TEW Linear Algebra, Analysis of several variables, Probability Theory (2016)
Venue: 
Brahmananda Keshab Chandra College (BKC College), Kolkatta 
Dates: 
1^{st} to 6^{th} Feb 2016 
Convener(s)  Speakers, Syllabus and Time table  Applicants/Participants 
Name  Neeta Pandey  Prof. Mahuya Datta 
Mailing Address  Associate Professor Department of Mathematics BrahmanandaKeshab Chandra College Kolkata – 700 108 
Indian Statistical Institute, 203, B. T. Road, Kolkata 700108. 
Syllabus Covered
(a) Linear Algebra (7 lectures)
Resource Person: Prof. Sumitra Purakayastha, Applied Statistics Division, Indian Statistical Institute, Kolkata
Vector space over a field. Subspaces. Sum and intersection of two subspaces.Linearly independent set. Linear span. Basis of a vector space. Existence of Basis, Replacement Theorem. Extension theorem. Extraction of basis from a set of generators. Linear transformation. Rank and Nullity theorem.
Matrix of a Linear transformation. Row and column rank of a matrix. Linear homogeneous system of equations : Solution space as a subspace. Homogeneous system AX = 0 in n unknowns : Necessary and sufficient condition for the consistency of the system. Solution of the system of equations (Matrix method, Cramer's Rule). Characteristic equation of a square matrix. Eigen value and Eigenvector. CayleyHamilton Theorem. Simple properties of Eigen value and Eigen vector.
Inner Product Spaces. Norm. Euclidean vector spaces (EVS), Triangle Inequality and CauchySchwarz Inequality in EVS. Orthogonality of vectors. Orthonormal basis, GramSchmidt process of orthonormalisation. Elementary matrices. Congruence of matrices. Real Quadratic form Reduction to Normal Form.
Texts followed:
(i) Rao, A.R. and Bhimasankaram P. (2000). Linear Algebra. Second edition. Hindustan Book Agency.
(ii) Kumaresan, K. (2000). Linear Algebra: A Geometric Approach. PHI.
(b) Analysis of Several Variables (6 lectures)
Resource Persons: Prof. Swagato K. Ray (4lectures), Theoretical Statistics and Mathematics Division, Indian Statistical Institute, Kolkata
And
Prof. Rudra P. Sarkar (2 lectures), Theoretical Statistics and Mathematics Division, Indian Statistical Institute, Kolkata
Functions of several variables, Continuity, Partial derivatives, Differentiability, Chain Rule, Inverse function theorem and Implicit function theorem. Taylor’s theorem, Maxima and minima. Lagrange’s multiplier method.Multiple integrals, Repeated integrals, The Jacobian theorem, Line, surface and volume integrals.
(c) Probability (5 lectures)
Resource Person: Prof. KrishanuMaulik ,Theoretical Statistics and Mathematics Division, Indian Statistical Institute, Kolkata
Notion of random experiments, events and their probability. Probability of some basic models using combinatorial methods. Axiomatic definition of probability and study of conditional probability, Bayes theorem, independence. Univariate and multivariate distribution functions, their moments and their properties. Probability generating functions and their applications. Continuous distributions, examples and properties. Transformations of random variables with some interesting examples. A quick introduction to Poisson process. A brief review of different modes of convergence with reference to laws of large numbers and central limit theorem.
TimeTable
01.02.2016 Monday 
Inauguration 
Lecture I 10:2511:40 
Lecture II 11:451:00 
Lunch 1:002:00 
Lecture III 2:003:15 
Tea 3:153:30 
Discussion 3:304:45 
Snacks 4:455:00 

S.P. 
K .M. 

S. K. R. 

S.K.R. 


Date and Day 
Lecture I 10:0011:15 
Tea 11:1511:45 
Lecture II 11:451:00 
Lunch 1:002:00 
Lecture III 2:003:15 
Tea 3:153:30 
Discussion 3:304:45 
Snacks 4:455:00 
02.02.2016 Tuesday 
S. P. 

S. K. R. 

K. M. 

K.M 

03.02.2016 Wednesday 
S. P. 

S. K. R 

K. M 

S.K.R. 

04.02.2016 Thursday 
S. P. 

S. K. R 

K. M 

K.M 

05.02.2016 Friday 
S. P. 

R. P. S. 

K. M 

S. P. 

06.02.2016 Saturday 
S. P. 

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R. P. S. 

