IST Linear Algebra and Multivariable Calculus (2017)

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

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.

• Here is the Dibrugarh University official homepage: https://www.dibru.ac.in
• More informations about Dibrugarh city can be found at http://dibrugarh.nic.in