Data.tex

\chapter{Data}
\section{Interview}
Some students remembered taking proofs in high school in geometry.
Some students were taking proofs contemporaneously in philosophy.
Some of the students studying proof in philosophy found them disturbing, expressing a preference for geometrical proofs.
Some students remembered having to furnish proofs of geometrical facts, also facts about prime numbers and sets.
Some students knew that CSE2500 treated proofs because they would be used in later courses. Students did not know why proofs would be used later, and were generally happy to hear some example uses.
Though students were asked whether they made use of proofs spontaneously, none of those interviewed gave an example.
Some students preferred to articulate with code, and some (who were dual computer science / math) sometimes preferred mathematical symbols, depending upon the context.
Some students do wish to convince themselves of things, such as tractable execution times, and correctness. Though students were asked whether they made use of proofs for this purpose, none of those interviewed claimed to do so, rather they mentioned going carefully over their algorithm construction, and considering cases.

In interviews, the students almost all chose to dicuss proofs by mathematical induction.


\section{Homework}
Table : Some example errors
Let x be empty
$|xy| \leq p, so xy = 0^p$\\
$|xy| \leq p; let x = 0^{p+r}, y = 0^{p+r}, 0 < r < p$\\
Let’s choose $|xy| = p$\\
$0^{p+1}0^b1^p \neq 0^{p+1}1^p \therefore xy^2z \not\in \mathcal{L}$
where $\mathcal{L} = \{0^i1^j, i \neq j\}$\\
we choose $s = 0^{p+1}1^p$ within $|xy|$\\
thus $\neq 0^p1^{p+1}$\\
Let $x = 0^a, y = 0^b1^a$\\
$x = 0^{p-h}, y = 0^h$\\
$x = 0^i, y = 0^i, z = 0^i1^j$