R.P.S 
Valedictory

S. P. – Prof. Sumitra Purakayastha (Linear Algebra)
S. K. R. – Prof. Swagato K. Ray (Analysis of Several variables (Differentiation)
K. M. – Prof. Krishanu Maulik (Probability Theory)
R. P. S. – Prof. Rudra P. Sarkar (Analysis of Several variables (Integration))
Actual Participants 
Sr.n  SID  Full Name  Gender  Affiliation  State  Position in College/ University  University / Institute M.Sc./M.A.  Year of Passing M.Sc./ M.A  Ph.D. Degree Date 
1  5551  Mr Vineet Kumar  Male  SABOUR COLLEGE  Bihar  Student  Appeared / Awaiting Result  
2  5572  Dr. Gopal Chandra Ghosh  Male  RISHI BANKIM CHANDRA COLLEGE  West Bengal  Asst. Professor  University of Kalyani  2000  Sep 25, 2006 
3  5581  Dr. Kapil Gupta  Male  Department of Computer Applications  Haryana  Asst. Professor  Jawaharlal Nehru University  2005  Dec 27, 2012 
4  5599  Mr. Rajib Mukherjee  Male  K N College (Employed)  West Bengal  Asst. Professor  University of Kalyani  2003  
5  5608  Dr. Shyamali Dewan  Female  Bhairab Ganguly College  West Bengal  Asst. Professor  University of Kalyani  2000  Jun 1, 2006 
6  5619  Mr. Subhasis Saha  Male  Guru Nanak Institute of Technology  West Bengal  Asst. Professor  University of Calcutta  2013  
7  5635  Mr. Sagar Chakraborty  Male  UNIVERSITY OF KALYANI  West Bengal  MSc STUDENT  University of Kalyani  2015  
8  5764  Mr. Ahmed Sheikh Hossain  Male  Brahmananda Keshab Chandra College, Kolkata  West Bengal  Asst. Professor  University of Calcutta  1999  
9  5769  Mr. Sanjoy Biswas  Male  Gurunnak Institute of Technology  West Bengal  Asst. Professor  University of Kalyani  2012  
10  5770  Mr. Ranjan Das  Male  SERAMPORE COLLEGE  West Bengal  Asst. Professor  CALCUTTA UNIVERSITY  1997  
11  5771  Dr. Md. Sabiar Rahman  Male  GOBARDANGA HINDU COLLEGE  West Bengal  Asst. Professor  VISVABHARATI  2000  Jun 23, 2014 
12  5790  Dr. Sampa Mitra  Female  Rishi Bankim Chandra College for Women  West Bengal  Asst. Professor  University of Calcutta  2000  Nov 12, 2010 
13  5840  Ms. Munmun Biswas  Female  Brahmananda Keshab Chandra College  West Bengal  Asst. Professor  Indian Statistical Institute  2010  
14  5856  Mr. Nabin Chandra Biswas  Male  DUM DUM MOTIJHEEL COLLEGE  West Bengal  Asst. Professor  IIT GUWAHATI  2012  
15  5866  Miss Paramita Sen  Female  Dum Dum Motijheel College  West Bengal  Assoc. Professor  Calcutta University  1988  Sep 1, 2005 
16  5890  Dr. Subhrojyoti Debnath  Male  Brahmananda Keshab Chandra College  West Bengal  Asst. Professor  University of Kalyani  2006  Jun 12, 2013 
17  6045  Dr. Alakesh Maity  Male  VIDYASAGAR METROPOLITAN COLLEGE  West Bengal  Asst. Professor  University of Calcutta  1997  Feb 16, 2009 
How to reach
 Bus: Get down at either Dunlop or ISI or BonHooghly bus stop. Then take a cycle rickshaw from rickshaw stand to the college.
 Local Trains: Either of the following:
 Sealdah –Dankuni local train to Baranagar Road Station. Then take a cycle rickshaw from rickshaw stand to the college.
 Any local train to Belghoria station. Any one of the bus numbers 201, 237 or 234/1 to either Dunlop or ISI or BonHooghly bus stop. Then take a cycle rickshaw from rickshaw stand to the college.
 Metro train: Get down at Dumdum station. Take bus number DN 9/1 to either Dunlop or ISI or BonHooghly bus stop.
 Car: From Shyambazar take B. T. Road and turn right at BonHooghly crossing. From Barrackpore take B. T. Road and turn left at ISI bus stop.