From 6a5e02a8ac5e5b4ce37af0036056edc170c003a1 Mon Sep 17 00:00:00 2001 From: Mark Date: Sat, 9 Dec 2023 18:17:22 -0800 Subject: [PATCH] Typos --- Advanced/Continued Fractions/parts/00 euclidean.tex | 2 +- Advanced/Cryptography/parts/0 euclidean.tex | 2 +- Advanced/Cryptography/parts/3 DLP.tex | 2 +- Advanced/DFAs/parts/0 DFA.tex | 2 +- Advanced/Definable Sets/parts/3 sets.tex | 2 +- Advanced/Euler's Number/parts/1 limits.tex | 2 +- Advanced/Graph Algorithms/parts/01 flow.tex | 2 +- Advanced/Lambda Calculus/main.tex | 2 +- Advanced/Lambda Calculus/parts/00 intro.tex | 2 +- Advanced/Lattices/parts/2 orchard.tex | 5 ++++- Advanced/Linear Algebra 101/parts/1 vectors.tex | 2 +- Advanced/Linear Algebra 101/parts/2 dotprod.tex | 2 +- Advanced/Proof Techniques/parts/0 intro.tex | 4 ++-- Advanced/Proof Techniques/parts/1 contradiction.tex | 6 +++--- Advanced/Proof Techniques/parts/2 induction.tex | 2 +- Advanced/Quotient Groups/parts/0 mod.tex | 2 +- Advanced/Random Walks/parts/1 circuits.tex | 4 ++-- Advanced/Random Walks/parts/3 effective.tex | 6 +++--- Advanced/Retrograde Analysis/parts/02 easy.tex | 2 +- Advanced/Retrograde Analysis/parts/04 hard.tex | 2 +- .../An Introduction to Graph Theory/parts/0 intro.tex | 2 +- Intermediate/Probability/main.tex | 2 +- Misc/Moscow Puzzles/problems/120.tex | 2 +- Misc/Moscow Puzzles/problems/239.tex | 2 +- Misc/Warm-Ups/regex.tex | 2 +- resources/macros.sty | 2 +- resources/ormc_handout.cls | 2 +- 27 files changed, 36 insertions(+), 33 deletions(-) diff --git a/Advanced/Continued Fractions/parts/00 euclidean.tex b/Advanced/Continued Fractions/parts/00 euclidean.tex index eacf5e1..da044f8 100755 --- a/Advanced/Continued Fractions/parts/00 euclidean.tex +++ b/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} diff --git a/Advanced/Cryptography/parts/0 euclidean.tex b/Advanced/Cryptography/parts/0 euclidean.tex index 9bd167e..c054ab8 100755 --- a/Advanced/Cryptography/parts/0 euclidean.tex +++ b/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} diff --git a/Advanced/Cryptography/parts/3 DLP.tex b/Advanced/Cryptography/parts/3 DLP.tex index e080b05..03c826e 100755 --- a/Advanced/Cryptography/parts/3 DLP.tex +++ b/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 diff --git a/Advanced/DFAs/parts/0 DFA.tex b/Advanced/DFAs/parts/0 DFA.tex index 5e9a9a2..2f6ad24 100644 --- a/Advanced/DFAs/parts/0 DFA.tex +++ b/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 diff --git a/Advanced/Definable Sets/parts/3 sets.tex b/Advanced/Definable Sets/parts/3 sets.tex index bea0e09..e22498e 100644 --- a/Advanced/Definable Sets/parts/3 sets.tex +++ b/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 diff --git a/Advanced/Euler's Number/parts/1 limits.tex b/Advanced/Euler's Number/parts/1 limits.tex index 4aea0ed..2b44172 100644 --- a/Advanced/Euler's Number/parts/1 limits.tex +++ b/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 diff --git a/Advanced/Graph Algorithms/parts/01 flow.tex b/Advanced/Graph Algorithms/parts/01 flow.tex index 538f83b..8acdab2 100755 --- a/Advanced/Graph Algorithms/parts/01 flow.tex +++ b/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. diff --git a/Advanced/Lambda Calculus/main.tex b/Advanced/Lambda Calculus/main.tex index 0c979f4..6032a54 100755 --- a/Advanced/Lambda Calculus/main.tex +++ b/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 diff --git a/Advanced/Lambda Calculus/parts/00 intro.tex b/Advanced/Lambda Calculus/parts/00 intro.tex index 4c7c00f..5d785b2 100755 --- a/Advanced/Lambda Calculus/parts/00 intro.tex +++ b/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 diff --git a/Advanced/Lattices/parts/2 orchard.tex b/Advanced/Lattices/parts/2 orchard.tex index e5712f5..08b2cff 100644 --- a/Advanced/Lattices/parts/2 orchard.tex +++ b/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 diff --git a/Advanced/Linear Algebra 101/parts/1 vectors.tex b/Advanced/Linear Algebra 101/parts/1 vectors.tex index e37ea1c..97c20f9 100755 --- a/Advanced/Linear Algebra 101/parts/1 vectors.tex +++ b/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} diff --git a/Advanced/Linear Algebra 101/parts/2 dotprod.tex b/Advanced/Linear Algebra 101/parts/2 dotprod.tex index 3ff7f6b..9f52b2d 100644 --- a/Advanced/Linear Algebra 101/parts/2 dotprod.tex +++ b/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.