dihedral and quaternion groups, matrix
groups and permutation groups. Review of normal subgroups and isomorphism
theorems, internal and direct products.
Dr. Jayanthan A V IIT Madras 4 Isometries of Rnand plane. Group actions, finite subgroups of SO(2) and SO(3).
D. Krishna Hanumanthu CMI 4 Sylow Theory, classification of finite groups of order 12, simplicity of the alternating groups and PSL(V)
solvable groups, p-groups,Jordan-HÖlder theorem.
Dr. Manoj Kummini CMI 4 Linear groups Classical groups, SU (2), latitudes and longitudes on the 3-sphere,
simplicity of SO(3), normal subgroups of SL(2, F ).
Dr. M. Thamban Nair IIT Madras 8 Basics Abstract measure spaces and the concept of measurability, simple functions, basic properties of measures, Lebesgue integration of positive functions and complex values functions, measure zero sets, completion of a measure and outer measure. Positive Borel Measures: Topological preliminaries on locally compact Hausdorff spaces, Riesz representation theorem (outline of the proof), Borel measures, Lebesgue measure on Rn , comparison with Riemann integration. Approximation by continuous functions,Generalized Riesz representation theorem.
 Dr. S. H. Kulkarni    8 Differentiation Maximal functions, Lebesgue points, First Fundamental Theorem of integral calculus, Absolutely continuous functions, Second Fundamental theorem of integral calculus. Change of variable formula. Integration on products Monotone classes, algebra on products, product measure, Fibini, completion, convolution.
 Dr. T. E. Venkata Balaji   IIT Madras  8 Open sets and closed sets, limit points, closure and boundary points, subspace. Bases and subbases. Continuous functions, open functions,closed functions,homeomorphisms. Separation axioms: Hausdorffness regularity and normality.Urysohn’s lemma and Tietze extension theorem. Compactness and LindelÖff property, local compactness.I and II countability separability. Path connectedness, connectedness, local connectedness. Product topology.
Dr. Suhas Pandit    IIT Madras   8 Induced and coinduced topologies. Quotient topology, separation axioms under quotient topology, criterion for a restriction of a quotient map to be a quotient map, examples such as cones, cylinders, Mobius strips etc. Paracompactness and partition of unity, Stone’s theorem (paracompactness of metric topology). Topological groups and orbit spaces. Examples from matrix groups. Function spaces, compact-open-topology and exponential correspondence.
Dr. Dishant
CMI 4 Differentiability of functions on open subsets of Rn , relation with partial/directional derivative, Taylor’s theorem etc. Inverse and implicit function theorems, rank theorem, Differentiability of functions on arbitrary subsets of subsets of Rn, diffeomorphisms,smooth version of invariance of domain. Richness of smooth functions, smooth partition of unity and consequences on subspaces of Rn such as approximation of continuous functions by smooth functions. Sard’s theorem for smooth functions RnRm and some applications.


  1. M. Artin, Algebra, Second Edition, Prentice Hall of India, 2011.
  2. N. Jacobson, Basic Algebra Volume 1, Second Edition, Dover Publications, 2009.
  3. I. K. Rana, Introduction to Measure and Integration, II edition, Narosa Publishing House, New Delhi.
  4. Royden H. L. Real Analysis, III edition, Macmillan, New York, 1963.
  5. M.A. Armstrong, Basic Topology, Springer.
  6. K. D. Joshi, Introduction to General Topology, New Age International (P) Limited.
  7. A. R. Shastri, Elements of Differential Topology, CRC Press, Taylor and Francis Group, Boca Raton, 2011.


