IST Linear Algebra and Multivariable Calculus (2017)

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Venue: Dibrugarh University,  Dibrugarh, Assam
Date:  18th, Dec 2017 to 30th, Dec 2017

 


 

School Convener(s)

Name Dhrubajit Choudhury Diganta Borah
Mailing Address Department of Mathematics
Dibrugarh University, Dibrugarh,
Assam
IISER Pune
Dr Homi Bhabha Road, Pashan
Pune-411008

 


 

Speakers and Syllabus

List of Speakers

  1. Bhaba Kumar Sharma, IIT Guwahati
  2. Krishna B Athreya, Iowa State University
  3. Anupam Kumar Singh, IISER Pune
  4. Diganta Borah, IISER Pune

List of course associates

  1. Neelam Saikia, IIT Guwahati
  2. Sudhir Pujahari, HRI Allahabad
  3. Ratna Pal, IISER Pune
  4. Dhrubajit Choudhury, Dibrugarh University

Summary of lectures

Module 1 (Prof. Bhaba Kumar Sharma).

  • Lecture I: Definition of vector spaces and examples of vector spaces.
  • Lecture II: Subspaces of vector spaces and examples.
  • Lecture III: Basis and dimension of vector spaces and Linear transformation.
  • Lecture IV: Direct sum and Invariant subspaces.
  • Lecture V: Linear transformation in matrix form and eigenvalues and eigenvectors.
  • Lecture VI: Primary decomposition Theorem.

 

Module 2 (Prof. Krishna B. Athreya).

  • Lecture I: Definition of open balls and open sets.
  • Lecture II: Convergence sequence, limits, cauchy sequence and completeness.
  • Lecture III: Continuous functions and uniform continuity.
  • Lecture IV: Compact Spaces and their properties.
  • Lecture V: Characterization of compact metric spaces.
  • Lecture VI: Connected spaces and path connected spaces.

 

Module 3 (Prof. Anupam Kumar Singh).

  • Lecture I: Story of classification of finite simple groups, GL(V) action on P(V)
  •  Lecture II: Gaussian elimination, Bruhat decomposition, Action of GL(V) on flags, parabolic subgroups
  • Lecture III: Motivation from computational group theory, Orthogonal groups, O(2), SO(2) and finite subgroups, Dihedral groups
  • Lecture IV: O(3), SO(3), reflections, finite subgroups
  • Lecture V: Platonic solids, demonstration of platonic solids, groups of symmetry
  • Lecture VI: Isometry groups of Rn, Affine Linear transformations, groups of symmetry in plane,Application to robotics and 3D graphics

 

Module 3 (Prof. Diganta Borah).

  • Lecture I: Motivation for Gauss theorema Egregium and its intuitive statement, space curves
  • Lecture II: Geometry of space curves, curvature and torsion.
  • Lecture III: Differential calculus on Rn
  • Lecture IV: Definition of surfaces, examples
  • Lecture V: Differential calculus on surfaces
  • Lecture VI: Definition of Gaussian curvature, computation for the plane, cylinder and sphere, Gauss theorema Egregium, idea of the proof.


Time Table

First Week (Dec 18-23)

Day 9:30-11:00 11:00-11:30 11:30-1:00 1:00-2:30 2:30-3:30 3:30-4:00 4:00-5:00 5:00-5:30
Mon BKS Tea KBA Lunch BKS, NS, SP Tea KBA, DC, RP Snacks
Tue BKS Tea KBA Lunch BKS, NS, SP Tea KBA, DC, RP Snacks
Wed BKS Tea KBA Lunch BKS, NS, SP Tea KBA, DC, RP Snacks
Thu BKS Tea KBA Lunch BKS, NS, SP Tea KBA, DC, RP Snacks
Fri BKS Tea KBA Lunch BKS, NS, SP Tea KBA, DC, RP Snacks
Sat BKS Tea KBA Lunch BKS, NS, SP Tea KBA, DC, RP Snacks
Second Week (Dec 25-30)
Day 9:30-11:00 11:00-11:30 11:30-1:00 1:00-2:30 2:30-3:30 3:30-4:00 4:00-5:00 5:00-5:30
Mon AKS Tea DB Lunch AKS, NS, SP Tea DB, DC, RP Snacks
Tue AKS Tea DB Lunch AKS, NS, SP Tea DB, DC, RP Snacks
Wed AKS Tea DB Lunch AKS, NS, SP Tea DB, DC, RP Snacks
Thu AKS Tea DB Lunch AKS, NS, SP Tea DB, DC, RP Snacks
Fri AKS Tea DB Lunch AKS, NS, SP Tea DB, DC, RP Snacks
Sat AKS Tea DB Lunch AKS, NS, SP Tea DB, DC, RP Snacks

