DRAFT

authors.toml

@@ -0,0 +1,3 @@
+[authors."mark"]
+email = "mark@betalupi.com"
+webpage = "betalupi.com"

src/Advanced/Tropical Polynomials/parts/00 arithmetic.typ

@@ -62,8 +62,7 @@ Let's expand $#sym.RR$ to include a tropical additive identity.
 #problem()
 Do tropical additive inverses exist? \
 #note([
-  Is there an inverse $y$ for every $x$ so that $x #tp y = #sym.infinity$? \
-  Remember that $#sym.infinity$ is the additive identity.
+  Is there an inverse $y$ for every $x$ so that $x #tp y = #sym.infinity$?
 ])
 
 #solution([
@@ -278,7 +277,7 @@ Fill the following tropical addition and multiplication tables
 
 #problem()
 Expand and simplify $f(x) = (x #tp 2)(x #tp 3)$, then evaluate $f(1)$ and $f(4)$ \
-#hint([Adjacent parenthesis imply tropical multiplication])
+Adjacent parenthesis imply tropical multiplication
 
 #solution([
   $

src/Advanced/Tropical Polynomials/parts/01 polynomials.typ

@@ -20,7 +20,7 @@ for some nonnegative integer $n$ and coefficients $c_0, c_1, ..., c_n$. \
 The _degree_ of a polynomial is the largest $n$ for which $c_n$ is nonzero.
 
 #theorem()
-The _fundamental theorem of algebra_ states that any non-constant polynomial with real coefficients
+The _fundamental theorem of algebra_ implies that any non-constant polynomial with real coefficients
 can be written as a product of polynomials of degree 1 or 2 with real coefficients.
 
 #v(2mm)
@@ -30,8 +30,8 @@ can be written as $(x^2 + 2x+5)(x-2)(x+4)(x+4)$
 
 #v(2mm)
 A similar theorem exists for polynomials with complex coefficients. \
-These coefficients may be found using the _roots_ of this polynomial. \
-As you already know, there are formulas that determine the roots of quadratic, cubic, and quartic #note([(degree 2, 3, and 4)]) polynomials. There are no formulas for the roots of polynomials with larger degrees---in this case, we usually rely on appropriate roots found by computers.
+These coefficients may be found using the roots of this polynomial. \
+As it turns out, there are formulas that determine the roots of quadratic, cubic, and quartic #note([(degree 2, 3, and 4)]) polynomials. There are no formulas for the roots of polynomials with larger degrees---in this case, we usually rely on approximate roots found by computers.
 
 #v(2mm)
 In this section, we will analyze tropical polynomials:
@@ -100,7 +100,7 @@ In other words, find $r$ and $s$ so that
   ),
 )
 
-#note([Naturally, we will call $r$ and $s$ the _roots_ of $f$.])
+we will call $r$ and $s$ the _roots_ of $f$.
 
 #solution([
   Because $(x #tp r)(x #tp s) = x^2 #tp (r #tp s)x #tp s r$, we must have $r #tp s = 1$ and $r #tm s = 4$. \
@@ -116,8 +116,7 @@ In other words, find $r$ and $s$ so that
 #v(1fr)
 
 #problem()
-Can you see the roots of this polynomial in the graph? \
-#hint([Yes, you can. What "features" do the roots correspond to?])
+How can we use the graph to determine these roots?
 
 #solution([The roots are the corners of the graph.])
 
@@ -317,7 +316,7 @@ into linear factors.
 #v(2mm)
 
 Whenever we say "the roots of $f$", we really mean "the roots of $accent(f, macron)$." \
-Also, $f$ and $accent(f, macron)$ might be the same polynomial.
+$f$ and $accent(f, macron)$ might be the same polynomial.
 
