Most of the course information is now at the Spring 2015 Laulima “Wiki”.

## Word Distance Project

Word distance metrics in one of the following databases:

Make a definition of distance between words. For instance, you could use *the number of occurrences of $A$ and $B$ exactly 9 words apart, divided by the number of occurrences of $A$ and $B$ at most 9 words apart*.

Select 10 words (or more) and compute all distances between them.

Check whether your distance $d(A,B)$ satisfies the following axioms for a metric (if they don’t, your definition may still be okay if it has other nice features):

$d(A,A)=0$

$d(A,B)=d(B,A)$

$d(A,B)\le d(A,C)+d(C,A)$

Make a graphic representation of the 10 words so that words $A$ and $B$ are close to eachother in the graphic if $d(A,B)$ is small.

## Pocket cube project

There are many articles available about Rubik’s cube but not as many about the simpler pocket cube (2x2x2).

Here are some draft instructions:

First solve the white side.

Get two of same color in the layer

Face the opposite two and have white face up.

Do:

$$

R^{-1} D R L D^{-1} L^{-1} R^{-1} D R

$$

Now we have the layer.

Now to swap two corners (recall that yellow should be opposite white),

face them towards you and do

$$

L^{-1} U^{-1} L F U F^{-1} L^{-1} U L U^2

$$

Then finally do (with problem corners facing you and white at bottom)

$$R U R^{-1} U R U^2 R^{-1} U^2

$$

(possibly repeat)

But if two already solved put solved corners furthest away from you

do $R U …$

If not done yet,

put the newly solved bottom *right* in bottom *left* and repeat $R U…$ maybe twice (this may intermittently mess up the two solved ones!).

*To complete this project, your write-up will have to show exactly how the algorithm works on a couple of random cubes that I provide.
*