 


 

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 13295 Mr Dilli Ram Chhetri Male Sikkim University Student Sikkim University 2015  
2 13368 Ms Waikhom Warseen Chanu Female NIT Guest Lecturer Manipur University 2009 5/10/2016
3 13504 Mr. Jyoti Bhusan Saha Male National Institute of Technology, Arunachal Pradesh Asst. Prof. Dibrugarh University 2014  
4 13833 Mr Anupam Das Male Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh Asst. Prof. IIT KGP 2008  
5 13869 Mr Gete Umbrey Male RGU PhD Scholar RGU 2014  
6 14024 Dr. Biju Kumar Dutta Male Kaziranga University Asst. Prof. Gauhati University 2003 4/3/2014
7 14261 Mr. Kshittiz Chettri Male SGC Tadong Asst. Prof. Sikkim Manipal University 2006  
8 14459 Mrs Kabita Phukon Female Gargaon College Asst. Prof. Dibrugarh University 2002  
09 14558 Mr. Rajdeep Bora Male Kakojan college Asst. Prof. Gauhati University 2007  
10 14679 Ms. Anushree Das Female Arunachaluniversity Of Studies LECTURER Dibrugarh University 2015  
11 14852 Mr. Ajay Sharma Male Tezpur University Research Scholar Tezpur University 2015  
12 15381 Mr. Nazeer Ansari Male North Eastern Regional Institute Of Science And Tecnology PhD Tezpur University 2015  
13 15388 Mrs. Karabi Saikia Female Dhakuakhana College Asst. Prof. Gauhati University 2004  
14 15503 Mr. Debakanta Buragohain Male Tinsukia College Asst. Prof. Tezpur University 2009  
15 15649 Mr. Chinglensana Phanjoubam Male North Eastern Hill University, Shillong Asst. Prof. Delhi University 2006  
16 15849 Dr. Avinoy Paul Male Cachar College Asst. Prof. Gauhati University 2004 7/1/2014
17 13417  Mr. Birinchi Kumar  Boruah Male  Tezpur University MSc Student  Tezpur University 2015  
18   Dr Dibjyoti Sarma   Sibsagar College        
19   Dr Pranab Kalita   DDU College        
Local  participants (no accommodation)
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 13776 Mr. Jadav Konch Male Dibrugarh University Ph.D. Student Dibrugarh University 2013  
2 13955 Ms. Nijara Konch Female Dibrugarh University M. PHIL Tezpur University 2016  
3 14199 Ms. Sujata Goala Female Dibrugarh University M. Phil Tezpur University 2016  
4 14238 Dr. Nisha Gohain Female Dibrugarh University Asst. Prof Dibrugarh University 2011  
5 15458 Mrs. Dimpee Baruah Female Dibrugarh University Ph D Student Dibrugarh University 2013  
6 15863 Mr Amir Barhoi Male Dibrugarh University Asst. Prof. Dibrugarh University 2014  

 


How to reach

The school will take place in the Department of Mathematics at Dibrugarh University.
Accommodation for the participants and speakers are arranged at the university guest house. One can reach the university by any of the following means:

  1. By air: The Dibrugarh airport (DIB) is located at Mohanbari. From the airport, the university is about 20 km away and can be reached by taxi / auto rickshaw.
  2. By rail: There are two major railway stations--DBRT and DBRG. The university is around 5/6 km away from each of these stations and can be reached by taxi / auto rickshaw.
  3. By bus: When arriving by bus you can alight at Dibrugarh town bus stand which is in front of the DBRT railway station. From there, the university is 5/6 km away and can be reached by taxi / auto rickshaw.

 

 

 

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