Minor edits.

D3127_Terminology/tex/terminology_0.tex

@@ -27,7 +27,7 @@ \section{Summary of Key Takeaways}
   \item A graph comprises a set of \emph{vertices} $\{V\}$ and a set of \emph{edges} $\{E\}$, and is written $G=\{V, E\}$.
   \item Expressing algorithms (mathematically as well as in code) requires a \emph{representation} of a graph, the most basic of which is an \emph{adjacency matrix}.  An adjacency matrix is constructed using an \emph{enumeration} of the vertices, not the vertices themselves.
     \item In addition to the (dense) adjacency matrix representation, we consider three sparse representations: coordinate, compressed, and packed coordinate.  The sparse forms store \emph{indices} defined by the enumeration.
-    \item The \emph{coordinate} and \emph{compressed} forms of the adjacency matrix\footnote{the terems coordinate and compressed are taken from linear algebra.} respectively correspond to representations of the graph theoretical 
+    \item The \emph{coordinate} and \emph{compressed} forms of the adjacency matrix\footnote{the terms coordinate and compressed are taken from linear algebra.} respectively correspond to representations of the graph theoretical 
 \emph{edge list} and \emph{adjacency list}.
 \end{itemize}
 
@@ -135,7 +135,7 @@ \subsection{Graph Representation: Enumerating the Vertices}
   \item A \emph{subgraph} of $G=\{V,E\}$ is a graph $H=\{V, F\}$ such that $F$ is a subset of $E$.
 \item A \emph{spanning tree} is a subgraph of $G$ that is also a tree.
 \end{itemize}
-If any of these properties is important to the correct functioning of an algorithm, either positively or negatively, it will be part of the corresponding requirements of the algorithm.  In general we assume that graphs are not multigraphs, not hyperspase, and that they do not have self-loops.
+If any of these properties is important to the correct functioning of an algorithm, either positively or negatively, it will be part of the corresponding requirements of the algorithm.  In general we assume that graphs are not multigraphs, not hypersparse, and that they do not have self-loops.
 
 \andrew{We should probably have pictures for all of these -- and others -- saves 1k (or 10k) words.}
 

D3129_Views/tex/views.tex

@@ -23,8 +23,8 @@ \section{Introduction}
 % because there is likely a way to get the return value in O(1) time instead of O(log n) when using an id.
 %
 
-The views in this paper provide common ways that algorithms use to traverse graphs. They are a simple as iterating 
-through the set of vertices, or more complex ways such as depth-first search and breadth-first search. They also 
+The views in this paper provide common ways that algorithms use to traverse graphs. They are as simple as iterating 
+through the set of vertices, or more complex such as iterating through the vertices in a depth-first and breadth-first order. They also 
 provide a consistent and reliable way to access related elements using the View Return Types, and guaranteeing expected 
 values, such as that the target is really the target on unordered edges.
 

tex/P1709-preamble.tex

@@ -87,7 +87,7 @@
 
 %% Shortcut for inline code
 \newcommand{\tcode}[1]{%
-  \lstinline[breaklines=true,columns=fullflexible]{#1}
+  \lstinline[breaklines=true,columns=fullflexible]{#1}%
 }
 
 % \usepackage{underscore}   % remove special status of '_' in ordinary text