} diff --git a/Advanced/Proof Techniques/parts/0 intro.tex b/Advanced/Proof Techniques/parts/0 intro.tex index 86737bc..6744c7a 100644 --- a/Advanced/Proof Techniques/parts/0 intro.tex +++ b/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 diff --git a/Advanced/Proof Techniques/parts/1 contradiction.tex b/Advanced/Proof Techniques/parts/1 contradiction.tex index 5d8eebd..7de6416 100644 --- a/Advanced/Proof Techniques/parts/1 contradiction.tex +++ b/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 -\textit{proof by contradiction}. It works as follows: +A very common proof technique is \textit{proof by contradiction}. +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} diff --git a/Advanced/Proof Techniques/parts/2 induction.tex b/Advanced/Proof Techniques/parts/2 induction.tex index fee07a7..7f5be5a 100644 --- a/Advanced/Proof Techniques/parts/2 induction.tex +++ b/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{} diff --git a/Advanced/Quotient Groups/parts/0 mod.tex b/Advanced/Quotient Groups/parts/0 mod.tex index 6eb2d08..7885b8a 100644 --- a/Advanced/Quotient Groups/parts/0 mod.tex +++ b/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 $, diff --git a/Advanced/Random Walks/parts/1 circuits.tex b/Advanced/Random Walks/parts/1 circuits.tex index 38cb0ec..bbf067e 100644 --- a/Advanced/Random Walks/parts/1 circuits.tex +++ 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{} -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 $x$} diff --git a/Advanced/Random Walks/parts/3 effective.tex b/Advanced/Random Walks/parts/3 effective.tex index 46e89bf..614edb1 100644 --- a/Advanced/Random Walks/parts/3 effective.tex +++ b/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)} diff --git a/Advanced/Retrograde Analysis/parts/02 easy.tex b/Advanced/Retrograde Analysis/parts/02 easy.tex index a1c4d45..d0a658f 100644 --- a/Advanced/Retrograde Analysis/parts/02 easy.tex +++ b/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} diff --git a/Advanced/Retrograde Analysis/parts/04 hard.tex b/Advanced/Retrograde Analysis/parts/04 hard.tex index 8f84d96..f8c2160 100644 --- a/Advanced/Retrograde Analysis/parts/04 hard.tex +++ b/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} diff --git a/Intermediate/An Introduction to Graph Theory/parts/0 intro.tex b/Intermediate/An Introduction to Graph Theory/parts/0 intro.tex index 9ac93c0..08207d1 100644 --- a/Intermediate/An Introduction to Graph Theory/parts/0 intro.tex +++ b/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} diff --git a/Intermediate/Probability/main.tex b/Intermediate/Probability/main.tex index 8b82e0a..a6eee42 100755 --- a/Intermediate/Probability/main.tex +++ b/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. diff --git a/Misc/Moscow Puzzles/problems/120.tex b/Misc/Moscow Puzzles/problems/120.tex index e4a2652..4757edb 100755 --- a/Misc/Moscow Puzzles/problems/120.tex +++ b/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. \\ diff --git a/Misc/Moscow Puzzles/problems/239.tex b/Misc/Moscow Puzzles/problems/239.tex index 8af0036..644a528 100755 --- a/Misc/Moscow Puzzles/problems/239.tex +++ b/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. diff --git a/Misc/Warm-Ups/regex.tex b/Misc/Warm-Ups/regex.tex index dbd9a0b..fc42e3b 100644 --- a/Misc/Warm-Ups/regex.tex +++ b/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} \ No newline at end of file diff --git a/resources/macros.sty b/resources/macros.sty index 9252766..cddf991 100644 --- a/resources/macros.sty +++ b/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 diff --git a/resources/ormc_handout.cls b/resources/ormc_handout.cls index 1bebf74..6098163 100755 --- a/resources/ormc_handout.cls +++ b/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<> }{