 #problem()
 If $f(x) = a x^2 #tp b x #tp c$, then $accent(f, macron)(x) = a x^2 #tp B x #tp c$ for some $B$. \

src/Warm-Ups/A Familiar Concept/main.tex

@@ -0,0 +1,35 @@
+\documentclass[
+	solutions,
+	hidewarning,
+	singlenumbering,
+	nopagenumber
+]{../../../lib/tex/ormc_handout}
+\usepackage{../../../lib/tex/macros}
+
+
+
+\title{Warm-Up: A Familiar Concept}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today}
+
+
+\begin{document}
+
+	\maketitle
+
+
+	\problem{}<one>
+	Let $v = [-5, -2, 0, 1, 4, 1000]$. Find all $x$ that minimize the following metric. \par
+	$$
+		\sum_{\forall i} |v_i - x| = |v_1 - x| + |v_2 - x| + ... + |v_6 - x|
+	$$
+	\vfill
+
+	\problem{}
+	Let $v = [-5, -2, 0, 1, 4, 1000, 1001]$. Find all $x$ that minimize the metric in \ref{one}.
+	\vfill
+
+	\problem{}
+	What is this metric usually called?
+
+\end{document}

src/Warm-Ups/A Familiar Concept/main.typ

@@ -1,39 +0,0 @@
-#import "@local/handout:0.1.0": *
-
-#show: doc => handout(
-  doc,
-  quarter: link(
-    "https://betalupi.com/handouts",
-    "betalupi.com/handouts",
-  ),
-
-  title: [Warm-Up: A Familiar Concept],
-  by: "Mark",
-)
-
-#problem()
-Let $v = [-5, -2, 0, 1, 4, 1000]$. Find all $x$ that minimize the following metric:
-
-#align(
-  center,
-  box(
-    inset: 3mm,
-    $
-      sum_(#sym.forall i) |v_i - x| = |v_1 - x| + |v_2 - x| + ... + |v_6 - x|
-    $,
-  ),
-)
-
-#v(1fr)
-
-#problem()
-Let $v = [-5, -2, 0, 1, 4, 1000, 1001]$. Find all $x$ that minimize the metric in the previous problem.
-
-#v(1fr)
-
-
-#problem()
-What is this metric usually called?
-
-
-#v(0.25fr)

src/Warm-Ups/Fuse Timers/main.tex

@@ -0,0 +1,31 @@
+\documentclass[
+	solutions,
+	hidewarning,
+	singlenumbering,
+	nopagenumber
+]{../../../lib/tex/ormc_handout}
+\usepackage{../../../lib/tex/macros}
+
+
+
+\title{Warm-Up: Fuse Timers}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today.}
+
+\begin{document}
+
+	\maketitle
+
+
+	\problem{}
+	Suppose we have two strings and a lighter. Each string takes an hour to fully burn. \par
+	However, we do not know how fast each part of the string burns:
+	half might burn in 1 minute, and the rest could take 59.
+
+	\vspace{2mm}
+
+	How would we measure exactly 45 minutes using these strings?
+
+	\vfill
+
+\end{document}

src/Warm-Ups/Fuse Timers/main.typ

@@ -1,21 +0,0 @@
-#import "@local/handout:0.1.0": *
-
-#show: doc => handout(
-  doc,
-  quarter: link(
-    "https://betalupi.com/handouts",
-    "betalupi.com/handouts",
-  ),
-
-  title: [Warm-Up: Fuse Timers],
-  by: "Mark",
-)
-
-#problem()
-Suppose we have two strings and a lighter. Each string takes exactly an hour to fully burn. \
-However, we do not know how fast each part of the string burns:
-half might burn in 1 minute, and the rest could take 59.
-
-#v(2mm)
-
-How can we measure exactly 45 minutes using these two strings?

