Typos

Advanced/Continued Fractions/parts/00 euclidean.tex

@@ -38,7 +38,7 @@ Using the two theorems above, detail an algorithm for finding $\gcd(a, b)$. \par
 Then, compute $\gcd(1610, 207)$ by hand. \par
 
 \begin{solution}
-	Using \ref{gcd_abc} and the division algorthm,
+	Using \ref{gcd_abc} and the division algorithm,
 
 	% Minipage prevents column breaks inside body
 	\begin{multicols}{2}

Advanced/Cryptography/parts/0 euclidean.tex

@@ -36,7 +36,7 @@ Using the two theorems above, detail an algorithm for finding $\gcd(a, b)$. \par
 Then, compute $\gcd(1610, 207)$ by hand. \par
 
 \begin{solution}
-	Using \ref{gcd_abc} and the division algorthm,
+	Using \ref{gcd_abc} and the division algorithm,
 
 	% Minipage prevents column breaks inside body
 	\begin{multicols}{2}

Advanced/Cryptography/parts/3 DLP.tex

@@ -16,7 +16,7 @@ This is the \textit{discrete logarithm problem}, often abbreviated \textit{DLP}.
 \problem{}
 Does the discrete log function even exist? \par
 Show that $\exp$ is a bijection, which will guarantee the existence of $\log$. \par
-\note[Note]{Why does this guarantee the existence of log? Recall our lesson on funtions.}
+\note[Note]{Why does this guarantee the existence of log? Recall our lesson on functions.}
 
 \vfill
 

Advanced/DFAs/parts/0 DFA.tex

@@ -510,7 +510,7 @@ Draw a state diagram for a DFA over an alphabet of your choice that accepts exac
 	\end{tikzpicture}
 	\end{center}
 
-	This automaton rejects all strings with three \texttt{'a'}s in a row. If we count accepted strings, we get the Tribonacci numbers with an offest: $f(0) = 1$, $f(1) = 2$, $f(2)=4$, ... \par
+	This automaton rejects all strings with three \texttt{'a'}s in a row. If we count accepted strings, we get the Tribonacci numbers with an offset: $f(0) = 1$, $f(1) = 2$, $f(2)=4$, ... \par
 
 	\pagebreak
 

Advanced/Definable Sets/parts/3 sets.tex

@@ -112,7 +112,7 @@ Define $\{-2, 2\}$ in $S$.
 
 \problem{}
 Let $P$ be the set of all subsets of $\mathbb{Z}^+_0$. This is called a \textit{power set}. \par
-Let $S$ be the stucture $( P ~|~ \{\subseteq\})$ \par
+Let $S$ be the structure $( P ~|~ \{\subseteq\})$ \par
 
 \problempart{}
 Show that the empty set is definable in $S$. \par

Advanced/Euler's Number/parts/1 limits.tex

@@ -99,7 +99,7 @@ Show that if a sequence $a_n$ has a limit, that limit is unique. \par
 
 	Let $N = \max(N_A, N_B)$. \par
 	Then, $|a_n - A| + |a_n - B| < 2\epsilon\ \forall n > N$, \par
-	which can be writen as $|a_n - A| + |B - a_n| < 2\epsilon\ \forall n > N$. \par
+	which can be written as $|a_n - A| + |B - a_n| < 2\epsilon\ \forall n > N$. \par
 
 	By the triangle inequality, we have \par
 	$|a_n - A + B - a_n| \leq |a_n - A| + |B - a_n|$, \par

Advanced/Graph Algorithms/parts/01 flow.tex

@@ -5,7 +5,7 @@ Say have a network: a sequence of pipes, a set of cities and highways, an electr
 
 \vspace{1ex}
 
-We can draw this network as a directed weighted graph. If we take a transporation network, for example, edges will represent highways and nodes will be cities. There are a few conditions for a valid network graph:
+We can draw this network as a directed weighted graph. If we take a transportation network, for example, edges will represent highways and nodes will be cities. There are a few conditions for a valid network graph:
 
 \begin{itemize}
 	\item The weight of each edge represents its capacity, e.g, the number of lanes in the highway.

