Annual Foundation Schools Part I - (2014 IIT Madras)
1st to 27th Dec ,2014
|Convener(s)||Speakers, Syllabus and Time table||Applicants/Participants|
|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.
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
|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.|
|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 Rn →Rm and some applications.|
- M. Artin, Algebra, Second Edition, Prentice Hall of India, 2011.
- N. Jacobson, Basic Algebra Volume 1, Second Edition, Dover Publications, 2009.
- I. K. Rana, Introduction to Measure and Integration, II edition, Narosa Publishing House, New Delhi.
- Royden H. L. Real Analysis, III edition, Macmillan, New York, 1963.
- M.A. Armstrong, Basic Topology, Springer.
- K. D. Joshi, Introduction to General Topology, New Age International (P) Limited.
- A. R. Shastri, Elements of Differential Topology, CRC Press, Taylor and Francis Group, Boca Raton, 2011.
(2.30 – 3.30)
(4.00 - 5.00)
|1||R. Balajkrishnan||IIT Madras|
|2||Susobhan Mazumdar||IIT Madras|
|4||Suhas B. N.||IIT Madras|
|5||Arundhathi Krishnan||IIT Madras|
|6||Saswata Adhikari||IIT Madras|
Instructions to selected candidates:
- 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.
- 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.
- Selected candidates will correspond with the respective conveners for all further matters concerning the school.
- All wait-listed candidates are also advised to make advance booking in anticipation of getting a chance.
- 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.
- Click here for wait list
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|
|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.
|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.