feat: epigraphs

lamv.typ

@@ -1,10 +1,13 @@
 #import "@local/evan:1.0.0":*
 #let poonen = link("https://math.mit.edu/~poonen/notes02.pdf")[Poonen's notes]
-#let epigraph(quote_src, quote_text) = pad(left: 35%)[
-  #emph(quote_text) \
-  #line(length: 100%)
-  #align(right)[--- #quote_src]
-]
+#let epigraph(quote_text, attribution: none) = {
+  set text(size: 10pt)
+  pad(left: 35%)[
+    #emph(quote_text)
+    #line(length: 100%)
+    #if attribution != none { align(right)[--- #attribution] }
+  ]
+}
 
 #show: evan.with(
   title: [Linear Algebra and Multivariable Calculus],
@@ -28,6 +31,12 @@
 #pagebreak()
 
 #part[Part Alfa: Linear Algebra of Vectors]
+#epigraph(attribution: [_Infinite Jest_, by David Foster Wallace])[
+  It's a very American illness,
+  the idea of giving yourself away entirely to the idea
+  of working in order to achieve some sort of brass ring
+  that usually involves people feeling some way about you.
+]
 For comparison, Part Alfa corresponds roughly to §1, §2, §3.9 of #poonen.
 #include "src/vectors.typ"
 #pagebreak()
@@ -39,6 +48,14 @@ For comparison, Part Alfa corresponds roughly to §1, §2, §3.9 of #poonen.
 #pagebreak()
 
 #part[Part Bravo: Linear Algebra of Matrices]
+#epigraph(attribution: [Lydia's opening line in
+  #link("https://anserena.com/other/writing/")[_Holding on to Her Words_], by Serena An])[
+  Translation is a bridge. It can bridge two languages, time periods, cultures.
+  The pages of a book and your mind.  Even the space between two people.
+  Translation involves reflecting on yourself and your relationships with others.
+  That’s at the heart of why I study Chinese literature.
+  But it took me many years to realize that.
+]
 For comparison, Part Bravo corresponds roughly to §3, §4, §6 of #poonen.
 #include "src/matrix.typ"
 #pagebreak()
@@ -48,18 +65,31 @@ For comparison, Part Bravo corresponds roughly to §3, §4, §6 of #poonen.
 #pagebreak()
 
 #part[Part Charlie: Review of complex numbers]
+#epigraph(attribution: [#link("https://w.wiki/Tpof")[_Stephen's Sausage Roll_]])[
+  Learned people cast great shadows.
+]
 For comparison, Part Charlie corresponds roughly to §11 of #poonen.
 #include "src/complex.typ"
 #pagebreak()
 #include "src/mt1.typ"
 #pagebreak()
 
 #part[Part Delta: Parametric side-quest]
+#epigraph(attribution: [Koro-sensei in _Assassination Classroom_])[
+  Broadly speaking, there are two reasons a person feels the desire to teach something:
+  Either he wants to pass on his successes or he wants to pass on his failures.
+]
 For comparison, Part Delta corresponds roughly to §5 and §7 of #poonen.
 #include "src/param.typ"
 #pagebreak()
 
 #part[Part Echo: Multivariable differentiation]
+#epigraph(attribution: [#link("https://www.ams.org/notices/201005/rtx100500608p.pdf")[What is mathematics for?], by Underwood Dudley])[
+  However, when I am before a bar of judgment, heavenly or otherwise,
+  and asked to justify my life, I will draw myself up proudly and say,
+  "I was one of the stewards of mathematics, and it came to no harm in my care".
+  I will not say, "I helped people get jobs".
+]
 For comparison, Part Echo corresponds roughly to §8 and §12.1-§12.3 of #poonen.
 #include "src/level.typ"
 #pagebreak()
@@ -71,6 +101,9 @@ For comparison, Part Echo corresponds roughly to §8 and §12.1-§12.3 of #poone
 #pagebreak()
 
 #part[Part Foxtrot: Optimization]
+#epigraph(attribution: [Queen in #link("https://w.wiki/6WCE")[_Deltarune_], by Toby Fox])[
+  Teens Are Merely Big Children #text(size:7pt)[And Adults Are Even Bigger Children]
+]
 For comparison, Part Foxtrot corresponds roughly to §9 and §12.4-§12.6 of #poonen.
 #include "src/minmax.typ"
 #pagebreak()
@@ -82,6 +115,10 @@ For comparison, Part Foxtrot corresponds roughly to §9 and §12.4-§12.6 of #po
 #pagebreak()
 