Day Date





Lecture 2





(2.30 – 3.30)
(4.00 - 5.00)
    (name/initial of
the speaker)
  (name/initial of
the speaker)
  (name/initial of
the speaker/tutor)
  (name/initial of
the speaker/tutor)
Mon 1.12.2014 VU   TEVB   RB,SM   PP,BNS  
Tues 2.12.2014 MTN   VU   AK,SA   RB,SM  
Wed 3.12.2014 TEVB   MTN   PP,BNS   AK,SA  
Thu 4.12.2014 VU   TEVB   RB,SM   PP,BNS  
Fri 5.12.2014 MTN   VU   AK,SA   RB,SM  
Sat 6.12.2014 TEVB   MTN   PP,BNS   AK,SA  
Mon 8.12.2014 AVJ   SP   RB,SM   PP,BNS  
Tues 9.12.2014 MTN   AVJ   AK,SA   RB,SM  
Wed 10.12.2014 SP   MTN   PP,BNS   AK,SA  
Thu 11.12.2014 AVJ   SP   RB,SM   PP,BNS  
Fri 12.12.2014 MTN   AVJ   AK,SA   RB,SM  
Sat 13.12.2014 SP   MTN   PP,BNS   AK,SA  
Mon 15.12.2014 KH   TEVB   RB,SM   PP,BNS  
Tues 16.12.2014 SHK   KH   AK,SA   RB,SM  
Wed 17.12.2014 TEVB   SHK   PP,BNS   AK,SA  
Thu 18.12.2014 KH   TEVB   RB,SM   PP,BNS  
Fri 19.12.2014 SHK   KH   AK,SA   RB,SM  
Sat 20.12.2014 TEVB   SHK   PP,BNS   AK,SA  
Mon 22.12.2014 MK   DP   RB,SM   PP,BNS  
Tues 23.12.2014 SHK   MK   AK,SA   RB,SM  
Wed 24.12.2014 DP   SHK   PP,BNS   AK,SA  
Thu 25.12.2014 MK   DP   RB,SM   PP,BNS  
Fri 26.12.2014 SHK   MK   AK,SA   RB,SM  
Sat 27.12.2014 DP   SHK   PP,BNS   AK,SA  

Tutorial Assistants:

S.No. Name Affiliation
1 R. Balajkrishnan IIT Madras
2 Susobhan Mazumdar IIT Madras
3 Poornapushkala IIT Madras
4 Suhas B. N. IIT Madras
5 Arundhathi Krishnan IIT Madras
6 Saswata Adhikari IIT Madras


Selected Applicants

Instructions to selected candidates:


  1. Selected candidates will confirm their participation by 5th October by sending scanned copies of their forward journey tickets to the respective conveners, (NOT  to the coordinator A. R. Shastri)  failing which corresponding number of candidates from the wait-list will be selected.
  2. Even after the confirmation, for any reason what-so-ever, if a candidate decides to drop out, he/she is requested to inform this immediately to the organizers.
  3. Selected candidates will correspond with the respective conveners for all further matters concerning the school.
  4. All wait-listed  candidates are also advised to make advance booking in anticipation of getting a chance. 
  5. KEEP VISITING THE NCM PAGE and the links of the respective pages for further instructions regarding the school such as preparation, course material,  how to reach etc.
  6. Click here for wait list


First List


C.S=Confirmation status

C = Confirmed

NC = Participation not confirmed by participant

NAS = No Accommodation Support

Sr. SID Full name Gender Affiliation City , State Position in College/ Univ. University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A


