Math 331: Mathematical Problem Solving with Computers
Fall 2001

• Prof. Rasul Shafikov. email: shafikov@math.sunysb.edu
• Office hours: Mon 2-3 PM in Math Learning Center (Physics, A-127); Thu 1-2 PM in Math Tower 4-102

• A description of the course, including grading policies, text , etc.
• The preferred email client is pine, but you are welcome to use something else if you are more comfortable with it. The tutorial Getting Started with Pine covers all the basic stuff, and a bit more, and the Pine User's Guide has some more information, as well.
• Using a web browser (which you must already be doing if you are reading this) will also be quite handy. I like Netscape Navigator, (or its other version, Mozilla, but any other browser such as Microsoft Internet Explorer is OK if you want. You can get Netscape and MSIE from Instructional Computing, although more recent versions are available from Netscape and Micro$oft.
• We may sometimes have documents on the web which are in PDF form (Portable Document Format). To read these you will need to have a copy of the freely available Adobe Acrobat Reader on your machine. You can get this from Adobe.
• In fact, I prefer PostScript to PDF for various reasons, but will usually (not always) provide both. If you need to look at a PostScript document, a free viewer can be had from the GhostScript site.
• We will be using Maple extensively. Some locally produced notes (which will change as the semester progresses) are available HERE Other useful information about using Maple can be found in various places on the web, including a nice collection of some stock answers to maple questions at MIT, a collection of maple resources (including a tutorial or two) at Indiana University, the Maple lab manual from Worcester Polytechnical Institute, and, of course, the home of Maple at Waterloo Maple Software. You can purchase a student version of maple for your own computer, if you want.
• Since we will be doing most of our work (in class at least) on a Unix system, you should look over Using Unix. Also useful are the UNIXhelp tutorial, and sections of UNIX is a four-letter word.

• Homework assignment 1 (in pdf format). Due September 22 by 11:59 PM. Maple work sheet with solutions
• Homework assignment 2 (in pdf format). Due October 20 by 11:59 PM. Maple work sheet with solutions
• Homework assignment 3 (in pdf format). Due November 3 by 11:59 PM.
• Homework assignment 4 (in pdf format). Due December 1 by 11:59 PM. A picture that illustrates Newton's method described in the assignment.
• How to submit your homework: From a Unix shell, use the command

  submit331 -sectno file1 file2 ... filen
  

  where sectno is your section number (1 or 2) and file1, file2, etc. are the Maple worksheets you want to submit
  We strongly recommend that you use one worksheet per problem, and that you choose appropriate names for your files. For example, suppose you are in section 1 and you solved problems 01, 03, 06, saving the corresponding worksheets in the files prob01.mws, prob03.mws, prob06.mws. Then you can submit them by typing

  submit331 -1 prob01.mws prob03.mws prob06.mws
  

• In order to make it easier for you to keep up with the lectures, any Maple worksheets from each lecture will be available from this page. These are saved in files named by the date of the lecture HERE. Depending on how your browser is set up, you might be able to just click on the worksheets, or you might have to right-click and select "save link as..." and then open them from maple once you have saved a copy. If you are logged in to the mathlab system, this directory is /home/mat331/Worksheets and should be readable by anyone, so you can load the worksheets directly into your maple session.

  Note that Maple 6 can load worksheets directly from the web.

• Homework policy: Each exercise is worth 10 points and can be turned in at any time before its ``expiration date''. You can work on any number of problems per homework sheet (none to all, usually 5). However, at the end of the semester, we will expect you to have turned in at least 2/5 of the exercises assigned. If you do more, we will pick your best grades. If you do less, the missing grades will be counted as zeros. This will determine 20% of your final grade for the class.

• Recommended reading for Project 1 (in pdf). A printed copy of the document can be purchased from the Math Undegraduate office.
• The first project, dealing with least-squares fitting, is due on October 9 before class. The data you need to do the project can be found here, in a file corresponding to your username. If you find fitting lines insufficiently challenging, you may instead fit an ellipse to some randomly generated data. Make sure that you give a complete explanation of the method you are using. (Explain the method, not the maple used to implement it.)
• The second project, dealing with the Julia and Mandelbrot sets of a quadratic polynomial in C, is due November 15 before class. The data you need to do the project can be found HERE. Use the constant c that corresponds to your name.
• Here's a list of some books that you might find useful for project 2:
  1. L.Carlson, T. Gamelin, "Complex Dynamics", (Springer Verlag);
  2. K. Falconer, "Fractal Geometry", (Wiley & Sons);
  3. M. Barnsley, "Fractals Everywhere", (Academic Press Professional);
  4. H. Peitgen, H. Jurgens, D. Saupe "Fractals for the Classroom : Introduction to Fractals and Chaos" (Springer Verlag);
• Recommended reading for Project 3 is HERE
• NEW Project Three deals with different fractals and their dimensions. Due date: December 13 in class. This is the last assignment.

• You can check your grades online HERE (Final Grades posted)

• Sorting algorithms: visualization demos (Java enabled browser required)
• Java applets visualizing Julia and Manderbrot sets