Mark/handouts
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11
Advanced/Cryptography/main.tex
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@ -5,18 +5,17 @@
singlenumbering singlenumbering
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{multicol} \usepackage{multicol}
\uptitlel{Advanced 1A}
\uptitler{Spring 2022}
\title{Intro to Cryptography}
\subtitle{Prepared by Mark on \today{}}
\begin{document} \begin{document}
\maketitle \maketitle
<Advanced 1A>
<Spring 2022>
{Intro to Cryptography}
{Prepared by Mark on \today{}}
\input{parts/part 1} \input{parts/part 1}
\input{parts/part 2} \input{parts/part 2}

11
Advanced/DFAs/main.tex
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@ -6,14 +6,15 @@
\input{tikxset.tex} \input{tikxset.tex}
\uptitlel{Advanced 2}
\uptitler{Winter 2022}
\title{Finite Automata}
\subtitle{Prepared by Mark and Nikita on \today{}}
\begin{document} \begin{document}
\maketitle \maketitle
<Advanced 2>
<Winter 2022>
{Finite Automata}
{Prepared by Mark and Nikita on \today}
\input{parts/0 DFA.tex} \input{parts/0 DFA.tex}
\input{parts/1 regular.tex} \input{parts/1 regular.tex}

15
Advanced/Definable Sets/main.tex
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@ -8,15 +8,14 @@
% for \coloneqq, a centered := % for \coloneqq, a centered :=
\usepackage{mathtools} \usepackage{mathtools}
\begin{document} \uptitlel{Advanced 2}
\maketitle \uptitler{Spring 2023}
<Advanced 2> \title{Definable Sets}
<Spring 2023> \subtitle{Prepared by Mark on \today{}}
{Definable Sets}
{
Prepared by Mark on \today
}
\begin{document}
\maketitle
\input{parts/0 logic.tex} \input{parts/0 logic.tex}
\input{parts/1 structures.tex} \input{parts/1 structures.tex}

17
Advanced/Error-Correcting Codes/main.tex
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@ -1,22 +1,23 @@
% use [nosolutions] flag to hide solutions. % use [nosolutions] flag to hide solutions.
% use [solutions] flag to show solutions. % use [solutions] flag to show solutions.
\documentclass[ \documentclass[
solutions solutions,
singlenumbering
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\usepackage{tikz} \usepackage{tikz}
\begin{document} \uptitlel{Advanced 2}
\uptitler{Fall 2022}
\maketitle \title{Error-Correcting Codes}
<Advanced 2> \subtitle{
<Fall 2022>
{Error-Correcting Codes}
{
Based on a handout by Yingkun Li \\ Based on a handout by Yingkun Li \\
Revised by Mark on \today Revised by Mark on \today
} }
\begin{document}
\maketitle
\input{parts/00 detection} \input{parts/00 detection}
\input{parts/01 correction} \input{parts/01 correction}

22
Advanced/Euler's Number/main.tex
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@ -1,13 +1,10 @@
% use [nosolutions] flag to hide solutions. % use [nosolutions] flag to hide solutions.
% use [solutions] flag to show solutions. % use [solutions] flag to show solutions.
\documentclass[ \documentclass[
solutions,
singlenumbering, singlenumbering,
nosolutions
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{multicol} \usepackage{multicol}
\usepackage{tikz} \usepackage{tikz}
\usepackage{graphicx} \usepackage{graphicx}
@ -17,20 +14,19 @@
\newcommand{\qgt}{\stackrel{?}{>}} \newcommand{\qgt}{\stackrel{?}{>}}
\newcommand{\qlt}{\stackrel{?}{<}} \newcommand{\qlt}{\stackrel{?}{<}}
\uptitlel{Advanced 2}
\begin{document} \uptitler{Fall 2022}
\title{Euler's Number}
\maketitle \subtitle{
<Advanced 2>
<Fall 2022>
{Euler's Number}
{
By Oleg Gleizer and Olga Radko. \\ By Oleg Gleizer and Olga Radko. \\
Prepared by Mark on \today Prepared by Mark on \today
} }
\paragraph{} \begin{document}
\maketitle
The goal of this mini-course is to construct Euler's number, one of the most important constants in mathematics, physics, economics, and finance. Make sure you fully understand all definitions before trying to solve problems that use them. The goal of this mini-course is to construct Euler's number, one of the most important constants in mathematics, physics, economics, and finance. Make sure you fully understand all definitions before trying to solve problems that use them.
\section{Compound Interest} \section{Compound Interest}

