Here are hints for some of the definitions in the crossword puzzle.
Definition 1 (click to display)
A term in group theory = Distance traveled in a year by a planet.
Definition 2 (click to display)
A term in vector algebra = long and narrow (as a shape) + type of long sandwich + space
Definition 3 (click to display)
P(x)/Q(x)
Definition 4 (click to display)
A term in ring algebra: I=aR.
Definition 5 (click to display)
$ z \in \mathbb{C} $
Definition 6 (click to display)
A labeled structure in a poset.
Definition 7 (click to display)
$ sts = tst $, for example.
Definition 8 (click to display)
A dividing wall in a flying machine.
Definition 9 (click to display)
$ G \times X \to X, (g,x) \mapsto g \cdot x $
Definition 10 (click to display)
A set of cones whose union is the whole space.
Definition 11 (click to display)
Which language is this?
Definition 12 (click to display)
$ \mathbbm{1}_A: A \to \{0,1\} $
Definition 20 (click to display)
A dividing wall that doesn’t traverse.
Definition 22 (click to display)
See also this image.
Definition 25 (click to display
Look up the name of the corresponding geological period.
Definition 26 (click to display)
A certain type of commutative ring.
Definition 29 (click to display)
A term in graph theory = a big vegetal thing that spreads out.
Definition 31 (click to display)
Also known as Gaussian elimination.