Advanced/Lambda Calculus/main.tex

@@ -33,7 +33,7 @@
 % Lazy evaluation (alternate Y)
 % Add a few theorems
 % Better ending -> applications?
-% - nix, comparison to imperitive
+% - nix, comparison to imperative
 
 
 

Advanced/Lambda Calculus/parts/00 intro.tex

@@ -332,7 +332,7 @@ If we look closely, we'll find that $C$ pretends to take three arguments.
 
 \vspace{1mm}
 
-What does $C$ do? Evaluate $(C~a~b~x)$ for arbitary expressions $a, b,$ and $x$. \par
+What does $C$ do? Evaluate $(C~a~b~x)$ for arbitrary expressions $a, b,$ and $x$. \par
 \hint{Evaluate $(C~a)$ first. Remember, function application is left-associative.}
 
 \vfill

Advanced/Lattices/parts/2 orchard.tex

@@ -1,6 +1,9 @@
 \section{Polya's Orchard Problem}
 
-You are standing in the center of a circular orchard of integer radius $R$. A tree of raduis $r$ has been planted at every integer point in the circle. If $r$ is small, you will have a clear line of sight through the orchard. If $r$ is large, there will be no clear line of sight through in any direction:
+You are standing in the center of a circular orchard of integer radius $R$.
+A tree of radius $r$ has been planted at every integer point in the circle.
+If $r$ is small, you will have a clear line of sight through the orchard.
+If $r$ is large, there will be no clear line of sight through in any direction:
 
 \begin{center}
 	\hfill

Advanced/Linear Algebra 101/parts/1 vectors.tex

@@ -58,7 +58,7 @@ Can you develop geometric intuition for their sum and difference?
 
 \definition{Euclidean Norm}
 A \textit{norm} on $\mathbb{R}^n$ is a map from $\mathbb{R}^n$ to $\mathbb{R}^+_0$ \\
-Usually, one thinks of a norm as a way of mesuring \say{length} in a vector space. \\
+Usually, one thinks of a norm as a way of measuring \say{length} in a vector space. \\
 The norm of a vector $v$ is written $||v||$. \\
 
 \vspace{2mm}

Advanced/Linear Algebra 101/parts/2 dotprod.tex

@@ -28,7 +28,7 @@ Show that the dot product is
 \begin{itemize}
 	\item Commutative
 	\item Distributive $a \cdot (b + c) = a \cdot b + a \cdot c$
-	\item Homogenous: $x(a \cdot b) = xa \cdot b = a \cdot xb$ \\
+	\item Homogeneous: $x(a \cdot b) = xa \cdot b = a \cdot xb$ \\
 	\note{$x \in \mathbb{R}$, and $a, b$ are vectors.}
 	\item Positive definite: $a \cdot a \geq 0$, with equality iff $a = 0$ \\
 	\note{$a \in \mathbb{R}^n$, and $0$ is the zero vector.}

Advanced/Proof Techniques/parts/0 intro.tex

@@ -75,7 +75,7 @@ This is a trick we often use when showing that two quantities are equal.
 
 
 \problem{}
-Although $A \iff B$ looks like a single statement, we often need to prove each direction seperately. \par
+Although $A \iff B$ looks like a single statement, we often need to prove each direction separately. \par
 Show that $x \in \mathbb{Z}$ iff $\lfloor x \rfloor = \lceil x \rceil$
 
 \begin{solution}
@@ -97,7 +97,7 @@ Show that $x \in \mathbb{Z}$ iff $\lfloor x \rfloor = \lceil x \rceil$
 \pagebreak
 
 \problem{}
-We don't always need to prove each direction of an iff statement seperately. \par
+We don't always need to prove each direction of an iff statement separately. \par
 
 \begin{itemize}[itemsep = 1mm]
 	\item Convince yourself that we can \say{chain} iffs together: \par

Advanced/Proof Techniques/parts/1 contradiction.tex

@@ -1,8 +1,8 @@
 \section{Proofs by Contradiction}
 
 \definition{}
-A very common (and somewhat contraversial) proof technique is
+A very common proof technique is \textit{proof by contradiction}.
-\textit{proof by contradiction}. It works as follows: 
+It works as follows: 
 
 \vspace{2mm}
 
@@ -18,7 +18,7 @@ Show that the set of integers has no maximum using a proof by contradiction.
 \begin{solution}
 	Assume there is a maximal integer $x$. \par
 	$x + 1$ is also an integer. \par
-	$x + 1$ is larger than $x$, which contradicts our original assumtion!
+	$x + 1$ is larger than $x$, which contradicts our original assumption!
 