src/Warm-Ups/Mario Kart/main.tex

@@ -0,0 +1,54 @@
+\documentclass[
+	solutions,
+	hidewarning,
+	singlenumbering,
+	nopagenumber
+]{../../../lib/tex/ormc_handout}
+\usepackage{../../../lib/tex/macros}
+
+
+\title{Warm-Up: Mario Kart}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today}
+
+
+\begin{document}
+
+	\maketitle
+
+	\problem{}
+	A standard Mario Kart cup consists of 12 players and four races. \par
+	Each race is scored as follows:
+	\begin{itemize}
+		\item 15 points are awarded for first place;
+		\item 12 for second;
+		\item and $(13 - \text{place})$ otherwise.
+	\end{itemize}
+	In any one race, no players may tie.
+	A player's score at the end of a cup is the sum of their scores for each of the four races.
+
+	\vspace{2mm}
+
+	An $n$-way tie occurs when the top $n$ players have the same score at the end of a round. \par
+	What is the largest possible $n$, and how is it achieved?
+
+	\begin{solution}
+		A 12-way tie is impossible, since the total number of point is not divisible by 12.
+
+		\vspace{2mm}
+
+		A 11-way tie is possible, with a top score of 28:
+		\begin{itemize}
+			\item Four players finish $1^\text{st}$, $3^\text{ed}$, $11^\text{th}$, and $12^\text{th}$;
+
+			% spell:off
+			\item Four players finish $2^\text{nd}$, $4^\text{th}$, $9^\text{th}$, and $10^\text{th}$;
+			% spell:on
+
+			\item Two players finish fifth twice and seventh twice,
+			\item One player finishes sixth in each race.
+		\end{itemize}
+		The final player always finishes eighth, with a non-tie score of 20.
+	\end{solution}
+
+\end{document}

src/Warm-Ups/Mario Kart/main.typ

@@ -1,41 +0,0 @@
-#import "@local/handout:0.1.0": *
-
-#show: doc => handout(
-  doc,
-  quarter: link(
-    "https://betalupi.com/handouts",
-    "betalupi.com/handouts",
-  ),
-
-  title: [Warm-Up: Mario Kart],
-  by: "Mark",
-)
-
-#problem()
-A standard Mario Kart cup consists of 12 players and four races. \
-Each race is scored as follows:
-- 15 points are awarded for first place;
-- 12 for second;
-- and $(13 - #text("place"))$ otherwise.
-
-In any one race, no players may tie. \
-A player's score at the end of a cup is the sum of their scores for each of the four races.
-
-#v(2mm)
-
-An $n$-way tie occurs when the top $n$ players have the same score at the end of a round. \
-What is the largest possible $n$, and how is it achieved?
-
-#solution([
-  A 12-way tie is impossible, since the total number of point is not divisible by 12.
-
-  #v(2mm)
-
-  A 11-way tie is possible, with a top score of 28:
-  - Four players finish $1^#text("st")$, $3^#text("ed")$, $11^#text("th")$, and $12^#text("th")$;
-  - Four players finish $2^#text("nd")$, $4^#text("th")$, $9^#text("th")$, and $10^#text("th")$;
-  - Two players finish fifth twice and seventh twice,
-  - One player finishes sixth in each race.
-  The final player always finishes eighth, with a non-tie score of 20.
-
-])

src/Warm-Ups/Odd Dice/meta.toml

@@ -4,3 +4,8 @@ title = "Odd Dice"
 [publish]
 handout = true
 solutions = true
+
+[[attribution]]
+who = "mark"
+when = 2024-02-13
+what = "Initial version of handout"

