The Annual Foundation School (AFS)-II

Venue:	BP and Pune University.
Dates:	1 - 28 June 2006

Convener(s)

Speakers, Syllabus and Time table

Applicants/Participants

 

School Convener(s)
Name	S. A. Katre
Mailing Address	University of Pune

AFS being organised in Pune in June 2006 is the Second of the 2nd Annual Foundation Schools being organised on behalf of NBHM.

National Coordinating Committee

Director: R. S. Kulkarni 
Secretary: J. K. Verma 
Members : S. D. Adhikari, Satya Deo, Shobha Madan, I. B. S. Passi, R. A. Rao

Members of the Local Organising Committee

Bhaskaracharya Pratishthana: C. S. Inamdar (Custodian), R. V. Gurjar (Res. Director, Hon.)
University of Pune: B .N. Waphare (HOD, Maths.), S. A. Katre, H. Bhate

 

Speakers and Syllabus

Lecture notes and Problems at AFS-II
Algebra                  

•       S. R. Ghorpade
•       Balwant Singh
•       S. A. Katre

Complex Analysis                  

•       Ravi Kulkarni      
•       R. R. Simha            
•       Kaushal Verma

Algebraic Topology                  

•       Anandteertha Mangasuli      
•       Ravi Kulkarni      
•       A. Parameswaran

(Note: lecture notes and problems are available as attachment at end of page)

Objectives of AFS

Basic knowledge in algebra, analysis, discrete mathematics and topology forms the core of all advanced instructional schools the schools to be organized in this programme. 
The objective of the Annual Foundation Schools, to be offered in Winter and Summer every year, is two fold:

1. To bring up students with diverse backgrounds to a common level.
2. To identify those who are fit for further training.

Any student who wishes to attend the advanced instructional schools is strongly encouraged to enroll in the Annual Foundation Schools.

Format of AFS

The topics listed in the syllabi will be quickly covered in the lectures. There will be intensive problem sessions in the afternoons. The objective will not be to cover the syllabus prescribed, but to inculcate the habit of problem solving. However, the participants will be asked to study all the topics in the syllabus at home since the syllabi of these schools will be assumed in all the advanced instructional schools devoted to individual subjects.

Participants in AFS

These schools will admit 40 students in their first and second years of Ph. D. programme, students of M. Sc. (II Year), university lecturers and college teachers who lack the knowledge of basic topics covered in these schools.

A participant who has attended AFS-I and II will never be allowed to attend these again.

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Syllabus for the Annual Foundation School (AFS)-II (Jun., 2006)

Algebra-II

(1) Basic commutative algebra-I: Prime ideals and maximal ideals, Zariski topology, Nil and Jacobson radicals, Localization of rings and modules, Noetherian rings, Hilbert Basis theorem, modules, primary decomposition, integral dependence, Noether normalization lemma, principal ideal theorem, Hilbert's Nullstellensatz, structure of artinian rings, Dedekind domains. (12 lectures) 
(2) Introduction to Algebraic Number Theory: (6 lectures) 
(3) Introduction to Algebraic Geometry: (6 lectures)

Text/References: 
1. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra. 
2. D. Eisenbud, Commutative algebra with a view towards algebraic geometry. 
3. P. Samuel, Algebraic Number Theory.

Complex Analysis

(1) Euclidean similarity geometry, inversive geometry, hyperbolic geometry and complex analysis. 
(2) Analytic functions, Path integrals, Winding number, Cauchy integral formula and consequences. Hadamard gap theorem, Isolated singularities, Residue theorem, Liouville theorem.4 
(3) Casorati-Weierstrass theorem, Bloch-Landau theorem, Picard's theorems, Mobius transformations, Schwartz lemma, Extremal metrics, Riemann mapping theorem, Argument principle, Rouche's theorem. 
(4) Runge's theorem, Infinite products, Weierstrass p-function, Mittag-Leffler expansion.

Text/References: 
1. Murali Rao & H. Stetkaer, Complex Analysis, World Scientific, 1991 
2. L. V. Ahlfors, Complex Analysis, McGraw-Hill, Inc., 1996 
3. A. R. Shastri, Complex Analysis 
4. Krantz 
5. A. F. Beardon, Geometry of Discrete Groups, GTM Springer Verlag.

