Projects: Numerical Methods and Applications


    Objective of projects is to achieve an indepth look of a particular numerical technique and an application of it to a question in another area. It is an oppurtunity for you to explore an interest of yours. Projects are optional and are not mandatory part of this course. To see how they affect the grade please view the midterm information sheet.




    Basic Plan: The basic plan for a project is that: you will be given a brief summary of a subject, a list of key words for you to learn. Each one of us will be responsible for finding references, learning these key words and general aspects of the subject. Then two weeks later (say) you will be given some problems to work on. Finally, you will then assemble what you have learnt (brief description of the project and solution to the problems) into a report for submission (say 3-4 weeks after you get the questions).

    Grading: The link provides information on how the projects were graded in the past. I should essentially follow the same.

    Benefits: As will be evident from the link or otherwise, this is not like a test. You can always consult--check the solutions with me. Regular and responsible work are the keys to success. Overwhelming majority of my past students (96 out of 100 odd) really liked doing such a project, they found that learning (a bit) of a related subject quite rewarding. I have some of the past project reports with me, do drop by my office if you would like to see them. Apart from the material one will also get experinence of how to submit a paper/report.


    Areas in which I (think I can) assign Projects are,
    1. Algebra
      • Identifying Abelian Groups with Matrix presentations.
      • Computation in Groups.
      • Finding irreducible factors in polynomials over fields.
    2. Probability
      • Markov Chain Monte Carlo.
      • Applications in Genetics.
    3. Linear Algebra and its applications.
      • Electrical Networks
      • Equilibrium Temperature Distributions
      • Linear Programming
      • Forest management
      • Computer graphics
      • Animal Harvesting
      • Fractals.
    4. Numerical Analysis
      • Stability Analysis for various problems
      • Estimating condition number
      • Toeplitz approximation
      • Convergence properties of iterative mechanisms

    This page : http://www.isibang.ac.in/~athreya/cs205
    [CS II]