1 6548 Mr Mritunjay Kumar Singh Male Central University Of Bihar Patna , Bihar M.Phil BHU 2012 C
2 6549 Mr Rajeev Kumar Male Central University Of Bihar Patna , Bihar M.Phil BHU 2012 C
3 6561 Mr. Thomas John Male Indian Institute of Technology Bombay Mumbai , Maharashtra Phd St. Thomas College 2012 NC
4 6573 Ms. Kavita Khandelwal Female Malaviya National Institute of Technology, Jaipur Jaipur , Rajasthan PhD University of Rajasthan 2008 NC
5 6611 Ms. Kavitha R Female Manonmaniam Sundaranar University Tirunelveli , Tamil Nadu Ph.D Manonmaniam Sundaranar University, 2011 C
6 6676 Mr. Ahmed Mohammed Male National Institute Of Technology Karnataka- Surathkal Mangalore , Karnataka Research scholar National Institute Of Technology - Warangal 2013 C
7 6690 Mr. Manik Das Male University of Calcutta Kolkata , West Bengal Ph.D Visva-Bharati University 2012 C
8 6740 Mr. Vishvesh Kumar Male Indian Institute of Technology ,Delhi New Delhi , Delhi Ph.D. Indian Institute of Technology Bombay 2014 C
9 6787 Mr Ramasamy Subramaniyam Male Gandhigram Rural Institute - Deemed University Dindigul , Tamil Nadu Phd Student Periyar University 2006 C
10 6808 Ms Mallika A Female Manonmaniam Sundaranar University Tirunelveli , Tamil Nadu Ph.D. Studied Manonmaniam Sundaranar University 2010 C
11 6812 Mr. Gorachand Chakraborty Male IIT Bhubaneswar Bhubaneswar , Orissa Ph.D Student IIT Guwahati 2012 C
12 6866 Mr. Santosh Kumar Male Aligarh Muslim University Aligarh Aligarh , Uttar Pradesh Phd Dr.B.R.A.University Agra 2009 NC
13 6873 Mr. Arindam Das Male NIT ROURKELA Rourkela , Orissa M.SC STUDENT NIT ROURKELA Appeared / Awaiting Result C
14 6962 Mr. V. Ramanathan Male Manonmaniam Sundarnar University Tirunelveli , Tamil Nadu PhD Manonmaniam Sundarnar University 2010 C
15 6964 Ms. Sunanda Sinha Female University of Calcutta Kolkata , West Bengal Ph.D Student University of Calcutta 2010 C
16 6969 Mr Veeramani . S Male Indian Institute of Technology Hyderabad Medak , Andhra Pradesh Ph. D Manonmanium Sundaranar University 2010 C
17 6975 Ms Pravisha P Female IISER Thiruvananthapuram , Kerala MS Student IISER-TVM Integrated M.S programme Appeared / Awaiting Result C
18 7040 Ms. Jayeeta Saha Female University of Calcutta Kolkata , West Bengal PhD student University of Calcutta 2009 C
19 7048 Mrs. K Saranya Female Sri Sarada College for Women Salem , Tamil Nadu Ph.D student Meenakshi College for women, Chennai 2011 C
20 7079 Mr. Aziz Ahmed Male Swami Ramanandh Teerth Marathwada University, Nanded. Nanded , Maharashtra M.Phill. Science College, Nanded. 2005 C
21 7089 Mr Safeer K M Male IISER Pune , Maharashtra MS student IISER PUNE Appeared / Awaiting Result C
22 7103 Ms. Bidisha Roy Female IIT Madras Chennai , Tamil Nadu MSc student IIT Madras Appeared / Awaiting Result C
23 7125 Mr. Monirul Islam Male ALIGARH MUSLIM UNIVERSITY Aligarh , Uttar Pradesh M.PHIL ALIGARH MUSLIM UNIVERSITY 2012 C
24 7147 Ms. Dhanya V S Female UNIVERSITY COLLEGE Thiruvananthapuram , Kerala MPhil student University of Hyderabad 2012 C
25 7149 Ms. Sunitha J M Female UNIVERSITY COLLEGE Thiruvananthapuram , Kerala MPhil student UNIVERSITY OF KERALA 2013 C
26 7150 Ms. Remya R Female UNIVERSITY COLLEGE Thiruvananthapuram , Kerala MPHIL STUDENT PONDICHERRY UNIVERSITY 2013 NC
27 7152 Ms Reshmi P S Female UNIVERSITY COLLEGE Thiruvananthapuram , Kerala MPhil student St.THOMAS COLLEGE ( affilated to MG UNIVERSITY) 2013 C
28 7188 Ms Bijal Rohit Amlani Female IISER Thiruvananthapuram Trivandrum , Kerala Integrated PhD Student IISER Thiruvananthapuram Appeared / Awaiting Result C
29 6543 Mr Jeevaraj S Male National Institute Of Technology Tiruchirappalli (NIT Trichy) Tamil Nadu PhD Anna University Chennai 2012 C
30 6751 Mr. T Kalaimani Male Thiruvalluvar Government Arts College. Tamil Nadu PhD Student. GOVERNMENT ARTS COLLEGE, SALEM, TAMIL NADU. 2010 C
31 7072 Mrs. N Krithika Female Sri Sarada College For Women Tamil Nadu Ph.D student Tamilnadu Open University 2009 C
32 6613 Mr Radhakrishnan Mohanasundaram Male Ramanujan Institute For Advanced Study In Mathematics Tamil Nadu PhD UNIVERSITY OF MADRAS, CHENNAI 2011 NAS
33 6782 Mr. Prakash Ponnusamy Male Ramanujan Institute For Advanced Study In Mathematics, University Of Madras. Tamil Nadu PhD Bharathiar University 2012 NAS
34 6783 Mr. V.Shankar Veerabathiran Male Ramanujam Institute For Advanced Study In Mathematics, University Of Madras. Tamil Nadu PhD Ramanujan Institute For Advanced Study in Mathematics, University of Madras 2012 NAS
35 6638 Mr. Prabakaran P Male Periyar University. Tamil Nadu Ph.D Periyar University, Salem. 2012 C
36 6785 Ms Saranya R Female Bharathidasan University Tamil Nadu PhD BHARATHIDASAN UNIVERSITY 2012 C
37 6996 Ms. M Subajini Female Manonmaniam Sundaranar University Tamil Nadu PhD MANONMANIAM SUNDARANAR UNIVERSITY 2012 C
38 7121 Mr. Mohd. Sarfaraz Male Aligarh Muslim University Uttar Pradesh Ph. D ALIGARH MUSLIM UNIVERSITY 2012 C