src/Warm-Ups/Partition Products/main.tex

@@ -0,0 +1,57 @@
+\documentclass[
+	solutions,
+	singlenumbering,
+	nopagenumber
+]{../../../lib/tex/ormc_handout}
+\usepackage{../../../lib/tex/macros}
+
+
+\title{Warm-Up: Partition Products}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today.}
+
+\begin{document}
+
+	\maketitle
+
+	\problem{}
+	Take any positive integer $n$. \par
+	Now, write it as sum of smaller positive integers: $n = a_1 + a_2 + ... + a_k$ \par
+	Maximize the product $a_1 \times a_2 \times ... \times a_k$
+
+
+
+	\begin{solution}
+
+		\textbf{Interesting Solution:}
+
+		Of course, all $a_i$ should be greater than $1$. \par
+		Also, all $a_i$ should be smaller than four, since $x \leq x(x-2)$ if $x \geq 4$. \par
+		Thus, we're left with sequences that only contain 2 and 3. \par
+		\note{Note that two twos are the same as one four, but we exclude fours for simplicity.}
+
+		\vspace{2mm}
+
+		Finally, we see that $3^2 > 2^3$, so any three twos are better repackaged as two threes. \par
+		The best sequence $a_i$ thus consists of a maximal number of threes followed by 0, 1, or 2 twos.
+
+		\linehack{}
+
+
+
+		\textbf{Calculus Solution:}
+
+		First, solve this problem for equal, non-integer $a_i$:
+
+		\vspace{2mm}
+
+		We know $n = \prod{a_i}$, thus $\ln(n) = \sum{\ln(a_i)}$. \par
+		If all $a_i$ are equal, we get $\ln(n) = k \times \ln(n / k)$. \par
+		Derive wrt $k$ and set to zero to get $\ln(n / k) = 1$ \par
+		So $k = n / e$ and $n / k = e \approx 2.7$
+
+		\vspace{2mm}
+
+		If we try to approximate this with integers, we get the same solution as above.
+	\end{solution}
+\end{document}

src/Warm-Ups/Partition Products/main.typ

@@ -1,47 +0,0 @@
-#import "@local/handout:0.1.0": *
-
-#show: doc => handout(
-  doc,
-  quarter: link(
-    "https://betalupi.com/handouts",
-    "betalupi.com/handouts",
-  ),
-
-  title: [Warm-Up: Partition Products],
-  by: "Mark",
-)
-
-#problem()
-Take any positive integer $n$. \
-Now, write it as sum of smaller positive integers: $n = a_1 + a_2 + ...  a_k$ \
-Maximize the product $a_1 #sym.times a_2 #sym.times ... #sym.times a_k$
-
-
-#solution([
-  *Interesting Solution:*
-
-  Of course, all $a_i$ should be greater than $1$. \
-  Also, all $a_i$ should be smaller than four, since $x <= x(x-2)$ if $x >= 4$. \
-  Thus, we're left with sequences that only contain 2 and 3. \
-  #note([Note that two twos are the same as one four, but we exclude fours for simplicity.])
-
-  #v(2mm)
-
-  Finally, we see that $3^2 > 2^3$, so any three twos are better repackaged as two threes. \
-  The best sequence $a_i$ thus consists of a maximal number of threes followed by 0, 1, or 2 twos.
-
-  #v(8mm)
-
-  *Calculus Solution:*
-
-  First, solve this problem for equal, real $a_i$:
-  #v(2mm)
-  We know $n = product(a_i)$, thus $ln(n) = sum(ln(a_i))$. \
-  If all $a_i$ are equal, we get $ln(n) = k #sym.times ln(n / k)$. \
-  Derive wrt $k$ and set to zero to get $ln(n / k) = 1$ \
-  So $k = n / e$ and $n / k = e #sym.approx 2.7$
-
-  #v(2mm)
-
-  If we try to approximate this with integers, we get the same solution as above.
-])

src/Warm-Ups/Prime Factors/main.tex

@@ -0,0 +1,34 @@
+\documentclass[
+	solutions,
+	singlenumbering,
+	nopagenumber,
+	hidewarning
+]{../../../lib/tex/ormc_handout}
+\usepackage{../../../lib/tex/macros}
+
+\title{Warm-Up: Prime Factors}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today.}
+
+\begin{document}
+
+	\maketitle
+
+	\problem{}
+	What proportion of integers have $2$ as their smallest prime factor?
+	% 1^2
+	\vfill
+
+
+	\problem{}
+	What proportion of integers have $3$ as their second-smallest prime factor?
+	% 1/6
+	\vfill
+
+
+	\problem{}
+	What is the median second-smallest prime factor?
+	% 37
+	\vfill
+
+\end{document}

