auto-update(nvim): 2025-01-06 15:32:17

documents/by-course/math-8/course-notes/dvd.typ

@@ -45,10 +45,12 @@
       if loc.page() == 1 {
         return
       }
-      box(stroke: (bottom: 0.7pt), inset: 0.2em)[#text(
+      box(stroke: (bottom: 0.7pt), inset: 0.4em)[#text(
           font: "New Computer Modern",
         )[
-          #author #h(1fr)#title
+          *#author* --- #datetime.today().display("[day] [month repr:long] [year]")
+          #h(1fr)
+          *#title*
         ]]
     }),
     paper: paper-size,
@@ -86,7 +88,7 @@
     #if author != none [#text(16pt)[by #author]]
     #v(1.2em, weak: true)
     #if subtitle != none [#text(12pt, weight: 500)[#(
-          datetime.today().display("[month repr:long] [day], [year]")
+          datetime.today().display("[day] [month repr:long] [year]")
         )]]
 
   ]

documents/by-course/pstat-120a/course-notes/dvd.typ

@@ -0,0 +1,282 @@
+#import "@preview/ctheorems:1.1.2": *
+#import "@preview/showybox:2.0.1": showybox
+
+#let colors = (
+  rgb("#9E9E9E"),
+  rgb("#F44336"),
+  rgb("#E91E63"),
+  rgb("#9C27B0"),
+  rgb("#673AB7"),
+  rgb("#3F51B5"),
+  rgb("#2196F3"),
+  rgb("#03A9F4"),
+  rgb("#00BCD4"),
+  rgb("#009688"),
+  rgb("#4CAF50"),
+  rgb("#8BC34A"),
+  rgb("#CDDC39"),
+  rgb("#FFEB3B"),
+  rgb("#FFC107"),
+  rgb("#FF9800"),
+  rgb("#FF5722"),
+  rgb("#795548"),
+  rgb("#9E9E9E"),
+)
+
+#let dvdtyp(
+  title: "",
+  subtitle: "",
+  author: "",
+  abstract: none,
+  bibliography: none,
+  paper-size: "a4",
+  body,
+) = {
+  set document(title: title, author: author)
+
+  set std.bibliography(style: "springer-mathphys", title: [References])
+
+  show: thmrules
+
+  set page(
+    numbering: "1",
+    number-align: center,
+    header: locate(loc => {
+      if loc.page() == 1 {
+        return
+      }
+      box(stroke: (bottom: 0.7pt), inset: 0.4em)[#text(
+          font: "New Computer Modern",
+        )[
+          *#author* --- #datetime.today().display("[day] [month repr:long] [year]")
+          #h(1fr)
+          *#title*
+        ]]
+    }),
+    paper: paper-size,
+    // The margins depend on the paper size.
+    margin: (
+      left: (86pt / 216mm) * 100%,
+      right: (86pt / 216mm) * 100%,
+    ),
+  )
+
+
+  set heading(numbering: "1.")
+  show heading: it => {
+    set text(font: "Libertinus Serif")
+    set par(first-line-indent: 0em)
+
+    if it.numbering != none {
+      text(rgb("#2196F3"), weight: 500)[#sym.section]
+
+      text(rgb("#2196F3"))[#counter(heading).display() ]
+    }
+    it.body
+  }
+
+  set text(font: "New Computer Modern", lang: "en")
+
+  show math.equation: set text(weight: 400)
+
+
+  // Title row.
+  align(center)[
+    #set text(font: "Libertinus Serif")
+    #block(text(weight: 700, 26pt, title))
+    #v(1.8em, weak: true)
+    #if author != none [#text(16pt)[by #author]]
+    #v(1.2em, weak: true)
+    #if subtitle != none [#text(12pt, weight: 500)[#(
+          datetime.today().display("[day] [month repr:long] [year]")
+        )]]
+
+  ]
+
+  if abstract != none [
+    #v(2em)
+    #set text(font: "Libertinus Serif")
+    #pad(x: 14%, abstract)
+    #v(1em)
+  ]
+
+  set outline(fill: repeat[~.], indent: 1em)
+
+  show outline: set heading(numbering: none)
+  show outline: set par(first-line-indent: 0em)
+
+  show outline.entry.where(level: 1): it => {
+    text(font: "Libertinus Serif", rgb("#2196F3"))[#strong[#it]]
+  }
+  show outline.entry: it => {
+    h(1em)
+    text(font: "Libertinus Serif", rgb("#2196F3"))[#it]
+  }
+
+
+  // Main body.
+  set par(
+    justify: true,
+    first-line-indent: 1em,
+  )
+
+  body
+
+  // Display the bibliography, if any is given.
+  if bibliography != none {
+    show std.bibliography: set text(footnote-size)