12
Advanced/Graph Algorithms/main.tex
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@ -4,17 +4,17 @@
solutions solutions
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\input{tikxset} \input{tikxset}
\uptitlel{Advanced 2}
\uptitler{Fall 2022}
\title{Algorithms on Graphs: Flow}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
<Advanced 2>
<Fall 2022>
{Algorithms on Graphs: Flow}
{Prepared by Mark on \today}
\input{parts/00 review} \input{parts/00 review}
\input{parts/01 flow} \input{parts/01 flow}

12
Advanced/Group Theory/main.tex
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@ -6,16 +6,14 @@
\usepackage{tikz} \usepackage{tikz}
\uptitlel{Advanced 2}
\uptitler{Fall 2022}
\title{Group Theory}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
<Advanced 2>
<Fall 2022>
{Group Theory}
{
Prepared by Mark on \today
}
\input{parts/00 review} \input{parts/00 review}
\input{parts/01 groups} \input{parts/01 groups}

12
Advanced/Lambda Calculus/main.tex
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@ -29,16 +29,14 @@
% Notice that I a b = 1 a b! % Notice that I a b = 1 a b!
\uptitlel{Advanced 2}
\uptitler{Fall 2022}
\title{Lambda Calculus}
\subtitle{Prepared by Mark on \today{}}
\begin{document} \begin{document}
\maketitle \maketitle
<Advanced 2>
<Fall 2022>
{Lambda Calculus}
{
Prepared by Mark on \today
}
\begin{minipage}{8cm} \begin{minipage}{8cm}
Beware of the Turing tar-pit in which everything is possible but nothing of interest is easy. Beware of the Turing tar-pit in which everything is possible but nothing of interest is easy.

16
Advanced/Lattices/main.tex
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@ -6,23 +6,21 @@
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\usepackage{ifthen} \usepackage{ifthen}
%\usepackage{lua-visual-debug} %\usepackage{lua-visual-debug}
\renewcommand{\arraystretch}{1.2} \renewcommand{\arraystretch}{1.2}
\uptitlel{Advanced 2}
\uptitler{Spring 2023}
\title{Lattices}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
<Advanced 2>
<Spring 2023>
{Lattices}
{
Prepared by Mark on \today \\
}
\input{parts/0 intro.tex} \input{parts/0 intro.tex}
\input{parts/1 minkowski.tex} \input{parts/1 minkowski.tex}
\input{parts/2 orchard.tex} \input{parts/2 orchard.tex}
\end{document} \end{document}

15
Advanced/Linear Algebra 101/main.tex
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@ -2,7 +2,7 @@
% use [solutions] flag to show solutions. % use [solutions] flag to show solutions.
\documentclass[ \documentclass[
solutions, solutions,
nowarning, hidewarning,
%singlenumbering %singlenumbering
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
@ -20,16 +20,15 @@
} }
\input{tikzset} \input{tikzset}
\uptitlel{Advanced 2}
\uptitler{Spring 2023}
\title{Linear Algebra 101}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
<Advanced 2>
<Spring 2023>
{Linear Algebra 101}
{
Prepared by Mark on \today \\
}
\input{parts/0 notation} \input{parts/0 notation}
\input{parts/1 vectors} \input{parts/1 vectors}

15
Advanced/Mock a Mockingbird/main.tex
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@ -63,18 +63,21 @@
\newcommand{\qed}{\(\blacksquare\)} \newcommand{\qed}{\(\blacksquare\)}
\begin{document}
\maketitle \uptitlel{Advanced 2}
<Advanced 2> \uptitler{Spring 2023}
<Spring 2023> \title{To Mock a Mockingbird}
{To Mock a Mockingbird} \subtitle{
{
Prepared by Mark on \today \\ Prepared by Mark on \today \\
Based on a book of the same name. Based on a book of the same name.
} }
\begin{document}
\maketitle
\input{parts/00 intro} \input{parts/00 intro}
\input{parts/01 tmam} \input{parts/01 tmam}
\input{parts/02 kestrel} \input{parts/02 kestrel}
\end{document} \end{document}

5
Advanced/Origami/main.tex
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@ -7,6 +7,11 @@
\graphicspath{ {./images/} } \graphicspath{ {./images/} }
\uptitlel{Advanced 2}
\uptitler{Winter 2022}
\title{Origami}
\subtitle{Prepared by everyone on \today}
\begin{document} \begin{document}
\maketitle \maketitle

12
Advanced/Pidgeonhole Problems/main.tex
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@ -8,16 +8,14 @@
\usepackage{amssymb} \usepackage{amssymb}
\usepackage{tikz} \usepackage{tikz}
\uptitlel{Advanced 2}
\uptitler{Winter 2022}
\title{Pidgeonhole Problems}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
<Advanced 2>
<Winter 2023>
{Pidgeonhole Problems}
{Prepared by Mark on \today}
\vspace{3ex}
\problem{} \problem{}