 #part[Part Golf: 2D integrals of scalar functions]
+#epigraph(attribution: [Calvin in _Calvin and Hobbes_ (May 3, 1989)])[
+  Mom says Hobbes wouldn't have stolen because he's not valuable. \
+  ... (sniff) well, *I* think he's valuable.
+]
 For comparison, Part Golf corresponds to §13.1-§13.5 of #poonen.
 #include "src/ipep.typ"
 #pagebreak()
@@ -95,6 +132,15 @@ For comparison, Part Golf corresponds to §13.1-§13.5 of #poonen.
 #pagebreak()
 
 #part[Part Hotel: 3D integrals of scalar functions]
+#epigraph(attribution: [Author notes for
+  #link("https://puzzles.mit.edu/2023/puzzlefactory.place/puzzles/5d-barred-diagramless-with-multiverse-time-travel")[5D Barred Diagramless with Multiverse Time Travel],
+  by Alex Irpan])[
+  At some points, I was not convinced this puzzle should even exist,
+  but editors and testsolvers encouraged me to finish it, saying it was
+  "exactly the bullshit I expect to see in Mystery Hunt".
+  (The lucky postprodder for the puzzle would also like to voice his support.)
+  Hope you had fun! Really, it could have been much worse.
+]
 For comparison, Part Hotel corresponds to §13.6-13.9 and §17.1-§17.6 of #poonen.
 #include "src/triple.typ"
 #pagebreak()
@@ -108,6 +154,12 @@ For comparison, Part Hotel corresponds to §13.6-13.9 and §17.1-§17.6 of #poon
 #pagebreak()
 
 #part[Part India: Line integrals of vector fields over a curve]
+#epigraph(attribution: [EWD 1036, by Edsger W. Dijkstra (1988)])[
+  My point today is that, if we wish to count lines of code,
+  we should not regard them as "lines produced" but as "lines spent":
+  the current conventional wisdom is so foolish as to book
+  that count on the wrong side of the ledger.
+]
 For comparison, Part India corresponds to §14, §15, §20, §21 of #poonen.
 #include "src/vecfield.typ"
 #pagebreak()
@@ -125,6 +177,10 @@ For comparison, Part India corresponds to §14, §15, §20, §21 of #poonen.
 #pagebreak()
 
 #part[Part Juliett: Flux integrals of vector fields over a surface]
+#epigraph(attribution: [Monokuma in _Danganronpa_])[
+  Every human has regrets, has things they'd like to go back and change.
+  But I don't! 'Cause I'm a bear!
+]
 For comparison, Part Juliett corresponds to §17.7, §18, §19, §21 of #poonen.
 #include "src/flux.typ"
 #pagebreak()
@@ -134,10 +190,17 @@ For comparison, Part Juliett corresponds to §17.7, §18, §19, §21 of #poonen.
 #pagebreak()
 
 #part[Part Kilo: Practice questions]
+#epigraph(attribution: [Lester Gardner])[
+  The beaver is noted for his engineering, mechanical skills, and industry.
+  His habits are nocturnal. He does his best work in the dark.
+]
 #include "src/practice.typ"
 #pagebreak()
 
 #part[Part Lima: Solutions]
+#epigraph(attribution: [#link("https://mitadmissions.org/discover/life-culture/hacks-tomfoolery-pranks/")[MIT hacker code of ethics]])[
+  Brute force is the last resort of the incompetent.
+]
 #include "src/sol-alfa.typ"
 #pagebreak()
 #include "src/sol-bravo.typ"
@@ -162,4 +225,10 @@ For comparison, Part Juliett corresponds to §17.7, §18, §19, §21 of #poonen.
 #pagebreak()
 
 #part[Part Mike: Appendix]
+#epigraph[
+  You all have a little bit of "I want to save the world" in you,
+  that's why you're here, in college.
+  I want you to know that it's okay if you only save one person,
+  and it's okay if that person is you.
+]
 #include "src/appendix.typ"

recitations/r03.typ

@@ -7,7 +7,7 @@
   date: [11 September 2024],
 )
 