+    show std.bibliography: set block(above: 11pt)
+    show std.bibliography: pad.with(x: 0.5pt)
+    bibliography
+  }
+}
+
+#let thmtitle(t, color: rgb("#000000")) = {
+  return text(
+    font: "Libertinus Serif",
+    weight: "semibold",
+    fill: color,
+  )[#t]
+}
+#let thmname(t, color: rgb("#000000")) = {
+  return text(font: "Libertinus Serif", fill: color)[(#t)]
+}
+
+#let thmtext(t, color: rgb("#000000")) = {
+  let a = t.children
+  if (a.at(0) == [ ]) {
+    a.remove(0)
+  }
+  t = a.join()
+
+  return text(font: "New Computer Modern", fill: color)[#t]
+}
+
+#let thmbase(
+  identifier,
+  head,
+  ..blockargs,
+  supplement: auto,
+  padding: (top: 0.5em, bottom: 0.5em),
+  namefmt: x => [(#x)],
+  titlefmt: strong,
+  bodyfmt: x => x,
+  separator: [#h(0.1em).#h(0.2em) \ ],
+  base: "heading",
+  base_level: none,
+) = {
+  if supplement == auto {
+    supplement = head
+  }
+  let boxfmt(name, number, body, title: auto, ..blockargs_individual) = {
+    if not name == none {
+      name = [ #namefmt(name)]
+    } else {
+      name = []
+    }
+    if title == auto {
+      title = head
+    }
+    if not number == none {
+      title += " " + number
+    }
+    title = titlefmt(title)
+    body = bodyfmt(body)
+    pad(
+      ..padding,
+      showybox(
+        width: 100%,
+        radius: 0.3em,
+        breakable: true,
+        padding: (top: 0em, bottom: 0em),
+        ..blockargs.named(),
+        ..blockargs_individual.named(),
+        [#title#name#titlefmt(separator)#body],
+      ),
+    )
+  }
+
+  let auxthmenv = thmenv(
+    identifier,
+    base,
+    base_level,
+    boxfmt,
+  ).with(supplement: supplement)
+
+  return auxthmenv.with(numbering: "1.1")
+}
+
+#let styled-thmbase = thmbase.with(
+  titlefmt: thmtitle,
+  namefmt: thmname,
+  bodyfmt: thmtext,
+)
+
+#let builder-thmbox(color: rgb("#000000"), ..builderargs) = styled-thmbase.with(
+  titlefmt: thmtitle.with(color: color.darken(30%)),
+  bodyfmt: thmtext.with(color: color.darken(70%)),
+  namefmt: thmname.with(color: color.darken(30%)),
+  frame: (
+    body-color: color.lighten(92%),
+    border-color: color.darken(10%),
+    thickness: 1.5pt,
+    inset: 1.2em,
+    radius: 0.3em,
+  ),
+  ..builderargs,
+)
+
+#let builder-thmline(
+  color: rgb("#000000"),
+  ..builderargs,
+) = styled-thmbase.with(
+  titlefmt: thmtitle.with(color: color.darken(30%)),
+  bodyfmt: thmtext.with(color: color.darken(70%)),
+  namefmt: thmname.with(color: color.darken(30%)),
+  frame: (
+    body-color: color.lighten(92%),
+    border-color: color.darken(10%),
+    thickness: (left: 2pt),
+    inset: 1.2em,
+    radius: 0em,
+  ),
+  ..builderargs,
+)
+
+#let problem-style = builder-thmbox(
+  color: colors.at(11),
+  shadow: (offset: (x: 2pt, y: 2pt), color: luma(70%)),
+)
+
+#let problem = problem-style("problem", "Problem")
+
+#let theorem-style = builder-thmbox(
+  color: colors.at(6),
+  shadow: (offset: (x: 3pt, y: 3pt), color: luma(70%)),
+)
+
+#let theorem = theorem-style("theorem", "Theorem")
+#let lemma = theorem-style("lemma", "Lemma")
+#let corollary = theorem-style("corollary", "Corollary")
+
+#let definition-style = builder-thmline(color: colors.at(8))
+
+#let definition = definition-style("definition", "Definition")
+#let proposition = definition-style("proposition", "Proposition")
+#let remark = definition-style("remark", "Remark")
+#let observation = definition-style("observation", "Observation")
+
+#let example-style = builder-thmline(color: colors.at(16))
+
+#let example = example-style("example", "Example").with(numbering: none)
+
+#let proof(body, name: none) = {
+  thmtitle[Proof]
+  if name != none {
+    [ #thmname[#name]]
+  }
+  thmtitle[.]
+  body
+  h(1fr)
+  $square$
+}

