The Annual Foundation School I (2010 )

Venue: PU, Chandigarh
Dates: 9-29 December 2010


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


School Convener(s)

Name Sudesh Kaur Khanduja
Gurmeet Kaur Bakshi
Mailing Address Professor, Centre for Advanced Study in Mathematics
Panjab University
Associate Professor,
Centre for Advanced Study in Mathematics
Panjab University


Speakers and Syllabus 


Algebra SKK-Sudesh Kaur Khanduja

Panjab University, Chandigarh

PS-Parvati Shastri

University of Bombay

GKB-Gurmeet Kaur Bakshi

Panjab University, Chandigarh

Analysis AK - Ajay Kumar

University of Delhi

SB-Savita Bhatnagar

Panjab University, Chandigarh

RBJ-Renu Bajaj

Panjab University, Chandigarh

Differential Geometry &Topology CSA - C.S. Arvinda

TIFR, Banglore

SD-Satya Deo

HRI, Allahabad

ARS-A.R. Shastri

IIT Bombay

UM-Lecture Series I.B.S.P-I.B.S. Passi

Panjab University, Chandigarh




Speaker Lectures  Detailed  Syllabus
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. 
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 Gibb’s Phenomenon.
Dr Renu Bajaj 6 Existence of local solutions for first order systems, maximal time of existence, finite time blow-up, global solutions. Gronwall inequality,Continuous dependence on initial data and on the vector field on  bounded intervals. Examples of linearsystems, Fundamental solutions.
Prof  A R Shastri 12 Revision of  Calculus of n-variables, smoothness of maps defined  on  arbitrary subsets of Rn Inverse and  implicit function  theorem. Manifolds in Rn(as `submanifolds'), tangent space,  induced map on the tangent spaces. Regular and critical points,  Sard's theorem(statement only),  regular inverse image.  Classification of 1-dim. 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 Frenet-Serret 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 E3, 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, Borsuk-Ulam Theorem

Hopf Degree theorem  Lefschetz Theory of vector fields, Poincare-Hopf Theorem.  


 Selected Applicants



AFS-I 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


AFS-I 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 12-14 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, ISBT-sector 17 and ISBT-sector 43. ISBT-sector 17 is about 4 km and ISBT-sector 43 is about 8 km from Panjab University. Cycle rickshaw/Auto rickshaw/Taxi charging approx. Rs. 30/ Rs 50/ Rs 100 from ISBT-sector 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)
0172-2541132 (O)
09872989234 (M)