-#quote(attribution: [Monokuma in _Danganropa_])[
+#quote(attribution: [Monokuma in _Danganronpa_])[
   Every human has regrets, has things they'd like to go back and change.
   But I don't! 'Cause I'm a bear!
 ]

src/divthm.typ

@@ -185,9 +185,9 @@ We can jump straight into examples now!
   Obviously $int_(theta=0)^(2pi) dif theta = 2pi$.
   The double integral can be evaluated as
   $ int_(r=0)^1 r int_(z=0)^(r^2) z dif z dif r
-    &= int_(r=0)^1 r dot [z^2/2]_(z=0)^(r^2) dif r \
-    &= int_(r=0)^1 r^5/2 dif r \
-    &= [r^6/12]_(r=0)^1 = 1/12. $
+    = int_(r=0)^1 r dot [z^2/2]_(z=0)^(r^2) dif r
+    = int_(r=0)^1 r^5/2 dif r
+    = [r^6/12]_(r=0)^1 = 1/12. $
   Hence the final answer is
   $  1/12 dot 2 pi = #boxed[$ pi / 6 $]. #qedhere $
 ]

src/flux.typ

@@ -75,10 +75,6 @@ in addition to the actual points,
 we need to specify an _orientation_.
 To be more precise, at every point $P$ of the surface $cal(S)$,
 the cross product from our parametrization could point in one of two opposite directions.
-#definition(title: [Definition of orienting a surface])[
-  To _orient_ the surface $cal(S)$ is to specify, at each point,
-  which way you want the cross product of your parametrization to point.
-]
 
 #figure(
   image("figures/flux-cross-sign.svg", width: auto),
@@ -89,6 +85,11 @@ the cross product from our parametrization could point in one of two opposite di
   ],
 ) <fig-flux-cross-sign>
 
+#definition(title: [Definition of orienting a surface])[
+  To _orient_ the surface $cal(S)$ is to specify, at each point,
+  which way you want the cross product of your parametrization to point.
+]
+
 Algebraically, this corresponds to choosing the _order of $u$ and $v$_;
 as if you flip the order of the two parameters it will negate the entire cross product:
 $ (partial bf(r))/(partial u) times (partial bf(r))/(partial v)

src/ipep.typ

@@ -11,6 +11,14 @@ If you've been following my advice to pay attention to type safety so far, it'll
 I'll freely admit that I (Evan) often make type-errors in this part of 18.02 as well,
 so don't let your guard down.
 
+#figure(
+  image("figures/integrals-triangle.svg", width: 100%),
+  caption: [
+    For each $0 <= d <= n <= 3$, we draw the kind of integral and give it a name.
+    Download at #url("https://web.evanchen.cc/textbooks/poster-ints.pdf").
+  ]
+) <poster-triangle>
+
 Remember that:
 #idea[
   Suppose $f : RR^n -> RR$ is given, and $0 <= d <= n$.
@@ -25,19 +33,10 @@ So philosophically, a $0$-dimensional integral is just a finite sum of $f$ at so
 This might seem stupid that I bring up this degenerate case,
 but it turns out later when we cover div/grad/curl the $0$-dimensional case is relevant.
 
-Here's a giant chart in @poster-triangle.
+We give a giant chart in @poster-triangle.
 (The chart is so big it doesn't quite fit in the page,
 but you can download a
 #link("https://web.evanchen.cc/textbooks/poster-ints.pdf")[large PDF version]).
-
-#figure(
-  image("figures/integrals-triangle.svg", width: 100%),
-  caption: [
-    For each $0 <= d <= n <= 3$, we draw the kind of integral and give it a name.
-    Download at #url("https://web.evanchen.cc/textbooks/poster-ints.pdf").
-  ]
-) <poster-triangle>
-
 This chart has ten different kinds of integrals,
 one for each $(d,n)$ with $0 <= d <= n <= 3$.
 Here's a rundown of the things in the chart.

src/practice.typ

@@ -54,8 +54,8 @@ Solutions are in @ch-sol-kilo.
   with normal vector oriented outwards (thus $cal(S)$ is the curved part of a cylinder).
   Compute the divergence of $bf(F)$.
   Then compute the flux of $bf(F)$ through $cal(S)$.
-  (Recommended approach: add two "lids" to $cal(S)$, calculate flux through the lids by hand,
-  then use the divergence theorem.)
+  (Recommended approach: add two "lids" to $cal(S)$
+  and use the divergence theorem.)
 ] <exer-mf-8>
 