src/Warm-Ups/Prime Factors/main.typ

@@ -1,29 +0,0 @@
-#import "@local/handout:0.1.0": *
-
-#show: doc => handout(
-  doc,
-  quarter: link(
-    "https://betalupi.com/handouts",
-    "betalupi.com/handouts",
-  ),
-
-  title: [Warm-Up: Prime Factors],
-  by: "Mark",
-)
-
-#problem()
-What proportion of integers have $2$ as their smallest prime factor?
-#solution([$1 div 2$])
-#v(1fr)
-
-
-#problem()
-What proportion of integers have $3$ as their second-smallest prime factor?
-#solution([$1 div 6$])
-#v(1fr)
-
-
-#problem()
-What is the median second-smallest prime factor?
-#solution([37])
-#v(1fr)

src/Warm-Ups/Regex/main.tex

@@ -0,0 +1,153 @@
+\documentclass[
+	solutions,
+	hidewarning,
+]{../../../lib/tex/ormc_handout}
+\usepackage{../../../lib/tex/macros}
+
+
+\usepackage{xcolor}
+\usepackage{soul}
+\usepackage{hyperref}
+
+\definecolor{Light}{gray}{.90}
+\sethlcolor{Light}
+\newcommand{\htexttt}[1]{\texttt{\hl{#1}}}
+
+
+\title{The Regex Warm-Up}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today}
+
+\begin{document}
+
+	\maketitle
+
+
+	Last time, we discussed Deterministic Finite Automata. One interesting application of these mathematical objects is found in computer science: Regular Expressions. \par
+	This is often abbreviated \say{regex}, which is pronounced like \say{gif.}
+
+	\vspace{2mm}
+
+	Regex is a language used to specify patterns in a string. You can think of it as a concise way to define a DFA, using text instead of a huge graph. \par
+
+	Often enough, a clever regex pattern can do the work of a few hundred lines of code.
+
+	\vspace{2mm}
+
+	Like the DFAs we've studied, a regex pattern \textit{accepts} or \textit{rejects} a string. However, we don't usually use this terminology with regex, and instead say that a string \textit{matches} or \textit{doesn't match} a pattern.
+
+	\vspace{5mm}
+
+	Regex strings consist of characters, quantifiers, sets, and groups.
+
+	\vspace{5mm}
+
+	\textbf{Quantifiers} \par
+	Quantifiers specify how many of a character to match. \par
+	There are four of these: \htexttt{+}, \htexttt{*}, \htexttt{?}, and \htexttt{\{ \}}
+
+	\vspace{2mm}
+
+	\htexttt{+} means \say{match one or more of the preceding token} \par
+	\htexttt{*} means \say{match zero or more of the preceding token}
+
+	For example, the pattern \htexttt{ca+t} will match the following strings:
+	\begin{itemize}
+		\item \texttt{cat}
+		\item \texttt{caat}
+		\item \texttt{caaaaaaaat}
+	\end{itemize}
+	\htexttt{ca+t} will \textbf{not} match the string \texttt{ct}. \par
+	The pattern \htexttt{ca*t} will match all the strings above, including \texttt{ct}.
+	\vspace{2mm}
+
+
+	\htexttt{?} means \say{match one or none of the preceding token} \par
+	The pattern \htexttt{linea?r} will match only \texttt{linear} and \texttt{liner}.
+	\vspace{2mm}
+
+	Brackets \htexttt{\{min, max\}} are the most flexible quantifier. \par
+	They specify exactly how many tokens to match: \par
+	\htexttt{ab\{2\}a} will match only \texttt{abba}. \par
