Convert "Travellers" to typst

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

@@ -1,54 +0,0 @@
-\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

@@ -0,0 +1,41 @@
+#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 $10^#text("th")$; // spell:disable-line
+  - 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/Partition Products/main.tex

@@ -1,57 +0,0 @@
-\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

@@ -0,0 +1,47 @@
+#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

@@ -1,34 +0,0 @@
-\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

@@ -0,0 +1,29 @@
+#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

@@ -1,153 +0,0 @@
-\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

@@ -0,0 +1,141 @@
+#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. // spell:disable-line
+
+#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

@@ -1,30 +0,0 @@
-\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

@@ -0,0 +1,26 @@
+#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.
+])