Skip to main content
Contents Dark Mode Prev Up Next \(\newcommand{\inv}{\mathrm{inv}} \newcommand{\deg}{\mathrm{deg}} \newcommand{\des}{\mathrm{des}} \newcommand{\Des}{\mathrm{Des}} \newcommand{\Inv}{\mathrm{Inv}} \newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\Bin}{\mathrm{Bin}} \newcommand{\comp}{\mathrm{Comp}} \newcommand{\ss}{\mathfrak{S}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Section 1.1 Eight Foundational Questions
We will be studying combinatorics and graph theory. We will be addressing the first six of the following eight foundational questions of combinatorics and graph theory:
Enumeration: How many ____ are there?
Classification: Which objects have ____ property?
Expectation: How likely is ____?
Optimization: What is the best ____?
Ethics: What are the ethical implications that arise when applying ____ to the physical, biological, health, or social sciences?
Sampling and Construction: How do I generate examples of ____?
Existence: Does ____ exist?
Estimation: Approximately how many ____ are there?
