The Annual Foundation School I (2010 )
Venue:  PU, Chandigarh 
Dates:  929 December 2010 
Convener(s)  Speakers, Syllabus and Time table  Applicants/Participants 
Name  Sudesh Kaur Khanduja 
Gurmeet Kaur Bakshi 
Mailing Address  Professor, Centre for Advanced Study in Mathematics Panjab University Chandigarh160014 
Associate Professor, Centre for Advanced Study in Mathematics Panjab University Chandigarh160014 
Speakers
Algebra  SKKSudesh Kaur Khanduja
Panjab University, Chandigarh 
PSParvati Shastri
University of Bombay 
GKBGurmeet Kaur Bakshi
Panjab University, Chandigarh 
Analysis  AK  Ajay Kumar
University of Delhi 
SBSavita Bhatnagar
Panjab University, Chandigarh 
RBJRenu Bajaj
Panjab University, Chandigarh 
Differential Geometry &Topology  CSA  C.S. Arvinda
TIFR, Banglore 
SDSatya Deo
HRI, Allahabad 
ARSA.R. Shastri
IIT Bombay 
UMLecture Series  I.B.S.PI.B.S. Passi
Panjab University, Chandigarh 
Syllabus
Speaker  Lectures  Detailed Syllabus 
Algebra  
Prof Parvati Shastri  8  Modules over commutative rings, Modules over a PID, Matrices over a PID and Structure Theorem, canonical forms 
Prof Sudesh Khanduja  8  Review of basic field theory, Separable and normal extensions, algebraically closed fields, splitting fields, Norm and Trace and their properties. Hilbert Theorem 90, The idea behind Galois theory , Fundamental theorem of Galois theory. 
Dr Gurmeet K. Bakshi  8  Cyclotomic Extensions & Cyclic Extensions, Application of the Cyclotomic extensions and Galois theory to the constructability of regular polygons. Historical aspects of the solvability of polynomial equations, Solvability of polynomial equations by radicals, The inverse problem of Galois theory. Computation of Galois groups over Q for small degree polynomials. 
Analysis  
Prof Savita Bhatnagar  12  Measures, Integration, Normed spaces, Baire category theorem.Open mapping theorem, Closed graph theorem, Uniform boundedness theorem. 
Prof Ajay Kumar  6  Review of Fourier series, Basic Fourier Analysis on groups Z of integers, unit circle T and the real line R generalized Reimann lebesgue lemma, The Gibbâ€™s Phenomenon. 
Dr Renu Bajaj  6  Existence of local solutions for first order systems, maximal time of existence, finite time blowup, global solutions. Gronwall inequality,Continuous dependence on initial data and on the vector field on bounded intervals. Examples of linearsystems, Fundamental solutions. 
Topology  
Prof A R Shastri  12  Revision of Calculus of nvariables, smoothness of maps defined on arbitrary subsets of R^{n }Inverse and implicit function theorem. Manifolds in R^{n}(as `submanifolds'), tangent space, induced map on the tangent spaces. Regular and critical points, Sard's theorem(statement only), regular inverse image. Classification of 1dim. Manifolds.
Richness of smooth functions, smooth partition of unity, immersions,submersions, embeddings. Abstract manifolds, different definitions of tangent space, examples Orientability. Embedding theorems for manifolds in to Euclidean spaces. Normal bundleand tubular nbd theorem. Homotopy and stability. Transversality, Vector fields and isotopies. 
Prof C S Aravinda  6  FrenetSerret Theory of Curves, congruence of curves, classification of compact surfaces with boundary (examples, and statement), tangent and cotangent bundles, Riemannian metrics, differential forms, first and second fundamental form of surfaces in E^{3}, normal curvature, Codazzi equations, congruence of surfaces, Gauss Bonnet theorem(statement). 
Prof Satya Deo  6  Transversality, Oriented intersection theory, Brauwer degree Winding number and Brauwer separation theorem, BorsukUlam Theorem
Hopf Degree theorem Lefschetz Theory of vector fields, PoincareHopf Theorem. 

