auto-update(nvim): 2025-01-06 17:45:05

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

@@ -1,5 +1,5 @@
-#import "@preview/ctheorems:1.1.2": *
-#import "@preview/showybox:2.0.1": showybox
+#import "@preview/ctheorems:1.1.3": *
+#import "@preview/showybox:2.0.3": showybox
 
 #let colors = (
   rgb("#9E9E9E"),
@@ -257,27 +257,33 @@
   shadow: (offset: (x: 2pt, y: 2pt), color: luma(70%)),
 )
 
-#let problem = problem-style("problem", "Problem")
+#let exercise = problem-style("item", "Exercise")
+#let problem = exercise
 
 #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 example-style = builder-thmbox(
+  color: colors.at(16),
+  shadow: (offset: (x: 3pt, y: 3pt), color: luma(70%)),
+)
+
+#let theorem = theorem-style("item", "Theorem")
+#let lemma = theorem-style("item", "Lemma")
+#let corollary = theorem-style("item", "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 definition = definition-style("definition", "Definition")
+#let proposition = definition-style("item", "Proposition")
+#let remark = definition-style("item", "Remark")
+#let observation = definition-style("item", "Observation")
 
-#let example-style = builder-thmline(color: colors.at(16))
+// #let example-style = builder-thmline(color: colors.at(16))
 
-#let example = example-style("example", "Example").with(numbering: none)
+#let example = example-style("item", "Example").with(numbering: none)
 
 #let proof(body, name: none) = {
   thmtitle[Proof]
@@ -289,3 +295,26 @@
   h(1fr)
   $square$
 }
+
+#let fact = thmplain(
+  "item",
+  "Fact",
+  titlefmt: strong,
+  separator: ".",
+
+  inset: 0pt,
+)
+#let abuse = thmplain(
+  "item",
+  "Abuse of Notation",
+  titlefmt: strong,
+  separator: ".",
+  inset: 0pt,
+)
+#let definition = thmplain(
+  "item",
+  "Definition",
+  titlefmt: strong,
+  separator: ".",
+  inset: 0pt,
+)

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

@@ -1,8 +1,11 @@
 #import "./dvd.typ": *
+#import "@preview/ctheorems:1.1.3": *
 
 #show: dvdtyp.with(
-  title: "Probability and Statistics",
+  title: "PSTAT120A Course Notes",
   author: "Youwen Wu",
+  date: "Winter 2024",
+  subtitle: "Taught by Brian Wainwright",
 )
 
 #outline()
@@ -11,9 +14,9 @@
 
 == Preliminaries
 
-#definition("Statistics")[
-  The science dealing with the collection, summarization, analysis, and
-  interpretation of data.
+#definition[
+  Statistics is the science dealing with the collection, summarization,
+  analysis, and interpretation of data.
 ]
 
 == Set theory for dummies
@@ -21,8 +24,8 @@
 A terse introduction to elementary set theory and the basic operations upon
 them.
 
-#definition[Set][
-  A collection of elements.
+#definition[
+  A Set is a collection of elements.
 ]
 
 #example[Examples of sets][
@@ -42,12 +45,12 @@ $ {"expression with" x | "conditions on" x} $
 
 We also have notation for working with sets:
 
-With arbitrary sets $A$, $B$, $Omega$:
+With arbitrary sets $A$, $B$:
 
 + $a in A$ ($a$ 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: $A != Omega$)
++ $A subset.eq B$ (Set theory: $A$ is a subset of $B$) (Stats: $A$ is a sample space in $B$)
++ $A subset B$ (Proper subset: $A != B$)
 + $A^c$ 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 $B$)
@@ -56,13 +59,14 @@ With arbitrary sets $A$, $B$, $Omega$:
 
 We can also write a few of these operations precisely as set comprehensions.
 
-+ $A subset Omega => A = {a | a in Omega, forall a in A}$
++ $A subset B => A = {a | a in B, forall a in A}$
 + $A union B = {x | x in A or x in B}$ (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.
+Take a moment and 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.
@@ -70,14 +74,15 @@ Convince yourself that these definitions are equivalent to the previous ones.
   $ 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 $RR$?
+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:
+#fact[Properties of set operations][
+  For any sets $A$ and $B$, we have DeMorgan's Laws:
   + $(A union B)' = A' sect B'$
   + $(A sect B)' = A' union B'$
 ]
@@ -87,9 +92,9 @@ Check your intuition that this makes sense. Why do you think $RR^n$ was chosen a
   + $(sect_i A_i)' = union_i A_i'$
 ]
 
-=== Sizes of infinity
+== Sizes of infinity
 
-#definition("Cardinality")[
+#definition[
   Let $N(A)$ be the number of elements in $A$. $N(A)$ is called the _cardinality_ of $A$.
 ]
 
@@ -119,3 +124,4 @@ When a set is uncountably infinite, its cardinality is greater than $aleph_0$.
 ]
 
 
+