Weekly outline

  • CT 501 - Systems and Signal theory (3-0-0-3)
    Instructor: Aditya Tatu, Room 1206, Ext: 540
    • ForumNews forum
    • FileCT501_summary File
    • 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
    • Fileendsemsoln File

  • 25 July - 31 July

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


    • Lectures 2 & 3: Canceled.

  • 1 August - 7 August

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

  • 8 August - 14 August

  • 15 August - 21 August

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

  • 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
    • FileAssignment 3 File
    • 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
    • FileAssignment 4 File


    • 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

  • 3 October - 9 October

  • 10 October - 16 October

  • 17 October - 23 October

    • FileAssignment 5: Metric spaces File
    • 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
    • FileAdvanced Mathematics- SC 511 File
    • Assignment 6: Convergence of sequences
    • FileAssignment 6 File
    • Assignment 7: NVS & Operator norm
    • FileAssignment 7 File
    • Reference on Completion of Normed Vector Spaces & Lp spaces:
      The Lebesgue Stieltjes Integral- A Practical Introduction, M. Carter & B. van Brunt.
      e-book in Lecture/Aditya Tatu/CT501/
      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)
    • FileMATLAB Assignment File

  • 24 October - 30 October

  • 31 October - 6 November

  • 7 November - 13 November

  • 14 November - 20 November

  • 21 November - 27 November