Understand how to use mathematical induction to prove a statement
about an arbitrary number $n$ (see notes
with homework 7). Be able to prove that the sum of the first $n$
numbers (i.e. $1+2+3+\cdots +n$) is equal to $\frac{1}{2}n(n+1)$.
Be able to prove that the sum of the first $n$
odd numbers (i.e. $1+3+5+\cdots +(2n-1)$)
is equal to $n^2$.
Know how to construct the Fibonacci numbers (p. 55). Understand
the "converging quotients" discussion on pp. 56, 57, 58 and why
the limit of the fractions defined by adjacent Fibonacci
numbers (the $(n+1)$st over the $n$th) is equal to $\frac{1}{2}
(1+\sqrt{5})$.
Most facts about the Fibonacci numbers need to be proved using
induction (since the numbers themselves are defined inductively).
See Mindscapes 7 and 8 on pp. 62, 63.
Be able to convert numbers from base-$10$ to base-$2$ and back (see notes). Be able to perform long division with base-$10$ and base-$2$ numbers, in order to implement the division algorithm (p. 69). Understand why the remainder is always strictly less than the divisor.