Annual Foundation Schools Part I - (2014 IIT Madras)

Venue:	IIT, Madras
Dates:	1^st to 27^th 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 Pancholi	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 →R^m and some applications.

References:

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.

Time-Table

Day	Date	Lecture1 (09.30-11.00)	Tea (11.00)	Lecture 2 (11.30-01.00)	Lunch (01.00-02.30)	Tutorial (2.30 – 3.30)	Tea (3.30)	Tutorial (4.00 - 5.00)	Snacks (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:

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

First List

Note-

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	C.S
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.