AFSI being organised in Chandigarh in December 2010 and is funded by NBHM.
List of selected participants
Ms Margam Archana  University of Hydrabad 
Mr Anuj Kumar More  IISER Pune 
Ms Debika Dey  Hydrabad University 
Ms Dilpreet Kaur  IISER, Mohali 
Mr Husney Parvez Sarwar  IIT Bombay 
Mr James Philip  ST Dominc's college ,Kerala 
Ms Julee Srivastava  University of Allahabad 
Mr K. Premkumar  Pondicherry University 
Ms Kalpana  Banasthali University 
Mr Koteswara Rao Gulla  University of Hyderabad 
Ms Kuldeep Kaur  IIT Ropar 
Ms Leetika  PU ,Chandigarh 
Mr Madhav Reddy B  University of Hydrabad 
Ms Megha Goyal  PU ,Chandigarh 
Mr Munish Kansal  PU, Chandigarh 
Mr Nilesh Dagadu Mundlik  University of pune 
Ms Nisha Sharma  PU ,Chandigarh 
Mr P.Ramulu  University Of Hydrabad 
Mr Parkash E  Madurai Kamraj University 
Mr Prasad Tayaji Bathe  Pune University 
Ms Pratibha Manohar  University of Rajasthan 
Ms Pratima Rai  PU ,Chandigarh 
Ms Priyanka Rastogi  University of Rajasthan 
Ms Radhamani V  Madurai Kamraj University 
Mr Rakesh Ratnakar Pawar  IIT, Bombay 
Mr Ramandeep Behl  PU, Chandigarh 
Mr Ramesh K  IIT Bombay 
Mr Rami Reddy Pasupula  University of Hyderabad 
Ms Rani Kumari  University of Delhi 
Ms Rashmi Agarwal  University of Rajasthan 
Ms Revathi V.M.  Madurai Kamraj University 
Mr Sanjeev Kumar  PU ,Chandigarh 
Mr Sayan Chakraborty  IIT Bombay 
Mr Shiv Prasad  IISER Mohali 
Mr Surinder Kumar  PU, Chandigarh 
Mr Surya Ratna Prakash Dumpa  NIT, Karnataka 
Mr Vikash  IIT Ropar 
Mr Srinivas Majeti  Osmania University, Hyderabad 
How to reach

AFSI being organised in Chandigarh in December 2010 and is funded by NBHM.
How to reach Panjab University
The city beautiful of Chandigarh located at the foot hills of Himalayas is the capital of both Punjab and Haryana states. The city is situated at a distance of 250 kms from Delhi. Chandigarh is well connected by public transport (rail, road, air). Panjab University is within a distance of 1214 km from ISBT/Railway Station / Airport. The weather during December is cold. Woolen clothes are required here in the month of December. All participants will be provided accommodation.
How to reach Panjab University from ISBT
There are two inter state bus terminus, ISBTsector 17 and ISBTsector 43. ISBTsector 17 is about 4 km and ISBTsector 43 is about 8 km from Panjab University. Cycle rickshaw/Auto rickshaw/Taxi charging approx. Rs. 30/ Rs 50/ Rs 100 from ISBTsector 17 and Rs. 40/ Rs 80/ Rs 125 from ISBT sector 43 are available at these inter state bus terminus. Local buses are also available.
How to reach Panjab University from Railway Station
Chandigarh railway station is about 10 km from Panjab University. Auto rickshaw/ taxi charges approximately Rs. 100/ 150 for transporting to Panjab University. Local buses are also available from the local bus stand near the railway station.
How to reach Panjab University from Air Port
Chandigarh air port is about 14 km from Panjab University. Auto rickshaw/ taxi charges are approximately Rs. 125/ 200.
Postal Address & telephone numbers:
Prof Madhu Raka & Dr. Gurmeet K. Bakshi
Department of Mathematics, Panjab University
Chandigarh 160014
Tel 0172 2534501(O)
01722541132 (O)
09872989234 (M)
09914001444(M)