## Weekly outline

• CT 501 - Systems and Signal theory (3-0-0-3)
Instructor: Aditya Tatu, Room 1206, Ext: 540

• Dear Students,
You can come tomorrow (Monday, 28 Nov) between 11:00 am - 12:30 pm to my office to inspect your answer sheets. Please pass this message to other colleagues.
• End-sem exam solutions
• ### 25 July - 31 July

• Lecture 1: Introduction to the course.
Why do we study Math? - Abstraction.

• Lectures 2 & 3: Canceled.

• ### 1 August - 7 August

• Lecture 4: Equivalence relations
• Lecture 5: Introduction to Vector Spaces
• Lecture 6: Examples of Vector spaces, Subspaces.
• Assignment 1: Equivalence relations.
Due date: Thursday August 1, 2011. (Submission in class)

• ### 15 August - 21 August

• Assignment 2: Vector spaces
Due date: 25 August, 2011
• Lecture 10: Linear transformations
• Lecture 11: Matrix multiplication as the only linear transformation between finite dimensional vector spaces

• ### 22 August - 28 August

• Lecture 12: Range and Nullspace of a linear transformation, Geometry of linear equations.
• Lecture 13: Gaussian Elimination, LU factorization

• ### 29 August - 4 September

• Lecture 14: Permutation matrices, Matrix Inverse, Relation between pivots and solvability of linear equations (n x n case)

• ### 5 September - 11 September

• Lecture 15: Solving a homogeneous linear system with n variables and m equations
• Lecture 16: Solving Ax = b, with m equations in n variables with n > m. Introduction to scalar product.
• Assignment 3: Vector spaces and Linear transformations
To be discussed on Friday 16 Sept 2011
• Assignment 4 (Self study). Starts from the 2nd page in the pdf. From the book: Analysis in Vector spaces - Mustafa Ackoglu, Paul Bartha & Dzung Minh Ha

• References for Vector space:

1) Analysis in Vector space: Ackoglu, Bartha & Ha (Short loan)
2) Survey of Modern Algebra: Birkhoff, MacLane
3) Lectures on Linear Algebra: I. M. Gelfand
4) Abstract Linear Algebra: Morton L. Curtis
(Short loan)
5) Linear Algebra, An introductory approach: Charles W. Curtis (Short loan)
6) Linear Algebra (UTM): Serge Lang
7) Finite-Dimensional Vector Spaces: Paul R. Halmos
8) You will find what you want in most books on Abstract Algebra, for eg: books by Michael Artin, Hoffman & Kunze, Herstein etc.
• Lecture 17: Four fundamental subspaces for a matrix

• ### 12 September - 18 September

• Lecture 18: Four fundamental subspaces for a matrix
• Lecture 19: Four fundamental subspaces of a matrix
• Lecture 20: Direct sum, Orthogonal subspaces.

• ### 19 September - 25 September

• Lecture 21: Least Square solution to Ax = b
• Lecture 22: Least square solution to Ax = b, Projection to Range(A)
• Lecture 23: Gram-Schmidt Orthogonalization

• ### 26 September - 2 October

• Lecture 24: QR Factorization, Fourier transforms, Field of Complex numbers

• ### 17 October - 23 October

• Whosoever notices the assignment, please pass it on to your colleagues.
We will discuss this in the week after Diwali.

• Advanced Mathematics: PC-511, Winter 2011-12
Instructor: Prof. Samaresh Chatterji
• Assignment 6: Convergence of sequences
• Assignment 7: NVS & Operator norm
• Reference on Completion of Normed Vector Spaces & Lp spaces:
The Lebesgue Stieltjes Integral- A Practical Introduction, M. Carter & B. van Brunt.
Refer pages:
24-25: Definition of Step functions
39-40: Definition of Riemann Integral
46-48: Dirichlet function
135-138: Completion of spaces (general)
138-150: L1,Lp spaces

For those interested in understanding Lebesgue Integral, refer Chapter 4
• MATLAB assignment (Voluntary)