Let's look at how E.coli replicates itself.
E.coli grows exponentially (during some period)The consequence is..
Clone of me
On each day, a clone of me will clone herself into two. How many days do I need to wait to see 1M of me?
A logarithm of base $b$ for value $y$ is the power to which $b$ is raised to get $y$: $log_b(y)=x$ ($b^x=y$).
e.g,
$log_28=3$ ($2^3=8$)
Logarithmic algorithms, sweet!
Floor and ceiling
The floor of $x$ (written as $\lfloor x \rfloor$) takes real value $x$ and returns the greatest integer $\le x$; the ceiling of $x$ (written as $\lceil x \rceil$) takes real value $x$ and returns the least integer $\ge x$
Modulus
The modulus (or mod) function returns the remainder of an integer division; written as $n \% m $.
Summations
Useful summations that have closed-form solutions.
$\sum\limits_{i=1}^n i = \frac{n(n + 1)}{2}$
$\sum\limits_{i=1}^n i^2 = \frac{2n^3 + 3n^2 + 1}{6} = \frac{n(2n+1)(n+1)}{6}$
$\sum\limits_{i=1}^{logn} n = n logn$
$\sum\limits_{i=1}^n \frac{1}{2^i} = 1 - \frac{1}{2^n}$
$\sum\limits_{i=0}^{n}2^i = 2^{n+1} - 1$
$\sum\limits_{i=1}^{n}\frac{i}{2^i} = 2 - \frac{n + 2}{2^n}$
