auto-update(nvim): 2025-01-06 12:48:48

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

@@ -0,0 +1,255 @@
+#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,
+  body,
+) = {
+  set document(title: title)
+
+  show: thmrules
+
+  set page(
+    numbering: "1",
+    number-align: center,
+    header: locate(loc => {
+      if loc.page() == 1 {
+        return
+      }
+      box(stroke: (bottom: 0.7pt), inset: 0.2em)[#text(
+          font: "Libertinus Serif",
+        )[
+          #author #h(1fr)#title
+        ]]
+    }),
+  )
+
+  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
+    v(0.6em)
+  }
+
+  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, 25pt, title))
+    #v(0.4em, weak: true)
+    #if subtitle != none [#text(18pt, weight: 500)[#subtitle]]
+    #v(0.3em, weak: true)
+    #if author != none [#text(14pt)[by #author]]
+
+  ]
+
+  if abstract != none [#align(center)[#abstract]]
+
+  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
+}
+
+#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/math-8/course-notes/main.typ

@@ -0,0 +1,69 @@
+#import "./dvd.typ": *
+
+#show: dvdtyp.with(
+  title: "Math 8",
+  subtitle: [UC Santa Barbara],
+  author: "Youwen Wu",
+)
+
+#outline()
+
+= Chapter 1: Logic and Proofs
+
+== Trivial Preliminaries
+
+Definitions barely worth considering. Included purely for posterity.
+
+#definition("Proposition")[
+  A proposition is a sentence which is either true or false.
+]
+
+#example("Primes")[
+  The numbers 5 and 7 are prime.
+]
+
+#example("Not a proposition")[
+  $x^2 + 6x + 8 = 0$
+]
+
+Propositions may be stated in the formalism of mathematics using connectives, as *propositional forms*.
+
+#definition("Propositional forms")[
+  Let $P$ and $Q$ be propositions. Then:
+
+  + The conjunction of $P$ and $Q$ is written $P and Q$ ($P$ and $Q$).
+  + The disjunction of $P$ and $Q$ is written $P or Q$ ($P$ or $Q$) (here "or" is the inclusive or).
+  + The negation of $P$ is written $not P$.
+]
+
+#definition("Tautology")[
+  A propositional form for which all of its values are true. In other words, a statement which is always true.
+]
+
+#definition("Contradiction")[
+  A propositional form for which all of its values are false. In other words, a statement which is always false.
+]
+
+#problem[Prove that $(P or Q) or (not P and not Q)$ is a tautology][
+  Trivial, omitted.
+]
+
+#example[Several denials of the statement "integer $n$ is even"][
+  - It is not the case that integer $n$ is even.
+  - Integer $n$ is not even.
+  - $n != 2m, forall m in ZZ$
+  - $n = 2m + 1, exists m in ZZ$
+]
+
+DeMorgan's Laws tell us how to distribute logical connectives across parentheses.
+
+#theorem[DeMorgan's Laws][
+  + $not (P or Q) = not P and not Q$
+  + $not (P and Q) = not P or not Q$
+]
+
+#proof[
+  Trivially, by completing a truth table.
+]
+
+