Tom edits

lib/tex/ormc_handout.cls

@@ -1,18 +1,3 @@
-% Copyright (C) 2023 Mark (mark@betalupi.com)
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-%
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see <https://www.gnu.org/licenses/>.
-
 \NeedsTeXFormat{LaTeX2e}
 \ProvidesClass{../../../lib/tex/ormc_handout}[2023/05/29 2.0.2 ORMC Handout]
 

src/Advanced/Error-Correcting Codes/parts/00 detection.tex

@@ -19,7 +19,7 @@ Only one of the following ISBNs is valid. Which one is it?
 
 \begin{itemize}
 	\item \texttt{0-134-54896-2}
-	\item \texttt{0-895-77258-2}
+	\item \texttt{0-895-77258-2} % oliver twist
 \end{itemize}
 
 \begin{solution}
@@ -67,18 +67,19 @@ This is called a \textit{transposition error}.
 \vfill
 \pagebreak
 
-\problem{}
+\definition{}
 ISBN-13 error checking is slightly different. Given a partial ISBN-13 $n_1 n_2 n_3 ... n_{12}$, the final digit is given by
 
 $$
  n_{13} = \Biggr[ \sum_{i=1}^{12} n_i \times (2 + (-1)^i) \Biggl] \text{ mod } 10
 $$
 
+\problem{}
 What is the last digit of the following ISBN-13? \par
-\texttt{978-0-380-97726-?}
+\texttt{978-030-7292-06*} % foundation
 
 \begin{solution}
-	The final digit is 0.
+	The final digit is 3.
 \end{solution}
 
 \vfill
@@ -127,7 +128,7 @@ Take a valid ISBN-13 and swap two adjacent digits. When will the result be a val
 \vfill
 
 \problem{}<isbn-nocorrect>
-\texttt{978-0-08-2066-46-6} was a valid ISBN until I changed a single digit. \par
+\texttt{978-008-2066-466} was a valid ISBN until I changed a single digit. \par
 Can you find the digit I changed? Can you recover the original ISBN?
 
 \begin{solution}

src/Advanced/Error-Correcting Codes/parts/02 hamming.tex

@@ -570,8 +570,45 @@ If we know which parity bits are inconsistent, how can we find where the error i
 \vfill
 
 \problem{}<generalize-hamming>
-Can you generalize this system for messages of 4, 64, or 256 bits?
+Generalize this system for messages of 4, 64, or 256 bits. \par
+\begin{itemize}
+	\item How does the resilience of this scheme change if we use a larger message size?
+	\item How does the efficiency of this scheme change if we send larger messages?
+\end{itemize}
+
+\vfill
+\pagebreak
+
+
+\definition{}
+A \textit{deletion} error occurs when one bit of the message is deleted. \par
+Likewise, an \textit{insertion} error consists of a random inserted bit. \par
+
+\definition{}
+A \textit{message stream} is an infinite string of binary digits.
+
+\problem{}
+Show that Hamming codes do not reliably detect bit deletions: \par
+\hint{
+	Create a 17-bit message whose first 16 bits are a valid Hamming block, \par
+	and which is still valid when a bit (chosen by you; not the $17^\text{th}$) is deleted.
+}
 
 \vfill
 
+\problem{}
+Convince yourself that Hamming codes cannot correct insertions. \par
+Then, create a 16-bit message that...
+\begin{itemize}
+	\item is a valid Hamming block, and
+	\item incorrectly "corrects" a single bit error when it encounters an insertion error.
+\end{itemize}
+
+\vfill
+
+
+As we have seen, Hamming codes effectively handle substitutions, but cannot reliably
+detect (or correct) insertions and deletions. Correcting those errors is a bit more difficult:
+if the number of bits we receive is variable, how can we split a stream into a series of messages? \par
+\note{This is a rhetorical question, which we'll discuss another day.}
 \pagebreak

src/Advanced/Fast Inverse Root/parts/00 intro.typ

@@ -36,7 +36,7 @@ This code defines a function `Q_sqrt`, which was used as a fast approximation of
 
 #v(3mm)
 
-The key word here is "fast": _Quake_ ran on very limited hardware, and traditional approximation techniques (like Taylor series)#footnote[In fact, Taylor series aren't used today, and for the same reason: there are better ways.] were too computationally expensive to be viable.
+The key word here is "fast": _Quake_ ran on very limited hardware, and traditional approximation techniques (like Taylor series)#footnote[Taylor series aren't used today, and for the same reason. There are better ways.] were too computationally expensive to be viable.
 