Wait List


Sr. SID Full Name Gender Affiliation State Position Univ/ Inst. Ms.C/M.A. Year of Passing M.Sc. / M.A Ph.D. Degree Date
1 6679 Ms Kavitha S Female Manonmaniam Sundaranar University Tamil Nadu Ph.D Manonmaniam Sundaranar University 2010  
2 6753 Mr. M. Suresh Kumar Male National Institute Of Technology Karnataka, Karnataka Ph.D Manonmaniam Sundaranar University 2010  
3 6916 Mr. Purnendu Shekhar Pandey Male Indian Institute Of Information Technology Allahabad Uttar Pradesh PhD M.Tech (Gautam Buddha University) 2013  
4 6957 Ms. Sathya M Female Periyar University Tamil Nadu PhD Muthayammal College of Arts and Science, Rasipuram. 2010  
5 7062 Mr. Kislay Kishor Male Jawaharlal Nehru University Delhi Ph.D UNIVERSITY OF DELHI, DELHI 2010  
6 7179 Mr. Gobinda Rakshit Male IIT Bombay Maharashtra PhD IIT Kanpur 2011  


 How To Reach

The IIT campus is located on the Sardar Patel Road, midway between the Raj Bhavan and Adyar bus terminus and is around 12 km from Chennai Central Railway Station. Other landmarks include the Guindy Snake Park near the IIT main gate and the Central Leather Reasearch Institute (CLRI) campus opposite the IIT campus.

If you are coming by train to Chennai Central Station and have light luggage (a bag or an attache) you could consider taking a bus to IIT. The bus stop is just across the road from the Central Railway Station. You could use the subway to cross the road which is perpetually busy. There are direct buses to IIT, which start at the Central Station bus stop. If you take any of them, get down at Gandhi Mandapam, which is at walking distance from the IIT main gate. Otherwise, take any bus to Saidapet and from there, any bus heading for Adyar or Besant Nagar which will drop you right in front of the IIT gate. You could also take any bus to Adyar; there are frequent buses from Adyar Signal to the campus. Once you reach the In gate, there are
buses to Gajendra Circle (near the administrative block and Central Library), the academic zone and the Taramani Guest House close to it, almost every 30 minutes.

From To              Buses Nos.
Central Station Gandhi Mandapam, IIT, Adyar 18B, 19S
Saidapet IIT, Besant Nagar 5B, 23C, 47A, 47
Egmore Station IIT, Adyar   23C, 23E, 23A, 23G
Adyar Traffic Signal IIT           1LSS, 4LSS, 6LSS

If you have luggage and are coming from the railway station, an auto-rickshaw or taxi would be the most comfortable option. The fare will be about Rs. 150 for an auto-rickshaw and Rs. 300 for a taxi. If you arrive at Egmore Station, you could take buses to IIT, Gandhi Mandapam or Adyar from where there are number of buses to the IIT. Current auto-rickshaw and taxi fares from Egmore are approximately Rs.130 and Rs.250 respectively.

From the airport, probably the only convenient way is to take a prepaid taxi which is available at the exit point of the terminal.

A strong warning regarding the autorikshaws in Chennai: As soon as you get down at the railway station (Egmore or Central), there would be many autorikshaws trying to offer you to take you to IIT for a "cheap" price or a price which is "same as the prepaid ones". Do not heed them. Just come out and look for the prepaid autorikshaw counter and get the auto from there.