Algebraic Topology

(1) Basic notion of homotopy; contractibility, deformation etc. Some basic constructions such as cone, suspension, mapping cylinder etc. fundamental group; computation for the circle. Covering spaces and fundamental group. Simplicial Complexes, CW complexes. 
(2) Simplicial Complexes, CW complexes. Homology theory and applications: Simplicial homology, Singular homology, Cellular homology of CW-complexes, Jordan-Brouwer separation theorem, invariance of domain, Lefschetz fixed point theorem etc. 
(3) Categories and functors; Axiomatic homology theory.

Texts/References: 
1. E. H. Spanier, Algebraic Topology, Tata-McGraw-Hill 
2. A. Hatcher, Algebraic topology, Cambridge University Press.

 

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Syllabus for Annual Foundation School-II (December 2004)

Algebra II

(1) Homological algebra: Derived functors, projective modules, injective modules, free and projective resolutions, tensor, exterior and symmetric algebras, injective resolutions, Ext and Tor. ( 12 lectures)
(2) Basic commutative algebra: Prime ideals and maximal ideals, Zariski topology, Nil and Jacobson radicals, Localization of rings and modules, Noetherian rings, Hilbert Basis theorem, modules, primary decomposition, integral dependence, Noether normalization lemma, principal ideal theorem, Hilbert's Nullstellensatz, structure of artinian rings, Dedekind domains. (12 lectures) 
Text/References: 
1. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra.
2. D. Eisenbud, Commutative algebra with a view towards algebraic geometry.

Complex analysis

(1) Analytic functions, Path integrals, Winding number, Cauchy integral formula and consequences. Hadamard gap theorem, Isolated singularities, Residue theorem, Liouville theorem.4
(2) Casorati-Weierstrass theorem, Bloch-Landau theorem, Picard's theorems, Mobius transformations, Schwartz lemma, Extremal metrics, Riemann mapping theorem, Argument principle, Rouche's theorem.
(3) Runge's theorem, Infinite products, Weierstrass p-function, Mittag-Leffler expansion. 
Text: Complex analysis by Murali Rao & H. Stetkaer, World Scientific, 1991

Algebraic topology

(1) Basic notion of homotopy; contractibility, deformation etc. Some basic constructions such as cone, suspension, mapping cylinder etc. fundamental group; computation for the circle. Covering spaces and fundamental group. Simplicial Complexes, CW complexes.
(2) Simplicial Complexes, CW complexes. Homology theory and applications: Simplicial homology, Singular homology, Cellular homology of CW-complexes, Jordan-Brouwer separation theorem, invariance of domain, Lefschetz fixed point theorem etc. 
(3) Categories and functors; Axiomatic homology theory.
Texts/References
1. E. H. Spanier, Algebraic Topology, Tata-McGraw-Hill
2. A. Hatcher, Algebraic topology, Cambridge University Press. 
Number Theory Arithmetic functions, congruences, quadratic residues, quadratic forms, Diophantine approximations, quadratic fields, Diophantine equations.
Text/References : 
1. A. Baker, Theory of numbers.
2. K. Ireland and M. Rosen, A classical introduction to modern number theory.

Algebra II

 

Balwant Singh (co-ordinator), e-mail: balwantbagga at gmail.com (from 12th to 20th June) 
Sudhir Ghorpade, e-mail: srg at math.iitb.ac.in (from 5th to 14th June) 
S. A. Katre, e-mail: sakatre at math.unipune.ernet.in (from 1st to 28th June)

 

Complex Analysis

 

R. R. Simha (co-ordinator), e-mail: simhahome at yahoo.com (from 12th to 20th June) 
Ravi Kulkarni, e-mail: kulkarni at mri.ernet.in (from 3rd to 28th June) 
Kaushal Verma , e-mail: kverma at math.iisc.ernet.in (from 20th to 28th June)

 

Algebraic Topology

 

Anandateertha Mangasuli, e-mail: anandateertha at gmail.com (from 1st to 17th June) 
Ravi Kulkarni, e-mail: kulkarni at mri.ernet.in (from 3rd to 28th June) 
A. J. Parameshwaran (co-ordinator), param at math.tifr.res.in (from 3rd-5th, 19th to 28th June )

Special Lecture Series (Unity of Mathematics Lectures)

DINESH THAKUR, e-mail: thakur at math.arizona.edu

Associates:

Algebra II

Anuradha Gadre (ganura at math.unipune.ernet.in) 
Himanee Apte (himanee at math.bprim.org) 
Habeeb Basha (habeeb at math.iitb.ac.in)

