Math 331: Mathematical Problem Solving with Computers
Professor Sutherland
Spring 1998

• A description of the course, including grading policies, text (there is none), etc.
• We suggest you use pine for dealing with email. 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. We suggest Netscape Navigator, but Microsoft Internet Explorer is OK if you want. You can get either from IC's Network Apps page. Very useful search sites are Yahoo! and AltaVista. Acme Labs provides an interface to many search engines on a single page.
• We will be using Maple extensively. Some locally produced notes (which will change as the semester progresses) are available, either web browsable or as a PostScript document. 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.
• Here are a few things about unix inPostscript. You might also care to browse the UNIXhelp tutorial, or sections of UNIX is a four-letter word, both of which have tutorials.
• Cryptography related items:

  The chapter of my course notes devoted to doing cryptography in maple. This is, of course, still being worked on.

  Some notes on cryptography written by Charles Blair of the University of Illinois (also available as Postscript or LaTex).

  Learning About Cryptography, by Terry Ritter of Ritter Software Engineering. He also provides a good list of cryptography-related books. Two I particularly like are

  • A Course in Number Theory and Cryptography (Graduate Texts in Mathematics, No 114) by Neal I. Koblitz. (Hardcover, 235 pages, Springer Verlag, 1994)
  • The Codebreakers; The Comprehensive History of Secret Communication from Ancient Times to the Internet, by David Kahn. (Hardcover, 1181 pages, 1996, basically a reprint of the 1967 classic.)

  The Cryptography FAQ has all sorts of good stuff in it.

  There are a large number of links to cryptography related sites on the Quadralay Cryptography Archive, and on Crypto-Log: The Internet Guide to Cryptography. However, the latter hasn't been updated since 1996, and has quite a few dead links. Also, the International Cryptography Pages has both links and brief descriptions of currently used cryptographic algorithms.

  The ideas of several classical cryptosystems are breifly covered in Classic Ciphers and their Weaknesses, as well as a summary of RSA.

  RSA Data Security, owners of the patent on the RSA algorithm, provide Frequently Asked Questions on Cryptography, which is good, if a little self-serving.

  Edgar Allan Poe's story "The Gold Bug"(1853) is one of the earliest short stories to have cryptography play a prominent role in the plot, and also one of the best. Its certainly worth reading, if you never have.

Maple Worksheets on Assorted Topics

• Maple worksheets from class sessions (by date).

• Adaptive plotting, and in particular graphing y=sin(1/x) ( , .)
• 2D parametric plots. (, .)
• Using tubeplot (,
.)
• Using least squares to fit data to a line (, ), and to a cubic polynomial ( ), ). See also some notes on this.
  
• Four different ways to plot a circle: as functions, polar, parametrically, and implicitly. (, .)
• Some samples of fractals: One way to make a Sierpinski gasket (also ), a fractal living in 3-d, namely a Sierpinski pyramid (also ), and a function with a self-similar, fractal graph.

Deliverables

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Exercise 1: pretty basic email.   due by 30 January.

Send an email message to the instructor of this course.

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Exercise 2: Elementary Maple.   due 2/14/98.

There are 5 pretty easy problems, which you should use maple to solve. Hand in a printout of the maple worksheet you used to solve them. The problems are available in PostScript format for easy printing.
The solutions solutions are also now available, in the usual collection of formats ( , , or ).

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Project 1: Least Squares Fitting.   due 3/2/98.

This project is to explore the method of fitting a curve to data known as "least squares". In it, you need to explain the method, and fit data to a circle, and examine two ways of fitting to a line. The description is also available as PostScript for easy printing. You may find it helpful to glance at my notes for this subject (also ).


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Exercise 3: Secret Stuff.   due 4/2/98.

There are three problems related to cryptography to solve; the second one is different for each student, and was sent to you via email. If you didn't get one or want to look at somebody else's, you can find them here.

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Project 2: Cryptography.   due 4/9/98.

You are to research, implement, and describe a cipher of your choosing, avoiding, of course, the ones covered in class. As usual, there is a PostScript description, as well.

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Project 3: Fractally Stuff   due 5/14/98.

For this project, you are to make and discuss some self-similar fractals. As usual, we also have it in some other formats ( , ). Also of use might be the support file turtle.txt.

You may find it useful to look around the web for pages about fractals. For example, Fractals for Beginners and Exploring Fractals might be worth a look. (There are plenty more where those came from, but be forewarned: there are lots of pages with many mathematically incorrect statements on the web. The above documents are mostly correct, though some statements should be taken with a grain of salt).

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