14
Intermediate/An Introduction to Graph Theory/main.tex
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@ -8,17 +8,17 @@
\usepackage{tkz-graph} \usepackage{tkz-graph}
\begin{document} \uptitlel{Intermediate 2}
\uptitler{ORMC Summer Sessions}
\maketitle \title{An Introduction to Graph Theory}
<Intermediate 2> \subtitle{
<ORMC Summer Sessions>
{An Introduction to Graph Theory}
{
Prepared by Mark on \today \\ Prepared by Mark on \today \\
Based on a handout by Oleg Gleizer Based on a handout by Oleg Gleizer
} }
\begin{document}
\maketitle
\section{Graphs} \section{Graphs}

10
Intermediate/Combinatorics/main.tex
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@ -14,14 +14,14 @@
} }
} }
\uptitlel{Intermediate 2}
\uptitler{ORMC Summer Sessions}
\title{Combinatorics}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
<Intermediate 2>
<ORMC Summer Sessions>
{Combinatorics}
{Prepared by Mark on \today}
\section{Getting started} \section{Getting started}
@ -241,7 +241,7 @@
\problem{} \problem{}
A stressed-out student consumes at least one espresso every day of a particular year, drinking $500$ overall. Prove that on some consecutive sequence of whole days the student drinks exactly $100$ espressos. A stressed-out student consumes at least one espresso every day of a particular year, drinking $500$ overall. Prove that on some consecutive sequence of whole days the student drinks exactly $100$ espressos.
\note<Warning>{This problem is significantly harder than anything else in the handout.} \note[Warning]{This problem is significantly harder than anything else in the handout.}
\vfill \vfill

15
Intermediate/Instant Insanity/main.tex
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@ -8,17 +8,18 @@
\usepackage{tkz-graph} \usepackage{tkz-graph}
\begin{document} \uptitlel{Intermediate 2}
\uptitler{ORMC Summer Sessions}
\maketitle \title{Graph Theory and Instant Insanity}
<Intermediate 2> \subtitle{
<ORMC Summer Sessions>
{Graph Theory and Instant Insanity}
{
Prepared by Mark on \today \\ Prepared by Mark on \today \\
Based on a handout by Oleg Gleizer Based on a handout by Oleg Gleizer
} }
\begin{document}
\maketitle
\section{Instant Insanity} \section{Instant Insanity}

15
Intermediate/Newton's Laws/main.tex
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@ -5,17 +5,18 @@
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\begin{document} \uptitlel{Intermediate 2}
\uptitler{ORMC Summer Sessions}
\maketitle \title{Newton's Laws of Motion}
<Intermediate 2> \subtitle{
<ORMC Summer Sessions>
{Newton's Laws of Motion}
{
Prepared by Mark on \today \\ Prepared by Mark on \today \\
Based on a handout by Oleg Gleizer Based on a handout by Oleg Gleizer
} }
\begin{document}
\maketitle
\section{Newton's First Law} \section{Newton's First Law}
If the net force acting on an object is zero, the velocity of that object does not change. \\ If the net force acting on an object is zero, the velocity of that object does not change. \\
Conversely, if the velocity of an object doesn't change, the net force acting on it is zero. Conversely, if the velocity of an object doesn't change, the net force acting on it is zero.

15
Intermediate/Probability/main.tex
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@ -11,17 +11,20 @@
\ensuremath{\P{\text{#1}}} \ensuremath{\P{\text{#1}}}
} }
\begin{document}
\maketitle \uptitlel{Intermediate 2}
<Intermediate 2> \uptitler{ORMC Summer Sessions}
<ORMC Summer Sessions> \title{Probability}
{Probability} \subtitle{
{
Prepared by Mark on \today \\ Prepared by Mark on \today \\
Based on a handout by Oleg Gleizer Based on a handout by Oleg Gleizer
} }
\begin{document}
\maketitle
\problem{} \problem{}
A Zoo manager thinks of a way A Zoo manager thinks of a way
to set up a new pavilion. to set up a new pavilion.