 	\vspace{2mm}
 

Advanced/Proof Techniques/parts/2 induction.tex

@@ -229,7 +229,7 @@ For example, see the proof of the statement in \ref{binomsum} on the next page.
 	\textbf{Solution 2:}\par
 	We could also observe that there are $x - 1$ places to put a \say{bar} in
 	the array of ones. This corresponds to $x - 1$ binary positions, and thus
-	$2^{x-1}$ ways to seperate our array of $1$s with bars.
+	$2^{x-1}$ ways to separate our array of $1$s with bars.
 
 	\linehack{}
 

Advanced/Quotient Groups/parts/0 mod.tex

@@ -103,7 +103,7 @@ Show that every element of $A$ is in \textit{exactly one} equivalence class\foot
 
 We now have a proper definition of \say{mod $n$:} \par
 it is the equivalence relation $a \equiv_n b$, which is usually written as $a \equiv b \pmod{n}$. \par
-We will use this definition thoughout this handout.
+We will use this definition throughout this handout.
 
 \note[Note]{
 	This is different than the \say{mod} operator $a ~\%~ b $,

Advanced/Random Walks/parts/1 circuits.tex

@@ -23,7 +23,7 @@ In the definitions below, let $X$ be the set of nodes in a circuit.
 
 		Note that this is different than current and resistance, which aren't functions
 		of two arbitrary nodes --- rather, they are functions of \textit{edges}
-		(i.e, two adjecent nodes).
+		(i.e, two adjacent nodes).
 	}
 
 
@@ -136,7 +136,7 @@ It exists only to create a potential difference between the two nodes.
 \end{center}
 
 \problem{}<onecurrents>
-From the circuit diagram above, we immediatly know that $V(A) = 1$ and $V(B) = 0$. \par
+From the circuit diagram above, we immediately know that $V(A) = 1$ and $V(B) = 0$. \par
 What equations related to the currents out of $x$ and $y$ does Kirchoff's law give us? \par
 \hint{Current into $x$ = current out of $x$}
 

Advanced/Random Walks/parts/3 effective.tex

@@ -168,7 +168,7 @@ Using Ohm's law and Kirchoff's law, calculate the effective resistance $R_{\text
 \pagebreak
 
 We can now use effective resistance to simplify complicated circuits. Whenever we see the above constructions
-(resistors in parellel or in series) in a graph, we can replace them with a single resistor of appropriate value.
+(resistors in parallel or in series) in a graph, we can replace them with a single resistor of appropriate value.
 
 
 \problem{}
@@ -243,13 +243,13 @@ If we place $A$ and $B$ at opposing vertices, what is the effective resistance o
 	and $B$ at \texttt{111...1}. We can divide our cube into $n+1$ layers based on how many ones are in each
 	node's binary string, with the $k^\text{th}$ layer having $k$ ones. By symmetry, all the nodes in each layer
 	have the same voltage. This means we can think of the layers as connected in series, with the resistors
-	inside each layer connected in parellel.
+	inside each layer connected in parallel.
 
 	\vspace{2mm}
 
 	There are $\binom{n}{k}$ nodes in the $k^\text{th}$ layer. Each node in this layer has $k$ ones, so
 	there are $n - k$ ways to flip a zero to get to the $(k + 1)^\text{th}$ layer. In total, there are 
-	$\binom{n}{k}(n - k)$ parellel connections from the $k^\text{th}$ layer to the $(k + 1)^\text{th}$
+	$\binom{n}{k}(n - k)$ parallel connections from the $k^\text{th}$ layer to the $(k + 1)^\text{th}$
 	layer, creating an effective resistance of 
 	$$
 		\frac{1}{\binom{n}{k}(n - k)}

Advanced/Retrograde Analysis/parts/02 easy.tex

@@ -197,7 +197,7 @@ There is one more piece on the board, which isn't shown. What color square does
 \begin{solution}
 
 	Which piece performed the last capture on a black square? It couldn't have been a white pawn, which haven't moved.
-	It couldn't have been the white king, which is trapped; or the black king, which is restriced to white squares.
+	It couldn't have been the white king, which is trapped; or the black king, which is restricted to white squares.
 