 #v(3mm)
 

src/Advanced/Fast Inverse Root/parts/01 int.typ

@@ -6,7 +6,7 @@
 A _bit string_ is a string of binary digits. \
 In this handout, we'll denote bit strings with the prefix `0b`. \
 #note[This prefix is only notation---it is _not_ part of the string itself.] \
-For example, $1010$ is the number "one thousand and one," while $#text([`0b1001`])$ is the string of bits "1 0 0 1".
+For example, $1001$ is the number "one thousand and one," while $#text([`0b1001`])$ is the string of bits "1 0 0 1".
 
 #v(2mm)
 We will separate long bit strings with underscores for readability. \
@@ -69,19 +69,19 @@ Find the value of each of the following 32-bit unsigned integers:
 
 
 #definition()
-In general, fast division of `uints` is difficult.#footnote([One may use repeated subtraction, but this isn't efficient.]). \
+In general, fast division of `uints` is difficult#footnote([One may use repeated subtraction, but this isn't efficient.]). \
 Division by powers of two, however, is incredibly easy: \
 To divide by two, all we need to do is shift the bits of our integer right.
 
 #v(2mm)
 
 For example, consider $#text[`0b0000_0110`] = 6$. \
-If we insert a zero at the left end of this bit string and delete the digit at the right \
+If we insert a zero at the left end of this string and delete the zero at the right \
 (thus "shifting" each bit right), we get `0b0000_0011`, which is 3. \
 
 #v(2mm)
 
-Of course, we lose the remainder when we left-shift an odd number: \
+Of course, we lose the remainder when we right-shift an odd number: \
 $9$ shifted right is $4$, since `0b0000_1001` shifted right is `0b0000_0100`.
 
 #problem()

src/Advanced/Fast Inverse Root/parts/02 float.typ

@@ -3,7 +3,7 @@
 
 = Floats
 #definition()
-_Binary decimals_#footnote([Note that "binary decimal" is a misnomer---"deci" means "ten"!]) \
+_Binary decimals_#footnote([Note that "binary decimal" is a misnomer---"deci" means "ten"!]) are very similar to base-10 decimals.\
 In base 10, we interpret place value as follows:
 - $0.1 = 10^(-1)$
 - $0.03 = 3 times 10^(-2)$
@@ -113,7 +113,7 @@ Floats represent a subset of the real numbers, and are interpreted as follows: \
   They are interpreted as the fractional part of a binary decimal. \
   For example, the bits `0b10100000_00000000_00000000` represent $0.5 + 0.125 = 0.625$. \
   We'll call the value of these bits as a binary integer $F$. \
-  Their value as a binary decimal is then $F div 2^23$. #note([(Convince yourself that this is true!)])
+  Their value as a binary decimal is then $F div 2^23$. #note([(convince yourself of this)])
 
 
 #problem(label: "floata")
@@ -145,7 +145,7 @@ $
 
 #note[
   We subtract 127 from $E$ so we can represent positive and negative numbers. \
-  $E$ is an eight bit binary integer, so $0 <= E <= 255$ and $-127 <= (E - 127) <= 127$.
+  $E$ is an eight bit binary integer, so $0 <= E <= 255$ and thus $-127 <= (E - 127) <= 127$.
 ]
 
 #problem()

src/Advanced/Fast Inverse Root/parts/03 approx.typ

@@ -64,7 +64,7 @@ This allows us to improve the average error of our linear approximation:
       Max error: 0.086 \
       Average error: 0.0573
     ],
-  [$log(1+x)_2$ and $x + 0.045$]
+  [$log_2(1+x)$ and $x + 0.045$]
     + cetz.canvas({
       import cetz.draw: *
 