documents/by-course/pstat-120a/course-notes/main.typ

@@ -0,0 +1,121 @@
+#import "./dvd.typ": *
+
+#show: dvdtyp.with(
+  title: "Probability and Statistics",
+  author: "Youwen Wu",
+)
+
+#outline()
+
+= Lecture 1
+
+== Preliminaries
+
+#definition("Statistics")[
+  The science dealing with the collection, summarization, analysis, and
+  interpretation of data.
+]
+
+== Set theory for dummies
+
+A terse introduction to elementary set theory and the basic operations upon
+them.
+
+#definition[Set][
+  A collection of elements.
+]
+
+#example[Examples of sets][
+  + Trivial set: ${1}$
+  + Empty set: $emptyset$
+  + $A = {a,b,c}$
+]
+
+We can construct sets using set-builder notation (also sometimes called set comprehension).
+
+$ {"expression with" x | "conditions on" x} $
+
+#example("Set builder notation")[
+  + The set of all even integers: ${2n | n in ZZ}$
+  + The set of all perfect squares in $RR$: ${x^2 | x in NN}$
+]
+
+We also have notation for working with sets:
+
+With arbitrary sets $A$, $B$, $Omega$:
+
++ $a in A$ ($a$ is a member of the set $A$)
++ $a in.not A$ ($a$ is not a member of the set $A$)
++ $A subset.eq Omega$ (Set theory: $A$ is a subset of $Omega$) (Stats: $A$ is a sample space in $Omega$)
++ $A subset Omega$ (Proper subset: $A != Omega$)
++ $A^c$ or $A'$ (read "complement of $A$")
++ $A union B$ (Union of $A$ and $B$. Gives a set with both the elements of $A$ and $B$)
++ $A sect B$ (Intersection of $A$ and $B$. Gives a set consisting of the elements in *both* $A$ and $B$)
++ $A \\ B$ (Set difference. The set of all elements of $A$ that are not also in $B$)
++ $A times B$ (Cartesian product. Ordered pairs of $(a,b)$ $forall a in A$, $forall b in B$)
+
+We can also write a few of these operations precisely as set comprehensions.
+
++ $A subset Omega => A = {a | a in Omega, forall a in A}$
++ $A union B = {x | x in A or x in B}$ (here $or$ is the logical OR)
++ $A sect B = {x | x in A and x in B}$ (here $and$ is the logical AND)
++ $A \\ B = {a | a in A and a in.not B}$
++ $A times B = {(a,b) | forall a in A, forall b in B}$
+
+Convince yourself that these definitions are equivalent to the previous ones.
+
+#example[The real plane][
+  The real plane $RR^2$ can be defined as a Cartesian product of $RR$ with itself.
+
+  $ RR^2 = RR times RR $
+]
+
+Check your intuition that this makes sense. Why do you think $RR^n$ was chosen as the notation for $n$ dimensional spaces in $RR$?
+
+#remark[Disjoint sets][
+  If $A sect B$ = $emptyset$, then we say that $A$ and $B$ are *disjoint*.
+]
+
+#theorem[Properties of set operations][
+  + DeMorgan's Laws:
+    + $(A union B)' = A' sect B'$
+    + $(A sect B)' = A' union B'$
+]
+
+#remark[Generalized DeMorgan's][
+  + $(union_i A_i)' = sect_i A_i'$
+  + $(sect_i A_i)' = union_i A_i'$
+]
+
+=== Sizes of infinity
+
+#definition("Cardinality")[
+  Let $N(A)$ be the number of elements in $A$. $N(A)$ is called the _cardinality_ of $A$.
+]
+
+Sets are either finite or infinite. Finite sets have a fixed finite cardinality.
+
+Infinite sets can be either _countably infinite_ or _uncountably infinite_.
+
+When a set is countably infinite, its cardinality is $aleph_0$ (here $aleph$ is
+the Hebrew letter aleph and read "aleph null").
+
+When a set is uncountably infinite, its cardinality is greater than $aleph_0$.
+
+#example("Countable sets")[
+  + The natural numbers $NN$.
+  + The rationals $QQ$.
+  + The natural numbers $ZZ$.
+]
+
+#example("Uncountable sets")[
+  + The real numbers $RR$.
+  + The real numbers in the interval $[0,1]$.
+]
+
+#remark[Bijection][
+  If a set is countably infinite, then it has a bijection with $ZZ$. This means
+  every set with cardinality $aleph_0$ has a bijection to $ZZ$.
+]
+
+