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\title{Chapter 1, Intro}

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\section*{functions you should be familiar with}
polynomials, rational functions, roots/rational powers, trig functions
(and their ``inverses''), exponential (and their inverse, the logarithm)

(etymology of trig functions, draw triangle and show the relations)

\section*{techniques of proof}
$\sqrt{2}$ is irrational
infinitely many primes
(like an essay: intro, body, conclusion)
inductive proof

other stuff...

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