+	\htexttt{ab\{1,3\}a} will match only \texttt{aba}, \texttt{abba}, and \texttt{abbba}. \par
+	% spell:off
+	\htexttt{ab\{2,\}a} will match any \texttt{ab...ba} with at least two \texttt{b}s.
+	% spell:on
+
+	\vspace{5mm}
+
+	\problem{}
+	Write the patterns \htexttt{a*} and \htexttt{a+} using only \htexttt{\{ \}}.
+	\vfill
+
+	\problem{}
+	Draw a DFA equivalent to the regex pattern \htexttt{01*0}.
+	\vfill
+
+	\pagebreak
+
+
+
+
+
+
+	\textbf{Characters, Sets, and Groups} \par
+	In the previous section, we saw how we can specify characters literally: \par
+	\texttt{a+} means \say{one or more \texttt{a} character}
+
+	\vspace{2mm}
+
+	There are, of course, other ways we can specify characters.
+
+	\vspace{2mm}
+
+	The first such way is the \textit{set}, denoted \htexttt{[ ]}. A set can pretend to be any character inside it. \par
+	For example, \htexttt{m[aoy]th} will match \texttt{math}, \texttt{moth}, or \texttt{myth}. \par
+	\htexttt{a[01]+b} will match \texttt{a0b}, \texttt{a111b}, \texttt{a1100110b}, and any other similar string. \par
+	You may negate a set with a \htexttt{\textasciicircum}. \par
+	\htexttt{[\textasciicircum abc]} will match any character except \texttt{a}, \texttt{b}, or \texttt{c}, including symbols and spaces.
+
+	\vspace{2mm}
+
+	If we want to keep characters together, we can use the \textit{group}, denoted \htexttt{( )}. \par
+
+	Groups work exactly as you'd expect, representing an atomic\footnotemark{} group of characters. \par
+	\htexttt{a(01)+b} will match \texttt{a01b} and \texttt{a010101b}, but will \textbf{not} match \texttt{a0b}, \texttt{a1b}, or \texttt{a1100110b}.
+
+	\footnotetext{In other words, \say{unbreakable}}
+
+
+	\problem{}<regex>
+	You are now familiar with most of the tools regex has to offer. \par
+	Write patterns that match the following strings:
+	\begin{enumerate}[itemsep=1mm]
+		\item An ISO-8601 date, like \texttt{2022-10-29}. \par
+		\hint{Invalid dates like \texttt{2022-13-29} should also be matched.}
+
+		\item An email address. \par
+		\hint{Don't forget about subdomains, like \texttt{math.ucla.edu}.}
+
+		\item A UCLA room number, like \texttt{MS 5118} or \texttt{Kinsey 1220B}.
+
+		\item Any ISBN-10 of the form \texttt{0-316-00395-7}. \par
+		\hint{Remember that the check digit may be an \texttt{X}. Dashes are optional.}
+
+		\item A word of even length. \par
+		\hint{The set \texttt{[A-z]} contains every english letter, capitalized and lowercase. \\
+		\texttt{[a-z]} will only match lowercase letters.}
+
+		\item A word with exactly 3 vowels. \par
+		\hint{The special token \texttt{\textbackslash w} will match any word character. It is equivalent to \texttt{[A-z0-9\_]} \\ \texttt{\_} stands for a literal underscore.}
+
+		\item A word that has even length and exactly 3 vowels.
+
+		\item A sentence that does not start with a capital letter.
+	\end{enumerate}
+
+	\vfill
+
+	\problem{}
+	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}