14
Intermediate/Slide Rules/main.tex
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@ -6,6 +6,7 @@
\usepackage{pdfpages} \usepackage{pdfpages}
\usepackage{sliderule} \usepackage{sliderule}
\usepackage{changepage}
% Args: % Args:
% x, top scale y, label % x, top scale y, label
@ -22,15 +23,16 @@
node [below] {#3}; node [below] {#3};
} }
\uptitlel{Intermediate 2}
\uptitler{Summer 2022}
\title{Slide Rules}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
<Intermediate 2>
<Summer 2022>
{Slide Rules}
{
Prepared by Mark on \today
}
\begin{center} \begin{center}
\begin{minipage}{6cm} \begin{minipage}{6cm}

31
Intermediate/Vectors 1/main.tex
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@ -3,23 +3,18 @@
\documentclass[solutions]{../../resources/ormc_handout} \documentclass[solutions]{../../resources/ormc_handout}
\usepackage{adjustbox} \usepackage{adjustbox}
\uptitlel{Intermediate 2}
\uptitler{ORMC Summer Sessions}
\title{Vectors 1}
\subtitle{
Prepared by Mark on \today \\
Based on a handout by Oleg Gleizer
}
\begin{document} \begin{document}
\begin{adjustbox}{minipage=0.7\textwidth, margin=0pt \smallskipamount,center} \maketitle
\begin{center}
\textsc{Intermediate 2 \hfill ORMC Summer Sessions} \\
\rule{\linewidth}{0.2mm}\\
\huge
Vectors 1\\
\normalsize
\vspace{1ex}
Prepared by Mark on \today. \\
Based on a handout by Oleg Gleizer.
\rule{\linewidth}{0.2mm}\\
\end{center}
\end{adjustbox}
\section{Warm-Up} \section{Warm-Up}
@ -113,11 +108,11 @@
In other words, two vectors are equivalent if they have the same length and direction. If this is the case, we write $v = w$. In other words, two vectors are equivalent if they have the same length and direction. If this is the case, we write $v = w$.
\note<Note 1>{ \note[Note 1]{
Convince yourself that this is true. Why are these two definitions of vector equivalence interchangeable? Convince yourself that this is true. Why are these two definitions of vector equivalence interchangeable?
} }
\note<Note 2>{ \note[Note 2]{
A vector is characterized by its direction and length. One cannot make a formal definition out of this observation, because a ``direction'' is formally defined in terms of a vector. A vector is characterized by its direction and length. One cannot make a formal definition out of this observation, because a ``direction'' is formally defined in terms of a vector.
} }
@ -450,7 +445,7 @@
\vfill \vfill
\note<Note>{ \note[Note]{
With the tools we have thus far, we can multiply vectors by any rational number using only a compass and a ruler. Multiplying a vector by an irrational number is a bit more tricky, but it is doable... With the tools we have thus far, we can multiply vectors by any rational number using only a compass and a ruler. Multiplying a vector by an irrational number is a bit more tricky, but it is doable...
} }

13
Intermediate/Vectors 2/main.tex
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@ -3,18 +3,17 @@
\documentclass[solutions]{../../resources/ormc_handout} \documentclass[solutions]{../../resources/ormc_handout}
\begin{document} \uptitlel{Intermediate 2}
\uptitler{ORMC Summer Sessions}
\maketitle \title{Vectors 2}
<Intermediate 2> \subtitle{
<ORMC Summer Sessions>
{Vectors 2}
{
Prepared by Mark on \today \\ Prepared by Mark on \today \\
Based on a handout by Oleg Gleizer Based on a handout by Oleg Gleizer
} }
\begin{document}
\maketitle
\section{Review} \section{Review}

14
Misc/Moscow Puzzles/main.tex
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@ -8,19 +8,21 @@
\usepackage{graphicx} \usepackage{graphicx}
\graphicspath{ {./images} } \graphicspath{ {./images} }
\begin{document}
\maketitle \uptitlel{Intermediate 2}
<Intermediate 2> \uptitler{ORMC Summer Sessions}
<ORMC Summer Sessions> \title{Warm - Up}
{Warm - Up} \subtitle{
{
Prepared by Mark on \today \\ Prepared by Mark on \today \\
\medskip \medskip
These problems were originally found in \\ These problems were originally found in \\
Boris Kordemsky's \textit{The Moscow Puzzles} Boris Kordemsky's \textit{The Moscow Puzzles}
} }
\begin{document}
\maketitle
\subfile{problems/217} \subfile{problems/217}
\vfill \vfill
\pagebreak \pagebreak