 	\vspace{2mm}
 

Advanced/Retrograde Analysis/parts/04 hard.tex

@@ -76,7 +76,7 @@ Show that he must be on C7.
 
 	The pawn on A6 came from B7 by capturing one piece, and the pawn on B5 came from D7 by capturing two.
 	(Note that this may not be true if we don't assume the pawn on C7 is real.)
-	We've counted three captures, all on white squares, so the white black-square bishop must have been captured seperately.
+	We've counted three captures, all on white squares, so the white black-square bishop must have been captured separately.
 
 	\vspace{2mm}
 

Intermediate/An Introduction to Graph Theory/parts/0 intro.tex

@@ -7,7 +7,7 @@ This means that the sets $\{1, 2, 3\}$ and $\{3, 2, 1\}$ are identical.
 
 \definition{}
 A \textit{graph} $G = (N, E)$ consists of two sets: a set of \textit{vertices} $V$, and a set of \textit{edges} $E$. \par
-Verticies are simply named \say{points,} and edges are connections between pairs of vertices. \par
+Vertices are simply named \say{points,} and edges are connections between pairs of vertices. \par
 In the graph below, $V = \{a, b, c, d\}$ and $E = \{~ (a,b),~ (a,c),~ (a,d),~ (c,d) ~\}$.
 
 \begin{center}

Intermediate/Probability/main.tex

@@ -252,7 +252,7 @@
 	\problem{}
 	A pharmaceutical study shows that a new drug causes negative side effects in 3 of every 100 patients.
 	To check the number, a researcher chooses 5 random people to survey.
-	Assuming the study is accurate, what is the probabilty of the following? \\
+	Assuming the study is accurate, what is the probability of the following? \\
 
 	\begin{enumerate}
 		\item None of the five patients experience side effects.

Misc/Moscow Puzzles/problems/120.tex

@@ -2,7 +2,7 @@
 
 \begin{document}
 
-	\problem{One Hundred and Fourty-Five Doors}
+	\problem{One Hundred and Forty-Five Doors}
 	A prisoner was thrown into a medieval dungeon with 145 doors. Nine, shown by black bars, are locked, but each one will open if before you reach it you pass through exactly 8 open doors. \\
 	You don't have to go through every open door but you do have to go through every cell and all 9 locked doors. If you enter a cell or go through a door a second time, the doors clang shut, trapping you. \\
 

Misc/Moscow Puzzles/problems/239.tex

@@ -2,7 +2,7 @@
 
 \begin{document}
 
-	\problem{One Hundred and Fourty-Five Doors}
+	\problem{The Air Parade}
 
 	Volodya asked, ``What plane did you fly during the air parade?'' His father sketched a formation of 9 planes.
 

Misc/Warm-Ups/regex.tex

@@ -151,7 +151,7 @@
 
 
 	\problem{}
-	If you'd like to know more, check out \url{https://regexr.com}. It offers an interative regex prompt, as well as a cheatsheet that explains every other regex token there is. \par
+	If you'd like to know more, check out \url{https://regexr.com}. It offers an interactive regex prompt, as well as a cheatsheet that explains every other regex token there is. \par
 	You will find a nice set of challenges at \url{https://alf.nu/RegexGolf}.
 	I especially encourage you to look into this if you are interested in computer science.
 \end{document}

resources/macros.sty

@@ -30,7 +30,7 @@
 	\ifnum #1 > 0
 		% The $$ are required around \bigstar.
 		% the special \odot chess piece breaks
-		% star sizing if they are ommited.
+		% star sizing if they are omitted.
 		\loop
 			{\oncolor $\bigstar$}%
 		\ifnum\count255 < #1

resources/ormc_handout.cls

@@ -578,7 +578,7 @@
 	\IfNoValueF{#2}{\@customlabel{#2}{#1}}
 }
 
-% Make a new secion type.
+% Make a new section type.
 % Args: command, counter, title.
 \newcommand\@newobj[3]{
 	\NewDocumentCommand{#1}{ m d<> }{