TEW Real Analysis, Algebra and Linear Algebra (2019)

Venue:	Dibrugarh University, Dibrugarh, Assam
Date:	30th, Sep 2019 to 5th, Oct 2019

School Convener(s)
Name	Dr Ankur Bharali	Dr Palash Dutta
Mailing Address	Department of Mathematics Dibrugarh University Assam-786004	Department of Mathematics Dibrugarh University Assam-786004

Speakers with their affiliations:

Name of the speaker	Position	Affiliation
Bhaba Kumar Sarma	Professor	Department of Mathematics IIT Guwahati, Assam-781039
Tazid Ali	Professor	Department of Mathematics Dibrugarh University, Assam-786004
Surajit Borkotokey	Professor	Department of Mathematics Dibrugarh University, Assam-786004

List of tutors:

Name of the tutor	Position	Affiliation / official postal address
Dr. Ankur Bharali	Associate Professor	Department of Mathematics Dibrugarh University, Assam-786004
Dr. Palash Dutta	Assistant Professor	Department of Mathematics Dibrugarh University, Assam-786004
Dhrubajit Choudhury	Assistant Professor	Department of Mathematics Dibrugarh University, Assam-786004

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 9:30-10:30	10:35 to 10:55	Lecture 2 11:00-12:00	Lecture 3 12:00-1:00	1:00 to 2:20	Lecture 4 2:30-3:30	3:35 to 3:55	Discussion/ Tutorial 4:00-5:00	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 n a c k 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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