@@ -125,7 +125,7 @@ We won't bother with this---we'll simply leave the correction term as an opaque
   [
     "Average error" above is simply the area of the region between the two graphs:
     $
-      integral_0^1 abs( #v(1mm) log(1+x) - (x+epsilon) #v(1mm))
+      integral_0^1 abs( #v(1mm) log(1+x)_2 - (x+epsilon) #v(1mm))
     $
     Feel free to ignore this note, it isn't a critical part of this handout.
   ],

src/Advanced/Fast Inverse Root/parts/04 quake.typ

@@ -20,9 +20,8 @@ This code defines a function `Q_rsqrt` that consumes a float `number` and approx
 If we rewrite this using notation we're familiar with, we get the following:
 $
   #text[`Q_sqrt`] (n_f) =
-  #h(5mm)
   6240089 - (n_i div 2)
-  #h(5mm)
+  #h(10mm)
   approx 1 / sqrt(n_f)
 $
 
@@ -70,7 +69,7 @@ In other words,
 $
   r_f := 1 / (sqrt(n_f))
 $
-This is the value we want to approximate.
+This is the value we want to approximate. \
 
 #problem(label: "finala")
 Find an approximation for $log_2(r_f)$ in terms of $n_i$ and $epsilon$ \
@@ -92,7 +91,11 @@ Let's call the "magic number" in the code above $kappa$, so that
 $
   #text[`Q_sqrt`] (n_f) = kappa - (n_i div 2)
 $
-Use @convert and @finala to show that $#text[`Q_sqrt`] (n_f) approx r_i$
+Use @convert and @finala to show that $#text[`Q_sqrt`] (n_f) approx r_i$ \
+#note(type: "Note")[
+  If we know $r_i$, we know $r_f$. \
+  We don't even need to convert between the two---the underlying bits are the same!
+]
 
 #solution[
   From @convert, we know that

src/Advanced/Introduction to Quantum/src/main.tex

@@ -1,18 +1,3 @@
-% Copyright (C) 2023 <Mark (mark@betalupi.com)>
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-%
-% You may have received a copy of the GNU General Public License
-% along with this program. If not, see <https://www.gnu.org/licenses/>.
-%
-%
-%
-% If you edit this, please give credit!
-% Quality handouts take time to make.
-
 % use the [nosolutions] flag to hide solutions,
 % use the [solutions] flag to show solutions.
 \documentclass[

src/Advanced/Nonstandard Analysis/main.tex

@@ -1,19 +1,3 @@
-% Copyright (C) 2023 <Mark (mark@betalupi.com)>
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-%
-% You may have received a copy of the GNU General Public License
-% along with this program. If not, see <https://www.gnu.org/licenses/>.
-%
-%
-%
-% If you edit this, please give credit!
-% Quality handouts take time to make.
-
-
 % use [nosolutions] flag to hide solutions.
 % use [solutions] flag to show solutions.
 \documentclass[

src/Advanced/Nonstandard Analysis/parts/dual.tex

@@ -1,19 +1,3 @@
-% Copyright (C) 2023 <Mark (mark@betalupi.com)>
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-%
-% You may have received a copy of the GNU General Public License
-% along with this program. If not, see <https://www.gnu.org/licenses/>.
-%
-%
-%
-% If you edit this, please give credit!
-% Quality handouts take time to make.
-
-
 \section{Dual Numbers}
 
 \definition{}

src/Advanced/Nonstandard Analysis/parts/extensions.tex

@@ -1,18 +1,3 @@
-% Copyright (C) 2023 <Mark (mark@betalupi.com)>
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-%
-% You may have received a copy of the GNU General Public License
-% along with this program. If not, see <https://www.gnu.org/licenses/>.
-%
-%
-%
-% If you edit this, please give credit!
-% Quality handouts take time to make.
-
 \section{Extensions of $\mathbb{R}$}
 
 \definition{}

src/Advanced/Nonstandard Analysis/parts/supremum.tex

@@ -1,19 +1,3 @@
-% Copyright (C) 2023 <Mark (mark@betalupi.com)>
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-%
-% You may have received a copy of the GNU General Public License
-% along with this program. If not, see <https://www.gnu.org/licenses/>.
-%
-%
-%
-% If you edit this, please give credit!
-% Quality handouts take time to make.
-
-
 \section*{The supremum \& the infimum}
 
 \definition{}