TEW Real Analysis, Algebra and Linear Algebra (2019)
Venue:  Dibrugarh University, Dibrugarh, Assam 
Date:  30th, Sep 2019 to 5th, Oct 2019 
Name  Dr Ankur Bharali  Dr Palash Dutta 
Mailing Address 
Department of Mathematics 
Department of Mathematics 
Speakers with their affiliations:
Name of the speaker 
Position 
Affiliation 
Bhaba Kumar Sarma  Professor  Department of Mathematics IIT Guwahati, Assam781039 
Tazid Ali  Professor  Department of Mathematics Dibrugarh University, Assam786004 
Surajit Borkotokey  Professor  Department of Mathematics Dibrugarh University, Assam786004 
List of tutors:
Name of the tutor 
Position 
Affiliation / official postal address 
Dr. Ankur Bharali 
Associate Professor 
Department of Mathematics 
Dr. Palash Dutta 
Assistant Professor 
Department of Mathematics 
Dhrubajit Choudhury 
Assistant Professor 
Department of Mathematics 
Syllabus:
The topics covered covered by Speakers
Name of the Speaker with affiliation  No.of Lectures  Detailed Syllabus 
Prof. S. Borkotokey Dibrugarh University 
8  Finite, countable and uncountable sets, ℝ as complete ordered field, Sequences and their convergence, Continuous functions and their properties. 
Prof. Tazid Ali Dibrugarh University 
8  Groups, Subgroups, Quotient groups, Action of groups on set, Class equations, Sylow theorems and applications. 
Prof. B. K. Sarma IIT Guwahati 
8  Vector space, linearly independent, linear span, basis, linear transformation, eigenvalues and eigenvectors, diagonalization. 

Lectures by S. Borkotokey, Dibrugarh University

In the first two lectures the notions of countable and uncountable sets were introduced. Suitable examples were discussed and the participants were also asked to give their own examples. Then ℝ as complete ordered field was introduced and different properties were discussed. In the next two lectures the notion of sequence and their convergence was discussed. Sufficient examples were discussed to drive home the concepts. The next two lectures were devoted to the other properties of sequences placing Real sequences as the central focal point of discussion. In the last two classes the notion of continuous functions and their properties were discussed with many examples and exercises.

Lectures by Tazid Ali, Dibrugarh University

In the first two lectures the notion of symmetry of different objects was introduced to construct group structures. Suitable examples were discussed and the participants were also asked to give their own examples. Then gradually the notion of abstract idea of group was introduced. In the next two classes, different notions like subgroup, normal subgroup, quotient group were discussed with many examples. The notion of cyclic group was deliberated at length and different properties of cyclic group were discussed. In the next two lectures the notion of group action was introduced. Then the notion of conjugacy relation in a group was discussed. How the conjugacy relation introduces an equivalence relation and defines the conjugacy classed were elaborated. Sufficient examples were discussed to drive home the concepts. In the last two classes Sylow's three theorems were discussed one by one. Many exercises and related applications of the three theorems were solved.