Complex Analysis

Sameer Chavan (chavansameer at gmail.com) 
Vikram Aithal (vikram at mri.ernet.in), 
Dr. Sanjay Kumar Pant (sanjpant at yahoo.co.in)

Algebraic Topology

Vikram Aithal (vikram at mri.ernet.in), and others 
Sameer Chavan (chavansameer at gmail.com) 
Dr. Sanjay Kumar Pant (sanjpant at yahoo.com)

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 Syllabus

Algebra-II

 (1) Basic commutative algebra-I: Prime ideals and maximal ideals, Zariski topology, Nil and Jacobson radicals, Localization of rings and modules, Noetherian rings, Hilbert Basis theorem, modules, primary decomposition, integral dependence, Noether normalization lemma, principal ideal theorem, Hilbert's Nullstellensatz, structure of artinian rings, Dedekind domains. (12 lectures) 
(2) Introduction to Algebraic Number Theory: (6 lectures) 
(3) Introduction to Algebraic Geometry: (6 lectures)

 Text/References: 
1. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra. 
2. D. Eisenbud, Commutative algebra with a view towards algebraic geometry. 
3. P. Samuel, Algebraic Number Theory.

 Complex Analysis

 (1) Euclidean similarity geometry, inversive geometry, hyperbolic geometry and complex analysis. 
(2) Analytic functions, Path integrals, Winding number, Cauchy integral formula and consequences. Hadamard gap theorem, Isolated singularities, Residue theorem, Liouville theorem.4 
(3) Casorati-Weierstrass theorem, Bloch-Landau theorem, Picard's theorems, Mobius transformations, Schwartz lemma, Extremal metrics, Riemann mapping theorem, Argument principle, Rouche's theorem. 
(4) Runge's theorem, Infinite products, Weierstrass p-function, Mittag-Leffler expansion.

 Text/References: 
1. Murali Rao & H. Stetkaer, Complex Analysis, World Scientific, 1991 
2. L. V. Ahlfors, Complex Analysis, McGraw-Hill, Inc., 1996 
3. A. R. Shastri, Complex Analysis 
4. Krantz 
5. A. F. Beardon, Geometry of Discrete Groups, GTM Springer Verlag.

 Algebraic Topology

 (1) Basic notion of homotopy; contractibility, deformation etc. Some basic constructions such as cone, suspension, mapping cylinder etc. fundamental group; computation for the circle. Covering spaces and fundamental group. Simplicial Complexes, CW complexes. 
(2) Simplicial Complexes, CW complexes. Homology theory and applications: Simplicial homology, Singular homology, Cellular homology of CW-complexes, Jordan-Brouwer separation theorem, invariance of domain, Lefschetz fixed point theorem etc. 
(3) Categories and functors; Axiomatic homology theory.

 Texts/References: 
1. E. H. Spanier, Algebraic Topology, Tata-McGraw-Hill 
2. A. Hatcher, Algebraic topology, Cambridge University Press.
Schedule of Lectures

Lecture	9.00 - 10.00
Lecture	10.30 - 11.30
Lecture	11.45 - 12.45
Tutorial	2.15 - 4.15
UM Lecture	4.30 - 5.30

 Schedule of Lectures / Tutorials

 

Selected Applicants

 

