0. Write a question about Pattern Analysis, readings, or project. (The question can reflect thought about a fundamental issue.) .

1. Features' meaning involves decisions. Explain what a feature is. Give a definition of the term.

2. Choose a real pattern domain. Describe what could be ideal, prototype, template or paradigm patterns there. Indicate what could cause variation from such items.

3. The Bayes decision rule involves maximum values of a probability. If the symbol x represents a vector associated to a real pattern, and there are n different classes it could be from, write out the probabilities and express the rule in terms of them. (Hint: begin with conditional probability; consider classes as numbers 1, 2, ..., n)

4. There are (a. ten; b. ten million) given values of seventy-coordinate patterns from five classes. Describe the advantages and disadvantages of Nearest Neighbor and Nearest Prototype decision rules for these two situations.

5. If the 4.a information is available, a. what can be said about the utility of the data for describing the pattern sets? If we also know that only one class of pattern type is present, b. what can be said now (and what are any necessary assumptions)?

6. Symbols and signs present images that communicate information. Examples depict "skull and crossbones" signifying "poison" and "several curves" meaning "winding road". Choose a pattern of this type from any area; nonvisual examples, e.g., auditory, are fine. Show how the "element of a set of items that can in some useful way be treated alike" definition applies to your choice.

7. Dice and cards transform numbers and images into symbols via word descriptors. Make up a list of special terms that help people recognize patterns in the play of games involving those items.

8. Mathematics is a "science of patterns" according to K. Devlin and L. Steen. Support their belief with an example.

9. The Greeks knew that an integer (they had only positive ones) cubed could be represented as the sum of adjacent odd numbers. E.g., 8 as 5 + 3, 27 as 11 + 9 + 7. Find the representation of 7³. From it describe a feature of integers that helps establish this general truth.

10. The Game of Life due to J. Conway (Scientific American, Oct. 1970, p. 120) involves three rules governing behavior of elements on an array of arbitrary size nxn. "Born" elements mark some previously blank place in the array. "Die" is what happens to an element that fails to exist in the next "generation"; some persist. The rules involve the eight neighbors. Those elements with: a) two or three neighbors survive; b) four or more neighbors die from overcrowding (and are removed in the subsequent array), while those with no or one vanish because of isolation. Any empty array place with exactly three elements in the eight neighbors is a birth location: an element appears there in the next iteration. Two-by-two patterns persist; one-by-three and three-by-one alternate in sequence; many other patterns that persist (or travel) are known. Simulate five or more iterations of this game on an array with side equal to or greater than six. Did you find any interesting patterns?