Math 331: Mathematical Problem Solving with Computers
Professor Sutherland (section 1), or Stewart Mandell (section 2)
Fall 1997

• 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.

Maple Worksheets on Assorted Topics

• 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 ( ), ).
• Four different ways to plot a circle: as functions, polar, parametrically, and implicitly. (, .)
• Algebraic messing around: making the equation of an ellipse look like one (, .)
• Some glider related things: flying a glider exactly 10 units (also ), and the ancillary routines whereHit and bisect, both as maple worksheets only.
• 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

---

Exercise 1: pretty basic email.   due September 9 or 10.

Send an email message to the appropriate instructor of this course.

---

Exercise 2: Netsurfing.   due by 9/18/97.

You should have received a topic via email. Use the web to locate several URLs related to your topic, and email the best of them to your intructor. Note that sending the entire output of your search is inadequate; use judgement and pick the best of them.

---

Exercise 3: Elementary Maple.   due by 9/24/97.

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 ).

---

Project 1: Least Squares Fitting.   due 10/20/97 or 10/21/97.

This project is to write a paper about 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 line (two ways), a quadratic or a cubic, and a circle. The description is also available as PostScript for easy printing.

---

Exercise 4: More Maple.   due 10/29/97 or 10/30/94.

There are 3 problems, which you should solve. Maple will most likely be useful. The problems are also available in PostScript format for easy printing, or as a Maple worksheet.
The solutions are also now available, in the usual collection of formats ( , , or ).

---

Exercise 5: Animating Epi- and Hypo-cycloids.   due 11/10/97 or 11/11/94.

In this exercise, you need to produce an animation of a wheel rolling around the inside and outside of a circle. (This is the epicycloid and hypocycloid). The handout contains a fair amount of sample code, so you probably want a copy of the Maple worksheet, although PostScript is there too. The solutions are also now available, in the usual collection of formats ( , , or ).

---

Project 2: A differential equations model of a glider   due 12/3/97 or 12/4/94.

In this project, you are to analyze a simple model of glider flight, giving both a good expository discussion and answering some specific questions. It is also here in PostScript for your printing pleasure.

---

Project 3: Fractally Stuff   due 12/17/97 or 12/18/97.

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 drawlist.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).

---

---