Sr. No.	Name of Participant	Accommodation H- BP Guest House, F- BP Flat, R-Rooms at BP main building	Registration
1	Debasis Sen, ISI, Kolkata	F-3	yes
2	Vineet Kumar Singh, Banaras Hindu Univ.,Varanasi.	H-6	yes
3	Moriya Bhavin K., HRI, Allahabad.	R-5	yes
4	Amrutiya Sanjaykumar Hansraj, HRI, Allahabad.	R-5	yes
5	Ms. Kamlesh Tiwari, Chouksey Engg. College Bilaspur (C.G.)	R-1	yes
6	Sushil Gorai, IISc, Bangalore.	F-3	yes
7	Dr. N.V. Ramana Murty, Andhra Loyola College, Vijaywada, A.P.	F-2	yes
8	Ms. R. Lakshmi Lavanya, Ramanujan Institute, Univ. of Madras, Chennai.	R-2	yes
9	Musavvir Ali, A.M.U., Aligarh (U.P.).	H-8	yes
10	Saidur Rahman Barbhuiya, Hailakandi, Assam.	H-8	yes
11	Gurpreet Singh, Univ. of Delhi, Delhi.	H-7	yes
12	Varinder Kumar, Univ. of Delhi, Delhi.	H-7	yes
13	Venketasubramanian C. G., Univ. of Hyderabad, Hyderabad.	H-5	yes
14	Vadiraja Bhatta, National Institute of Technology, Karnataka, Surathkal	H-5	yes
15	Ms. Mamta D. Gondalia, M.S.University of Baroda, Baroda.	R-2	yes
16	Chandrajeet Singh Yadav, Ujjain, M.P.	R-5	yes
17	Ms. Mala Parihar, Ujjain, M.P.	R-1	yes
18	Chintamani Mohan Namdev, HRI, Allahabad.	R-5	yes
19	Dr. Bankteshwar Tiwari, B.R.D.P.G. College, Deoria, U.P.	F-1	yes
20	Dhorajia Alpesh Madhubhai, M.S.University of Barodara, Varodara.	H-5	yes
21	Ms. Soma Purkait, ISI-Bangalore, Bangalore.	R-2	yes
22	Ms. Soma Purkait, ISI-Bangalore, Bangalore.	R-2	yes
23	Surya Prasath, IITM, Chennai.	H-5	yes
24	Ms. Parvisha, Univ. of Jammu, Jammu, J & K.	R-1	yes
25	Pabitra Barik, ISIcal, Kolkata.	F-3	yes
26	Jagmohan Tanti, CMI, Chennai.	R-5	yes
27	Dr. Avanish Kumar, Bundelkhand University, Jhansi (UP)	F-1	yes
28	Mr. P. Pradhan, IITM, Chennai.	F-3	yes
29	Ms. Anuradha Namjoshi, Sathye College, Mumbai	Self accom.	yes
30	Mr. Dattatraya Patil, A.Nagar, (Mah.)	self Accom.	yes
31	Mr. Arun Kumar Patil, Dept. of Maths, IIT Powai, Mumbai	H-1	yes
32	Dr. Naik Uday H., Dept of Maths, Willingdon College, Sangli (Mah.)	F-2	yes
33	Rohit Joshi, IIT, Kanpur.	Self. Accom.	yes

List of Local participants for AFS-2.

1.	Shirolkar Devendra Dinkar, Dept. Maths, Univ. Pune, Pune.	Local	yes
2.	Ms. Kavita Sutar, BP, Pune	Local	yes
3.	Priyavrat Charudatta Deshpande, Pune.	Local	yes
4.	Vikas S. Jadhav, Pune.	Local	yes
5.	Mrs. Hurratulmalika Juzer Siamwalla, Abida Inamdar College, Pune.	Local	yes
6.	Ms. Manjusha Joshi, BP, Pune	Local	yes
7.	Ms. Aditi Marathe, SP, Pune	Local	yes

List of Students selected but not able to attend AFS-2.

1.	Avanish Kumar, Varanasi.	Not attended
2.	Mr. Gourab Bhattacharya, West Bengal	Not attended
3.	P. Paramanathan, Gandhigram, Tamilnadu	Not attended
4.	Susovan Pal, TIFR, Bangalore.	Not attended
5.	Nilakshi Goswami, Gauhati Univ., Guwahati.	Not attended
6.	Devendra Kumar, K.U., Kurukshetra.	Not attended
7.	Indu Pal, K.U., Kurukshetra.	Not attended
8.	Rahul Garg, A.M.U., Aligarh (U.P.).	Not attended
9.	Ms. Geetan Khurana, Univ. of Delhi, Delhi.	Not attended
10.	A. Thangam, Gandhigram Rural Institute, Gandhigram, TamilNadu.	Not attended
11.	Ratanesh Kumar Dikshit, HRI, Allahabad.	Not attended
12.	Ms. Meena S. Atak, Maharashtra Academy of Engineering, Alandi, Pune.	Not attended
13.	Manoj Kumar Savita, I.T. B.H.U., Varanasi.	Not attended
14.	Amit Kumar Singh, Banaras Hindu University, Varanasi.	Not attended
15.	Siraj Uddin, A.M.U. Aligarh.	Not attended
16.	Dr. Trilok Mathur, Banasthali Vidyapith, Rajasthan.	Not attended
17.	Pravin Garg, Banasthali Vidyapith, Rajasthan.	Not attended
18.	Sanjay Kumar Singh, ISI, Delhi.	Not attended
19.	Anoop T. V., HRI, Allahabad	Not attended
20.	Mr. Advait Kulkarni, Dept. of Maths, IIT Powai, Mumbai	Not attended
21.	Dr. T. Venkatesh, Karnatak University, Belgaum.	Not attended

 

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