1. Design a representation of an angle (ie a direction in the plane)
   such that a linear classifier (perceptron) can learn an arbitrary
   range of angles.  Eg "angles between 270 and 20 degrees -> yes,
   others -> no.  So 0 -> yes, 90 -> no.

2. Make up some data per problem 1 and train a perceptron on it.

3. Design a representation that allows a perceptron to learn a UNION
   of TWO ranges of angles, eg "angles between 10 and 20 or 70 and 120
   -> yes, others -> no".  You may assume some minimum separation and
   angular resolution in the target concept, but be sure to state your
   assumptions.

4. Make up some data per problem 3 and train a perceptron on it.

5. Design a representation of the location of a point on the surface
   of a sphere (usually latitude & longitude are used for the Earth)
   and design a representation that allows a linear classifier to
   handle the rule "all points within distance D of point X".

6. Figure out how to read in the digits dataset pointed to by the
   class home page.  Train a perceptron to distinguish one subset of
   digits from another, eg 7's from 9's or 3+5 from 1+7.  Plot it's
   learning curve (training set performance) & its generalization
   (test set performance) curve, ie as a function of training.
   (NOTE: just train on raw pixel values.  You won't get very good
   performance, that's okay.  You can downsample the images if you
   want.)

Hand this in as few pages of printed paper.
If you want to show me your code, you can give me a url or file
location.