src/Warm-Ups/Regex/main.typ

@@ -1,138 +0,0 @@
-#import "@local/handout:0.1.0": *
-
-#show: doc => handout(
-  doc,
-  quarter: link(
-    "https://betalupi.com/handouts",
-    "betalupi.com/handouts",
-  ),
-
-  title: [The Regex Warm-Up],
-  by: "Mark",
-)
-
-
-Last time, we discussed Deterministic Finite Automata. One interesting application of these mathematical objects is found in computer science: Regular Expressions. \
-This is often abbreviated "regex," which is pronounced like "gif."
-
-#v(2mm)
-
-Regex is a language used to specify patterns in a string. You can think of it as a concise way to define a DFA, using text instead of a huge graph. \
-
-Often enough, a clever regex pattern can do the work of a few hundred lines of code.
-
-#v(2mm)
-
-Like the DFAs we've studied, a regex pattern _accepts_ or _rejects_ a string. However, we don't usually use this terminology with regex, and instead say that a string _matches_ or _doesn't match_ a pattern.
-
-#v(5mm)
-
-Regex strings consist of characters, quantifiers, sets, and groups.
-
-#v(5mm)
-
-
-
-*Quantifiers* \
-Quantifiers specify how many of a character to match. \
-There are four of these: `+`, `*`, `?`, and `{ }`.
-
-#v(4mm)
-
-`+` means "match one or more of the preceding token" \
-`*` means "match zero or more of the preceding token"
-
-For example, the pattern `ca+t` will match the following strings:
-- `cat`
-- `caat`
-- `caaaaaaaat`
-`ca+t` will *not* match the string `ct`. \
-The pattern `ca*t` will match all the strings above, including `ct`.
-
-
-#v(4mm)
-
-
-`?` means "match one or none of the preceding token" \
-The pattern `linea?r` will match only `linear` and `liner`.
-
-#v(4mm)
-
-Brackets `{min, max}` are the most flexible quantifier. \
-They specify exactly how many tokens to match: \
-`ab{2}a` will match only `abba`. \
-`ab{1,3}a` will match only `aba`, `abba`, and `abbba`. \
-`ab{2,}a` will match any `ab...ba` with at least two `b`s.
-
-#problem()
-Write the patterns `a*` and `a+` using only `{ }`.
-#v(1fr)
-
-#problem()
-Draw a DFA equivalent to the regex pattern `01*0`.
-#v(1fr)
-
-#pagebreak()
-
-
-
-
-
-
-*Characters, Sets, and Groups* \
-In the previous section, we saw how we can specify characters literally: \
-`a+` means "one or more `a` characters" \
-There are, of course, other ways we can specify characters.
-
-#v(4mm)
-
-The first such way is the _set_, denoted `[ ]`. A set can pretend to be any character inside it. \
-For example, `m[aoy]th` will match `math`, `moth`, or `myth`. \
-`a[01]+b` will match `a0b`, `a111b`, `a1100110b`, and any other similar string. \
-
-#v(4mm)
-
-We can negate a set with a `^`. \
-`[^abc]` will match any single character except `a`, `b`, or `c`, including symbols and spaces.
-
-#v(4mm)
-
-If we want to keep characters together, we can use the _group_, denoted `( )`. \
-
-Groups work exactly as you'd expect, representing an atomic#footnote([In other words, "unbreakable"]) group of characters. \
-`a(01)+b` will match `a01b` and `a010101b`, but will *not* match `a0b`, `a1b`, or `a1100110b`.
-
-#problem()
-You are now familiar with most of the tools regex has to offer. \
-Write patterns that match the following strings:
-
-- An ISO-8601 date, like `2022-10-29`. \
-  #hint([Invalid dates like `2022-13-29` should also be matched.])
-
-- An email address. \
-  #hint([Don't forget about subdomains, like `math.ucla.edu`.])
-
-- A UCLA room number, like `MS 5118` or `Kinsey 1220B`.
-
-- Any ISBN-10 of the form `0-316-00395-7`. \
-  #hint([Remember that the check digit may be an `X`. Dashes are optional.])
-
-- A word of even length. \
-  #hint([The set `[A-z]` contains every english letter, capitalized and lowercase. \
-  `[a-z]` will only match lowercase letters.])
-
-- A word with exactly 3 vowels. \
-  #hint([The special token `\w` will match any word character. \
-  It is equivalent to `[A-z0-9_]`. `_` represents a literal underscore.
-])
-
-- A word that has even length and exactly 3 vowels.
-
-- A sentence that does not start with a capital letter.
-#v(1fr)
-
-#problem()
-If you'd like to know more, check out `https://regexr.com`.
-It offers an interactive regex prompt,
-as well as a cheatsheet that explains every other regex token there is. \
-You can find a nice set of challenges at `https://alf.nu/RegexGolf`.