Lectures by B. K. Sarma, IIT Guwahati

In the first two lectures, the basic notions of Vector spaces, subspaces, linear span, linearly dependent and independent sets, basis and dimension were discussed with plenty of examples and deriving the important results. In the next two lectures, linear transformations and their matrices were discussed at length with many examples and exercises. The next two lectures were devoted for discussing eigenvalues and eigenvectors of linear operators on finite dimensional vector spaces, placing diagonalizibility as the central focal point of discussion. The last two lectures were devoted to discuss inner products on vector spaces leading to the spectral theorem for normal operators on finite dimensional inner product spaces.
Time Table
Day  Date  Lecture 1 9:3010:30 
10:35 to 10:55 
Lecture 2 11:0012:00 
Lecture 3 12:001:00 
1:00 to 2:20 
Lecture 4 2:303:30 
3:35 to 3:55 
Discussion/ Tutorial 4:005:00 
5:05 to 5:30 
Mon  30/09  TA  Tea  SBK  BKS  L u n c h 
TA  Tea  AB, PD  T e a & S 
Tues  01/10  BKS  TA  SBK  BKS  PD, DC  
Wed  02/10  SBK  BKS  TA  SBK  AB, DC  
Thu  03/10  BKS  TA  SBK  BKS  AB, DC  
Fri  04/10  TA  SBK  BKS  TA  AB, DC  
Sat  05/10  SBK  BKS  TA  SBK  AB, DC 
Full forms for the abbreviations of speakers and tutors:
 BKS: B. K. Sarma
 TA: Tazid Ali
 SBK: Surajit Borkotokey
 AB: Ankur Bharali
 PD: Palash Dutta
 DC: Dhrubajit Choudhury
List of actual Participants
Sr  SID  Full Name  Gender  Affiliation  Position in College/ University  University/ Institute M.Sc./M.A.  Year of Passing M.Sc./ M.A  Ph.D. Deg Date 
1  27221  Mrs Smita Sahu  Female  Dibru college  Assistant professor  Dibrugarh University  2000  
2  28671  Ms. Pranami Phukan  Female  North eastern Regional Institute of Science and Technology  PhD  North eastern Regional Institute of Science and Technology  2017  
3  28672  Ms. Jyoti Saikia  Female  North eastern Regional Institute of Science and Technology  PhD  North eastern Regional Institute of Science and Technology  2018  
4  28758  Ms. Manjuri Dutta  Female  North eastern Regional Institute of Science and Technology  PhD  North eastern Regional Institute of Science and Technology  2018  
5  28805  Mr. Basanta Borah  Male  Majuli College  Asst. Prof.  65  1999  
6  28980  Mr. Surajit Dutta  Male  C N B College, Bokakhat  Asst. Prof.  Dibrugarh university.  1994  
7  28988  Mr Amir Barhoi  Male  Duliajan College  Asst. Prof.  Dibrugarh  2014  
8  28991  Mr Hrishikesh Boruah  Male  Duliajan College  Asst. Prof.  Dibrugarh  2004  07/05/2013 
9  29039  Dr. Nisha Gohain  Female  Directorate of Open and Distance LearningDibrugarh University  Asst. Prof.  Dibrugarh University  2011  24/10/2016 
10  29464  Mr. Birinchi Kumar Boruah  Male  Dibrugarh University  PhD  Tezpur University  2015  
11  29532  Mrs. Dimpee Baruah  Female  MAJULI COLLEGE  Asst. Prof.  Dibrugarh University  2013  
12  29676  Mr. Nazeer Ansari  Male  North eastern Regional Institute of Science and Technology  guest lecturer  Tezpur university  2015  
13  29708  Mr. Amitav Doley  Male  DHSK College  Asst. Prof.  Dibrugarh University  2011  
14  29774  Mr. Champak Kr. Neog  Male  North Eastern Regional Institute of Science and Technology  PhD  Tezpur University  2016  
15  29844  Mr. Lham Tashi  Male  North Eastern Regional Institute of Science and Technology  PhD  Rajiv Gandhi University  2017  
16  29958  Dr Dr Rupam Kr Kr Gogoi  Male  Sibsagar College, Joysagar  Asst. Professor  Gauhati University  1996  16/06/2015 
17  29998  Dr. Ananta Kumar Dutta  Male  DHSK College  Associate Professor  Guwahati University  1993  12/11/2018 
18  30025  Mr Raju Kumar Phukan  Male  JIST,JORHAT  Asst professor  Gauhati University,guwahati  2002  
19  30029  Mr. Mukul Buragohain  Male  Digboi college  Asst. Prof.  Dibrugarh university  1997  
20  30106  Mr. Mayzul Alom Hussain  Male  Rajiv Gandhi University  Research Scholar  GAUHATI UNIVERSITY  2014  
21  30124  Dr. Soumendra Goala  Male  Dibrugarh University  Ph. D.  Tezpur University  2013  02/09/2019 
22  30131  Mr. Abhigyan Mahanta  Male  Dibrugarh University  PhD Student  Dibrugarh University  2017  
23  30155  Dr. Devanjan Hazarika  Male  DHSK College  Asst. Prof.  University of Delhi  1993  14/12/2017 
24  30169  Mr. Madhurya Hazarika  Male  Dibrugarh University  PhD  Dibrugarh University  2017  
25  30170  Mr. Jibonjyoti Buragohain  Male  Pandu College  PhD  Dibrugarh University  2017  
26  30172  Dr. Debozani Borgohain  Female  Dibrugarh University  Asst. Prof.  Gauhati university  2010  21/07/2017 
27  30173  Ms. Parishmita Boruah  Female  Dibrugarh University  PhD  Tezpur University  2017  
28  30185  Mr. Joydeep Borah  Male  Dibrugarh University  PhD  M.Sc.  2016  
29  30188  Mr Bijit Bora  Male  Dibrugarh University  M.Phil Student  Dibrugarh University  2018  
30    Mr. Ritu Dutta  Male  Dibrugarh University  Research Scholar  
31    Mr. Idweep Jyoti Gogoi  Male  Dibrugarh University  Research Scholar  
32    Mr. Rubul Moran  Male  Dibrugarh University  Research Scholar  
33    Mr. Budheswar Deka  Male  Dibrugarh University  Research Scholar  
34    Mr. Hirak Jyoti Dehingia  Male  Dibrugarh University  Research Scholar 
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