11
Misc/Warm-Ups/ast.tex
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@ -1,19 +1,20 @@
\documentclass[ \documentclass[
solutions, solutions,
nowarning, hidewarning,
singlenumbering, singlenumbering,
nopagenumber nopagenumber
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\usepackage[linguistics]{forest} \usepackage[linguistics]{forest}
\title{Warm-Up: What's an AST?}
\subtitle{Prepared by Mark on \today. \\ Based on a true story.}
\begin{document} \begin{document}
\maketitle \maketitle
{Warm-Up: What's an AST?}
{Prepared by Mark on \today. \\ Based on a true story.}
\vspace{2mm}
Say you have a valid string of simple arithmetic that contains no unary operators (like $3!$ or $-4$) and no parenthesis: Say you have a valid string of simple arithmetic that contains no unary operators (like $3!$ or $-4$) and no parenthesis:
$$ $$

10
Misc/Warm-Ups/electician.tex
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@ -1,6 +1,6 @@
\documentclass[ \documentclass[
solutions, solutions,
nowarning, hidewarning,
singlenumbering, singlenumbering,
nopagenumber nopagenumber
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
@ -20,13 +20,15 @@
} }
} }
\title{The Electrician's Warm-Up}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
{The Electrician's Warm-Up}
{Prepared by Mark on \today}
\vspace{2mm}
Ivan the electician is working in an apartment. He has a box of switches, which come in three types: Ivan the electician is working in an apartment. He has a box of switches, which come in three types:
\begin{center} \begin{center}

11
Misc/Warm-Ups/median.tex
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@ -1,17 +1,20 @@
\documentclass[ \documentclass[
nosolutions, solutions,
warning, hidewarning,
singlenumbering, singlenumbering,
nopagenumber nopagenumber
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\usepackage[linguistics]{forest} \usepackage[linguistics]{forest}
\title{Warm-Up: A Familiar Concept}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
{Warm-Up: A Familiar Concept}
{Prepared by Mark on \today.}
\problem{}<one> \problem{}<one>

10
Misc/Warm-Ups/raid.tex
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@ -1,19 +1,21 @@
\documentclass[ \documentclass[
solutions, solutions,
nowarning, hidewarning,
singlenumbering, singlenumbering,
nopagenumber nopagenumber
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\usepackage{tikz} \usepackage{tikz}
\title{The Sysadmin's Warm-Up}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
{The Sysadmin's Warm-Up}
{Prepared by Mark on \today}
\vspace{2mm}
Most of you have seen a hard drive. Many have touched one, and a lucky few have poked around inside one. These devices have two interesting properties: Most of you have seen a hard drive. Many have touched one, and a lucky few have poked around inside one. These devices have two interesting properties:

9
Misc/Warm-Ups/regex.tex
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@ -1,6 +1,6 @@
\documentclass[ \documentclass[
solutions, solutions,
nowarning hidewarning,
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
@ -11,13 +11,14 @@
\sethlcolor{Light} \sethlcolor{Light}
\newcommand{\htexttt}[1]{\texttt{\hl{#1}}} \newcommand{\htexttt}[1]{\texttt{\hl{#1}}}
\title{The Regex Warm-Up}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
{The Regex Warm-Up}
{Prepared by Mark on \today}
\vspace{2mm}
Last time, we discussed Deterministic Finite Automata. One interesting application of these mathematical objects is found in computer science: Regular Expressions. \\ Last time, we discussed Deterministic Finite Automata. One interesting application of these mathematical objects is found in computer science: Regular Expressions. \\
(abbreviated \say{regex}, which is pronounced like \say{gif}) (abbreviated \say{regex}, which is pronounced like \say{gif})

11
Misc/Warm-Ups/sin.tex
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@ -1,19 +1,18 @@
\documentclass[ \documentclass[
nosolutions, solutions,
warning,
singlenumbering, singlenumbering,
nopagenumber nopagenumber
]{../../resources/ormc_handout} ]{../../resources/ormc_handout}
\usepackage[linguistics]{forest} \usepackage[linguistics]{forest}
\title{Warm-Up: Exact answers}
\subtitle{Prepared by Mark on \today}
\begin{document} \begin{document}
\maketitle \maketitle
{Warm-Up: Exact answers}
{Prepared by Mark on \today.}
\vspace{2mm}
Compute the exact value of $\sin(x^\circ)$ for as many integers $x \in [0, 90]$ as you can. Compute the exact value of $\sin(x^\circ)$ for as many integers $x \in [0, 90]$ as you can.

8
Problems/all.tex
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@ -1,6 +1,6 @@
\documentclass[ \documentclass[
solutions, solutions,
nowarning hidewarning,
]{../resources/ormc_handout} ]{../resources/ormc_handout}
@ -88,6 +88,12 @@
} }
\title{Mark's Problem Library}
\subtitle{
This document lists all problems in this library. \\
Use it to find problems or debug the source.
}
\begin{document} \begin{document}
\maketitle \maketitle
{Mark's Problem Library} {Mark's Problem Library}