src/Warm-Ups/Travellers/main.tex

@@ -0,0 +1,30 @@
+\documentclass[
+	solutions,
+	singlenumbering,
+	nopagenumber
+]{../../../lib/tex/ormc_handout}
+\usepackage{../../../lib/tex/macros}
+
+\title{Warm-Up: Travellers}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today}
+
+\begin{document}
+
+	\maketitle
+
+	\problem{}
+	Four travellers are on a plane, each moving along a straight line at an arbitrary constant speed. \par
+	No two of their paths are parallel, and no three intersect at the same point. \par
+	We know that traveller A has met travelers B, C, and D, \par
+	and that traveller B has met C and D (and A). Show that C and D must also have met. \par
+
+	\begin{solution}
+		When a body travels at a constant speed, its graph with respect to time is a straight line. \par
+		So, we add time axis in the third dimension, perpendicular to our plane. \par
+		Naturally, the projection of each of these onto the plane corresponds to a road.
+
+		Now, note that two intersecting lines define a plane and use the conditions in the problem to show that no two lines are parallel.
+	\end{solution}
+
+\end{document}

src/Warm-Ups/Travellers/main.typ

@@ -1,26 +0,0 @@
-#import "@local/handout:0.1.0": *
-
-#show: doc => handout(
-  doc,
-  quarter: link(
-    "https://betalupi.com/handouts",
-    "betalupi.com/handouts",
-  ),
-
-  title: [Warm-Up: Travellers],
-  by: "Mark",
-)
-
-#problem()
-Four travellers are on a plane, each moving along a straight line at an arbitrary constant speed. \
-No two of their paths are parallel, and no three intersect at the same point. \
-We know that traveller A has met travelers B, C, and D, \
-and that traveller B has met C and D (and A). Show that C and D must also have met.
-
-#solution([
-  When a body travels at a constant speed, its graph with respect to time is a straight line. \
-  So, we add time axis in the third dimension, perpendicular to our plane. \
-  Naturally, the projection of each of these onto the plane corresponds to a road.
-
-  Now, note that two intersecting lines define a plane and use the conditions in the problem to show that no two lines are parallel.
-])

src/Warm-Ups/fmod/main.tex

@@ -0,0 +1,22 @@
+\documentclass[
+	solutions,
+	hidewarning,
+	singlenumbering,
+	nopagenumber
+]{../../../lib/tex/ormc_handout}
+\usepackage{../../../lib/tex/macros}
+
+
+\title{Warm-Up: \texttt{fmod}}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today.}
+
+\begin{document}
+
+	\maketitle
+
+	\problem{}
+	I'm sure you're all familiar with how \texttt{mod(a, b)} and \texttt{remainder(a, b)} work with integers. \par
+	Devise an equivalent for floats (i.e, real numbers).
+
+\end{document}

src/Warm-Ups/fmod/main.typ

@@ -1,16 +0,0 @@
-#import "@local/handout:0.1.0": *
-
-#show: doc => handout(
-  doc,
-  quarter: link(
-    "https://betalupi.com/handouts",
-    "betalupi.com/handouts",
-  ),
-
-  title: [Warm-Up: `fmod`],
-  by: "Mark",
-)
-
-#problem()
-I'm sure you're all familiar with how `mod(a, b)` and `remainder(a, b)` \ work when `a` and `b` are integers.
-Devise an equivalent for floats (i.e, real numbers).