LinearAlgebra
MT 1223 Linear Algebra
(January-April 2020)
Instructors: Dr Anupam Singh (January-February)
Dr Kaneenika Sinha (March-April)
Follow the link https://sites.google.com/site/iisermth1223/home/notes for the rest of the semester.
Audience: 1st year, 2nd semester BS-MS students at IISER Pune
Tutors: Prashant Gitte, Snehal Lawande, Tumpa Mahato, Jewel Mahajan, Kuntal Chakraborty, Mitesh Modasiya
Schedule: Thursday and Friday 2:45 - 3:45
Tutorial: Wednesday (B1, B2) 10:15 - 11:15, (B3, B4) 11:30 - 12:30
Quizzes will be held at 5:30 pm on Tuesdays (except Feb first week). Please see the "weekly topics covered" section below.
Evaluation: Continuous evaluation! Mid sem 30%, end-sem 30%, Quizzes (best 8 out of 10) 5% each.
Prerequisite: None from mathematics but a lot from individuals such as willingness to work hard, pay attention to what is going on in the class, do home-works etc.
Goal of the course: To learn Linear Algebra which is a foundational course to science and engineering.
Proposed content:
Structure of finite dimensional vector spaces, matrix operations and systems of linear equations, Gauss-Jordan elimination, Matrix inversions, determinants, subspaces, linear combinations, basis and dimension, linear transformations and geometry, rank nullity theorem, coordinates and change of basis.
Dot product on R^n, orthogonality and Gram Schmidt process, eigenvalues and eigenvectors, diagonalizability, applications to linear ODE, discrete dynamical systems, least squares method.
Textbooks:
Linear algebra : K. Hoffman and R. Kunze
Introduction to linear algebra : G. Strang
Linear algebra done right: S. Axler
Linear algebra with applications: O. Bretscher
Computational Softwares : We plan to learn how to use SAGEmath. http://www.sagemath.org
Weekly Topics Covered
02/01/2020 - Solving a system of linear equations - Algebraic, Geometric and Computational method for 2-by-2
03/01/2020 - Solution of 2-by-2 equations, "three rules" and reduction.
09/01/2020 - Field, Equivalent system of equations, Row operations
10/01/2020 - Row-reduced matrix, row-reduced echelon matrix, Gaussian elimination
14/01/2020 - Quiz at 5:30 pm
16/01/2020 - Vector space and examples
17/01/2020 - Liner combination, linear independence
21/01/2020 - Quiz at 5:30 pm
23/01/2020 - Basis, subspace
2401/2020 - Coordinates with respect to a basis, change of basis
28/01/2020 - Quiz at 5:30 pm
30/01/2020 - Linear transformation
31/01/2020 - Matrix of a linear transformation w.r.t fixed basis
01/02/2020 - Extra class at 10AM on SAGEmath
Here are SAGE practice sheets
Sage-I, Sage-II, Sage-III, Sage-IV, Sage-V
Sage for Linear Algebra by Beezer
03/02/2020 - Quiz at 5:30 pm
06/02/2020 - Matrix of linear transformation with base change, Similarity of matrices
07/02/2020 - Applications - Page ranking algorithm, Leslie matrix for population growth
The original paper of Brin & Page
Page-ranking + Leslie matrix notes
11/02/2020 - Quiz at 5:30 pm
13/02/2020 - no class
14/02/2020 - no class
Assignment - VII (questions I asked in class)
Mid sem exam 24/02/2020 at 3pm
Please follow the link below for the rest of the classes.