 == Miscellaneous practice questions without solutions

src/sol-alfa.typ

@@ -140,10 +140,10 @@ $ op("comp")_(bf(w))(bf(v)) = frac(bf(v) dot bf(w), |bf(w)|)
 The vector projection of $bf(v)$ along $bf(w)$ is
 given by:
 $ op("proj")_(bf(w))(bf(v))
-  &= frac(bf(v) dot bf(w), |bf(w)|) (bf(w) / (|bf(w)|)) \
-  &= -11/5 dot vec(-3000, -4000, 0) / 5000 \
-  &= -11/5 dot vec(-3 slash 5, -4 slash 5, 0) \
-  &= #boxed[$ vec(33 slash 25, 44 slash 25, 0) $]. $
+  = frac(bf(v) dot bf(w), |bf(w)|) (bf(w) / (|bf(w)|))
+  = -11/5 dot vec(-3000, -4000, 0) / 5000
+  = -11/5 dot vec(-3 slash 5, -4 slash 5, 0)
+  = #boxed[$ vec(33 slash 25, 44 slash 25, 0) $]. $
 
 == Solution to @exer-dot-reverse (dot product $3$)
 
@@ -156,6 +156,13 @@ See @fig-sol-alfa-dot-reverse for a picture.
 (You might already guess one of the solutions ---
 $bf(v) = chevron.l 1,0 chevron.r $ obviously works --- but we'll pretend we didn't notice that.)
 
+#figure(
+  image("figures/sol-alfa-dot-reverse.svg", width: auto),
+  caption: [The two answers to @exer-dot-reverse,
+    which are two unit vectors spaced at an equal angle away from $chevron.l 3,4 chevron.r$.
+  ],
+) <fig-sol-alfa-dot-reverse>
+
 Translating the givens algebraically,
 we have the following system of equations:
 $ bf(v) dot bf(w) = 3 &==> 3 x + 4 y = 3 \
@@ -180,13 +187,6 @@ In conclusion the answer is
 $ #boxed[$ chevron.l 1,0 chevron.r " and " lr(chevron.l -7/25, 24/25 chevron.r) $]. $
 See @fig-sol-alfa-dot-reverse for a picture of the two answers.
 
-#figure(
-  image("figures/sol-alfa-dot-reverse.svg", width: auto),
-  caption: [The two answers to @exer-dot-reverse,
-    which are two unit vectors spaced at an equal angle away from $chevron.l 3,4 chevron.r$.
-  ],
-) <fig-sol-alfa-dot-reverse>
-
 == Solution to @exer-cauchy ($2$ and $5$)
 
 #recall-thm(<exer-cauchy>)

src/triple.typ

@@ -82,19 +82,16 @@ so one needs different letters.
       2sqrt(1-x^2)
       int_(y=-sqrt(1-x^2))^(sqrt(1-x^2)) 1 dif y dif x \
     &= int_(x=-1)^1
-      2sqrt(1-x^2) dot 2sqrt(1-x^2) dif x \
-    &= int_(x=-1)^1 4(1-x^2) dif x \
+      2sqrt(1-x^2) dot 2sqrt(1-x^2) dif x
+    = int_(x=-1)^1 4(1-x^2) dif x \
     &= 4[x - x^3 / 3]_(x=-1)^1 = 4[(1 - 1 / 3) - (-1 + 1/3)] = #boxed[$ 16 /3 $]. #qedhere $
 ]
 #digression(title: [Digression on picture])[
   If you draw a picture of the region,
   you get the intersection of these two cylinders
   which forms something apparently called a _Steinmetz solid_.
-  (I say "apparently" because ChatGPT told me this name;
-  I didn't know this had a name before either.)
 
-  Surprisingly, you actually _don't_ want to use polar (or cylindrical) coordinates
-  on this example.
+  Surprisingly, you actually _don't_ want to use polar (or cylindrical) coordinates on this example.
   If you try to do so, I think you'll actually get stuck.
   Straight $x y z$-integration turns out to work because of the
   unexpectedly convenient fact that you get two square roots that miraculously cancel.
@@ -167,13 +164,12 @@ If you were able to do the earlier example with
 $z = 3(x^2+y^2)$ and $z = 72-5(x^2+y^2)$ by yourself without reading the solution,
 then you can safely skip this entire section!
 
-The transition map $ (r, theta, z) |-> (x, y, z)$ is given by
+The transition map $(r, theta, z) |-> (x, y, z)$, illustrated in @fig-triple-cylinder, is given by
 $
   x &= r cos theta \
   y &= r sin theta \
   z &= z.
 $
-This is illustrated in @fig-triple-cylinder.
 #figure(
   image("figures/triple-cylinder.svg", width: auto),
   caption: [Picture of cylindrical coordinates.